Estimation of activity coefficients for aqueous organic redox-flow batteries: Theoretical basis and equations
The pre-print of the paper can be generated by executing the "main.tex" file in the "final_version_LaTeX" folder.
In the folder "Sections", the code used to generate the figures can be accessed, and will look something like this:
\begin{figure}[!hbtp]
\begin{subfigure}[hb]{0.49\textwidth}
\resizebox{\linewidth}{!}{\begin{tikzpicture}
\pgfplotsset{
scale only axis,
}
%axis options:
\begin{axis}[
xlabel=b (mol/kg),
ylabel= $\phi_{NaCl} $,
legend pos=north west,
xmin = 0,
xmax = 5,
cycle list name=temperaturelist
]
\addplot+[only marks] table[y index =1]{\PhiNaClExp};
\addplot+[only marks] table[y index =2]{\PhiNaClExp};
\addplot+[only marks] table[y index =3]{\PhiNaClExp};
\addplot+[only marks] table[y index =4]{\PhiNaClExp};
\addplot+[only marks] table[y index =5]{\PhiNaClExp};
\addplot+[only marks] table[y index =6]{\PhiNaClExp};
\addplot+[t1, no markers] table[y index =1]{\PhiNaClCalc};
\addplot+[t2, no markers] table[y index =2]{\PhiNaClCalc};
\addplot+[t3, no markers] table[y index =3]{\PhiNaClCalc};
\addplot+[t4, no markers] table[y index =4]{\PhiNaClCalc};
\addplot+[t5, no markers] table[y index =5]{\PhiNaClCalc};
\addplot+[t6, no markers] table[y index =6]{\PhiNaClCalc};
\end{axis}
\end{tikzpicture}
}
\caption{}
\end{subfigure}
\hfill
%crop 1
\begin{subfigure}[hb]{0.49\textwidth}
\resizebox{\linewidth}{!}{\begin{tikzpicture}
\pgfplotsset{
scale only axis,
}
%axis options:
\begin{axis}[
xlabel=b (mol/kg),
ylabel= $\gamma_s $,
legend pos=north west,
xmin = 0,
xmax = 5,
ymax = 1.01,
cycle list name=temperaturelist
]
\addplot+[only marks] table[y index =1]{\GammaNaClExp};
\addplot+[only marks] table[y index =2]{\GammaNaClExp};
\addplot+[only marks] table[y index =3]{\GammaNaClExp};
\addplot+[only marks] table[y index =4]{\GammaNaClExp};
\addplot+[only marks] table[y index =5]{\GammaNaClExp};
\addplot+[only marks] table[y index =6]{\GammaNaClExp};
\addplot+[t1, no markers] table[y index =1]{\GammaNaClCalc};
\addplot+[t2, no markers] table[y index =2]{\GammaNaClCalc};
\addplot+[t3, no markers] table[y index =3]{\GammaNaClCalc};
\addplot+[t4, no markers] table[y index =4]{\GammaNaClCalc};
\addplot+[t5, no markers] table[y index =5]{\GammaNaClCalc};
\addplot+[t6, no markers] table[y index =6]{\GammaNaClCalc};
\end{axis}
\end{tikzpicture}
}
\caption{ }
\end{subfigure}
\vspace*{0.5cm}
\newline
\begin{subfigure}[hb]{\textwidth}
\centering
\resizebox{\linewidth}{!}{
\begin{tikzpicture}
\begin{axis}[%
hide axis,
xmin=10,
xmax=50,
ymin=0,
ymax=0.4,
legend style={draw=white!15!black,
cells={align=center},
legend columns=7}
]
\addlegendimage{only marks}
\addlegendentry{literature values};
\addlegendimage{t1,only marks, mark=triangle*}
\addlegendentry{0°C \\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020} \cite{gibbardLiquidvaporEquilibriumAqueous1974}};
\addlegendimage{t2, only marks, mark=diamond*}
\addlegendentry{10°C\\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020}};
\addlegendimage{t3, only marks, mark=otimes}
\addlegendentry{15°C\\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020}};
\addlegendimage{t4, only marks, mark=star}
\addlegendentry{25°C\\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020} \cite{gibbardLiquidvaporEquilibriumAqueous1974}};
\addlegendimage{t5, only marks, mark=diamond}
\addlegendentry{40°C\\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020}};
\addlegendimage{t6, only marks, mark=triangle}
\addlegendentry{60°C\\ \cite{clarkeEvaluationThermodynamicFunctions1985} \cite{partanenTraceableValuesActivity2020}};
\addlegendimage{}
\addlegendentry{calculated values};
\addlegendimage{t1, no markers}
\addlegendentry{0°C};
\addlegendimage{t2, no markers}
\addlegendentry{10°C};
\addlegendimage{t3, no markers}
\addlegendentry{15°C};
\addlegendimage{t4, no markers}
\addlegendentry{25°C};
\addlegendimage{t5, no markers}
\addlegendentry{40°C};
\addlegendimage{t6, no markers}
\addlegendentry{60°C};
\end{axis}
\end{tikzpicture}
}
\end{subfigure}
\caption{Reference literature values and calculated values for (a) the osmotic coefficient and (b) the activity coefficient of NaCl(aq) as a function of molality and temperature}
\label{NaClresults}
\end{figure}
The input data, e.g. \GammaNaClCalc, is generated in the "Header.tex" file using the \pgfplotstableread command:
\pgfplotstableread[col sep=comma]{Data/gammaNaClExp.csv}{\GammaNaClExp}
\pgfplotstableread[col sep=comma]{Data/gammaNaClCalc.csv}{\GammaNaClCalc}
\pgfplotstableread[col sep=comma]{Data/phiNaClExp.csv}{\PhiNaClExp}
\pgfplotstableread[col sep=comma]{Data/phiNaClCalc.csv}{\PhiNaClCalc}
\pgfplotstableread[col sep=comma]{Data/phiNaClresiduals.csv}{\PhiNaClresiduals}
\pgfplotstableread[col sep=comma]{Data/gammaNaClresiduals.csv}{\GammaNaClresiduals}
\pgfplotstableread[col sep=comma]{Data/gammaKClExp.csv}{\GammaKClExp}
\pgfplotstableread[col sep=comma]{Data/gammaKClCalc.csv}{\GammaKClCalc}
\pgfplotstableread[col sep=comma]{Data/phiKClExp.csv}{\PhiKClExp}
\pgfplotstableread[col sep=comma]{Data/phiKClCalc.csv}{\PhiKClCalc}
\pgfplotstableread[col sep=comma]{Data/phiKClresiduals.csv}{\PhiKClresiduals}
\pgfplotstableread[col sep=comma]{Data/gammaKClresiduals.csv}{\GammaKClresiduals}
\pgfplotstableread[col sep=comma]{Data/CaClExp.csv}{\GammaCaClExp}
\pgfplotstableread[col sep=comma]{Data/CaClCalc.csv}{\GammaCaClCalc}
\pgfplotstableread[col sep=comma]{Data/phiCaClExp.csv}{\PhiCaClExp}
\pgfplotstableread[col sep=comma]{Data/phiCaClCalc.csv}{\PhiCaClCalc}
\pgfplotstableread[col sep=comma]{Data/phiCaClresiduals.csv}{\PhiCaClresiduals}
\pgfplotstableread[col sep=comma]{Data/gammaCaClresiduals.csv}{\GammaCaClresiduals}
\pgfplotstableread[col sep=comma]{Data/phiNaClFP.csv}{\PhiNaClFP}
\pgfplotstableread[col sep=comma]{Data/phiKClFP.csv}{\PhiKClFP}
\pgfplotstableread[col sep=comma]{Data/phiCaClFP.csv}{\PhiCaClFP}
\pgfplotstableread[col sep=comma]{Data/LNaClFP.csv}{\LNaClFP}
\pgfplotstableread[col sep=comma]{Data/LNaClFPexp.csv}{\LNaClFPexp}
\pgfplotstableread[col sep=comma]{Data/CpNaClFP.csv}{\CpNaClFP}
\pgfplotstableread[col sep=comma]{Data/CpNaClFPexp.csv}{\CpNaClFPexp}
\pgfplotstableread[col sep=comma]{Data/rawcurves.csv}{\rawcurves}
\pgfplotstableread[col sep=comma]{Data/deconvolutedcurves.csv}{\deconvolutedcurves}
\pgfplotstableread[col sep=comma]{Data/heatingcurve1.csv}{\heatingcurva}
\pgfplotstableread[col sep=comma]{Data/heatingcurve2.csv}{\heatingcurvb}
\pgfplotstableread[col sep=comma]{Data/heatingcurve5.csv}{\heatingcurvc}
\pgfplotstableread[col sep=comma]{Data/heatingcurve05.csv}{\heatingcurvd}
The .csv files located in the "Data" folder are themselves generated using the MATLAB code located in the "MATLAB_code" folder
#NaCl Folder
For convenience, input files are available in both .xslx and .txt format and correspond to data manually copied from the reference paper indicated in the paper manuscript. Authors are indicated in the file header.
The file "FittingVirialCoefficientsToClarkeData.m" makes use of the data from the paper from Clarke et al. compiled in the file "data_NaCl.txt"
Data = readmatrix('Data_NaCl.txt');
The formulas described in the manuscript are applied to calculate the activity coefficient and osmotic coefficient from this input data. For the complete virial matrix, coefficients were hard-coded from the paper of Clarke et al. into the Matlab code.
Figure 2 is generated using the VisulaisationSurfaceXX.m" files.
For the reduced virial matrix, the procedure makes use of the MATLAB curve fitting tool (cftool in the command line) and the files "ReducedMatrixFitEnthalpy.m", "ReducedMatrixFitHeatCapacity.m" and "ReducedMatrixFitOsmoticCoefficient.m".
#KCl and CaCl2 folders
Similar files are available in the KCl and CaCl2 folders, although the input files may be compiled from different sources indicated in the manuscript.
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