Mathcad Professional 14.0 <description/> <author>gulaboskirubin@outlook.de</author> <company/> <keywords/> <revisedBy>Media</revisedBy> </userData> <identityInfo> <revision>4</revision> <documentID>C842F6AB-7F37-4A54-894D-8F5357D2EB34</documentID> <versionID>54A1EC90-2857-42F9-B83E-0A84CD252FBD</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" 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automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="mks" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <polar item-idref="1"/> <xy item-idref="2"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="1488" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="790" left="12" top="15" width="440.25" height="42" align-x="24" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="16"> <b>EC</b> </f> <f family="Georgia" charset="0" size="16"> <b> <sub>rev</sub> </b> </f> <f family="Georgia" charset="0" size="16"> <b> electrode mechanism at a planar electrode of a dissolved redox couple in Cyclic Staircse Voltammetry</b> </f> </p> </text> </region> <region region-id="1485" left="36" top="84.75" width="187.5" height="24" align-x="43.5" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="14"> <b>Red = Ox + </b> </f> <f family="Georgia" charset="0" size="14"> <b>e</b> </f> <f family="Georgia" charset="0" size="14"> <b> <sup>- <tab/> <tab/> </sup> </b> </f> <f family="Georgia" charset="0" size="14"> <b>(</b> </f> <f family="Georgia" charset="0" size="14"> <i> <b>k</b> </i> </f> <b> <sub> <f family="Georgia" charset="0" size="14">s</f> </sub> </b> <f family="Georgia" charset="0" size="14"> <b>, </b> </f> <f family="Symbol" charset="2" size="14"> <b> <i>a</i> </b> </f> <f family="Georgia" charset="0" size="14"> <b>)</b> </f> </p> </text> </region> <region region-id="1486" left="318" top="96.75" width="47.25" height="13.5" align-x="318" align-y="108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(1)</b> </f> </p> </text> </region> <region region-id="1483" left="42" top="139.5" width="261" height="23.25" align-x="49.5" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="14"> <b>Ox = Y<tab/> </b> </f> <f family="Georgia" charset="0" size="14"> <b> <sup> <sp/> <tab/> <tab/> </sup> </b> </f> <f family="Georgia" charset="0" size="14"> <b>(</b> </f> <f family="Georgia" charset="0" size="14"> <i> <b>k</b> </i> </f> <f family="Georgia" charset="0" size="14"> <b> <i> <sub>f</sub> </i> </b> </f> <f family="Georgia" charset="0" size="14"> <b>, </b> </f> <f family="Georgia" charset="0" size="14"> <b> <i>k</i> </b> </f> <b> <i> <sub> <f family="Georgia" charset="0" size="14">b</f> </sub> </i> </b> <f family="Georgia" charset="0" size="14"> <b> <i>, K</i> </b> </f> <f family="Georgia" charset="0" size="14"> <b> <inlineAttr font-style="normal"> <sub>eq</sub> </inlineAttr> </b> </f> <f family="Georgia" charset="0" size="14"> <b>)</b> </f> </p> </text> </region> <region region-id="1487" left="318" top="150.75" width="45.75" height="13.5" align-x="318" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(2)</b> </f> </p> </text> </region> <region region-id="783" left="6" top="165" width="464.25" height="12.75" align-x="237" align-y="174" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">________________________________________________________________________________________</ml:id> </math> <rendering item-idref="3"/> </region> <region region-id="1237" left="30" top="213" width="42" height="12.75" align-x="47.25" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Es</ml:id> <ml:real>-0.5</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="1198" left="108" top="210.75" width="255.75" height="13.5" align-x="122.25" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">startiung potential (in V vs. the formal potential)</f> </p> </text> </region> <region region-id="1236" left="30" top="249" width="36.75" height="12.75" align-x="47.25" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Ef</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="1199" left="108" top="246.75" width="254.25" height="27" align-x="122.25" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">switching potential (in V vs. the formal potential)</f> </p> </text> </region> <region region-id="1235" left="30" top="279" width="45.75" height="12.75" align-x="47.25" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">dE</ml:id> <ml:real font="0">0.005</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="1200" left="108" top="276.75" width="162" height="13.5" align-x="122.25" align-y="288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">potential step increment (in V)</f> </p> </text> </region> <region region-id="1234" left="30" top="315" width="61.5" height="12.75" align-x="50.25" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:provenance expr-id="1" xmlns:ml="http://schemas.mathsoft.com/math30"> <originRef doc-id="5FE9E937-8CB1-49F7-99E8-EAA4226B0FDA" version-id="422E8821-760F-45AB-815C-A07E9F47D78F" branch-id="00000000-0000-0000-0000-000000000000" revision-num="303748516" is-modified="false" region-id="0" href="C:\Users\Rubin\Desktop\Mathcad fajlovi rubin\E-Catal difuzionen Cyclic-2014-TOCHEN.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </originRef> <parentRef doc-id="B9EB42A0-B946-4A76-9693-28D649555FEB" version-id="736F387A-8EB4-4165-8A8F-371F07A04E75" branch-id="00000000-0000-0000-0000-000000000000" revision-num="303748916" is-modified="false" region-id="0" href="C:\Users\Rubin\Desktop\Mathcad fajlovi rubin\EC difuzionen-reverzibilna-CV-2016-1.xmcd" xmlns="http://schemas.mathsoft.com/provenance10"> <hash/> </parentRef> <comment xmlns="http://schemas.mathsoft.com/provenance10"/> <originComment xmlns="http://schemas.mathsoft.com/provenance10"/> <contentHash xmlns="http://schemas.mathsoft.com/provenance10">8825f726ca548242bfcb8b4e7661b548</contentHash> <ml:define> <ml:id xml:space="preserve">ΔE</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">Ef</ml:id> <ml:id xml:space="preserve">Es</ml:id> </ml:apply> </ml:define> </ml:provenance> </math> <rendering item-idref="7"> <element-image-map> <box left="1.5" top="0.75" width="60" height="11.25" expr-idref="1" xmlns="http://schemas.mathsoft.com/worksheet30"/> </element-image-map> </rendering> </region> <region region-id="1201" left="108" top="312.75" width="90" height="13.5" align-x="122.25" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">potential window</f> </p> </text> </region> <region region-id="1233" left="30" top="351" width="31.5" height="12.75" align-x="42" align-y="360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v</ml:id> <ml:real>0.1</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="1223" left="114" top="348.75" width="156.75" height="13.5" align-x="120.75" align-y="360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">potential scan rate in V/s </f> </p> </text> </region> <region region-id="1232" left="30" top="386.25" width="34.5" height="27.75" align-x="42.75" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">τ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">dE</ml:id> <ml:id xml:space="preserve">v</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="1202" left="108" top="390.75" width="156.75" height="13.5" align-x="114.75" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">duartion of a single step (in s)</f> </p> </text> </region> <region region-id="1231" left="30" top="423" width="40.5" height="12.75" align-x="41.25" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">τ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.049999999999999996</ml:real> </result> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="1230" left="30" top="453" width="33" height="12.75" align-x="45.75" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">M</ml:id> <ml:real>25</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="1203" left="108" top="450.75" width="294.75" height="13.5" align-x="114.75" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">numer of time increments in a single potential step</f> </p> </text> </region> <region region-id="1229" left="30" top="482.25" width="33" height="27.75" align-x="42.75" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">d</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">τ</ml:id> <ml:id xml:space="preserve">M</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1204" left="108" top="486.75" width="112.5" height="13.5" align-x="114.75" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">time increment (in s)</f> </p> </text> </region> <region region-id="1228" left="30" top="536.25" width="56.25" height="27.75" align-x="59.25" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>400</ml:real> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="1206" left="108" top="540.75" width="157.5" height="27" align-x="114.75" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">total number of potential steps</f> </p> </text> </region> <region region-id="1227" left="30" top="584.25" width="69.75" height="27.75" align-x="43.5" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">m</ml:id> <ml:range> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> <ml:real>25</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="1207" left="108" top="588.75" width="171" height="27" align-x="114.75" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">serial number of time inceremnts</f> </p> </text> </region> <region region-id="1327" left="6" top="641.25" width="352.5" height="42.75" align-x="25.5" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve">m</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> <ml:real>25</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Es</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:real>25</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">Ef</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">ceil</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> <ml:real>25</ml:real> </ml:apply> </ml:parens> </ml:apply> <ml:real>25</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1329" left="384" top="660.75" width="93" height="13.5" align-x="390.75" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">potential ramp</f> </p> </text> </region> <region region-id="1328" left="498" top="660.75" width="30" height="13.5" align-x="498" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(3)</b> </f> </p> </text> </region> <region region-id="731" left="6" top="699" width="474.75" height="12.75" align-x="242.25" align-y="708" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">__________________________________________________________________________________________</ml:id> </math> <rendering item-idref="16"/> </region> <region region-id="1026" left="12" top="738" width="246" height="153.75" align-x="12" align-y="738" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="17"/> <rendering item-idref="18"/> </region> <region region-id="1250" left="12" top="921" width="42.75" height="12.75" align-x="24" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">F</ml:id> <ml:real>96485</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1067" left="114" top="918.75" width="81.75" height="27" align-x="120.75" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">Farady constant</f> </p> </text> </region> <region region-id="1249" left="12" top="945" width="45.75" height="12.75" align-x="24.75" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T</ml:id> <ml:real>298.15</ml:real> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="1066" left="114" top="942.75" width="153.75" height="27" align-x="143.25" align-y="954" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">theromodynamic temperature</f> </p> </text> </region> <region region-id="1248" left="12" top="981" width="42" height="12.75" align-x="25.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R</ml:id> <ml:real>8.314</ml:real> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="1065" left="114" top="978.75" width="72" height="27" align-x="122.25" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">Gass constant</f> </p> </text> </region> <region region-id="1247" left="12" top="1005" width="24.75" height="12.75" align-x="24" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="1064" left="114" top="1002.75" width="177.75" height="27" align-x="138" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">stoichiometric number of electrons</f> </p> </text> </region> <region region-id="1347" left="12" top="1034.25" width="72" height="27.75" align-x="33" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">F</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R</ml:id> <ml:id xml:space="preserve">T</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1348" left="114" top="1038.75" width="123" height="13.5" align-x="132.75" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">dimensionless potential</f> </p> </text> </region> <region region-id="1349" left="276" top="1038.75" width="30" height="13.5" align-x="276" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(4)</b> </f> </p> </text> </region> <region region-id="1245" left="12" top="1077" width="50.25" height="18.75" align-x="25.5" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">D</ml:id> <ml:apply> <ml:mult/> <ml:real>5</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1062" left="114" top="1077.75" width="224.25" height="16.5" align-x="120.75" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">common diffusion coefficient in cm</f> <f family="Georgia" charset="0" size="12"> <sup>2</sup> </f> <f family="Georgia" charset="0" size="12">/s</f> </p> </text> </region> <region region-id="1244" left="12" top="1107" width="44.25" height="12.75" align-x="27.75" align-y="1116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ks</ml:id> <ml:real>0.005</ml:real> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="1061" left="114" top="1104.75" width="269.25" height="13.5" align-x="141.75" align-y="1116" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">electrochemical standard rate constant in cm/s</f> </p> </text> </region> <region region-id="1243" left="12" top="1131" width="32.25" height="12.75" align-x="24.75" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="1060" left="114" top="1128.75" width="137.25" height="27" align-x="127.5" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">electron transfer coeffcient</f> </p> </text> </region> <region region-id="1242" left="12" top="1155" width="44.25" height="12.75" align-x="27.75" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">kf</ml:id> <ml:real>0.010</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="1059" left="114" top="1149.75" width="286.5" height="16.5" align-x="128.25" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">forward rate constant of the chemical recation in s</f> <f family="Georgia" charset="0" size="12"> <sup>-1</sup> </f> </p> </text> </region> <region region-id="1241" left="12" top="1185" width="29.25" height="12.75" align-x="28.5" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">kb</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1058" left="114" top="1179.75" width="289.5" height="16.5" align-x="132.75" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">backward rate constant of the chemical reaction </f> <f family="Georgia" charset="0" size="12">in s</f> <f family="Georgia" charset="0" size="12"> <sup>-1</sup> </f> </p> </text> </region> <region region-id="1240" left="12" top="1214.25" width="44.25" height="27.75" align-x="35.25" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Keq</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">kf</ml:id> <ml:id xml:space="preserve">kb</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="1057" left="114" top="1218.75" width="306" height="13.5" align-x="133.5" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">equilibrium contant of the follow up chemical reaction</f> </p> </text> </region> <region region-id="1239" left="12" top="1254.75" width="50.25" height="30.75" align-x="26.25" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ks</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">τ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">D</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="1056" left="114" top="1260.75" width="283.5" height="13.5" align-x="138" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">dimensionless electrode kinetic parameter</f> </p> </text> </region> <region region-id="1238" left="12" top="1305" width="90" height="12.75" align-x="46.5" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kchem</ml:id> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">kf</ml:id> <ml:id xml:space="preserve">kb</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">τ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1055" left="114" top="1302.75" width="264" height="13.5" align-x="135.75" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">dimensioless chemical kinetic parameter</f> </p> </text> </region> <region region-id="1121" left="6" top="1353" width="464.25" height="12.75" align-x="237" align-y="1362" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">________________________________________________________________________________________</ml:id> </math> <rendering item-idref="32"/> </region> <region region-id="1363" left="18" top="1381.5" width="82.5" height="19.5" align-x="36.75" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">S</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="1362" left="270" top="1380.75" width="166.5" height="27" align-x="287.25" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">numerical integration parameter</f> </p> </text> </region> <region region-id="1361" left="474" top="1380.75" width="51" height="13.5" align-x="474" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(5)</b> </f> </p> </text> </region> <region region-id="1123" left="18" top="1428.75" width="205.5" height="29.25" align-x="40.5" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">M</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">erf</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kchem</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:real>25</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:id xml:space="preserve">erf</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kchem</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>25</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="1126" left="270" top="1434.75" width="166.5" height="27" align-x="287.25" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">numerical integration parameter</f> </p> </text> </region> <region region-id="1357" left="474" top="1434.75" width="36.75" height="13.5" align-x="474" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(6)</b> </f> </p> </text> </region> <region region-id="1122" left="6" top="1467" width="464.25" height="12.75" align-x="237" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">________________________________________________________________________________________</ml:id> </math> <rendering item-idref="35"/> </region> <region region-id="1472" left="6" top="1512.75" width="288" height="64.5" align-x="25.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>-2</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">25</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Keq</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">M</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">Kchem</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Keq</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="1467" left="444" top="1542.75" width="37.5" height="13.5" align-x="444" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(7)</b> </f> </p> </text> </region> <region region-id="1251" left="384" top="1566.75" width="297" height="27" align-x="401.25" align-y="1578" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>Recurent formulas for calculating the dimensioless current</b> </f> </p> </text> </region> <region region-id="1473" left="6" top="1620.75" width="444.75" height="88.5" align-x="27.75" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">25</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Keq</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">S</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Keq</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">Kchem</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">M</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">m</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">α</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>-2</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">25</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Keq</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:parens> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">K</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:apply> <ml:neg/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Φ</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">M</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">Kchem</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Keq</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="1474" left="582" top="1656.75" width="42.75" height="13.5" align-x="582" align-y="1668" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(8)</b> </f> </p> </text> </region> <region region-id="1120" left="6" top="1737" width="585" height="12.75" align-x="297.75" align-y="1746" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">_______________________________________________________________________________________________________________</ml:id> </math> <rendering item-idref="38"/> </region> <region region-id="1388" left="24" top="1778.25" width="73.5" height="27.75" align-x="36.75" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">p</ml:id> <ml:range> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="1383" left="264" top="1782.75" width="171" height="13.5" align-x="270.75" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">serial number of potential steps</f> </p> </text> </region> <region region-id="1479" left="492" top="1782.75" width="30.75" height="13.5" align-x="492" align-y="1794" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(9)</b> </f> </p> </text> </region> <region region-id="1419" left="24" top="1821" width="90" height="33" align-x="44.25" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Ψ</ml:id> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">τ</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">d</ml:id> <ml:real>25</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:parens> <ml:real>25</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="1420" left="264" top="1818.75" width="171" height="27" align-x="264" align-y="1830" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">dimesnioless current at the end of each potential step</f> </p> </text> </region> <region region-id="1408" left="492" top="1824.75" width="41.25" height="13.5" align-x="492" align-y="1836" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(10)</b> </f> </p> </text> </region> <region region-id="1416" left="24" top="1868.25" width="215.25" height="27.75" align-x="50.25" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">pot</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Es</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">Ef</ml:id> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ΔE</ml:id> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:id xml:space="preserve">dE</ml:id> </ml:apply> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1417" left="264" top="1872.75" width="171" height="27" align-x="270.75" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">potential value of each potential step in V</f> </p> </text> </region> <region region-id="1418" left="492" top="1872.75" width="43.5" height="13.5" align-x="492" align-y="1884" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Georgia" charset="0" size="12"> <b>(11)</b> </f> </p> </text> </region> <region region-id="1425" left="6" top="1926" width="330" height="173.25" align-x="6" align-y="1926" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="42"/> <rendering item-idref="43"/> </region> <region region-id="1488" left="384" top="1992.75" width="164.25" height="27" align-x="390.75" align-y="2004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Georgia" charset="0" size="12">dimensionless cyclic staircase voltammogram</f> </p> </text> </region> <region region-id="1252" left="6" top="2103" width="485.25" height="12.75" align-x="247.5" align-y="2112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">____________________________________________________________________________________________</ml:id> </math> <rendering item-idref="44"/> </region> <region region-id="1325" left="12" top="2145" 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