{ "cells": [ { "cell_type": "markdown", "id": "373446bb-4986-4d21-ad58-b3ed06850829", "metadata": {}, "source": [ "### Mean Field theory of interacting fluids" ] }, { "cell_type": "markdown", "id": "a50ad70b-bfde-4b44-8002-1256ffe12cc8", "metadata": {}, "source": [ ":::{admonition} **What you need to know**\n", ":class: note\n", "- The van der Waals equation is the best known example of an equation of state that exhibits a\n", "first-order phase transition with a critical end point.\n", "- Since clearly the pressure remains a monotonic function of the volume in experiment, the van der Waals equation is amended by a Maxwell construction, in which the famous “equal area” cut of the van der Waals loop replaces that loop.\n", "\n", "- This equal area construction is equivalent to replacing the corresponding van der Waals Helmholtz\n", "free energy by its convex envelope.\n", ":::" ] }, { "cell_type": "markdown", "id": "314428dd-c229-4d67-9038-18bd190384a5", "metadata": {}, "source": [ "### Mean field approximation for a gas with interacting particles\n", "\n", "- The canonical partition function splits into kinetic and potential energy contributions for a pure fluid. The kinetic energy part is the same as that of ideal gas. In the ideal gas, the last term is simply equal to volume. For nonideal gas, the last term can't be evaluated exactly in general, hence the need to make approximations. \n", "\n", "$$Z(\\beta, N, V) = \\frac{1}{N!h^{3N}}\\int e^{-\\beta\\frac{p^2}{2m}}dp^N \\cdot \\int e^{-\\beta U(r)} dr^N$$\n", "\n", "- When making mean-field approximation, we assume that each particle moves in some effective potential $U(r) = \\sum_i U^i_{eff}(r)$ created by the rest of the particles. This allows us to use $Z=z^N$\n", "\n", "$$Z(\\beta, N, V) = \\frac{1}{N!} \\Bigg[\\frac{(2\\pi mk_B T)}{h^3} \\Bigg]^N \\cdot \\Bigg[ \\int e^{-\\beta U(r)} dr \\Bigg]^N$$\n", "\n", "### Van der Waals gas\n", "\n", "- Van der Waals is a mean-field model for non-ideal gases. The essence of the model is in its two additions or modifications to the partition function: \n", "- First, each gas atom can occupy finite volume b; hence, the free volume with N particle in the container is $(V-bN)$\n", "- Second, we write effective potential to be proportional to density; this is the essence of mean field approximation $U_{eff} = -a\\frac{N}{V}$\n", "\n", "$$Z(\\beta, N, V) = \\frac{1}{N!} \\Bigg[\\frac{(2\\pi mk_B T)^{3/2}}{h^3} \\Bigg]^N \\cdot \\Bigg[(V-bn) e^{\\frac{aN}{Vk_B T}} \\Bigg]^N$$\n", "\n", "\n", "- **Free energy at fixed volumes**\n", " \n", "$$F = -k_BT logZ = -Nk_BT log \\Bigg[\\frac{(2\\pi mk_B T)^{3/2}e}{h^3}\\Big(\\frac{V}{N}-b \\Big) \\Bigg] -\\frac{aN^2}{V}$$\n", "\n", "- **Free energy at fixed pressures**\n", "\n", "$$G = F+pV$$\n", "\n", "$$G = -Nk_BT log \\Bigg[\\frac{(2\\pi mk_B T)^{3/2}e}{h^3}\\Big(\\frac{V}{N}-b \\Big) \\Bigg] -\\frac{aN^2}{V} +pV$$\n", "\n", "**Equation of state**\n", "\n", "$$\\frac{\\partial G}{\\partial V}=0$$\n", "\n", "$$ \\Big( p+\\frac{aN^2}{V^2}\\Big)(V-bN) = Nk_B T $$" ] }, { "cell_type": "markdown", "id": "114ed814-d8d9-4847-afba-b3b5c652d1a2", "metadata": {}, "source": [ "### Reduced equation and correspondence state principle\n", "\n", "- The critical point is the unique point where both derivatives of pressure vanish $dP/dV = d^2P/dV^2=0$. solving for the critical values of P, V and T we get:\n", "\n", "$$V_c = 3Nb\\,\\,\\,\\, P_c =\\frac{a}{27b^2}\\,\\,\\,\\,\\,\\, k_BT_c = \\frac{8a}{27b}$$ \n", "\n", "- As we can see, different gases will have different critical points described by a and b parameters.\n", "- But if you normalize pressure, temperature, and volume by their critical values, we get a reduced equation that describes many gases with a single curve!\n", "\n", "- Taking $P_r = P/P_c$, $T_r = T/T_c$ and $V_r = V/V_c$ we get:\n", "\n", "$$P_r = 8\\frac{T_r}{(3 V_r-1)} - \\frac{3}{(V_r^2)}$$\n" ] }, { "cell_type": "markdown", "id": "49b60215-0c9a-4cf3-a9ac-11480efacdeb", "metadata": {}, "source": [ "### Maxwell Construction" ] }, { "cell_type": "markdown", "id": "30a74efc-4aaf-4dcf-bba0-1012dcdc5eb8", "metadata": {}, "source": [ "- Note that the area between liquid and gas shows unphysical dependence of pressure on volume\n", "- The equilibrium pressure can be identified by making use of Gibbs free energy change around liquid and gas volumes $v_{liq}$ and $v_{gas}$. Taking a cyclic integral\n", "\n", "$$\\oint \\frac{\\partial G}{\\partial P}dP = \\oint VdP =0 $$\n", "\n", "- In Maxwell, a construction line is drawn between the instability points in P vs V plot where the areas above and below it sum to one.\n", "- On this straight line, we learn that the second-order derivative of free energy is zero.\n", "- As a function of the extensive variable V, there is a region (between $v_{liq}$ and $v_{gas}$) of phase\n", "coexistence. The densities of the extensive variables of the two phases in equilibrium are\n", "discontinuous across the transition" ] }, { "cell_type": "code", "execution_count": 2, "id": "694bfe08-7232-4242-8df2-f766502cd900", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import quad\n", "from scipy.optimize import newton\n", "from scipy.signal import argrelextrema\n", "\n", "palette = iter(['#9b59b6', '#4c72b0', '#55a868', '#c44e52', '#dbc256'])\n", "\n", "# Critical pressure, volume and temperature\n", "# These values are for the van der Waals equation of state for CO2:\n", "# (p - a/V^2)(V-b) = RT. Units: p is in Pa, Vc in m3/mol and T in K.\n", "pc = 7.404e6\n", "Vc = 1.28e-4\n", "Tc = 304\n", "\n", "def vdw(Tr, Vr):\n", " \"\"\"Van der Waals equation of state.\n", "\n", " Return the reduced pressure from the reduced temperature and volume.\n", "\n", " \"\"\"\n", "\n", " pr = 8*Tr/(3*Vr-1) - 3/Vr**2\n", " return pr\n", "\n", "\n", "def vdw_maxwell(Tr, Vr):\n", " \"\"\"Van der Waals equation of state with Maxwell construction.\n", "\n", " Return the reduced pressure from the reduced temperature and volume,\n", " applying the Maxwell construction correction to the unphysical region\n", " if necessary.\n", "\n", " \"\"\"\n", "\n", " pr = vdw(Tr, Vr)\n", " if Tr >= 1:\n", " # No unphysical region above the critical temperature.\n", " return pr\n", "\n", " if min(pr) < 0:\n", " raise ValueError('Negative pressure results from van der Waals'\n", " ' equation of state with Tr = {} K.'.format(Tr))\n", "\n", " # Initial guess for the position of the Maxwell construction line:\n", " # the volume corresponding to the mean pressure between the minimum and\n", " # maximum in reduced pressure, pr.\n", " iprmin = argrelextrema(pr, np.less)\n", " iprmax = argrelextrema(pr, np.greater)\n", " Vr0 = np.mean([Vr[iprmin], Vr[iprmax]])\n", "\n", " def get_Vlims(pr0):\n", " \"\"\"Solve the inverted van der Waals equation for reduced volume.\n", "\n", " Return the lowest and highest reduced volumes such that the reduced\n", " pressure is pr0. It only makes sense to call this function for\n", " T= Vrmin) & (Vr <= Vrmax)] = pr0\n", " return pr\n", "\n", "Vr = np.linspace(0.5, 3, 500)\n", "\n", "def plot_pV(T):\n", " Tr = T / Tc\n", " c = next(palette)\n", " ax.plot(Vr, vdw(Tr, Vr), lw=2, alpha=0.3, color=c)\n", " ax.plot(Vr, vdw_maxwell(Tr, Vr), lw=2, color=c, label='{:.2f}'.format(Tr))\n", "\n", "fig, ax = plt.subplots()\n", "\n", "for T in range(270, 320, 10):\n", " plot_pV(T)\n", "\n", "ax.set_xlim(0.4, 3)\n", "ax.set_xlabel('Reduced volume')\n", "ax.set_ylim(0, 1.6)\n", "ax.set_ylabel('Reduced pressure')\n", "ax.legend(title='Reduced temperature')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cfc2abf3-f16b-4c9e-9306-1f86f331695d", "metadata": {}, "source": [ "### Problems\n" ] }, { "cell_type": "markdown", "id": "8cc41c04-a8f3-4a11-a767-4dede88e05c3", "metadata": {}, "source": [ "1. Using van der Waals gas with $a=1$, $b=1$, $m=1$, and $N=1$ and adopting simplified units where $k_B=1$, $h=1$ plot dimensionless free energy per particle $G/Nk_BT$ vs. molar volume $V/N$ for temperatures 0.2, 0.22, 0.24, 0.26 and 0.28.\n", "2. Minima on free energy correspond to equilibrium molar fractions of gas and liquid $v_{gas}$ and $v_{liq}$. For each of the temperatures in point 1, extract these molar volumes and then plot them on the same graph as a function of temperature $v_{gas}(T)$ and $v_{liq}(T)$\n", "3. Using van der Waals equation of state, make a 3D plot of volume vs pressure vs temperature.\n", "4. Find the critical volume, temperature, and pressure of Van der Waals gas $V_c, P_c, T_c$ by taking the first three derivatives of Gibbs free energy and setting it to zero, e.g $\\frac{\\partial^n G}{\\partial v^n}=$ (n=1,2,3)" ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:llpsmd3] *", "language": "python", "name": "conda-env-llpsmd3-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.16" } }, "nbformat": 4, "nbformat_minor": 5 }