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data-component-name="Pill" data-props="{"color":"gray","children":["Fuel Cell Vehicles"]}" data-trace="false" data-dom-id="Pill-react-component-b87f869d-882d-44b8-a9d4-3b06c8c96cc8"></div> <div id="Pill-react-component-b87f869d-882d-44b8-a9d4-3b06c8c96cc8"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="35962046" href="https://www.academia.edu/Documents/in/Plug_In_Hybrid_Electric_Vehicles"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Plug In Hybrid Electric Vehicles"]}" data-trace="false" data-dom-id="Pill-react-component-18536e27-9010-407b-b2e4-6e1b94e056d0"></div> <div id="Pill-react-component-18536e27-9010-407b-b2e4-6e1b94e056d0"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by J. Schmelzer</h3></div><div class="js-work-strip profile--work_container" data-work-id="92590385"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/92590385/Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry"><img alt="Research paper thumbnail of Size and rate dependence of crystal nucleation in single tin drops by fast scanning calorimetry" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/92590385/Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry">Size and rate dependence of crystal nucleation in single tin drops by fast scanning calorimetry</a></div><div class="wp-workCard_item"><span>The Journal of Chemical Physics</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="92590385"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="92590385"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 92590385; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=92590385]").text(description); $(".js-view-count[data-work-id=92590385]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 92590385; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='92590385']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 92590385, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=92590385]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":92590385,"title":"Size and rate dependence of crystal nucleation in single tin drops by fast scanning calorimetry","translated_title":"","metadata":{"abstract":"The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.","publisher":"AIP Publishing","publication_date":{"day":null,"month":null,"year":2013,"errors":{}},"publication_name":"The Journal of Chemical Physics"},"translated_abstract":"The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.","internal_url":"https://www.academia.edu/92590385/Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry","translated_internal_url":"","created_at":"2022-12-10T22:32:24.597-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":22300,"name":"Chemical Physics","url":"https://www.academia.edu/Documents/in/Chemical_Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":78753,"name":"Differential scanning calorimetry","url":"https://www.academia.edu/Documents/in/Differential_scanning_calorimetry"},{"id":80693,"name":"Tin","url":"https://www.academia.edu/Documents/in/Tin"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":125058,"name":"Nucleation","url":"https://www.academia.edu/Documents/in/Nucleation"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":274522,"name":"Supercooling","url":"https://www.academia.edu/Documents/in/Supercooling"}],"urls":[{"id":26878393,"url":"http://aip.scitation.org/doi/pdf/10.1063/1.4789447"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557591"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation"><img alt="Research paper thumbnail of Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation" class="work-thumbnail" src="https://attachments.academia-assets.com/90983146/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation">Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation</a></div><div class="wp-workCard_item"><span>Ukrainian Journal of Physics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The work considers the thermodynamics and the kinetics of initial decomposition stages in a super...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45605168503109018e78ebde26d88e5d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983146,"asset_id":86557591,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983146/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557591"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557591"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557591; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557591]").text(description); $(".js-view-count[data-work-id=86557591]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557591; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557591']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557591, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "45605168503109018e78ebde26d88e5d" } } $('.js-work-strip[data-work-id=86557591]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557591,"title":"Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation","translated_title":"","metadata":{"abstract":"The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...","publisher":"National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka) (Publications)","publication_date":{"day":null,"month":null,"year":2022,"errors":{}},"publication_name":"Ukrainian Journal of Physics"},"translated_abstract":"The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...","internal_url":"https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation","translated_internal_url":"","created_at":"2022-09-12T22:39:04.409-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983146,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983146/thumbnails/1.jpg","file_name":"2409.pdf","download_url":"https://www.academia.edu/attachments/90983146/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Evolution_of_New_Phase_Clusters_at_the_I.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983146/2409-libre.pdf?1663048810=\u0026response-content-disposition=attachment%3B+filename%3DEvolution_of_New_Phase_Clusters_at_the_I.pdf\u0026Expires=1732998830\u0026Signature=NyGqnIJ9ruT5kw-CHQQaHAXLk-BjKzZJ7XF6YrzLxowImOjhLFzCfj0wdN0UhLOqu~sx4Iafn5GtgOBU3oELo1xzoAT6NRirtAlLibB8m0DiUp9PrNmlJVMa4p-KOb3PlIemy~TbKa0-0k1AuyrP9UXK~UUobm5YXbmq2Ae4sUbZsuWpPhrnvdvE6Dmz8O4vfh3R3RLO1MnWeuzM2AFowFdK26Kw35FsLIvRY40nUvMqCRCDZxoA3MlCLhdn7503umqeyJtVE3Z6SJKd1OOaw2hCsUc4YyEL8rdcLwML1klNrhdoB4p8IM6W6ed7cCgQltZNbxMR86oe-nlgPPTLpw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation","translated_slug":"","page_count":8,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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It is shown, that the general scenario of first-order phase transitions in finite systems developed earlier is also applicable for this special case and a kinetic description of nucleation and subsequent growth of the bubbles is given.","publication_date":{"day":null,"month":null,"year":1988,"errors":{}},"publication_name":"Zeitschrift für Physikalische Chemie","grobid_abstract_attachment_id":90983170},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557590/Formation_and_Growth_of_Babbles_in_One_Component_Closed_Isochoric_Systems","translated_internal_url":"","created_at":"2022-09-12T22:39:04.236-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983170,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983170/thumbnails/1.jpg","file_name":"zpch-1988-2696820220913-1-1cijakm.pdf","download_url":"https://www.academia.edu/attachments/90983170/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Formation_and_Growth_of_Babbles_in_One_C.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983170/zpch-1988-2696820220913-1-1cijakm-libre.pdf?1663061618=\u0026response-content-disposition=attachment%3B+filename%3DFormation_and_Growth_of_Babbles_in_One_C.pdf\u0026Expires=1732998830\u0026Signature=KWI~ASHKn5QvwXJ9nrIvzL6zC1z06yqkQ~xHMgsYe0HdIC-C6SnNktQcGU4NWXxIySZgy8-EZiG5vXyPDNkhAiMZOsXz~d7YQgHOdqk47yWj6ktr1WFfukCNoTJsK9p39zSDj99co~X51XZXwAgZWTI8LbFXaEsl0o43Crs70NXISPmOEPgUA8rvKriZQ6oG-YRtTyP35hWiduDC2~mvW8pZ~0ph-il4L5i8kM~7db-nW5FGaO4abNkR03TSj~ggDiO3IXvA3uOvhwnPejtbeHf9Wzuwnkz5VYOtz0SjWhHpFrrpUje6oParAhw4nuhjroqRtfJYa3-BOzAEkfkAXw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Formation_and_Growth_of_Babbles_in_One_Component_Closed_Isochoric_Systems","translated_slug":"","page_count":14,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557588"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets"><img alt="Research paper thumbnail of A New General Formula for the Curvature Dependence of Surface Tension of Droplets" class="work-thumbnail" src="https://attachments.academia-assets.com/90983171/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets">A New General Formula for the Curvature Dependence of Surface Tension of Droplets</a></div><div class="wp-workCard_item"><span>Zeitschrift für Physikalische Chemie</span><span>, 1985</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbda82a9438f6ff0208748e5ec6f3fa2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983171,"asset_id":86557588,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983171/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557588"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557588"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557588; 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In Übereinstimmung mit früheren Arbeiten von GIBBS, TOLMAN U. a. sind krümmungsabhängige Korrekturen für kleine Tropfen mit Radien rS 6 nm von Bedeutung. Die Oberflächenspannung sinkt bei Verkleinerung des Keimradius. Für spezielle Werte eines Parameters, der die spezifischen Eigenschaften des betrachteten Systems wiederspiegelt, folgen als Spezialfälle die bekannten Formeln von GIBBS, TOLMAN, RAS-MUSSEN und VOGELSBERGER. In his fundamental paper \"On the Equilibrium of Heterogeneous Substances\" (1878) GIBBS [1] pointed out, that the value of the surface tension is independent of the position of the dividing surface when the surface is plane. Measurements of this flat interface surface tension a^ are known for a long time, and at present the experimental data of σ x as function of temperature for various substances are precisely given. If the surface between two homogeneous phases is curved the surface tension σ becomes a function of the curvature in general or for spherical droplets a function of the droplet radius r. Already GIBBS [1] derived the first approximative equation for a = a(r). The investigations of GIBBS were extended by TOLMAN [2] and others. Some of the equations proposed by different authors are listed below, eq. (l)-(4). r is the radius of the surface of tension and δ 0 (TOLMAN coefficient) represents the distance between the surface of tension and the equimolecular dividing surface. In agree","publication_date":{"day":null,"month":null,"year":1985,"errors":{}},"publication_name":"Zeitschrift für Physikalische Chemie","grobid_abstract_attachment_id":90983171},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets","translated_internal_url":"","created_at":"2022-09-12T22:39:04.052-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983171,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983171/thumbnails/1.jpg","file_name":"zpch-1985-26612520220913-1-yo3x2o.pdf","download_url":"https://www.academia.edu/attachments/90983171/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_New_General_Formula_for_the_Curvature.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983171/zpch-1985-26612520220913-1-yo3x2o-libre.pdf?1663061586=\u0026response-content-disposition=attachment%3B+filename%3DA_New_General_Formula_for_the_Curvature.pdf\u0026Expires=1732998830\u0026Signature=UV8seE4f1kswpz9AQAqzMLyORcncwfbbyWlEEGRWIUGMGdfFSoVClAZcmgDkuWbpRXQSK~2dJB6oFTHgSZxoSIDl4L71ntSZIhGDQYhlPav0qIUOVQKEInV6DsfhQ5BG16JDz71WB-JPx158QjyRIAKtjeCNnK-UvBfe2pzAPh2Mxnppb-BkR3iRDzlLMLHmZF5BpB458FHooAepFf8Vil3bjhuygDdwiOowsSU8YdfI7hLlqJXlzQtFTkxiZE~uoCRE5u9nFZbg~ml9GrV7cIL2AqYz7yzrpXmzYO7BtraS-kO0A47fjC0b-FgWF0kq-wSGOtukXaQUMfku0ZajCA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets","translated_slug":"","page_count":4,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman&#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557587"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557587"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557587; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557587]").text(description); $(".js-view-count[data-work-id=86557587]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557587; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557587']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557587, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557587]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557587,"title":"The curvature dependence of surface tension of small droplets","translated_title":"","metadata":{"abstract":"The curvature dependence of the surface tension has been calculated via a general thermodynamic route from results based on molecular dynamics and density gradient calculations on liquid drops. It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman\u0026#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.","publisher":"Royal Society of Chemistry (RSC)","publication_date":{"day":null,"month":null,"year":1986,"errors":{}},"publication_name":"Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases"},"translated_abstract":"The curvature dependence of the surface tension has been calculated via a general thermodynamic route from results based on molecular dynamics and density gradient calculations on liquid drops. It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman\u0026#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.","internal_url":"https://www.academia.edu/86557587/The_curvature_dependence_of_surface_tension_of_small_droplets","translated_internal_url":"","created_at":"2022-09-12T22:39:03.870-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"The_curvature_dependence_of_surface_tension_of_small_droplets","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":512,"name":"Mechanics","url":"https://www.academia.edu/Documents/in/Mechanics"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":118428,"name":"Curvature","url":"https://www.academia.edu/Documents/in/Curvature"},{"id":394521,"name":"Surface Tension","url":"https://www.academia.edu/Documents/in/Surface_Tension"}],"urls":[{"id":23806604,"url":"http://pubs.rsc.org/en/content/articlepdf/1986/F1/F19868201421"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557586"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles"><img alt="Research paper thumbnail of General formulae for the curvature dependence of droplets and bubbles" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles">General formulae for the curvature dependence of droplets and bubbles</a></div><div class="wp-workCard_item"><span>Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases</span><span>, 1986</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">General equations have been developed that describe the curvature dependence of the surface tensi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman&#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557586"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557586"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557586; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557586]").text(description); $(".js-view-count[data-work-id=86557586]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557586; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557586']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557586, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557586]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557586,"title":"General formulae for the curvature dependence of droplets and bubbles","translated_title":"","metadata":{"abstract":"General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman\u0026#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.","publisher":"Royal Society of Chemistry (RSC)","publication_date":{"day":null,"month":null,"year":1986,"errors":{}},"publication_name":"Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases"},"translated_abstract":"General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman\u0026#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.","internal_url":"https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles","translated_internal_url":"","created_at":"2022-09-12T22:39:03.728-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":118428,"name":"Curvature","url":"https://www.academia.edu/Documents/in/Curvature"},{"id":152114,"name":"Bubble","url":"https://www.academia.edu/Documents/in/Bubble"},{"id":360549,"name":"Radius","url":"https://www.academia.edu/Documents/in/Radius"},{"id":394521,"name":"Surface Tension","url":"https://www.academia.edu/Documents/in/Surface_Tension"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557585"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems"><img alt="Research paper thumbnail of Kinetics of First-Order Phase Transitions in Condensed Systems" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems">Kinetics of First-Order Phase Transitions in Condensed Systems</a></div><div class="wp-workCard_item"><span>Physica Status Solidi (a)</span><span>, 1992</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557585"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557585"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557585; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557585]").text(description); $(".js-view-count[data-work-id=86557585]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557585; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557585']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557585, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557585]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557585,"title":"Kinetics of First-Order Phase Transitions in Condensed Systems","translated_title":"","metadata":{"abstract":"ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.","publisher":"Wiley-Blackwell","publication_date":{"day":null,"month":null,"year":1992,"errors":{}},"publication_name":"Physica Status Solidi (a)"},"translated_abstract":"ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.","internal_url":"https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems","translated_internal_url":"","created_at":"2022-09-12T22:39:03.608-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems","translated_slug":"","page_count":null,"language":"de","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":505,"name":"Condensed Matter Physics","url":"https://www.academia.edu/Documents/in/Condensed_Matter_Physics"},{"id":4987,"name":"Kinetics","url":"https://www.academia.edu/Documents/in/Kinetics"},{"id":17733,"name":"Nanotechnology","url":"https://www.academia.edu/Documents/in/Nanotechnology"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557584"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts"><img alt="Research paper thumbnail of Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts" class="work-thumbnail" src="https://attachments.academia-assets.com/90983169/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts">Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts</a></div><div class="wp-workCard_item"><span>Journal of Non-Crystalline Solids</span><span>, 2003</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="994fa8059b9799ca972f58aa505f6ec2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983169,"asset_id":86557584,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557584"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557584"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557584; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557584]").text(description); $(".js-view-count[data-work-id=86557584]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557584; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557584']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557584, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "994fa8059b9799ca972f58aa505f6ec2" } } $('.js-work-strip[data-work-id=86557584]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557584,"title":"Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"Glassforming melts behave, in the vicinity of the temperature of vitrification T g , as viscoelastic bodies. A general theory of nucleation in a viscoelastic body developed elsewhere is applicable to the description of phase formation processes in such systems. The present contribution is directed to the demonstration of the relevance of this proposed general theory to describing phase transformation processes in glassforming melts. The application of the theory is shown to explain a number of experimental results on crystallization of glassforming melts, which have not found a satisfactory interpretation so far.","publication_date":{"day":null,"month":null,"year":2003,"errors":{}},"publication_name":"Journal of Non-Crystalline Solids","grobid_abstract_attachment_id":90983169},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts","translated_internal_url":"","created_at":"2022-09-12T22:39:03.431-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983169,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983169/thumbnails/1.jpg","file_name":"s0022-3093_2802_2901428-x20220913-1-11fbhj7.pdf","download_url":"https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_nucleation_in_viscoelastic_med.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983169/s0022-3093_2802_2901428-x20220913-1-11fbhj7-libre.pdf?1663061582=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_nucleation_in_viscoelastic_med.pdf\u0026Expires=1732998830\u0026Signature=AHaf1FLioE4cYAZrB8lgm~J6BHGt9zzCOj-XwMtwKdphVDa17~oduCr4KjsYMSpXBAMs-Blh~jhVVh9EGxEynAnNvubI1xntKODf3Onsyv6v5eYqpVc20aegDVmQl3-R6rMWq3Ei0lFyJYTfPiilCEOtj7btykW4zEzYPCUODhKI9K0KC-7ZT9M7f0pKXVbKjgLNV0HbR-VQm0SYFthIo20SNUkKLtcgUvp53X308gn1Iewkye7uWeESQZgtrXoDELwk~xLBlahXcq1dKh31h8y8LIC3vecGVMNs1Q9wpDTWYHzuWPiizCgDRJAokEvOwqw0MhobgyGibNv~BfxLig__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts","translated_slug":"","page_count":17,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[{"id":90983169,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983169/thumbnails/1.jpg","file_name":"s0022-3093_2802_2901428-x20220913-1-11fbhj7.pdf","download_url":"https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_nucleation_in_viscoelastic_med.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983169/s0022-3093_2802_2901428-x20220913-1-11fbhj7-libre.pdf?1663061582=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_nucleation_in_viscoelastic_med.pdf\u0026Expires=1732998830\u0026Signature=AHaf1FLioE4cYAZrB8lgm~J6BHGt9zzCOj-XwMtwKdphVDa17~oduCr4KjsYMSpXBAMs-Blh~jhVVh9EGxEynAnNvubI1xntKODf3Onsyv6v5eYqpVc20aegDVmQl3-R6rMWq3Ei0lFyJYTfPiilCEOtj7btykW4zEzYPCUODhKI9K0KC-7ZT9M7f0pKXVbKjgLNV0HbR-VQm0SYFthIo20SNUkKLtcgUvp53X308gn1Iewkye7uWeESQZgtrXoDELwk~xLBlahXcq1dKh31h8y8LIC3vecGVMNs1Q9wpDTWYHzuWPiizCgDRJAokEvOwqw0MhobgyGibNv~BfxLig__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":2383,"name":"Viscoelasticity","url":"https://www.academia.edu/Documents/in/Viscoelasticity"},{"id":125058,"name":"Nucleation","url":"https://www.academia.edu/Documents/in/Nucleation"},{"id":150216,"name":"Non crystalline solids","url":"https://www.academia.edu/Documents/in/Non_crystalline_solids"},{"id":308420,"name":"Phase Transformation","url":"https://www.academia.edu/Documents/in/Phase_Transformation"}],"urls":[{"id":23806603,"url":"https://api.elsevier.com/content/article/PII:S002230930201428X?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557583"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557583/Kinetics_of_first_order_phase_transitions_in_adiabatic_systems"><img alt="Research paper thumbnail of Kinetics of first-order phase transitions in adiabatic systems" class="work-thumbnail" src="https://attachments.academia-assets.com/90983167/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557583/Kinetics_of_first_order_phase_transitions_in_adiabatic_systems">Kinetics of first-order phase transitions in adiabatic systems</a></div><div class="wp-workCard_item"><span>Journal of Colloid and Interface Science</span><span>, 1989</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b122cba0ca405e2637aa589fc9acb538" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983167,"asset_id":86557583,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983167/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557583"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557583"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557583; 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It is shown that, in analogy to isothermal constraints, three main stages of the transition may be distinguished: a first stage of dominating nucleation and simultaneous growth of the already formed supercritical clusters, a second stage of independent growth of the clusters, their number being nearly constant, and a third stage of competitive growth, of Ostwald ripening. The change of the temperature of the system due to the latent heat of the transition can be considered hereby as an additional depletion effect. It leads to an increase of the critical size of the clusters and thus to a significant decrease of the nucleation rate, compared with isothermal conditions, especially for relatively large initial supersaturations. Further, it may result also in variations of the stable heterogeneous equilibrium state-that is, configurations of stable clusters in the otherwise homogeneous medium. In particular, for a one-component system under a constant external pressure it makes the existence of such a state possible and results therefore in a qualitative change of the whole course of the phase transition from independent nucleation and growth to the three-stage scenario as characterized above. A theoretical description of the independent growth of the drops and of Ostwald ripening under adiabatic conditions is developed. The results are compared with growth processes in isothermal systems and both quantitative and possible qualitative differences are discussed. 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Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557582"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557582"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557582; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557582]").text(description); $(".js-view-count[data-work-id=86557582]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557582; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557582']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557582, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557582]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557582,"title":"On the Kinetic Description of Condensation in Binary Vapours","translated_title":"","metadata":{"abstract":"Based on a thermodynamic analysis and an earlier developed general growth equation for clusters of a new phase, the kinetics of growth of droplets in a binary gaseous mixture under isothermal and isobaric conditions is described. Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.","publisher":"Wiley-Blackwell","publication_date":{"day":null,"month":null,"year":1987,"errors":{}},"publication_name":"Annalen der Physik"},"translated_abstract":"Based on a thermodynamic analysis and an earlier developed general growth equation for clusters of a new phase, the kinetics of growth of droplets in a binary gaseous mixture under isothermal and isobaric conditions is described. Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.","internal_url":"https://www.academia.edu/86557582/On_the_Kinetic_Description_of_Condensation_in_Binary_Vapours","translated_internal_url":"","created_at":"2022-09-12T22:39:03.018-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_the_Kinetic_Description_of_Condensation_in_Binary_Vapours","translated_slug":"","page_count":null,"language":"de","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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It is shown that in contrast to the conclusions derived by Ward et al. [1, 2], multi-bubble systems in the otherwise homgeneous medium are thermodynamically unstable. Based on thermodynamic investigations, a theory of Ostwald ripening of gas bubbles in liquid-gas solutions is presented which includes the description of the initial stage of this process. Differential equations describing the time development of the mean radius and the number of bubbles are derived. For the asymptotic region analytic solutions in agreement with the results of Lifshitz and Slyozov [3] are obtained. The results can also be applied to a description of the growth of single droplets and ensembles of droplets in multicomponent vapours, demonstrating the analogy between the time development of ensembles of droplets and bubbles. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="81136076"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/81136076/Dependence_of_the_width_of_the_glass_transition_interval_on_cooling_and_heating_rates"><img alt="Research paper thumbnail of Dependence of the width of the glass transition interval on cooling and heating rates" class="work-thumbnail" src="https://attachments.academia-assets.com/87286044/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/81136076/Dependence_of_the_width_of_the_glass_transition_interval_on_cooling_and_heating_rates">Dependence of the width of the glass transition interval on cooling and heating rates</a></div><div class="wp-workCard_item"><span>The Journal of Chemical Physics</span><span>, 2013</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7fd2e8578004578cd09a5117786e1e4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87286044,"asset_id":81136076,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87286044/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="81136076"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="81136076"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 81136076; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7fd2e8578004578cd09a5117786e1e4b" } } $('.js-work-strip[data-work-id=81136076]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":81136076,"title":"Dependence of the width of the glass transition interval on cooling and heating rates","translated_title":"","metadata":{"publisher":"AIP Publishing","grobid_abstract":"In a preceding paper [J. W. P. Schmelzer, J. Chem. Phys. 136, 074512 (2012)], a general kinetic criterion of glass formation has been advanced allowing one to determine theoretically the dependence of the glass transition temperature on cooling and heating rates (or similarly on the rate of change of any appropriate control parameter determining the transition of a stable or metastable equilibrium system into a frozen-in, non-equilibrium state of the system, a glass). In the present paper, this criterion is employed in order to develop analytical expressions for the dependence of the upper and lower boundaries and of the width of the glass transition interval on the rate of change of the external control parameters. It is shown, in addition, that the width of the glass transition range is strongly correlated with the entropy production at the glass transition temperature. The analytical results are supplemented by numerical computations. 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Chemie 266 (1985) 1057 a general equat ion describing the gro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In a preceding paper [12]: Z. phys. Chemie 266 (1985) 1057 a general equat ion describing the growth of a new phase in the rmodynamic phase transit ions of first order was derived. This equat ion is applie¿j here first to an investigation of the t ime development of single clusters of a new phase. Based on the proposed in [12] new theory of Ostwald ripening a general theory describing this process for elastic media is developed. This method leads to a set of differential equat ions for the mean cluster radius, the number of clusters and the total mass of the new phase concentrated in the clusters. These equations are valid and can be solved numerically for the whole ripening process including the initial stage. A criterion is established under which condit ions elastic strains lead to a s top of the growth of the clusters and, therefore, t o a quite different asymptotic behaviour of the solutions as compared with the theory of LIFSHITZ, S&#39;.YOZOV and others. In these cases for long times a stationary relatively monodisperse distribution of clusters is established in the system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75961373"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75961373"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75961373; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75961373]").text(description); $(".js-view-count[data-work-id=75961373]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75961373; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75961373']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 75961373, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75961373]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75961373,"title":"On the Kinetic Description of Ostwald Ripening in Elastic Media","translated_title":"","metadata":{"abstract":"In a preceding paper [12]: Z. phys. 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The influence of the finite size of the system or the depletion of the surrounding the clusters medium on the work of formation of critical clusters is determined for different thermodynamic constraints. Besides the variations of the parameters of the critical clusters finite-size effects lead to the existence of additional states obeying the necessary thermodynamic equilibrium conditions and to a correction term AW in the equation for the work of formation of critical clusters. It is shown that AW is always negativ. This term AW is, however, overcompensated by the changes of the nucleation work due to the variations of the parameters of the critical clusters. The general results are illustrated by an analysis of the process of an isochoric condensation of a one-component gas in a closed system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75961251"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75961251"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75961251; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75961251]").text(description); $(".js-view-count[data-work-id=75961251]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75961251; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75961251']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 75961251, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75961251]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75961251,"title":"Thermodynamik und Keimbildung","translated_title":"","metadata":{"abstract":"Based on the Gibbs\u0026#39; theory of surface effects a thermodynamic description of a heterogeneous system consisting of s clusters of a new phase in the otherwise homogeneous medium is given. 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The general results are illustrated by an analysis of the process of an isochoric condensation of a one-component gas in a closed system.","publisher":"Walter de Gruyter GmbH","publication_date":{"day":null,"month":null,"year":1985,"errors":{}},"publication_name":"Zeitschrift für Physikalische Chemie"},"translated_abstract":"Based on the Gibbs\u0026#39; theory of surface effects a thermodynamic description of a heterogeneous system consisting of s clusters of a new phase in the otherwise homogeneous medium is given. The influence of the finite size of the system or the depletion of the surrounding the clusters medium on the work of formation of critical clusters is determined for different thermodynamic constraints. 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The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="92590385"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="92590385"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 92590385; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=92590385]").text(description); $(".js-view-count[data-work-id=92590385]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 92590385; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='92590385']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 92590385, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=92590385]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":92590385,"title":"Size and rate dependence of crystal nucleation in single tin drops by fast scanning calorimetry","translated_title":"","metadata":{"abstract":"The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.","publisher":"AIP Publishing","publication_date":{"day":null,"month":null,"year":2013,"errors":{}},"publication_name":"The Journal of Chemical Physics"},"translated_abstract":"The experimentally accessible degree of undercooling of single micron-sized liquid pure tin drops has been studied via differential fast scanning calorimetry. The cooling rates employed ranged from 100 to 14,000 K/s. The diameter of the investigated tin drops varied in the range from 7 to 40 μm. The influence of the drop shape on the solidification process could be eliminated due to the nearly spherical shape of the single drop upon heating and cooling and the resultant geometric stability. As a result it became possible to study the effect of both drop size and cooling rate in rapid solidification experimentally. A theoretical description of the experimental results is given by assuming the existence of two different heterogeneous nucleation mechanisms leading to crystal nucleation of the single tin drop. In agreement with the experiment these mechanisms yield a shelf-like dependence of crystal nucleation on undercooling. A dependence of crystal nucleation on the size of the tin drop was observed and is discussed in terms of the mentioned theoretical model, which can possibly also describe the nucleation for other related rapid solidification processes.","internal_url":"https://www.academia.edu/92590385/Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry","translated_internal_url":"","created_at":"2022-12-10T22:32:24.597-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Size_and_rate_dependence_of_crystal_nucleation_in_single_tin_drops_by_fast_scanning_calorimetry","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":48,"name":"Engineering","url":"https://www.academia.edu/Documents/in/Engineering"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":22300,"name":"Chemical Physics","url":"https://www.academia.edu/Documents/in/Chemical_Physics"},{"id":26327,"name":"Medicine","url":"https://www.academia.edu/Documents/in/Medicine"},{"id":78753,"name":"Differential scanning calorimetry","url":"https://www.academia.edu/Documents/in/Differential_scanning_calorimetry"},{"id":80693,"name":"Tin","url":"https://www.academia.edu/Documents/in/Tin"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":125058,"name":"Nucleation","url":"https://www.academia.edu/Documents/in/Nucleation"},{"id":260118,"name":"CHEMICAL SCIENCES","url":"https://www.academia.edu/Documents/in/CHEMICAL_SCIENCES"},{"id":274522,"name":"Supercooling","url":"https://www.academia.edu/Documents/in/Supercooling"}],"urls":[{"id":26878393,"url":"http://aip.scitation.org/doi/pdf/10.1063/1.4789447"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557591"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation"><img alt="Research paper thumbnail of Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation" class="work-thumbnail" src="https://attachments.academia-assets.com/90983146/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation">Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation</a></div><div class="wp-workCard_item"><span>Ukrainian Journal of Physics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The work considers the thermodynamics and the kinetics of initial decomposition stages in a super...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="45605168503109018e78ebde26d88e5d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983146,"asset_id":86557591,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983146/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557591"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557591"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557591; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557591]").text(description); $(".js-view-count[data-work-id=86557591]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557591; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557591']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557591, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "45605168503109018e78ebde26d88e5d" } } $('.js-work-strip[data-work-id=86557591]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557591,"title":"Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation","translated_title":"","metadata":{"abstract":"The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...","publisher":"National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka) (Publications)","publication_date":{"day":null,"month":null,"year":2022,"errors":{}},"publication_name":"Ukrainian Journal of Physics"},"translated_abstract":"The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size...","internal_url":"https://www.academia.edu/86557591/Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation","translated_internal_url":"","created_at":"2022-09-12T22:39:04.409-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983146,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983146/thumbnails/1.jpg","file_name":"2409.pdf","download_url":"https://www.academia.edu/attachments/90983146/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Evolution_of_New_Phase_Clusters_at_the_I.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983146/2409-libre.pdf?1663048810=\u0026response-content-disposition=attachment%3B+filename%3DEvolution_of_New_Phase_Clusters_at_the_I.pdf\u0026Expires=1732998830\u0026Signature=NyGqnIJ9ruT5kw-CHQQaHAXLk-BjKzZJ7XF6YrzLxowImOjhLFzCfj0wdN0UhLOqu~sx4Iafn5GtgOBU3oELo1xzoAT6NRirtAlLibB8m0DiUp9PrNmlJVMa4p-KOb3PlIemy~TbKa0-0k1AuyrP9UXK~UUobm5YXbmq2Ae4sUbZsuWpPhrnvdvE6Dmz8O4vfh3R3RLO1MnWeuzM2AFowFdK26Kw35FsLIvRY40nUvMqCRCDZxoA3MlCLhdn7503umqeyJtVE3Z6SJKd1OOaw2hCsUc4YyEL8rdcLwML1klNrhdoB4p8IM6W6ed7cCgQltZNbxMR86oe-nlgPPTLpw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Evolution_of_New_Phase_Clusters_at_the_Initial_Stages_of_Binary_Alloy_Decomposition_Described_in_Terms_of_a_Modified_Theory_of_Nucleation","translated_slug":"","page_count":8,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557588"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets"><img alt="Research paper thumbnail of A New General Formula for the Curvature Dependence of Surface Tension of Droplets" class="work-thumbnail" src="https://attachments.academia-assets.com/90983171/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets">A New General Formula for the Curvature Dependence of Surface Tension of Droplets</a></div><div class="wp-workCard_item"><span>Zeitschrift für Physikalische Chemie</span><span>, 1985</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbda82a9438f6ff0208748e5ec6f3fa2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983171,"asset_id":86557588,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983171/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557588"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557588"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557588; 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In Übereinstimmung mit früheren Arbeiten von GIBBS, TOLMAN U. a. sind krümmungsabhängige Korrekturen für kleine Tropfen mit Radien rS 6 nm von Bedeutung. Die Oberflächenspannung sinkt bei Verkleinerung des Keimradius. Für spezielle Werte eines Parameters, der die spezifischen Eigenschaften des betrachteten Systems wiederspiegelt, folgen als Spezialfälle die bekannten Formeln von GIBBS, TOLMAN, RAS-MUSSEN und VOGELSBERGER. In his fundamental paper \"On the Equilibrium of Heterogeneous Substances\" (1878) GIBBS [1] pointed out, that the value of the surface tension is independent of the position of the dividing surface when the surface is plane. Measurements of this flat interface surface tension a^ are known for a long time, and at present the experimental data of σ x as function of temperature for various substances are precisely given. If the surface between two homogeneous phases is curved the surface tension σ becomes a function of the curvature in general or for spherical droplets a function of the droplet radius r. Already GIBBS [1] derived the first approximative equation for a = a(r). The investigations of GIBBS were extended by TOLMAN [2] and others. Some of the equations proposed by different authors are listed below, eq. (l)-(4). r is the radius of the surface of tension and δ 0 (TOLMAN coefficient) represents the distance between the surface of tension and the equimolecular dividing surface. In agree","publication_date":{"day":null,"month":null,"year":1985,"errors":{}},"publication_name":"Zeitschrift für Physikalische Chemie","grobid_abstract_attachment_id":90983171},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557588/A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets","translated_internal_url":"","created_at":"2022-09-12T22:39:04.052-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983171,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983171/thumbnails/1.jpg","file_name":"zpch-1985-26612520220913-1-yo3x2o.pdf","download_url":"https://www.academia.edu/attachments/90983171/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_New_General_Formula_for_the_Curvature.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983171/zpch-1985-26612520220913-1-yo3x2o-libre.pdf?1663061586=\u0026response-content-disposition=attachment%3B+filename%3DA_New_General_Formula_for_the_Curvature.pdf\u0026Expires=1732998830\u0026Signature=UV8seE4f1kswpz9AQAqzMLyORcncwfbbyWlEEGRWIUGMGdfFSoVClAZcmgDkuWbpRXQSK~2dJB6oFTHgSZxoSIDl4L71ntSZIhGDQYhlPav0qIUOVQKEInV6DsfhQ5BG16JDz71WB-JPx158QjyRIAKtjeCNnK-UvBfe2pzAPh2Mxnppb-BkR3iRDzlLMLHmZF5BpB458FHooAepFf8Vil3bjhuygDdwiOowsSU8YdfI7hLlqJXlzQtFTkxiZE~uoCRE5u9nFZbg~ml9GrV7cIL2AqYz7yzrpXmzYO7BtraS-kO0A47fjC0b-FgWF0kq-wSGOtukXaQUMfku0ZajCA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_New_General_Formula_for_the_Curvature_Dependence_of_Surface_Tension_of_Droplets","translated_slug":"","page_count":4,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman&#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557587"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557587"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557587; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557587]").text(description); $(".js-view-count[data-work-id=86557587]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557587; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557587']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557587, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557587]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557587,"title":"The curvature dependence of surface tension of small droplets","translated_title":"","metadata":{"abstract":"The curvature dependence of the surface tension has been calculated via a general thermodynamic route from results based on molecular dynamics and density gradient calculations on liquid drops. It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman\u0026#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.","publisher":"Royal Society of Chemistry (RSC)","publication_date":{"day":null,"month":null,"year":1986,"errors":{}},"publication_name":"Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases"},"translated_abstract":"The curvature dependence of the surface tension has been calculated via a general thermodynamic route from results based on molecular dynamics and density gradient calculations on liquid drops. It is shown that in the region of applicability of thermodynamics, the curvature corrections are small and are described asymptotically by Tolman\u0026#39;s equations. However, in contrast to earlier calculations the decrease in surface tension with decreasing droplet radius is succeeded by a region in which the surface tension increases again to values higher than the asymptotic value of the surface tension of a planar interface. Applications to nucleation theory are discussed.","internal_url":"https://www.academia.edu/86557587/The_curvature_dependence_of_surface_tension_of_small_droplets","translated_internal_url":"","created_at":"2022-09-12T22:39:03.870-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"The_curvature_dependence_of_surface_tension_of_small_droplets","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":512,"name":"Mechanics","url":"https://www.academia.edu/Documents/in/Mechanics"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":118428,"name":"Curvature","url":"https://www.academia.edu/Documents/in/Curvature"},{"id":394521,"name":"Surface Tension","url":"https://www.academia.edu/Documents/in/Surface_Tension"}],"urls":[{"id":23806604,"url":"http://pubs.rsc.org/en/content/articlepdf/1986/F1/F19868201421"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557586"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles"><img alt="Research paper thumbnail of General formulae for the curvature dependence of droplets and bubbles" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles">General formulae for the curvature dependence of droplets and bubbles</a></div><div class="wp-workCard_item"><span>Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases</span><span>, 1986</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">General equations have been developed that describe the curvature dependence of the surface tensi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman&#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557586"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557586"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557586; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557586]").text(description); $(".js-view-count[data-work-id=86557586]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557586; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557586']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557586, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557586]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557586,"title":"General formulae for the curvature dependence of droplets and bubbles","translated_title":"","metadata":{"abstract":"General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman\u0026#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.","publisher":"Royal Society of Chemistry (RSC)","publication_date":{"day":null,"month":null,"year":1986,"errors":{}},"publication_name":"Journal of the Chemical Society, Faraday Transactions 1: Physical Chemistry in Condensed Phases"},"translated_abstract":"General equations have been developed that describe the curvature dependence of the surface tension of droplets in the gas phase and of bubbles in a liquid. These are based on thermodynamic arguments and a special assumption concerning the Tolman parameter, δ. The equations derived by Gibbs, Tolman and Rasmussen are obtained as special cases for particular values of a parameter dependent both on the system considered and the thermodynamic constraints. Although the behaviour of the Tolman coefficient δ as a function of the radius, Rs, of the surface of tension can be quite different, the resulting equations describing the curvature dependence of surface tension are similar, thus confirming Tolman\u0026#39;s equation as a first, but accurate approximation.It is further shown that physically meaningful results for the surface tension of bubbles can be obtained only if the Tolman coefficient changes its sign for a specific value Rs=|b| of the radius of the bubble. Therefore in this case the surface tension has a maximum for a finite value of the radius of the surface of tension and there are two regions in which the surface tension either decreases (Rs |b|) with decreasing size of the bubble.","internal_url":"https://www.academia.edu/86557586/General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles","translated_internal_url":"","created_at":"2022-09-12T22:39:03.728-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"General_formulae_for_the_curvature_dependence_of_droplets_and_bubbles","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":118428,"name":"Curvature","url":"https://www.academia.edu/Documents/in/Curvature"},{"id":152114,"name":"Bubble","url":"https://www.academia.edu/Documents/in/Bubble"},{"id":360549,"name":"Radius","url":"https://www.academia.edu/Documents/in/Radius"},{"id":394521,"name":"Surface Tension","url":"https://www.academia.edu/Documents/in/Surface_Tension"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557585"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems"><img alt="Research paper thumbnail of Kinetics of First-Order Phase Transitions in Condensed Systems" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems">Kinetics of First-Order Phase Transitions in Condensed Systems</a></div><div class="wp-workCard_item"><span>Physica Status Solidi (a)</span><span>, 1992</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557585"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557585"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557585; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557585]").text(description); $(".js-view-count[data-work-id=86557585]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557585; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557585']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557585, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557585]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557585,"title":"Kinetics of First-Order Phase Transitions in Condensed Systems","translated_title":"","metadata":{"abstract":"ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.","publisher":"Wiley-Blackwell","publication_date":{"day":null,"month":null,"year":1992,"errors":{}},"publication_name":"Physica Status Solidi (a)"},"translated_abstract":"ABSTRACT The kinetics of first-order phase transitions – nucleation, independent cluster growth, and Ostwald ripening – in condensed systems is analysed based on the numerical solution of a Fokker-Planck equation for the cluster size distribution function. Particular attention is directed to the investigation of the transition period between independent growth and Ostwald ripening. An unexpected temporary slowing down of the growth rate of the mean cluster size is observed in this region and the parameter range for its occurrence is calculated. Moreover, a new analytic expression for the time evolution of the mean cluster radius for the period of nucleation and independent growth is developed. It is in good agreement with the numerical results.Die Kinetik von thermodynamischen Phasenübergängen 1. Art – Keimbildung, unabhängiges Clusterwachstum und Ostwaldreifung – wird analysiert basierend auf der numerischen Lösung einer Fokker-Planck-Gleichung für die Clustergrößenverteilungsfunktion. Besondere Aufmerksamkeit wird dabei auf die Übergangsperiode zwischen unabhängigem Wachstum und Ostwaldreifung gerichtet. Eine unerwartete Verlangsamung des Wachstums wird hier beobachtet und Abschätzungen für das Parametergebiet, für das ein derartiges Verhalten auftritt, werden vorgenommen. Zusätzlich wird eine analytische Beschreibung für die zeitliche Entwicklung des mittleren Clusterradius für die Phase von simultaner Keimbildung und unabhängigem Wachstum der Cluster vorgeschlagen. Die erhaltene Gleichung ist in guter Übereinstimmung mit den numerischen Ergebnissen.","internal_url":"https://www.academia.edu/86557585/Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems","translated_internal_url":"","created_at":"2022-09-12T22:39:03.608-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Kinetics_of_First_Order_Phase_Transitions_in_Condensed_Systems","translated_slug":"","page_count":null,"language":"de","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":505,"name":"Condensed Matter Physics","url":"https://www.academia.edu/Documents/in/Condensed_Matter_Physics"},{"id":4987,"name":"Kinetics","url":"https://www.academia.edu/Documents/in/Kinetics"},{"id":17733,"name":"Nanotechnology","url":"https://www.academia.edu/Documents/in/Nanotechnology"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557584"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts"><img alt="Research paper thumbnail of Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts" class="work-thumbnail" src="https://attachments.academia-assets.com/90983169/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts">Theory of nucleation in viscoelastic media: application to phase formation in glassforming melts</a></div><div class="wp-workCard_item"><span>Journal of Non-Crystalline Solids</span><span>, 2003</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="994fa8059b9799ca972f58aa505f6ec2" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983169,"asset_id":86557584,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557584"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557584"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557584; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557584]").text(description); $(".js-view-count[data-work-id=86557584]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557584; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557584']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557584, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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A general theory of nucleation in a viscoelastic body developed elsewhere is applicable to the description of phase formation processes in such systems. The present contribution is directed to the demonstration of the relevance of this proposed general theory to describing phase transformation processes in glassforming melts. The application of the theory is shown to explain a number of experimental results on crystallization of glassforming melts, which have not found a satisfactory interpretation so far.","publication_date":{"day":null,"month":null,"year":2003,"errors":{}},"publication_name":"Journal of Non-Crystalline Solids","grobid_abstract_attachment_id":90983169},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557584/Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts","translated_internal_url":"","created_at":"2022-09-12T22:39:03.431-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983169,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983169/thumbnails/1.jpg","file_name":"s0022-3093_2802_2901428-x20220913-1-11fbhj7.pdf","download_url":"https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_nucleation_in_viscoelastic_med.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983169/s0022-3093_2802_2901428-x20220913-1-11fbhj7-libre.pdf?1663061582=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_nucleation_in_viscoelastic_med.pdf\u0026Expires=1732998830\u0026Signature=AHaf1FLioE4cYAZrB8lgm~J6BHGt9zzCOj-XwMtwKdphVDa17~oduCr4KjsYMSpXBAMs-Blh~jhVVh9EGxEynAnNvubI1xntKODf3Onsyv6v5eYqpVc20aegDVmQl3-R6rMWq3Ei0lFyJYTfPiilCEOtj7btykW4zEzYPCUODhKI9K0KC-7ZT9M7f0pKXVbKjgLNV0HbR-VQm0SYFthIo20SNUkKLtcgUvp53X308gn1Iewkye7uWeESQZgtrXoDELwk~xLBlahXcq1dKh31h8y8LIC3vecGVMNs1Q9wpDTWYHzuWPiizCgDRJAokEvOwqw0MhobgyGibNv~BfxLig__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theory_of_nucleation_in_viscoelastic_media_application_to_phase_formation_in_glassforming_melts","translated_slug":"","page_count":17,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[{"id":90983169,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983169/thumbnails/1.jpg","file_name":"s0022-3093_2802_2901428-x20220913-1-11fbhj7.pdf","download_url":"https://www.academia.edu/attachments/90983169/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_nucleation_in_viscoelastic_med.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983169/s0022-3093_2802_2901428-x20220913-1-11fbhj7-libre.pdf?1663061582=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_nucleation_in_viscoelastic_med.pdf\u0026Expires=1732998830\u0026Signature=AHaf1FLioE4cYAZrB8lgm~J6BHGt9zzCOj-XwMtwKdphVDa17~oduCr4KjsYMSpXBAMs-Blh~jhVVh9EGxEynAnNvubI1xntKODf3Onsyv6v5eYqpVc20aegDVmQl3-R6rMWq3Ei0lFyJYTfPiilCEOtj7btykW4zEzYPCUODhKI9K0KC-7ZT9M7f0pKXVbKjgLNV0HbR-VQm0SYFthIo20SNUkKLtcgUvp53X308gn1Iewkye7uWeESQZgtrXoDELwk~xLBlahXcq1dKh31h8y8LIC3vecGVMNs1Q9wpDTWYHzuWPiizCgDRJAokEvOwqw0MhobgyGibNv~BfxLig__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":523,"name":"Chemistry","url":"https://www.academia.edu/Documents/in/Chemistry"},{"id":2383,"name":"Viscoelasticity","url":"https://www.academia.edu/Documents/in/Viscoelasticity"},{"id":125058,"name":"Nucleation","url":"https://www.academia.edu/Documents/in/Nucleation"},{"id":150216,"name":"Non crystalline solids","url":"https://www.academia.edu/Documents/in/Non_crystalline_solids"},{"id":308420,"name":"Phase Transformation","url":"https://www.academia.edu/Documents/in/Phase_Transformation"}],"urls":[{"id":23806603,"url":"https://api.elsevier.com/content/article/PII:S002230930201428X?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="86557583"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/86557583/Kinetics_of_first_order_phase_transitions_in_adiabatic_systems"><img alt="Research paper thumbnail of Kinetics of first-order phase transitions in adiabatic systems" class="work-thumbnail" src="https://attachments.academia-assets.com/90983167/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/86557583/Kinetics_of_first_order_phase_transitions_in_adiabatic_systems">Kinetics of first-order phase transitions in adiabatic systems</a></div><div class="wp-workCard_item"><span>Journal of Colloid and Interface Science</span><span>, 1989</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b122cba0ca405e2637aa589fc9acb538" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90983167,"asset_id":86557583,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90983167/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557583"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557583"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557583; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557583]").text(description); $(".js-view-count[data-work-id=86557583]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557583; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557583']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557583, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b122cba0ca405e2637aa589fc9acb538" } } $('.js-work-strip[data-work-id=86557583]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557583,"title":"Kinetics of first-order phase transitions in adiabatic systems","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"Based on thermodynamic investigations a general scenario and a kinetic description of the process of first-order phase transitions in adiabatically closed systems, starting from metastable initial states, is developed. It is shown that, in analogy to isothermal constraints, three main stages of the transition may be distinguished: a first stage of dominating nucleation and simultaneous growth of the already formed supercritical clusters, a second stage of independent growth of the clusters, their number being nearly constant, and a third stage of competitive growth, of Ostwald ripening. The change of the temperature of the system due to the latent heat of the transition can be considered hereby as an additional depletion effect. It leads to an increase of the critical size of the clusters and thus to a significant decrease of the nucleation rate, compared with isothermal conditions, especially for relatively large initial supersaturations. Further, it may result also in variations of the stable heterogeneous equilibrium state-that is, configurations of stable clusters in the otherwise homogeneous medium. In particular, for a one-component system under a constant external pressure it makes the existence of such a state possible and results therefore in a qualitative change of the whole course of the phase transition from independent nucleation and growth to the three-stage scenario as characterized above. A theoretical description of the independent growth of the drops and of Ostwald ripening under adiabatic conditions is developed. The results are compared with growth processes in isothermal systems and both quantitative and possible qualitative differences are discussed. Further, they are applied to an interpretation of molecular-dynamics simulations of first-order phase transitions in adsorbed layers.","publication_date":{"day":null,"month":null,"year":1989,"errors":{}},"publication_name":"Journal of Colloid and Interface Science","grobid_abstract_attachment_id":90983167},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557583/Kinetics_of_first_order_phase_transitions_in_adiabatic_systems","translated_internal_url":"","created_at":"2022-09-12T22:39:03.177-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983167,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983167/thumbnails/1.jpg","file_name":"0021-9797_2889_2990389-520220913-1-1wjvr1k.pdf","download_url":"https://www.academia.edu/attachments/90983167/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Kinetics_of_first_order_phase_transition.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983167/0021-9797_2889_2990389-520220913-1-1wjvr1k-libre.pdf?1663061580=\u0026response-content-disposition=attachment%3B+filename%3DKinetics_of_first_order_phase_transition.pdf\u0026Expires=1732998830\u0026Signature=adwfsPZlbbTqwRHgWGCrF14yDmvo0k7qpI3-ioLbxkG4XaRTNvaySPSzY5T8tyd-f-OdSjuEwZmP0USSN2zkU~P~uO2MPtmPDSHXz2ov2X8sLWL7lcNJAxEe7LdwJ~j27mtO1xkoFpfzxTgCtMRm0~fLTiqSIAVU42yUDPdDwfb6wfb~mFfJ7WP7D5zfCuT059LZ6bs1a88rM3WoBT33iSstNyS2QHC8xlr8i3w09ktGAUJeHdkYQMnwTumGrCuTdg-EYO5A32d1QqHzVgNn9WwgeaqI4YpUcXWukESXmv-S8oFj6Yc3PpjfwwRQ-j3UAd09t9QE23ntfxzT5Slkhg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Kinetics_of_first_order_phase_transitions_in_adiabatic_systems","translated_slug":"","page_count":11,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="86557582"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="86557582"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 86557582; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=86557582]").text(description); $(".js-view-count[data-work-id=86557582]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 86557582; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='86557582']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 86557582, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=86557582]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":86557582,"title":"On the Kinetic Description of Condensation in Binary Vapours","translated_title":"","metadata":{"abstract":"Based on a thermodynamic analysis and an earlier developed general growth equation for clusters of a new phase, the kinetics of growth of droplets in a binary gaseous mixture under isothermal and isobaric conditions is described. Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.","publisher":"Wiley-Blackwell","publication_date":{"day":null,"month":null,"year":1987,"errors":{}},"publication_name":"Annalen der Physik"},"translated_abstract":"Based on a thermodynamic analysis and an earlier developed general growth equation for clusters of a new phase, the kinetics of growth of droplets in a binary gaseous mixture under isothermal and isobaric conditions is described. Differential equations for the time development of the mean radius of the droplets, the number of droplets, and the overall mass concentrated in the droplets are obtained. These equations describe the evolution of the system of droplets beginning after the nucleation period has finished. The equations can be easily solved numerically. For long times analytic solutions are derived. It is shown that the growth of droplets proceeds accordingly to the mechanism of Ostwald ripening. Zur kinetischen Beschreibung der Kondensation binarer Dampfe Basierend auf einer thermodynamischen Analyse und unter Verwendung einer fruher entwickelten allgemeinen Wachstumsgleichung fur Keime einer neuen Phase wird die Kinetik des Wachstums von Tropfen in einer binaren Gasmischung unter isobar-isothermen Bedingungen mathematisch beschrieben. Es werden Ausdrucke fur die zeitliche Entwicklung des mittleren Tropfenradius, der Tropfenzahl und der Gesamtmenge der flussigen Phase erhalten. Diese Gleichungen beschreiben die zeitliche Entwicklung des Systems von Tropfen, beginnend unmittelbar nach Abschlus der Keimbildungsphase. Sie sind relativ einfach numerisch losbar, fur grose Zeiten konnen analytische Losungen angegeben werden. Es wird gezeigt, das das Wachstum von Tropfen in der Gasphase nach dem Mechanismus der Ostwaldreifung erfolgt.","internal_url":"https://www.academia.edu/86557582/On_the_Kinetic_Description_of_Condensation_in_Binary_Vapours","translated_internal_url":"","created_at":"2022-09-12T22:39:03.018-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_the_Kinetic_Description_of_Condensation_in_Binary_Vapours","translated_slug":"","page_count":null,"language":"de","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics"},{"id":4987,"name":"Kinetics","url":"https://www.academia.edu/Documents/in/Kinetics"},{"id":38050,"name":"Phase Transitions","url":"https://www.academia.edu/Documents/in/Phase_Transitions"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":125058,"name":"Nucleation","url":"https://www.academia.edu/Documents/in/Nucleation"},{"id":254626,"name":"Cluster","url":"https://www.academia.edu/Documents/in/Cluster"},{"id":401240,"name":"Change of State","url":"https://www.academia.edu/Documents/in/Change_of_State"},{"id":634545,"name":"Condensation","url":"https://www.academia.edu/Documents/in/Condensation"},{"id":670651,"name":"Ostwald Ripening","url":"https://www.academia.edu/Documents/in/Ostwald_Ripening"},{"id":765146,"name":"Differential equation","url":"https://www.academia.edu/Documents/in/Differential_equation"}],"urls":[]}, dispatcherData: dispatcherData }); 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It is shown that in contrast to the conclusions derived by Ward et al. [1, 2], multi-bubble systems in the otherwise homgeneous medium are thermodynamically unstable. Based on thermodynamic investigations, a theory of Ostwald ripening of gas bubbles in liquid-gas solutions is presented which includes the description of the initial stage of this process. Differential equations describing the time development of the mean radius and the number of bubbles are derived. For the asymptotic region analytic solutions in agreement with the results of Lifshitz and Slyozov [3] are obtained. The results can also be applied to a description of the growth of single droplets and ensembles of droplets in multicomponent vapours, demonstrating the analogy between the time development of ensembles of droplets and bubbles. It was stated by these authors that in a closed volume of a liquid-gas-solution there can exist configurations of a single bubble and a number of bubbles in stable thermodynamic equilibrium within the otherwise homgeneous solution. We would like to show here, that, while the first is true, the second statement is","publication_date":{"day":null,"month":null,"year":1987,"errors":{}},"publication_name":"Journal of Non-Equilibrium Thermodynamics","grobid_abstract_attachment_id":90983112},"translated_abstract":null,"internal_url":"https://www.academia.edu/86557490/Ostwald_Ripening_of_Bubbles_in_Liquid_Gas_Solutions","translated_internal_url":"","created_at":"2022-09-12T22:37:19.806-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90983112,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90983112/thumbnails/1.jpg","file_name":"Schmelzer__Schweitzer_-_1987_-_Ostwald_Ripening_of_Bubbles_in_Liquid-Gas_Solutions.pdf","download_url":"https://www.academia.edu/attachments/90983112/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Ostwald_Ripening_of_Bubbles_in_Liquid_Ga.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90983112/Schmelzer__Schweitzer_-_1987_-_Ostwald_Ripening_of_Bubbles_in_Liquid-Gas_Solutions-libre.pdf?1663048819=\u0026response-content-disposition=attachment%3B+filename%3DOstwald_Ripening_of_Bubbles_in_Liquid_Ga.pdf\u0026Expires=1732998830\u0026Signature=BWF1CVxdR-mzhwpQb2rrlNFy91q1n~faMR5A0jTO5BnMZdq92T5N0VoFXoWlekRTPSi8g2x2ETjtQ4GIBwxUMec6iq1PvGvhJItuHN3eYiZlsNTFM3Kg0CsPOfrJ~Y28PrVI7A7YSne8cnCsF~WPyRfvrQEUoKi3Jq4TICmk8LjA11M-1msmruRV9P8XUUPk5TNYW47jA-ycEFxD9FU8I8d0QBPEAUzwsobZ1XNI5GCpNrAOaPXF1Qtu~EMDrp08NflO1YwDhyE~XSg~AI40MTsNhC~AkP5DznmIje3~uaYnbs5vG1qARr-oFJahA2ApKq1kn86IZQhtgm3UA6XWbQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Ostwald_Ripening_of_Bubbles_in_Liquid_Gas_Solutions","translated_slug":"","page_count":16,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="81136076"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/81136076/Dependence_of_the_width_of_the_glass_transition_interval_on_cooling_and_heating_rates"><img alt="Research paper thumbnail of Dependence of the width of the glass transition interval on cooling and heating rates" class="work-thumbnail" src="https://attachments.academia-assets.com/87286044/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/81136076/Dependence_of_the_width_of_the_glass_transition_interval_on_cooling_and_heating_rates">Dependence of the width of the glass transition interval on cooling and heating rates</a></div><div class="wp-workCard_item"><span>The Journal of Chemical Physics</span><span>, 2013</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7fd2e8578004578cd09a5117786e1e4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87286044,"asset_id":81136076,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87286044/download_file?st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&st=MTczMjk5NTIzMCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="81136076"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="81136076"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 81136076; 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7fd2e8578004578cd09a5117786e1e4b" } } $('.js-work-strip[data-work-id=81136076]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":81136076,"title":"Dependence of the width of the glass transition interval on cooling and heating rates","translated_title":"","metadata":{"publisher":"AIP Publishing","grobid_abstract":"In a preceding paper [J. W. P. Schmelzer, J. Chem. Phys. 136, 074512 (2012)], a general kinetic criterion of glass formation has been advanced allowing one to determine theoretically the dependence of the glass transition temperature on cooling and heating rates (or similarly on the rate of change of any appropriate control parameter determining the transition of a stable or metastable equilibrium system into a frozen-in, non-equilibrium state of the system, a glass). In the present paper, this criterion is employed in order to develop analytical expressions for the dependence of the upper and lower boundaries and of the width of the glass transition interval on the rate of change of the external control parameters. It is shown, in addition, that the width of the glass transition range is strongly correlated with the entropy production at the glass transition temperature. The analytical results are supplemented by numerical computations. 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=81135949]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":81135949,"title":"Non-Stationary Nucleation and the Johnson-Mehl-Avrami Equation","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":1989,"errors":{}}},"translated_abstract":null,"internal_url":"https://www.academia.edu/81135949/Non_Stationary_Nucleation_and_the_Johnson_Mehl_Avrami_Equation","translated_internal_url":"","created_at":"2022-06-09T22:30:52.565-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Non_Stationary_Nucleation_and_the_Johnson_Mehl_Avrami_Equation","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. Schmelzer","url":"https://independent.academia.edu/JSchmelzer"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="75961373"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/75961373/On_the_Kinetic_Description_of_Ostwald_Ripening_in_Elastic_Media"><img alt="Research paper thumbnail of On the Kinetic Description of Ostwald Ripening in Elastic Media" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/75961373/On_the_Kinetic_Description_of_Ostwald_Ripening_in_Elastic_Media">On the Kinetic Description of Ostwald Ripening in Elastic Media</a></div><div class="wp-workCard_item"><span>Zeitschrift für Physikalische Chemie</span><span>, 1988</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In a preceding paper [12]: Z. phys. Chemie 266 (1985) 1057 a general equat ion describing the gro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In a preceding paper [12]: Z. phys. Chemie 266 (1985) 1057 a general equat ion describing the growth of a new phase in the rmodynamic phase transit ions of first order was derived. This equat ion is applie¿j here first to an investigation of the t ime development of single clusters of a new phase. Based on the proposed in [12] new theory of Ostwald ripening a general theory describing this process for elastic media is developed. This method leads to a set of differential equat ions for the mean cluster radius, the number of clusters and the total mass of the new phase concentrated in the clusters. These equations are valid and can be solved numerically for the whole ripening process including the initial stage. A criterion is established under which condit ions elastic strains lead to a s top of the growth of the clusters and, therefore, t o a quite different asymptotic behaviour of the solutions as compared with the theory of LIFSHITZ, S&#39;.YOZOV and others. In these cases for long times a stationary relatively monodisperse distribution of clusters is established in the system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75961373"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75961373"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75961373; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75961373]").text(description); $(".js-view-count[data-work-id=75961373]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75961373; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75961373']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 75961373, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75961373]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75961373,"title":"On the Kinetic Description of Ostwald Ripening in Elastic Media","translated_title":"","metadata":{"abstract":"In a preceding paper [12]: Z. phys. Chemie 266 (1985) 1057 a general equat ion describing the growth of a new phase in the rmodynamic phase transit ions of first order was derived. This equat ion is applie¿j here first to an investigation of the t ime development of single clusters of a new phase. Based on the proposed in [12] new theory of Ostwald ripening a general theory describing this process for elastic media is developed. This method leads to a set of differential equat ions for the mean cluster radius, the number of clusters and the total mass of the new phase concentrated in the clusters. These equations are valid and can be solved numerically for the whole ripening process including the initial stage. A criterion is established under which condit ions elastic strains lead to a s top of the growth of the clusters and, therefore, t o a quite different asymptotic behaviour of the solutions as compared with the theory of LIFSHITZ, S\u0026#39;.YOZOV and others. In these cases for long times a stationary relatively monodisperse distribution of clusters is established in the system.","publisher":"Walter de Gruyter GmbH","publication_date":{"day":null,"month":null,"year":1988,"errors":{}},"publication_name":"Zeitschrift für Physikalische Chemie"},"translated_abstract":"In a preceding paper [12]: Z. phys. Chemie 266 (1985) 1057 a general equat ion describing the growth of a new phase in the rmodynamic phase transit ions of first order was derived. This equat ion is applie¿j here first to an investigation of the t ime development of single clusters of a new phase. Based on the proposed in [12] new theory of Ostwald ripening a general theory describing this process for elastic media is developed. This method leads to a set of differential equat ions for the mean cluster radius, the number of clusters and the total mass of the new phase concentrated in the clusters. These equations are valid and can be solved numerically for the whole ripening process including the initial stage. A criterion is established under which condit ions elastic strains lead to a s top of the growth of the clusters and, therefore, t o a quite different asymptotic behaviour of the solutions as compared with the theory of LIFSHITZ, S\u0026#39;.YOZOV and others. In these cases for long times a stationary relatively monodisperse distribution of clusters is established in the system.","internal_url":"https://www.academia.edu/75961373/On_the_Kinetic_Description_of_Ostwald_Ripening_in_Elastic_Media","translated_internal_url":"","created_at":"2022-04-09T22:28:27.236-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":35962046,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_the_Kinetic_Description_of_Ostwald_Ripening_in_Elastic_Media","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":35962046,"first_name":"J.","middle_initials":null,"last_name":"Schmelzer","page_name":"JSchmelzer","domain_name":"independent","created_at":"2015-10-10T01:29:28.791-07:00","display_name":"J. 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The influence of the finite size of the system or the depletion of the surrounding the clusters medium on the work of formation of critical clusters is determined for different thermodynamic constraints. Besides the variations of the parameters of the critical clusters finite-size effects lead to the existence of additional states obeying the necessary thermodynamic equilibrium conditions and to a correction term AW in the equation for the work of formation of critical clusters. It is shown that AW is always negativ. This term AW is, however, overcompensated by the changes of the nucleation work due to the variations of the parameters of the critical clusters. The general results are illustrated by an analysis of the process of an isochoric condensation of a one-component gas in a closed system.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="75961251"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="75961251"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 75961251; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=75961251]").text(description); $(".js-view-count[data-work-id=75961251]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 75961251; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='75961251']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 75961251, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=75961251]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":75961251,"title":"Thermodynamik und Keimbildung","translated_title":"","metadata":{"abstract":"Based on the Gibbs\u0026#39; theory of surface effects a thermodynamic description of a heterogeneous system consisting of s clusters of a new phase in the otherwise homogeneous medium is given. 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