07-BET_isotherm.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. The BET isotherm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The BET (Brunauer, Emmet and Teller) isotherm allows to extend ideas and hypotheses that are adopted to obtain the Langmuir isotherm to describe the adsorption of a component from a gas phase in cases in which it can form multiple layers on the surface of the stationary phase, up to the limit in which it condenses into a macroscopic liquid phase. \n",
    "\n",
    "The hypotheses at the foundation of the BET theory are:\n",
    "\n",
    "- Lateral interactions between adsorbed molecules (i.e. interactions between molecules adsorbed in the same layer) are neglibile. In other words the adsorption process does not depend on the local environment around an adsorption site. This hypothesis is common to the derivation of the Langmuir isotherm. \n",
    "- Molecules can adsorb in an infinite number of layers. \n",
    "- The adsorption enthalpy on the first layer is constant and independent from the fractional occupation of that layer. \n",
    "- The adsorption enthalpy in layers from the second onwards is constant and corresponds to the condensation enthalpy.\n",
    "\n",
    "Following an approach similar to the one adopted for the derivation of the Langmuir isotherm let us begin by defining the rates of adsorption and desorption. In the case of th BET isotherm the rates will depend on the layer considered and will therefore have subscript $i$ that indicate the layer on which adsorption takes place. \n",
    "\n",
    "The adsorption rate on layer $i$ can be written as: \n",
    "\n",
    "$$\n",
    "R_{A,i}=k_{A,i}\\Gamma_iP\n",
    "$$(eq1)\n",
    "\n",
    "The desorption rate instead, explicitly introducing the dependence on the adsorption enthalpy through an Arrhenius-like functional form, is written as: \n",
    "\n",
    "$$\n",
    "R_{D,i}=k_{D,i}\\Gamma_i=A_ie^{\\frac{-E_i}{RT}}\\Gamma_i\n",
    "$$(eq2)\n",
    "\n",
    "where $E_i$ is the adsorption energy. Denoting with $E_0$ the adsorption energy on a free adsorption site, the adsorption energy on all successive layers is $E_2=E_3=...E_n=\\lambda$, where $\\lambda$ is the condensation enthalpy. \n",
    "\n",
    "Following the same criterion also the adsorption constant $k_{A,i}$, and the pre-exponential factor of the desorption constant $A_i$ are independent from the layer index - except for those related to the adsorption on a free surface and the desorption from the first layer: \n",
    "\n",
    "$$\n",
    "A_{i\\geq2}=const=A\n",
    "$$(eq3)\n",
    "\n",
    "$$\n",
    "k_{A,i\\geq1}=const=k_A\n",
    "$$(eq4)\n",
    "\n",
    "Having defined the rates of adsorption and desorption one can write population balances for every layer of the adsorbed phase. \n",
    "In the following $\\Gamma_0$ represents the fraction of free adsorption sites, $\\Gamma_i$ represents the fractional occupation of the $i^{th}$ layer. \n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    " \\frac{d\\Gamma_0}{dt}&=-k_{A,0}\\Gamma_0P +k_{D,1}\\Gamma_1 \\\\\n",
    " \\frac{d\\Gamma_1}{dt}&=+k_{A,0}\\Gamma_0P -k_{D,1}\\Gamma_1-k_{A,1}\\Gamma_1P+k_{D,2}\\Gamma_2 \\\\\n",
    " \\frac{d\\Gamma_2}{dt}&=+k_{A,1}\\Gamma_1P -k_{D,2}\\Gamma_2-k_{A,2}\\Gamma_2P+k_{D,3}\\Gamma_3 \\\\\n",
    " \\vdots \\\\\n",
    " \\frac{d\\Gamma_n}{dt}&=+k_{A,n-1}\\Gamma_{n-1}P -k_{D,n}\\Gamma_n-k_{A,n}\\Gamma_nP+k_{D,n+1}\\Gamma_{n+1} \\\\\n",
    " \\vdots\\\\\n",
    " \\end{cases}\n",
    "$$(eq5)\n",
    "\n",
    "At equilibrium the balances reduce to: \n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    " 0=-k_{A,0}\\Gamma_0P +k_{D,1}\\Gamma_1 \\\\\n",
    " 0=+k_{A,0}\\Gamma_0P -k_{D,1}\\Gamma_1-k_{A,1}\\Gamma_1P+k_{D,2}\\Gamma_2 \\\\\n",
    " 0=+k_{A,1}\\Gamma_1P -k_{D,2}\\Gamma_2-k_{A,2}\\Gamma_2P+k_{D,3}\\Gamma_3 \\\\\n",
    " \\vdots \\\\\n",
    " 0=+k_{A,n-1}\\Gamma_{n-1}P -k_{D,n}\\Gamma_n-k_{A,n}\\Gamma_nP+k_{D,n+1}\\Gamma_{n+1} \\\\\n",
    " \\vdots\\\\\n",
    " \\end{cases}\n",
    "$$(eq6)\n",
    "\n",
    "From the steady state balance on free sites we get: \n",
    "\n",
    "$$\n",
    "k_{A,0}\\Gamma_0P=k_{D,1}\\Gamma_1\n",
    "$$(eq7)\n",
    "\n",
    "hence, inserting this equality into the balance on the fraction of sites occupied by a single layer, $\\Gamma_1$ we get: \n",
    "\n",
    "$$\n",
    "k_{A,1}\\Gamma_1P=k_{D,2}\\Gamma_2\n",
    "$$(eq8)\n",
    "\n",
    "Introducing the Arrhenius expression for the adsorption rates we get: \n",
    "\n",
    "$$\n",
    "\\Gamma_1=\\frac{k_{A,0}}{k_{D,1}}\\Gamma_0P=\\frac{k_{A,0}}{A_{1}}e^{\\frac{E_1}{RT}}P\\Gamma_0\n",
    "$$(eq9)\n",
    "\n",
    "and analogously for $\\Gamma_2$: \n",
    "\n",
    "$$\n",
    "\\Gamma_2=\\frac{k_{A,1}}{k_{D,2}}\\Gamma_1P=\\frac{k_{A,1}}{A_{2}}e^{\\frac{E_2}{RT}}P\\Gamma_1\n",
    "$$(eq10)\n",
    "\n",
    "a similar procedure can now be followed recursively to obtain a compact expression for the fraction of sites occupied by an arbitrary number of layers $n$. To this aim we can introduce two constants, $\\alpha$ and $\\beta$ - defined as: \n",
    "\n",
    "$$\n",
    "\\alpha=\\frac{k_{A,0}}{A_{1}}e^{\\frac{E_1}{RT}}P\n",
    "$$(eq11)\n",
    "\n",
    "$$\n",
    "\\beta=\\frac{k_{A}}{A}e^{\\frac{\\lambda}{RT}}P\n",
    "$$(eq12)\n",
    "\n",
    "At this point the fraction of sites occupied by $n$ layers can be obtained as: \n",
    "\n",
    "$$\n",
    "\\Gamma_n=\\beta\\Gamma_{n-1}=\\beta^2\\Gamma_{n-2}=...=\\beta^{n-1}\\Gamma_{1}=\\beta^n\\frac{\\alpha}{\\beta}\\Gamma_0\n",
    "$$(eq13)\n",
    "\n",
    "Deining for the sake of compactness the constant $B_2=\\alpha/\\beta$ and introducing the volume of adsorbate per unit area  $v_s^1$ one can express the total volume adsorbed as: \n",
    "\n",
    "$$\n",
    "v_s=v_s^1\\sum_{i=1}^n{iB_2\\beta^i\\Gamma_0}=v_s^1B_2\\beta\\sum_{i=1}^ni\\beta^{i-1}=v_s^1B_2\\beta\\frac{d\\sum_{i=1}^n\\beta^{i}}{d\\beta}\n",
    "$$(eq14)\n",
    "\n",
    "By introducing the notable result for the term $\\sum_{i=1}^n\\beta^{i}$: \n",
    "\n",
    "$$\n",
    "\\sum_{i=1}^n\\beta^{i}=\\left(\\frac{1-\\beta^n}{1-\\beta}\\right)\\beta\n",
    "$$(eq15)\n",
    "\n",
    "one gets:\n",
    "\n",
    "$$\n",
    "\\frac{v_s}{v_s^1}=\\frac{B_2\\beta}{1-\\beta}\\frac{\\left[1-(n+1)\\beta^n+n\\beta^{n+1}\\right]}{\\left[1+(B_2-1)\\beta-B_2\\beta^{n+1}\\right]}\n",
    "\\label{eq:16}\n",
    "$$(eq16)\n",
    "\n",
    "In order to obtain the final formulation of the BET isotherm it is useful to consider the limit corresponding to macroscopic condensation, which corresponds to a buildup of an infinite number of adsorbed layers, which corresponds to $\\beta=1$. Since this condition is realised for $P=P^o$, it can be shown that $\\beta=\\frac{k_{A}}{A}e^{\\frac{\\lambda}{RT}}P=P/P^o$. \n",
    "\n",
    "Introducing this equality in {eq}`eq16` one gets the so called limited form of the BET isotherm:\n",
    "\n",
    "$$\n",
    "\\frac{v_s}{v_s^1}=\\frac{B_2\\left(\\frac{P}{P^o}\\right)}{1-\\left(\\frac{P}{P^o}\\right)}\\frac{\\left[1-(n+1)\\left(\\frac{P}{P^o}\\right)^n+n\\left(\\frac{P}{P^o}\\right)^{n+1}\\right]}{\\left[1+(B_2-1)\\left(\\frac{P}{P^o}\\right)-B_2\\left(\\frac{P}{P^o}\\right)^{n+1}\\right]}\n",
    "$$(eq17)\n",
    "\n",
    "note that the left hand side of this equation can be expressed in terms of unit mass of adsorbent, instead of unit surface. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1 Many isotherm shapes from the same expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending on the parameters introduced in the BET isotherm its functional form can adapt to capture all known shapes of adsorption isotherm. In the following we shall demonstrate combination of parameters that produce isotherms belonging to all five of the classes introduced by Brunauer (Brunauer et al. JACS 1940). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from matplotlib.pyplot import cm\n",
    "\n",
    "#Plotting\n",
    "figure=plt.figure()\n",
    "axes = figure.add_axes([0.1,0.1,1.2,1.2])\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "\n",
    "N=100;\n",
    "\n",
    "#Parameters\n",
    "P0 = np.array([5, 12, 12, 5, 11, 11]);\n",
    "B2 = np.array([10, 50, 2, 50, 2]);\n",
    "n  = np.array([1,500, 500, 5, 5]);\n",
    "\n",
    "P = np.linspace(0, 10, N)\n",
    "vv1 = np.zeros(np.size(P))\n",
    "   \n",
    "\n",
    "\n",
    "color=iter(cm.rainbow(np.linspace(0,1,np.size(B2))))\n",
    "\n",
    "for i in range(0,np.size(B2)):     \n",
    "    S=P/P0[i]\n",
    "    c=next(color)\n",
    "    \n",
    "    #Langmuir isotherm   \n",
    "    vv1=B2[i]*S/(1-S)*(1-(n[i]+1)*np.power(S,n[i])+n[i]*np.power(S,n[i]+1))/(1+(B2[i]-1)*S-B2[i]*np.power(S,n[i]+1));\n",
    "    \n",
    "    axes.plot(P,vv1, marker=' ' , c=c)\n",
    "\n",
    "    \n",
    "plt.title('BET isotherm types', fontsize=18);\n",
    "axes.set_xlabel('P [bar]', fontsize=18);\n",
    "axes.set_ylabel('$v_l$ / $v_l^1$',fontsize=18);\n",
    "axes.legend(['Type I','Type II','Type III','Type IV','Type V'], fontsize=18);"
   ]
  }
 ],
 "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
}