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Exactly solved models are especially important in the theory of phase transitions. A number of exactly solved models of phase transitions in a single polymer chain are discussed in this review. These are three models demonstrating the second order phase transitions with some unusual features: twodimensional model of β-structure formation, the model of coil-globule transition, and adsorption a polymer chain grafted on the solid surface. We discuss also models with first order phase transitions in a single macromolecule which admit not only exact analytical solutions for the partition function with explicit finite finite-size effects but also the non-equilibrium free energy as a function of the order parameter (Landau function) in closed analytical form. One of them is a model of mechanical desorption of a macromolecule which demonstrates an unusual first order phase transitions with phase coexistence within a single chain. Features of first and second order transitions become mixed here due to phase coexistence which is not accompanied by additional interfacial free energy.","publication_date":"2011,,","publication_name":"Journal of Physics A: Mathematical and Theoretical","grobid_abstract_attachment_id":"40200927"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Unconventional phase transitions in a constrained single polymer chain","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [38757218]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" 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E, Statistical, nonlinear, and soft matter physics, 2002</p><p class="ds-related-work--abstract ds2-5-body-sm">We report on the conformational properties and transitions of an ideal polymer chain near a solid surface. The chain is tethered with one of its ends at distance z(0) from an adsorbing surface. The surface is characterized by an adsorption parameter c. The exact expression for the partition function is available. We obtained the distribution of complex zeros of this function. The comparison with the Yang-Lee theory allows the characterization of the phase transitions. A first-order conformational transition from a coil to a (adsorbed) flower conformation occurs at c(*)=6z(0)/N. The flower is composed of a strongly stretched stem and a pancake that collects the remaining adsorbed segments. The degree of stretching of the coil or of the stem serves as an order parameter which parametrizes the analytical expressions of the Landau free energy. The phase diagram with one binodal and two spinodal lines is presented. 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