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</div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" 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src="//upload.wikimedia.org/wikipedia/commons/7/72/Potentiostat3.png" decoding="async" width="300" height="169" class="mw-file-element" data-file-width="300" data-file-height="169" /></a><figcaption>Fig. 1 : Schematic of a potentiostat.</figcaption></figure> <p>A <b>potentiostat</b> is the <a href="/wiki/Electronic_hardware" title="Electronic hardware">electronic hardware</a> required to control a <a href="/wiki/Voltammetry#Three_electrode_system" title="Voltammetry">three electrode cell</a> and run most <a href="/wiki/Electroanalytical_method" class="mw-redirect" title="Electroanalytical method">electroanalytical</a> experiments. A <i>Bipotentiostat</i> and <i>polypotentiostat</i> are potentiostats capable of controlling two working electrodes and more than two working electrodes, respectively.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The system functions by maintaining the <a href="/wiki/Voltage" title="Voltage">potential</a> of the <a href="/wiki/Working_electrode" title="Working electrode">working electrode</a> at a constant level with respect to the <a href="/wiki/Reference_electrode" title="Reference electrode">reference electrode</a> by adjusting the <a href="/wiki/Electric_current" title="Electric current">current</a> at an <a href="/wiki/Auxiliary_electrode" title="Auxiliary electrode">auxiliary electrode</a>. The heart of the different potentiostatic electronic circuits is an <a href="/wiki/Operational_amplifier" title="Operational amplifier">operational amplifier</a> (op amp).<sup id="cite_ref-Colburn_2021_5-0" class="reference"><a href="#cite_note-Colburn_2021-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> It consists of an <a href="/wiki/Electric_circuit" class="mw-redirect" title="Electric circuit">electric circuit</a> which is usually described in terms of simple <a href="/wiki/Op_amps" class="mw-redirect" title="Op amps">op amps</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Primary_use">Primary use</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=1" title="Edit section: Primary use"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This equipment is fundamental to modern <a href="/wiki/Electrochemical" class="mw-redirect" title="Electrochemical">electrochemical</a> studies using <a href="/wiki/Voltammetry" title="Voltammetry">three electrode systems</a> for investigations of <a href="/wiki/Electrochemical_reaction_mechanism" title="Electrochemical reaction mechanism">reaction mechanisms</a> related to <a href="/wiki/Redox" title="Redox">redox</a> chemistry and other <a href="/wiki/Chemistry" title="Chemistry">chemical</a> phenomena. The dimensions of the resulting data depend on the experiment. In <a href="/wiki/Voltammetry" title="Voltammetry">voltammetry</a>, <a href="/wiki/Electric_current" title="Electric current">electric current</a> in <a href="/wiki/Ampere" title="Ampere">amps</a> is plotted against <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> in <a href="/wiki/Voltage" title="Voltage">voltage</a>. In a <a href="/wiki/Bulk_electrolysis" title="Bulk electrolysis">bulk electrolysis</a> total <a href="/wiki/Coulomb" title="Coulomb">coulombs</a> passed (total <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a>) is plotted against time in seconds even though the experiment measures electric current (<a href="/wiki/Ampere" title="Ampere">amperes</a>) over time. This is done to show that the experiment is approaching an expected number of coulombs. </p><p>Most early potentiostats could function independently, providing data output through a physical data trace. Modern potentiostats are designed to interface with a <a href="/wiki/Personal_computer" title="Personal computer">personal computer</a> and operate through a dedicated <a href="/wiki/Software" title="Software">software</a> package. The automated software allows the user rapidly to shift between experiments and experimental conditions. The computer allows data to be stored and analyzed more effectively, rapidly, and accurately than the earlier standalone devices. </p> <div class="mw-heading mw-heading2"><h2 id="Basic_relationships">Basic relationships</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=2" title="Edit section: Basic relationships"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A potentiostat is a <a href="/wiki/Controller_(control_theory)" class="mw-redirect" title="Controller (control theory)">control</a> and <a href="/wiki/Measuring" class="mw-redirect" title="Measuring">measuring</a> device. It comprises an <a href="/wiki/Electric_circuit" class="mw-redirect" title="Electric circuit">electric circuit</a> which controls the potential across the cell by sensing changes in its <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a>, varying accordingly the current supplied to the system: a higher resistance will result in a decreased current, while a lower resistance will result in an increased current, in order to keep the voltage constant as described by <a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm's law</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {R}={E \over I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mi>I</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {R}={E \over I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d479ef0696ea31148238fc830f1e7eeb5710cd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.474ex; height:5.176ex;" alt="{\displaystyle {R}={E \over I}}"></span></dd></dl> <p>As a result, the variable system <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> and the controlled current are <a href="/wiki/Inversely_proportional" class="mw-redirect" title="Inversely proportional">inversely proportional</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{o}={E_{c} \over R_{v}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{o}={E_{c} \over R_{v}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c87b746c32814f8cc3845f717b758b02cd229d04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.781ex; height:5.676ex;" alt="{\displaystyle I_{o}={E_{c} \over R_{v}}}"></span> <ul><li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{o}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{o}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c462307420358828e01df3a8b777bc2fb54f5c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.053ex; height:2.509ex;" alt="{\displaystyle I_{o}}"></span></i> is the output electric current of the potentiostat</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f1a398c7e13c50d90d2e8d6a1434dfaf99887f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.659ex; height:2.509ex;" alt="{\displaystyle E_{c}}"></span></i> is the <a href="/wiki/Voltage" title="Voltage">voltage</a> that is kept constant</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40da33633288f9598f0c6f560681e91bcd8fcee2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.794ex; height:2.509ex;" alt="{\displaystyle R_{v}}"></span></i> is the <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">electrical resistance</a> that varies.</li></ul></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Principles_of_operation">Principles of operation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=3" title="Edit section: Principles of operation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since 1942, when the English electrochemist Archie Hickling (<a href="/wiki/University_of_Leicester" title="University of Leicester">University of Leicester</a>) built the first <a href="/wiki/Voltammetry#Three_electrode_system" title="Voltammetry">three electrode</a> potentiostat,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> substantial progress has been made to improve the instrument. Hickling's device used a third electrode, the <a href="/wiki/Reference_electrode" title="Reference electrode">reference electrode</a> to control the cell potential automatically. Up until the present day his principle has remained in use. At a glance, a potentiostat measures the potential difference between the working and the reference electrode, applies the current through the counter electrode and measures the current as an <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> voltage drop over a series resistor (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\textrm {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\textrm {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/032ed254f08780c162d9da52ca8dc685847e659f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.365ex; height:2.509ex;" alt="{\displaystyle R_{\textrm {m}}}"></span> in Fig. 1). </p><p>The control amplifier (CA) is responsible for maintaining the voltage between the reference and the working electrode as closely as possible to the voltage of the input source <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56ab82bee1e0e5ce146952cda795c4a32681db06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.405ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {i}}}"></span>. It adjusts its output to automatically control the cell current so that a condition of equilibrium is satisfied. The theory of operation is best understood using the equations below. </p><p>Prior to observing the following equations, one may note that, from an electrical point of view, the electrochemical cell and the current measurement resistor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\textrm {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\textrm {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/032ed254f08780c162d9da52ca8dc685847e659f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.365ex; height:2.509ex;" alt="{\displaystyle R_{\textrm {m}}}"></span> may be regarded as two impedances (Fig. 2). <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cea9e950915c77b3dcf9d4d54101820f538bc077" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle Z_{1}}"></span> includes <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{\textrm {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{\textrm {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/032ed254f08780c162d9da52ca8dc685847e659f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.365ex; height:2.509ex;" alt="{\displaystyle R_{\textrm {m}}}"></span> in series with the interfacial impedance of the <a href="/wiki/Counter_electrode" class="mw-redirect" title="Counter electrode">counter electrode</a> and the solution resistance between the counter and the reference. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c98d433ae289ecb2b88f895b407538b0e4183b28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle Z_{2}}"></span> represents the interfacial impedance of the working electrode in series with the solution resistance between the working and the reference electrodes. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Potentiostat4.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/06/Potentiostat4.png" decoding="async" width="300" height="169" class="mw-file-element" data-file-width="300" data-file-height="169" /></a><figcaption>Fig. 2 : Schematic of a potentiostat, with electrochemical cell replaced by two impedances.</figcaption></figure> <p>The role of the control amplifier is to amplify the potential difference between the positive (or noninverting) input and the negative (or inverting) input. This may be translated mathematically into the following equation: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {out}}=A\,(E^{+}-E^{-})=A\,(E_{\textrm {i}}-E_{\textrm {r}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mi>A</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>−</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mspace width="thinmathspace" /> <mo stretchy="false">(</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {out}}=A\,(E^{+}-E^{-})=A\,(E_{\textrm {i}}-E_{\textrm {r}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75aa67de2dc3af5396ca8c019ae2377c4c88a9c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.686ex; height:3.009ex;" alt="{\displaystyle E_{\textrm {out}}=A\,(E^{+}-E^{-})=A\,(E_{\textrm {i}}-E_{\textrm {r}})}"></span>. (1)</dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> is the amplification factor of the CA. At this point the assumption may be made that a negligible amount of current is flowing through the reference electrode. This correlates to physical phenomenon since the reference electrode is connected to a high impedance electrometer. Thus, the cell current may be described in two ways: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {out}}}{Z_{1}+Z_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </mrow> </msub> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {out}}}{Z_{1}+Z_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e4cb0d5c2ef69ddc3f3f23a206d0143cc630951" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.044ex; height:5.509ex;" alt="{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {out}}}{Z_{1}+Z_{2}}}}"></span>(2)</dd></dl> <p>and </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {r}}}{Z_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </mrow> </msub> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {r}}}{Z_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8881c84192057e3a7f6ddde9d8ad6a34f0d55ff3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:8.562ex; height:5.509ex;" alt="{\displaystyle I_{\textrm {c}}={\frac {E_{\textrm {r}}}{Z_{2}}}}"></span>. (3)</dd></dl> <p>Combining Eqs. (2) and (3) yields Eq. (4): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {r}}={\frac {Z_{2}}{Z_{1}+Z_{2}}}\,E_{\textrm {out}}=\beta \,E_{\textrm {out}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mi>β</mi> <mspace width="thinmathspace" /> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>out</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {r}}={\frac {Z_{2}}{Z_{1}+Z_{2}}}\,E_{\textrm {out}}=\beta \,E_{\textrm {out}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a06e0f7ab6b424d5e29e654af455958972f3eda6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:28.501ex; height:5.509ex;" alt="{\displaystyle E_{\textrm {r}}={\frac {Z_{2}}{Z_{1}+Z_{2}}}\,E_{\textrm {out}}=\beta \,E_{\textrm {out}}}"></span> (4)</dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> is the fraction of the output voltage of the control amplifier returned to its negative input; namely the feedback factor: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta ={\frac {Z_{2}}{Z_{1}+Z_{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {Z_{2}}{Z_{1}+Z_{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d60c8b97eddd71ec68c637147adfb1489e2a2c56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.39ex; height:5.509ex;" alt="{\displaystyle \beta ={\frac {Z_{2}}{Z_{1}+Z_{2}}}}"></span>.</dd></dl> <p>Combining Eqs. (1) and (4) yields Eq. (6): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {E_{\textrm {r}}}{E_{\textrm {i}}}}={\frac {\beta \,A}{1+\beta \,A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>β</mi> <mspace width="thinmathspace" /> <mi>A</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>β</mi> <mspace width="thinmathspace" /> <mi>A</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {E_{\textrm {r}}}{E_{\textrm {i}}}}={\frac {\beta \,A}{1+\beta \,A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13b86eb675d4bac0623df63680bfc46d0bcda9da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.828ex; height:5.843ex;" alt="{\displaystyle {\frac {E_{\textrm {r}}}{E_{\textrm {i}}}}={\frac {\beta \,A}{1+\beta \,A}}}"></span>. (6)</dd></dl> <p>When the quantity <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> becomes very large with respect to one, Eq. (6) reduces to Eq. (7), which is one of the negative feedback equations: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {i}}=E_{\textrm {r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>i</mtext> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {i}}=E_{\textrm {r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ecee6caaf592d311d37f4317ee62b1db015df2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.095ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {i}}=E_{\textrm {r}}}"></span>. (7)</dd></dl> <p>Eq. (7) proves that the control amplifier works to keep the voltage between the reference and the working close to the input source voltage. </p> <div class="mw-heading mw-heading2"><h2 id="Software_control">Software control</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=4" title="Edit section: Software control"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Replacing the CA, a control algorithm can maintain a constant voltage <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81d834a63ef65c315b4bd2d77ee410f782ea72d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.678ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {c}}}"></span> between the reference electrode and the working electrode.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> This algorithm is based on the <a href="/wiki/Rule_of_proportion" class="mw-redirect" title="Rule of proportion">rule of proportion</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {U_{\textrm {m}}}{E_{\textrm {c}}}}={\frac {U_{\textrm {n}}}{E_{\textrm {SP}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>n</mtext> </mrow> </mrow> </msub> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SP</mtext> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {U_{\textrm {m}}}{E_{\textrm {c}}}}={\frac {U_{\textrm {n}}}{E_{\textrm {SP}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f479120495437aad7fbf4ba422c16109c08c7318" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.94ex; height:5.676ex;" alt="{\displaystyle {\frac {U_{\textrm {m}}}{E_{\textrm {c}}}}={\frac {U_{\textrm {n}}}{E_{\textrm {SP}}}}}"></span>. (8)</dd></dl> <dl><dd><ul><li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\textrm {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\textrm {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1320b27754bf6da0640aa31a8b2e6118b17463ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle U_{\textrm {m}}}"></span></i> is the last measured cell voltage between the working electrode (WE) and the counter electrode (CE).</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81d834a63ef65c315b4bd2d77ee410f782ea72d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.678ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {c}}}"></span></i> is the last measured electrochemical potential, i.e. the voltage between the reference electrode and WE to be kept constant.</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\textrm {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>n</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\textrm {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe55324037633d3cca10a644b4ad03a969f06f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.734ex; height:2.509ex;" alt="{\displaystyle U_{\textrm {n}}}"></span></i> is the next cell voltage to be set, i.e. the controller output.</li> <li><i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {SP}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SP</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {SP}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e64a8c2ebb3639a87c3b1ff70739ffa245a37d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.981ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {SP}}}"></span></i> is the <a href="/wiki/Setpoint_(control_system)" title="Setpoint (control system)">setpoint</a>, i.e. the desired <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81d834a63ef65c315b4bd2d77ee410f782ea72d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.678ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {c}}}"></span>.</li></ul></dd></dl> <p>If the measurement intervals of Eq. (8) are kept constant, the control algorithm sets the cell voltage <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U_{\textrm {m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>U</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U_{\textrm {m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1320b27754bf6da0640aa31a8b2e6118b17463ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.189ex; height:2.509ex;" alt="{\displaystyle U_{\textrm {m}}}"></span> so to keep <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81d834a63ef65c315b4bd2d77ee410f782ea72d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.678ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {c}}}"></span> as close as possible to the setpoint <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\textrm {SP}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>SP</mtext> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\textrm {SP}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e64a8c2ebb3639a87c3b1ff70739ffa245a37d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.981ex; height:2.509ex;" alt="{\displaystyle E_{\textrm {SP}}}"></span>. The algorithm requires software-controllable hardware such as a <a href="/wiki/Digital_multimeter" class="mw-redirect" title="Digital multimeter">digital multimeter</a>, a <a href="/wiki/Power_supply" title="Power supply">power supply</a>, and a double-pole double-throw <a href="/wiki/Relay" title="Relay">relay</a>. The relay is necessary to switch polarity. </p> <div class="mw-heading mw-heading2"><h2 id="Significant_features">Significant features</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=5" title="Edit section: Significant features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In electrochemical experiments the electrodes are the pieces of equipment that comes in immediate contact with the <a href="/wiki/Analyte" title="Analyte">analyte</a>. For this reason the electrodes are very important for determining the experimental result. The electrode surface may or may not catalyze chemical reactions. The size of the electrodes affects the magnitude of the currents passed which can affect signal to noise. But electrodes are not the only limiting factor for electrochemical experiments, the potentiostat also has a limited range of operation. The following are a few significant features that vary between instruments. </p> <ul><li><i>Electric potential range (measured and applied)</i>: while the potential window is mostly based on the solvent window the electronics can also limit the possible range.</li> <li><i>Accuracy in potential (measured and applied)</i>: limits of deviations between the actual and reported.</li> <li><i>Range of scan rate</i>: how slow or fast a potential window can be scanned. This is most important for experiments that require high scan rates such as those involving <a href="/wiki/Ultramicroelectrode" title="Ultramicroelectrode">ultramicroelectrodes</a>.</li> <li><i>Sample rate</i>: the rate at which potential or voltage can be accurately sampled. This can be important for experiments that need high scan rates such as those involving ultramicroelectrodes.</li> <li><i>File size</i>: a limiting factor can be the file size limit. This would most likely affect the choice of the potential range swept or the potential sample rate.</li> <li><i>Electric current range (measured and applied)</i>: the maximum range over which current can be sampled. Applying large currents is important for experiments that pass a great deal of current like a large <a href="/wiki/Bulk_electrolysis" title="Bulk electrolysis">bulk electrolysis</a>. Measuring small currents is important for experiments that pass small currents like those involving ultramicroelectrodes.</li> <li><i>Current resolution</i>: determines the operational range of a specific experiment and the bit resolution of that data in the current dimension.</li> <li><i>Accuracy in current (measured and applied)</i>: limits of deviations between the actual and reported.</li> <li><i>Number of working channels</i>: how many <a href="/wiki/Working_electrode" title="Working electrode">working electrodes</a> can the instrument control. A <i>bipotentiostat</i> is necessary to controlling systems with two working electrodes like a <a href="/wiki/Rotating_ring-disk_electrode" title="Rotating ring-disk electrode">rotating ring-disk electrode</a>. A <i>polypotentiostat</i> may be important for controlling some biological experiments with three or more working electrodes. In conjunction with a Zero Resistance Ammeter per electrode many polarisations can be monitored at the same time in the same cell around the <sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (July 2023)">clarification needed</span></a></i>]</sup> he couple potential. If the Zero Resistance Ammeters have an offsetting ability, then multiple tests can be achieved at the same time in the same test cell around the individual rest potential of each electrode. Such features can be useful for corrosion monitoring of coated electrodes or segmented but otherwise coupled welds.</li> <li><i>Footprint</i>: potentiostats include small devices of about 20 x 10 x 5 cm weighing well under a kilogram or a simple board that can be installed in a desktop computer. A large bench-top model would be on the order of 50 x 20 x 10 cm and weigh up to or more than 5 kilograms.</li> <li><i>Interface</i>: can the instrument run independently or must it be slaved to a personal computer.</li> <li><i>Sweep generator</i>: can the system apply an analogue sweep or does it use a digital staircase generator as an approximation. If it does use a digital staircase then the resolution of the staircase is important.</li> <li><i>Rotating electrode</i>: can the instrument operate a rotating electrode. This is intrinsic for experiments that require a <a href="/wiki/Rotating_disk_electrode" title="Rotating disk electrode">rotating disk electrode</a> or <a href="/wiki/Rotating_ring-disk_electrode" title="Rotating ring-disk electrode">rotating ring-disk electrode</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Amperostat" class="mw-redirect" title="Amperostat">Amperostat</a></li> <li><a href="/wiki/Coulometry" title="Coulometry">Coulometry</a></li> <li><a href="/wiki/Electroanalytical_method" class="mw-redirect" title="Electroanalytical method">Electroanalytical method</a></li> <li><a href="/wiki/Galvanostat" title="Galvanostat">Galvanostat</a></li> <li><a href="/wiki/Operational_amplifier" title="Operational amplifier">Operational amplifier</a></li> <li><a href="/wiki/Polarography" title="Polarography">Polarography</a></li> <li><a href="/wiki/Potentiometry" class="mw-redirect" title="Potentiometry">Potentiometry</a></li> <li><a href="/wiki/Voltammetry" title="Voltammetry">Voltammetry</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Bard, A.J.; Faulkner, L.R. (2000). Electrochemical Methods: Fundamentals and Applications. New York: John Wiley & Sons, 2nd Edition, <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-40521-3" title="Special:BookSources/0-471-40521-3">0-471-40521-3</a>.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Cynthia G. Zoski (Editor) (2007). <a href="/wiki/Handbook_of_Electrochemistry" title="Handbook of Electrochemistry">Handbook of Electrochemistry</a>. Elsevier, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-444-51958-0" title="Special:BookSources/0-444-51958-0">0-444-51958-0</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Peter T. Kissinger, William R. Heineman (1996). Laboratory Techniques in Electroanalytical Chemistry. CRC Press, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8247-9445-1" title="Special:BookSources/0-8247-9445-1">0-8247-9445-1</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Douglas A. Skoog, F. James Holler, Timothy A. Nieman (1998). Principles of Instrumental Analysis. Harcourt Brace College Publishers,<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-03-002078-6" title="Special:BookSources/0-03-002078-6">0-03-002078-6</a>.</span> </li> <li id="cite_note-Colburn_2021-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Colburn_2021_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFW._ColburnJ._LeveyO'HareV._Macpherson2021" class="citation journal cs1">W. Colburn, Alex; J. Levey, Katherine; O'Hare, Danny; V. Macpherson, Julie (2021). <a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FD1CP00661D">"Lifting the lid on the potentiostat: a beginner's guide to understanding electrochemical circuitry and practical operation"</a>. <i>Physical Chemistry Chemical Physics</i>. <b>23</b> (14): 8100–8117. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PCCP...23.8100C">2021PCCP...23.8100C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FD1CP00661D">10.1039/D1CP00661D</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33875985">33875985</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Chemistry+Chemical+Physics&rft.atitle=Lifting+the+lid+on+the+potentiostat%3A+a+beginner%27s+guide+to+understanding+electrochemical+circuitry+and+practical+operation&rft.volume=23&rft.issue=14&rft.pages=8100-8117&rft.date=2021&rft_id=info%3Apmid%2F33875985&rft_id=info%3Adoi%2F10.1039%2FD1CP00661D&rft_id=info%3Abibcode%2F2021PCCP...23.8100C&rft.aulast=W.+Colburn&rft.aufirst=Alex&rft.au=J.+Levey%2C+Katherine&rft.au=O%27Hare%2C+Danny&rft.au=V.+Macpherson%2C+Julie&rft_id=https%3A%2F%2Fdoi.org%2F10.1039%252FD1CP00661D&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHickling1942" class="citation journal cs1">Hickling, A. (1942). "Studies in electrode polarisation. Part IV.-The automatic control of the potential of a working electrode". <i>Transactions of the Faraday Society</i>. <b>38</b>: 27–33. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FTF9423800027">10.1039/TF9423800027</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Faraday+Society&rft.atitle=Studies+in+electrode+polarisation.+Part+IV.-The+automatic+control+of+the+potential+of+a+working+electrode&rft.volume=38&rft.pages=27-33&rft.date=1942&rft_id=info%3Adoi%2F10.1039%2FTF9423800027&rft.aulast=Hickling&rft.aufirst=A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegert2018" class="citation journal cs1">Siegert, M. (2018). <a rel="nofollow" class="external text" href="https://doi.org/10.3389%2Ffenrg.2018.00131">"A scalable multi-channel software potentiostat"</a>. <i><a href="/wiki/Frontiers_in_Energy_Research" class="mw-redirect" title="Frontiers in Energy Research">Frontiers in Energy Research</a></i>. <b>6</b>: 131. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3389%2Ffenrg.2018.00131">10.3389/fenrg.2018.00131</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Frontiers+in+Energy+Research&rft.atitle=A+scalable+multi-channel+software+potentiostat&rft.volume=6&rft.pages=131&rft.date=2018&rft_id=info%3Adoi%2F10.3389%2Ffenrg.2018.00131&rft.aulast=Siegert&rft.aufirst=M.&rft_id=https%3A%2F%2Fdoi.org%2F10.3389%252Ffenrg.2018.00131&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=8" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060301201416/http://chemeducator.org/sbibs/s0011001/spapers/1110023dr.htm">"An Inexpensive Field-Portable Programmable Potentiostat"</a>. <i>The Chemical Educator</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1333%2Fs00897050972a">10.1333/s00897050972a</a>. Archived from <a rel="nofollow" class="external text" href="http://chemeducator.org/sbibs/s0011001/spapers/1110023dr.htm">the original</a> on 2006-03-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-10-06</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Chemical+Educator&rft.atitle=An+Inexpensive+Field-Portable+Programmable+Potentiostat&rft_id=info%3Adoi%2F10.1333%2Fs00897050972a&rft_id=http%3A%2F%2Fchemeducator.org%2Fsbibs%2Fs0011001%2Fspapers%2F1110023dr.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStaicopoulos1961" class="citation journal cs1">Staicopoulos, D. N. (1961). "High Current Electronic Potentiostat". <i>Review of Scientific Instruments</i>. <b>32</b> (2): 176–178. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961RScI...32..176S">1961RScI...32..176S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.1717304">10.1063/1.1717304</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Review+of+Scientific+Instruments&rft.atitle=High+Current+Electronic+Potentiostat&rft.volume=32&rft.issue=2&rft.pages=176-178&rft.date=1961&rft_id=info%3Adoi%2F10.1063%2F1.1717304&rft_id=info%3Abibcode%2F1961RScI...32..176S&rft.aulast=Staicopoulos&rft.aufirst=D.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFriedmanRosenbaumLeeLipson2012" class="citation journal cs1">Friedman, Elliot S.; Rosenbaum, Miriam A.; Lee, Alexander W.; Lipson, David. A.; Land, Bruce R.; Angenent, Largus T. (2012). "A cost-effective and field-ready potentiostat that poises subsurface electrodes to monitor bacterial respiration". <i>Biosensors and Bioelectronics</i>. <b>32</b> (1): 309–313. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.bios.2011.12.013">10.1016/j.bios.2011.12.013</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22209069">22209069</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Biosensors+and+Bioelectronics&rft.atitle=A+cost-effective+and+field-ready+potentiostat+that+poises+subsurface+electrodes+to+monitor+bacterial+respiration&rft.volume=32&rft.issue=1&rft.pages=309-313&rft.date=2012&rft_id=info%3Adoi%2F10.1016%2Fj.bios.2011.12.013&rft_id=info%3Apmid%2F22209069&rft.aulast=Friedman&rft.aufirst=Elliot+S.&rft.au=Rosenbaum%2C+Miriam+A.&rft.au=Lee%2C+Alexander+W.&rft.au=Lipson%2C+David.+A.&rft.au=Land%2C+Bruce+R.&rft.au=Angenent%2C+Largus+T.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFW._ColburnJ._LeveyO'HareV._Macpherson2021" class="citation journal cs1">W. Colburn, Alex; J. Levey, Katherine; O'Hare, Danny; V. Macpherson, Julie (2021). <a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FD1CP00661D">"Lifting the lid on the potentiostat: a beginner's guide to understanding electrochemical circuitry and practical operation"</a>. <i>Physical Chemistry Chemical Physics</i>. <b>23</b> (14): 8100–8117. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2021PCCP...23.8100C">2021PCCP...23.8100C</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1039%2FD1CP00661D">10.1039/D1CP00661D</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/33875985">33875985</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Chemistry+Chemical+Physics&rft.atitle=Lifting+the+lid+on+the+potentiostat%3A+a+beginner%27s+guide+to+understanding+electrochemical+circuitry+and+practical+operation&rft.volume=23&rft.issue=14&rft.pages=8100-8117&rft.date=2021&rft_id=info%3Apmid%2F33875985&rft_id=info%3Adoi%2F10.1039%2FD1CP00661D&rft_id=info%3Abibcode%2F2021PCCP...23.8100C&rft.aulast=W.+Colburn&rft.aufirst=Alex&rft.au=J.+Levey%2C+Katherine&rft.au=O%27Hare%2C+Danny&rft.au=V.+Macpherson%2C+Julie&rft_id=https%3A%2F%2Fdoi.org%2F10.1039%252FD1CP00661D&rfr_id=info%3Asid%2Fen.wikipedia.org%3APotentiostat" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Potentiostat&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Genady Ragoisha (webmaster), "<i><a rel="nofollow" class="external text" href="http://www.abc.chemistry.bsu.by/vi/">Potentiodynamic electrochemical impedance spectroscopy (PDEIS)</a></i>", Physico-Chemical Research Institute, Belarusian State University. A description of the use of a potentiostat in <a href="/wiki/Virtual_instrumentation" title="Virtual instrumentation">virtual instrumentation</a> for electrochemical experiments.</li> <li>Pierre R. Roberge (Webmaster) "<i><a rel="nofollow" class="external text" href="http://www.corrosion-doctors.org/Instrumentation/potentiostat.htm">Potentiostat</a></i>", corrosion-doctors.org <a rel="nofollow" class="external text" href="http://www.corrosion-doctors.org/Principles/Glossary.htm">Electrochemistry Dictionary</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.plosone.org/article/info:doi%2F10.1371%2Fjournal.pone.0023783">"CheapStat: An Open-Source, “Do-It-Yourself” Potentiostat..."</a>, Aaron A. Rowe <i>et al.</i>, University of California Santa Barbara</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Potentiostat&oldid=1247518594">https://en.wikipedia.org/w/index.php?title=Potentiostat&oldid=1247518594</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Electroanalytical_chemistry_devices" title="Category:Electroanalytical chemistry devices">Electroanalytical chemistry devices</a></li><li><a href="/wiki/Category:Electronic_engineering" title="Category:Electronic engineering">Electronic engineering</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_July_2023" title="Category:Wikipedia articles needing clarification from July 2023">Wikipedia articles needing clarification from July 2023</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 24 September 2024, at 17:12<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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