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@dansteingart
Created March 18, 2020 11:49
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# A \"Gentle\" Guide To Newman 1962\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This guide to [Newman 1962]() is based on Professor Josh Gallaway's (graduate of Columbia SEAS) excellent guide [here](http://www.joshuagallaway.com/?p=215a) adapted in python be [me](https://dansteingart.com).\n",
"\n",
"First let's get some python out of the way. We're using Python 2.7 because I'm too lazy to rewrite this for the modren era. We're pulling in all of the math libraries from [pithy](https://github.com/dansteingart/pithy/blob/master/static/prepend.txt) I might change this at some point. Not today."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"##Author: Dan Steingart\n",
"##Date Started: 2016-02-09\n",
"import sys\n",
"sys.path.append(\"/pithy/code\")\n",
"\n",
"#import pithy to make matlab like (imports numpy, matplotlib, bunch of other stuff)\n",
"from pithy import *\n",
"\n",
"#call this to show plots in line.\n",
"%matplotlib inline "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we have the main call to run the Newman simulation. Per Gallaway\n",
"\n",
"> (In the Newman model), the complex network of pores through an electrode are described as a single pore, which extends from separator to current collector. The direction across the electrode is given by x, and we use rectangular coordinates to keep the math simple. (Thus, this is one electrode or half of the battery above, but in a rectangular configuration instead of a cylindrical one.)\n",
"\n",
"> The separator will not allow electrons to pass, and thus only ionic current can come through at x = 0. The current collector will not allow ions to pass, so only electrons can flow out at x = L. This is the essence of the porous electrode model: the total current flow from separator to current collector is constant: the current across the circuit, denoted as I. However, across the porous electrode it may travel either as ions or as electrons. The only necessity is that it must be all-ionic at the separator and all-electronic at the current collector.\n",
"\n",
">Ionic current and electronic current may be converted to one another by an electrochemical reaction. In fact, this is the definition of electrochemistry: the study of reactions that involve both chemicals (ions) and electricity (electrons). In the picture above a unit of ionic current ends at the same location where one of electronic current begins. In reality, the ion causing the ionic current turns upward, contacts the pore wall, and there participates in the liberation of an electron. But for simplicity, we draw the entire thing as involving only motion in the x-direction.\n",
"\n",
"If we ignore solid state diffusion in the electrode, Four equations can define a steady state porous electrode:\n",
"\n",
"> 1. Conservation of charge. The equation states that any i2 that disappears must be matched by appearance of $i_1$ and vice versa. The boundary condition states all current is electronic at the current collector.\n",
"> $$\\frac{di_1}{dx} +\\frac{di_2}{dx} = 0 $$ \n",
"> with the boundary conditions \n",
"> $$ x = L; i_1 = I$$\n",
"\n",
"> 2. Rate of electrochemical reaction. The equation states that i2 disappears by an interfacial reaction that is driven (linearly) by the potential difference between the solid and liquid. The boundary condition states all current is ionic at the separator.\n",
"> $$\\frac{di_2}{dx} = ai_0 \\frac{nF}{RT}(\\phi_1 - \\phi_2)$$ \n",
"> with the boundary conditions \n",
"> $$x=0, i_2 = I$$\n",
"\n",
">3. Ohm’s law in the solid. This relates current to potential gradient. The boundary condition arbitrarily sets the \n",
"> $$i_1 = -\\sigma \\frac{d\\phi_1}{dx}$$ \n",
"> with the boundary conditions \n",
"> $$x=0,\\phi_1 = 0$$\n",
"\n",
">4. Solid potential to zero at the separator.\n",
"Ohm’s law in the liquid. The boundary condition states the liquid potential gradient is zero at the current collector.\n",
">$$i_2 = -\\kappa \\frac{d\\phi_2}{dx}$$ \n",
"> with the boundary conditions \n",
"> $$x=L,i_2 = 0 = \\frac{d\\phi_2}{dx} = 0$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All of these can be expressed by\n",
"> $$\\frac{d^2i_2}{dx^2} = a i_0 \\frac{nF}{RT}\\left[ \\frac{I}{\\sigma} - i_2 \\left(\\frac{1}{\\sigma}+\\frac{1}{\\kappa}\\right)\\right]$$ \n",
"\n",
"At with the boundary conditions\n",
"> $$ x = 0, i_2 = I ; x = L, i_2 = 0 $$\n",
"\n",
"we can solve to achieve the form\n",
"\n",
"> $$\\frac{i_2}{I} = \\frac{\\kappa}{\\kappa+\\sigma}\\left[ 1+ \\frac{\\sigma}{\\kappa}\\frac{\\sinh(\\nu(1-y)-\\sinh(\\nu y)}{\\sinh(\\nu)}\\right] $$\n",
"\n",
"where \n",
"\n",
"> $$\\nu = L \\sqrt{a i_0 \\frac{nF}{RT} \\frac{\\kappa+\\sigma}{\\kappa \\sigma}}; y = \\frac{x}{L}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below Gallaway applies this for the steady state treamtent of the zinc alkaline cathode (MnO<sub>2</sub>, where he assumes\n",
"\n",
"- $\\frac{a}{v} = 23,300 \\frac{cm^2}{cm^3}$\n",
"- $i_0 = 3.5 * 10^-6 \\frac{A}{cm^2}$\n",
"- $I = 0.1 \\frac{A}{cm^2}$\n",
"- $L = 1.0 cm$\n",
"- $\\kappa = 0.06 \\frac{S}{cm}$\n",
"- $\\sigma = 20.0 \\frac{S}{cm}$\n",
"\n",
"Below we'll create a function where these are the default, but we can change at will to tailor the properties of the electrode that we want."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def n62(a=23330,io=3.5e-6,I=0.1,L=1.0,kappa=6e-2,sigma=20.,anno=False):\n",
"\n",
" \n",
" n = 1 #number of electrons\n",
" F = 96487. #C/mol\n",
" R = 8.31446 #J(mol K)\n",
" T = 300 #K\n",
" \n",
" x = linspace(0,L,1000)\n",
" \n",
" v = L*sqrt(a*io*((n*F)/(R*T)) *(kappa+sigma)/(kappa*sigma))\n",
" y = x/L\n",
" \n",
" i_ion = (kappa/(kappa+sigma))*(1+((sigma/kappa)*sinh(v*(1-y))-sinh(v*y))/sinh(v))\n",
" \n",
" i_electron = 1-i_ion\n",
" \n",
" ilab = \"ionic\\n$\\sigma=%.1e$\\n$\\kappa=%.1e$\" %(sigma,kappa)\n",
" elab = \"electronic\\n$\\sigma=%.1e$\\n$\\kappa=%.1e$\" %(sigma,kappa)\n",
" plot(x,i_ion,label=ilab)\n",
" plot(x,i_electron,label=elab)\n",
" \n",
" if anno:\n",
" y = int(random()*len(x))\n",
" annotate(ilab,xy=(x[y],i_ion[y]),fontsize=10)\n",
" annotate(elab,xy=(x[y],i_electron[y]),fontsize=10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So for the default case:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f29b24e0610>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figure(figsize=(10,10))\n",
"\n",
"n62()\n",
"L = 1.0\n",
"xlabel(\"Distance (cm)\")\n",
"ylabel(\"Fraction Current (i/I)\")\n",
"xlim(0,L)\n",
"legend(fontsize=8,loc='best')\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Per Gallaway:\n",
"> The disparity in conductivities results in the general behavior we observe. The reaction driving force in equation 2 is the difference in these potentials, the surface potential. Thus there is substantially more reaction near the separator than elsewhere in the electrode.\n",
"\n",
"If we change the structure of the electrode to make it thinner, and alter the $\\kappa$ to $\\sigma$ ratio, we see in three different cases:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f29b2246b10>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"figure(figsize=(10,10))\n",
"LL = .1\n",
"\n",
"\n",
"#What will happend if:\n",
"n62(kappa=.01,sigma=.01,L=LL)\n",
"n62(kappa=.0001,sigma=100,L=LL)\n",
"n62(kappa=.1,sigma=.000001,L=LL)\n",
"\n",
"xlabel(\"Distance (cm)\")\n",
"ylabel(\"Fraction Current (i/I)\")\n",
"xlim(0,LL)\n",
"legend(fontsize=8,loc=5,ncol = 2)\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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