{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Colloids : DLVO theory and stability\n", "\n", "Cette théorie permet de calculer les interactions colloïdales dues aux effets électrostatiques et aux interactions de Van der Waals.\n", "\n", "Dans le code ci-dessous, le calcul est effectué pour entre 2 sphères dans un électrolyte symétrique.\n", "$$V=V_R+V_A=64\\pi a n_0k_BT\\lambda_D^2\\Gamma_0^2e^{-\\frac{d}{\\lambda_D}}-\\frac{Aa}{12d}$$\n", "où $\\Gamma_0=tanh(\\frac{z \\zeta e}{k_B T})$.\n", "\n", "Le code calcule la hauteur de la barrière de potentiel (maximum des énergies d'intéraction) et trace l'énergie potentielle d'interaction en fonction de la distance de séparation entre les deux sphères. \n", "\n", "Le code détermine ensuite la concentration critique de coagulation (c.c.c.) en cherchant pour quelle concentration en sel la barrière de potentiel est nulle.\n", "\n", "Le code calcule ensuite le rapport de stabilité par intégration du profil d'interaction :\n", "$$W=2a\\int_{2a}^{\\infty} e^{\\frac{V}{kT}} \\frac{dh}{(h+2a)^2} \\$$\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "c0 \t V_max\n", "1e-05 \t 36.26\n", "0.0001 \t 31.88\n", "0.001 \t 24.43\n", "0.01 \t 12.33\n", "0.1 \t -0.2\n", "la concentration critique de coagulation est = 0.055 mol/L\n", "La règle de Schulze-Hardy donne pour la ccc 51.671 mol/m3\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "c(M) \t W \t\t\t t 1/2 (s) \t\t t 1/2 (jrs)\n", "0.001 \t 336213004.46838474 \t 2567231213.998475 \t 29713.32423609346\n", "0.003 \t 1514190.3458081863 \t 11561946.349578086 \t 133.81882349048712\n", "0.01 \t 1066.9358226933077 \t 8146.832249045162 \t 0.09429203991950419\n", "0.03 \t 1.2287960457293512 \t 9.38275296406902 \t 0.00010859667782487292\n", "0.0551 \t 0.7828888737856383 \t 5.977926871248067 \t 6.918896841722299e-05\n", "0.1 \t 0.7775913818959482 \t 5.93747666154657 \t 6.872079469382604e-05\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#calcul des interactions colloïdales entre 2 sphères dans un électrolyte symétrique\n", "#détermination de la concentration critique de coagulation\n", "#calcul de la stabilité par intégration du profil d'interaction\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import newton\n", "\n", "k=1.38064852e-23 #m2 kg s-2 K-1\n", "T=298\n", "avo=6.02214076e23\n", "kT=k*T\n", "e=1.6e-19\n", "#colloids\n", "a=1e-7 \n", "A=1e-20\n", "zeta=-0.02\n", "#solution \n", "c0=[0.00001,0.0001,0.001, 0.01,0.1] #mol/L\n", "z=1.\n", "#allocation variable\n", "maxi=np.zeros(len(c0))\n", "print ('c0 \\t V_max')\n", "\n", "#Fonctions pour le calcul de VR -repulsion- et VA -attraction-\n", "def VR(d,zeta,c):\n", " I=z**2*c\n", " n0=c*1e3*avo\n", " lamD=3.07e-10/np.sqrt(I)\n", " gam0=np.tanh(z*zeta*e/(4*kT))\n", " return 64*np.pi*a*n0*kT*(lamD**2)*(gam0**2)*np.exp(-d/lamD)\n", "def VA(d):\n", " return -A*a/(12*d)\n", "\n", "#Calcul et tracé de l'énergie potentielle d'interaction en fonction de la distance, d, inter-particules\n", "#pour les différentes concentrations en sel\n", "d=np.logspace(-10,-7,1000)\n", "for i in range(len(c0)): \n", " V=(VR(d,zeta,c0[i])+VA(d))/kT\n", " maxi[i]=max(V)\n", " print (c0[i],'\\t',round(maxi[i],2))\n", " I=z**2*c0[i]\n", " plt.plot(d,V, label='I= %.5f mol/L' %I)\n", "\n", "#fonction pour le calcul du max de la barrière de potentiel -> ccc\n", "def f(c):\n", " V=(VR(d,zeta,c)+VA(d))/kT\n", " return max(V)\n", "\n", "ccrit= newton(f,x0=0.001)\n", "print ('la concentration critique de coagulation est =', round(ccrit,3),'mol/L')\n", "ccrit_SH=3.8e-36*(np.tanh(z*zeta*e/(4*kT)))**4/(A**2*z**6)\n", "print ('La règle de Schulze-Hardy donne pour la ccc', round(ccrit_SH,3),'mol/m3')\n", "\n", "\n", "V=(VR(d,zeta,ccrit)+VA(d))/kT\n", "plt.plot(d,V, 'r--', label='I= %.5f mol/L' %ccrit)\n", "plt.title('Evolution du potentiel d\\'interaction DLVO entre deux sphères')\n", "plt.xlabel('Distance inter-particule (m)')\n", "plt.ylabel('Energie potentielle d\\'interaction/kT (-)')\n", "plt.plot([0,1e-7],[0,0],'k--')\n", "plt.legend(loc='best')\n", "plt.ylim(-10,)\n", "plt.show()\n", "\n", "#calcul de la stabilité\n", "from scipy.integrate import quad\n", "print ('c(M) \\t W \\t\\t\\t t 1/2 (s) \\t\\t t 1/2 (jrs)')\n", "phi=1e-4\n", "mu=1e-3\n", "def stab(d, c):\n", " return 2*a*np.exp((VR(d,zeta,c)+VA(d))/kT)/((d+2*a)**2)\n", "\n", "for cw in [0.001,0.003,0.01,0.03,round(ccrit,4),0.1]:\n", " W = quad(stab, 1e-10, 1e-5, args=(cw))\n", " tdemi=W[0]*np.pi*mu*a**3/(kT*phi)\n", " print (cw,'\\t',W[0], '\\t', tdemi,'\\t', tdemi/(3600*24))\n", " plt.scatter(np.log10(cw),np.log10(W[0]))\n", "\n", "plt.title('Stabilité en fonction de la concentration en sels')\n", "plt.xlabel('Log10(c(M))')\n", "plt.ylabel('Log10(W)') \n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }