notebooks/Langmuir Isotherm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Langmuir isotherm\n",
    "This notebook shows an example use case modelling adsorption in MECSim. MECSim implements Longmuir isother for adsorption modelling. \n",
    "\n",
    "For example, if a specie `A` is undergoing an electron transfer reaction via adsorption, it can be modelled by assuming that there would be empty (filled) sites on the electrode where the specie `A` resides in. \n",
    "\n",
    "If `A` is being reduced `A+` via single electron transfer, adsoprtion part of the electron transfer is modelled by assuming that there are `S*` and `S*+` that faciliate the electron transfer via adsorption. \n",
    "\n",
    "As a result, we model the following reaction mechanism: $$ A^{+} + e \\rightarrow A \\\\ A^{+} +S^{*}_{+} \\rightarrow S^{*}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from pymecsim import * \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_langmuir_isotherm(exp, Keq, varname, speciename):\n",
    "    \"\"\"Utility function to plot the longmuir isotherm test\n",
    "    \n",
    "    Inputs:\n",
    "    -------\n",
    "        exp         :  A pymecsim experiment class\n",
    "        Keq         :  Equilibrium constant of adsorption reaction\n",
    "        varname     :  Concentration variable that s varied in a lograthim scale of (-4,4)\n",
    "        speciename  : Adsorption specie name to be plotted on the Langmuir isotherm\n",
    "        \n",
    "        \n",
    "    Output:\n",
    "    -------\n",
    "        theta       : array of shape (2,N) with theta values from a theoretical formula and computation using pymecsim\n",
    "    \"\"\"\n",
    "    surface_species = []\n",
    "    for s in exp.mechanism.species:\n",
    "        if s.surface_confined:\n",
    "            surface_species.append(s)\n",
    "    C0 = np.logspace(-4.0,4.0, num=15)\n",
    "    fig, ax = plt.subplots()\n",
    "    theta_mecsim = []\n",
    "    theta_theory = []\n",
    "    for c in C0:\n",
    "        sim = MECSIM(exp=exp)\n",
    "        sim.set_parameter(varname, c)\n",
    "        sim.solve()\n",
    "        concs = sim.get_surface_concentrations()\n",
    "        total_coverage = 0\n",
    "        for s in surface_species:\n",
    "            total_coverage += concs[s.name][-1]\n",
    "        theta_mecsim.append(concs[speciename][-1]/total_coverage)\n",
    "        theta_theory.append((Keq * c) / ( 1.0 + (Keq * c) ) )\n",
    "        \n",
    "    ax.plot(C0, theta_mecsim, label='pymecsim', lw=6)\n",
    "    ax.plot(C0, theta_theory, label='Theory', lw=2)\n",
    "    ax.set_yscale('log')\n",
    "    ax.set_xscale('log')\n",
    "    ax.set_xlabel(r'[A] $mol/cm^3$')\n",
    "    ax.set_ylabel(r'$\\theta_{A*}$')\n",
    "    ax.set_title('Langmuir Isotherm')\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "    theta = np.column_stack((theta_mecsim, theta_theory))\n",
    "    return theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Charge Transfer : 1 A+ + 1 e <=> 1 A  ks= 0.00e+00, E0 = 0.00e+00, alpha = 5.00e-01\n",
      "Chemical Reaction : 1 S+* + 1 A+ <=> 1 S*  kf= 1, kb= 1 \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Aplus = Specie('A+', D=1e-5, C0='$C0')\n",
    "A = Specie('A', D=1e-5, C0=0.0)\n",
    "S_plus_star = Specie('S+*', D=0, C0=1e-12, surface_confined=True)\n",
    "S_star = Specie('S*', D=0, C0=0, surface_confined=True)\n",
    "\n",
    "R1 = ChargeTransfer([(Aplus,1),('e',1)],[(A,1)], ks=0.0, E0=0.0)\n",
    "R2 = ChemicalReaction([(S_plus_star,1),(Aplus,1)],[(S_star,1)], kf=1, kb=1)\n",
    "\n",
    "Keq = R2.kf/R2.kb\n",
    "rxn = [R1, R2]\n",
    "\n",
    "mech = Mechanism(rxn)\n",
    "print(mech)\n",
    "\n",
    "cv = DCVoltammetry(E_start = -0.5, E_rev=0.5, nu=0.1)\n",
    "volt = Voltammetry(objs=[cv], N = 14)\n",
    "\n",
    "exp = Experiment(mech, voltammetry=volt)\n",
    "theta = test_langmuir_isotherm(exp, Keq, '$C0', 'S*')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}