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3.412742608200365*^9, 3.412742631084955*^9}, {3.412742689322583*^9, 3.412742690047667*^9}, {3.4127430519913797`*^9, 3.412743143607299*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`ao$$ = 0.5, $CellContext`d$$ = 1, $CellContext`DM$$ = 1.*^-8, $CellContext`L$$ = 0.001, $CellContext`logCdl$$ = -6, $CellContext`logka$$ = 6.30102999566398, $CellContext`logkd$$ = 6.477121254719662, $CellContext`logko$$ = 1., $CellContext`logkr$$ = 1., $CellContext`logwc$$ = 4, $CellContext`Mmax$$ = 0.00001, $CellContext`ROhm$$ = 0, $CellContext`V$$ = -0.05, $CellContext`wc1$$ = False, $CellContext`wc2$$ = False, $CellContext`wc3$$ = False, $CellContext`\[CapitalGamma]$$ = 2.*^-11, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style[ " \!\(\*SuperscriptBox[\(M\), \ \(+\)]\) + s + \!\(\*SuperscriptBox[\(e\), \(-\)]\) \!\(\*UnderoverscriptBox[\ \(\[LongLeftRightArrow]\), SubscriptBox[\(K\), \(o\)], SubscriptBox[\(K\), \ \(r\)]]\) M,s", Bold, Medium]], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Style[ " M,s + \[LeftAngleBracket] \ \[RightAngleBracket] \!\(\*UnderoverscriptBox[\(\[LongLeftRightArrow]\), \ SubscriptBox[\(k\), \(d\)], SubscriptBox[\(k\), \(a\)]]\) \ \[LeftAngleBracket]M\[RightAngleBracket] + s", Bold, Medium]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`logko$$], 1., "log(\!\(\*SubscriptBox[\(k\), \(o\)]\)/\!\(\*SuperscriptBox[\(s\), \ \(-1\)]\))"}, -2, 2}, {{ Hold[$CellContext`logkr$$], 1., "log(\!\(\*SubscriptBox[\(k\), \(r\)]\)\!\(\*SuperscriptBox[\(M\), \ \(+*\)]\)/\!\(\*SuperscriptBox[\(s\), \(-1\)]\))"}, -2, 2}, {{ Hold[$CellContext`ao$$], 0.5, "\!\(\*SubscriptBox[\(\[Alpha]\), \(o\)]\)"}, 0.1, 0.9}, {{ Hold[$CellContext`d$$], 1, "d"}, {1, 2, 3}}, {{ Hold[$CellContext`logka$$], 6.30102999566398, "log(\!\(\*SubscriptBox[\(k\), \(a\)]\)/(\!\(\*SuperscriptBox[\(mol\), \ \(-1\)]\) \!\(\*SuperscriptBox[\(cm\), \(3\)]\) \!\(\*SuperscriptBox[\(s\), \ \(-1\)]\)))"}, 2, 7}, {{ Hold[$CellContext`logkd$$], 6.477121254719662, "log(\!\(\*SubscriptBox[\(k\), \(d\)]\)/(\!\(\*SuperscriptBox[\(mol\), \ \(-1\)]\) \!\(\*SuperscriptBox[\(cm\), \(3\)]\) \!\(\*SuperscriptBox[\(s\), \ \(-1\)]\)))"}, 2, 7}, {{ Hold[$CellContext`DM$$], 1.*^-8, "\!\(\*SubscriptBox[\(D\), \ \(\[LeftAngleBracket]M\[RightAngleBracket]\)]\)/(\!\(\*SuperscriptBox[\(cm\), \ \(2\)]\) \!\(\*SuperscriptBox[\(s\), \(-1\)]\))"}, 1.*^-8, 1.*^-6}, {{ Hold[$CellContext`L$$], 0.001, "L/cm"}, 0.00001, Rational[1, 1000]}, {{ Hold[$CellContext`\[CapitalGamma]$$], 2.*^-11, "\[CapitalGamma]/(mol \!\(\*SuperscriptBox[\(cm\), \(-2\)]\))"}, 1.*^-11, 1.*^-9}, {{ Hold[$CellContext`Mmax$$], 0.00001, "\[LeftAngleBracket]M\!\(\*SubscriptBox[\(\[RightAngleBracket]\), \ \(max\)]\)/(mol \!\(\*SuperscriptBox[\(cm\), \(-3\)]\))"}, 1.*^-6, 0.0001}, {{ Hold[$CellContext`logCdl$$], -6, "log(\!\(\*SubscriptBox[\(C\), \(dl\)]\)/(F \ \!\(\*SuperscriptBox[\(cm\), \(-2\)]\)))"}, -6, -3}, {{ Hold[$CellContext`ROhm$$], 0, "\!\(\*SubscriptBox[\(R\), \(\[CapitalOmega]\)]\)/(\[CapitalOmega] \ \!\(\*SuperscriptBox[\(cm\), \(2\)]\))"}, 0, 1000.}, {{ Hold[$CellContext`V$$], -0.05, "E/V"}, -0.18, 0.18}, {{ Hold[$CellContext`logwc$$], 4, "log(\[Omega]/(rd \!\(\*SuperscriptBox[\(s\), \(-1\)]\)))"}, -3, 6}, {{ Hold[$CellContext`wc1$$], False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c1\)]\) = \ 1/(\!\(\*SubscriptBox[\(R\), \(ct\)]\)\!\(\*SubscriptBox[\(C\), \(dl\)]\))"}, \ {False, True}}, {{ Hold[$CellContext`wc2$$], False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c2\)]\)"}, {False, True}}, {{ Hold[$CellContext`wc3$$], False, "\!\(\*SubscriptBox[\(\[Omega]\), \(c3\)]\)"}, {False, True}}}, Typeset`size$$ = {498., {181.875, 187.125}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`logko$14488$$ = 0, $CellContext`logkr$14489$$ = 0, $CellContext`ao$14490$$ = 0, $CellContext`d$14491$$ = 0, $CellContext`logka$14492$$ = 0, $CellContext`logkd$14493$$ = 0, $CellContext`DM$14494$$ = 0, $CellContext`L$14495$$ = 0, $CellContext`\[CapitalGamma]$14496$$ = 0, $CellContext`Mmax$14497$$ = 0, $CellContext`wc1$14498$$ = False, $CellContext`wc2$14499$$ = False, $CellContext`wc3$14500$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`ao$$ = 0.5, $CellContext`d$$ = 1, $CellContext`DM$$ = 1.*^-8, $CellContext`L$$ = 0.001, $CellContext`logCdl$$ = -6, $CellContext`logka$$ = 6.30102999566398, $CellContext`logkd$$ = 6.477121254719662, $CellContext`logko$$ = 1., $CellContext`logkr$$ = 1., $CellContext`logwc$$ = 4, $CellContext`Mmax$$ = 0.00001, $CellContext`ROhm$$ = 0, $CellContext`V$$ = -0.05, $CellContext`wc1$$ = False, $CellContext`wc2$$ = False, $CellContext`wc3$$ = False, $CellContext`\[CapitalGamma]$$ = 2.*^-11}, "ControllerVariables" :> { Hold[$CellContext`logko$$, $CellContext`logko$14488$$, 0], Hold[$CellContext`logkr$$, $CellContext`logkr$14489$$, 0], Hold[$CellContext`ao$$, $CellContext`ao$14490$$, 0], Hold[$CellContext`d$$, $CellContext`d$14491$$, 0], Hold[$CellContext`logka$$, $CellContext`logka$14492$$, 0], Hold[$CellContext`logkd$$, $CellContext`logkd$14493$$, 0], Hold[$CellContext`DM$$, $CellContext`DM$14494$$, 0], Hold[$CellContext`L$$, $CellContext`L$14495$$, 0], Hold[$CellContext`\[CapitalGamma]$$, \ $CellContext`\[CapitalGamma]$14496$$, 0], Hold[$CellContext`Mmax$$, $CellContext`Mmax$14497$$, 0], Hold[$CellContext`wc1$$, $CellContext`wc1$14498$$, False], Hold[$CellContext`wc2$$, $CellContext`wc2$14499$$, False], Hold[$CellContext`wc3$$, $CellContext`wc3$14500$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`Cdl = 10^$CellContext`logCdl$$; $CellContext`ko = 10^$CellContext`logko$$; $CellContext`kr = 10^$CellContext`logkr$$; $CellContext`kd = 10^$CellContext`logkd$$; $CellContext`ka = 10^$CellContext`logka$$; $CellContext`mM = \ $CellContext`DM$$/$CellContext`L$$; $CellContext`taudM = \ $CellContext`L$$^2/$CellContext`DM$$; $CellContext`KoV = \ $CellContext`Ko[$CellContext`V$$]; $CellContext`KrV = \ $CellContext`Kr[$CellContext`V$$]; $CellContext`ao$$; $CellContext`yMV = \ $CellContext`yM[$CellContext`V$$]; $CellContext`\[Theta]MV = $CellContext`\ \[Theta]M[$CellContext`V$$]; $CellContext`Rct = ($CellContext`KoV + \ $CellContext`KrV)/(((($CellContext`f $CellContext`F) $CellContext`\ \[CapitalGamma]$$) $CellContext`KoV) $CellContext`KrV); $CellContext`Rab = \ $CellContext`Rct (($CellContext`KoV + $CellContext`KrV)/($CellContext`Mmax$$ \ ($CellContext`ka ( 1 - $CellContext`yMV) + $CellContext`kd $CellContext`yMV))); \ $CellContext`RM = $CellContext`Rct ((($CellContext`KoV + $CellContext`KrV) \ $CellContext`\[CapitalGamma]$$) (($CellContext`ka $CellContext`\[Theta]MV + \ $CellContext`kd ( 1 - $CellContext`\[Theta]MV))/(($CellContext`mM \ $CellContext`Mmax$$) ($CellContext`ka ( 1 - $CellContext`yMV) + $CellContext`kd $CellContext`yMV)))); \ $CellContext`Rbf = $CellContext`ROhm$$ + $CellContext`Rct + $CellContext`Rab + \ $CellContext`RM/($CellContext`d$$ + 2); $CellContext`MM = Which[$CellContext`d$$ == 1, Coth[($CellContext`taudM $CellContext`p)^ Rational[1, 2]]/($CellContext`taudM $CellContext`p)^ Rational[1, 2], $CellContext`d$$ == 2, BesselI[0, ($CellContext`p $CellContext`taudM)^ Rational[1, 2]]/(($CellContext`p $CellContext`taudM)^ Rational[1, 2] BesselI[1, ($CellContext`p $CellContext`taudM)^ Rational[1, 2]]), $CellContext`d$$ == 3, 1/(-1 + ($CellContext`taudM $CellContext`p)^Rational[1, 2] Coth[($CellContext`taudM $CellContext`p)^ Rational[ 1, 2]])]; $CellContext`ZX1 = ($CellContext`Rct \ ($CellContext`KoV + $CellContext`KrV)) (( 1 + ($CellContext`\[CapitalGamma]$$ ($CellContext`ka $CellContext`\ \[Theta]MV + $CellContext`kd ( 1 - $CellContext`\[Theta]MV))) \ ($CellContext`MM/$CellContext`mM))/($CellContext`Mmax$$ ($CellContext`ka ( 1 - $CellContext`yMV) + $CellContext`kd $CellContext`yMV) + ( 1 + ($CellContext`\[CapitalGamma]$$ ($CellContext`ka \ $CellContext`\[Theta]MV + $CellContext`kd ( 1 - $CellContext`\[Theta]MV))) \ ($CellContext`MM/$CellContext`mM)) $CellContext`p)); $CellContext`ZX1Et = \ $CellContext`ZX1/$CellContext`Rbf; $CellContext`Zf = $CellContext`Rct + \ $CellContext`ZX1; $CellContext`ZfEt = ($CellContext`ROhm$$ + \ $CellContext`Zf)/$CellContext`Rbf; $CellContext`Z = $CellContext`ROhm$$ + \ $CellContext`Zf/( 1 + ($CellContext`Zf $CellContext`Cdl) $CellContext`p); \ $CellContext`ZEt = $CellContext`Z/$CellContext`Rbf; $CellContext`wcdM = Which[$CellContext`d$$ == 1, 3.88/$CellContext`taudM, $CellContext`d$$ == 2, 11.7/$CellContext`taudM, $CellContext`d$$ == 3, 22.3/$CellContext`taudM]; $CellContext`lw = { 1/($CellContext`Rct $CellContext`Cdl), $CellContext`wcdM, \ (($CellContext`Mmax$$ $CellContext`ka) $CellContext`kd) (($CellContext`KoV + \ $CellContext`KrV)/($CellContext`kd $CellContext`KoV + $CellContext`ka \ $CellContext`KrV))}; Grid[{{ Plot[ 0, {$CellContext`VSta, $CellContext`Vmin, $CellContext`Vmax}, PlotRange -> {{$CellContext`Vmin, $CellContext`Vmax}, {-1, 1}}, PlotStyle -> AbsoluteThickness[2], Frame -> True, AxesOrigin -> {$CellContext`Vmin, 0}, FrameLabel -> { "\!\(\*\nStyleBox[\"E\",\nFontSlant->\"Italic\"]\)/V", "\!\(\*SubscriptBox[\"i\", \n StyleBox[\"\\\"f\\\"\",\n\ FontWeight->\"Plain\"]]\)/(A \!\(\*SuperscriptBox[\(cm\), \(-2\)]\))"}, Epilog -> { AbsolutePointSize[6], Point[{$CellContext`V$$, 0}]}, BaseStyle -> $CellContext`monStyle, ImageSize -> 250, FrameTicks -> {{-0.1, 0, 0.1}, {-1, 0, 1}, None, None}], Plot[ Evaluate[{ $CellContext`yM[$CellContext`VSta], 1 - $CellContext`yM[$CellContext`VSta], $CellContext`\[Theta]M[$CellContext`VSta], 1 - $CellContext`\[Theta]M[$CellContext`VSta]}], \ {$CellContext`VSta, $CellContext`Vmin, $CellContext`Vmax}, PlotRange -> {{$CellContext`Vmin, $CellContext`Vmax}, {-0.01, 1.01}}, Frame -> True, ImageSize -> 240, Axes -> None, PlotStyle -> {{Blue, AbsoluteThickness[1.5]}, {Purple, AbsoluteThickness[1.5]}, { Part[$CellContext`lHue, 3], AbsoluteThickness[1.5]}, { Part[$CellContext`lHue, 4], AbsoluteThickness[1.5]}}, FrameLabel -> { "\!\(\*\nStyleBox[\"E\",\nFontSlant->\"Italic\"]\)/V", "y, \[Theta]"}, Epilog -> { AbsolutePointSize[6], Point[{$CellContext`V$$, $CellContext`yM[$CellContext`V$$]}], Point[{$CellContext`V$$, 1 - $CellContext`yM[$CellContext`V$$]}], Point[{$CellContext`V$$, $CellContext`\[Theta]M[$CellContext`V$$]}], Point[{$CellContext`V$$, 1 - $CellContext`\[Theta]M[$CellContext`V$$]}], Blue, Text[ "\!\(\*SubscriptBox[\(y\), \(\[LeftAngleBracket]\"M\"\ \[RightAngleBracket]\)]\)", Scaled[{0.1, 0.9}]], Purple, Text[ "\!\(\*SubscriptBox[\(y\), \(\[LeftAngleBracket]\" \"\ \[RightAngleBracket]\)]\)", Scaled[{0.1, 0.8}]], Part[$CellContext`lHue, 3], Text["\!\(\*SubscriptBox[\(\[Theta]\), \(\"M\"\)]\)", Scaled[{0.1, 0.7}]], Part[$CellContext`lHue, 4], Text["\!\(\*SubscriptBox[\(\[Theta]\), \(\"s\"\)]\)", Scaled[{0.1, 0.6}]]}, BaseStyle -> $CellContext`monStyle, FrameTicks -> {{-0.1, 0, 0.1}, {0, 0.5, 1}, None, None}]}, { ParametricPlot[ ReplaceAll[{ Re[$CellContext`ZX1Et], - Im[$CellContext`ZX1Et]}, $CellContext`p -> I 10^$CellContext`logw], {$CellContext`logw, \ $CellContext`logwmin, $CellContext`logwmax}, AspectRatio -> Automatic, Frame -> True, ImageSize -> 200, PlotStyle -> {Blue, AbsoluteThickness[2]}, PlotRange -> {{0, 1.1}, {0, 1.1}}, Epilog -> { AbsolutePointSize[6], If[$CellContext`wc2$$, {Red, Point[ ReplaceAll[{ Re[$CellContext`ZX1Et], - Im[$CellContext`ZX1Et]}, $CellContext`p -> I Part[$CellContext`lw, 2]]]}, {}], If[$CellContext`wc3$$, {Red, Point[ ReplaceAll[{ Re[$CellContext`ZX1Et], - Im[$CellContext`ZX1Et]}, $CellContext`p -> I Part[$CellContext`lw, 3]]]}, {}], Point[ ReplaceAll[{ Re[$CellContext`ZX1Et], - Im[$CellContext`ZX1Et]}, $CellContext`p -> I 10^$CellContext`logwc$$]], AbsolutePointSize[6]}, FrameTicks -> {{0, 0.5, 1}, {0, 0.5, 1}, None, None}, FrameLabel -> If[$CellContext`ROhm$$ == 0, { "Re \!\(\*SubscriptBox[\(Z\), \ \(\[Theta]\)]\)/\!\(\*SubscriptBox[\(R\), \(LF\)]\)", "- Im \!\(\*SubscriptBox[\(Z\), \ \(\[Theta]\)]\)/\!\(\*SubscriptBox[\(R\), \(LF\)]\)"}, { "Re \!\(\*SubscriptBox[\(Z\), \ \(\[Theta]\)]\)/(\!\(\*SubscriptBox[\(R\), \ \(\[CapitalOmega]\)]\)+\!\(\*SubscriptBox[\(R\), \(LF\)]\))", "- Im \!\(\*SubscriptBox[\(Z\), \ \(\[Theta]\)]\)/(\!\(\*SubscriptBox[\(R\), \ \(\[CapitalOmega]\)]\)+\!\(\*SubscriptBox[\(R\), \(LF\)]\))"}], BaseStyle -> $CellContext`monStyle], ParametricPlot[{ ReplaceAll[{ Re[$CellContext`ZEt], -Im[$CellContext`ZEt]}, $CellContext`p -> I 10^$CellContext`logw], ReplaceAll[{ Re[$CellContext`ZfEt], -Im[$CellContext`ZfEt]}, $CellContext`p -> I 10^$CellContext`logw]}, {$CellContext`logw, \ $CellContext`logwmin, $CellContext`logwmax}, AspectRatio -> Automatic, Frame -> True, ImageSize -> 200, PlotStyle -> {{Purple, AbsoluteThickness[1]}, {Blue, AbsoluteThickness[2]}}, PlotRange -> {{0, 1.1}, {0, 1.1}}, Epilog -> { AbsolutePointSize[6], If[$CellContext`wc1$$, {Red, Point[ ReplaceAll[{ Re[$CellContext`ZEt], - Im[$CellContext`ZEt]}, $CellContext`p -> I Part[$CellContext`lw, 1]]]}, {}], If[$CellContext`wc2$$, {Red, Point[ ReplaceAll[{ Re[$CellContext`ZEt], - Im[$CellContext`ZEt]}, $CellContext`p -> I Part[$CellContext`lw, 2]]], Point[ ReplaceAll[