estimate_paths_per_area.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = 1.9858775 * 10**-3     # universal gas (kcal / mol K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0431 : ratio of actual/theoretical CNT packing density\n"
     ]
    }
   ],
   "source": [
    "# from https://doi.org/10.1002/advs.202001670 for SWCNTs with average diameter 1.7 nm\n",
    "\n",
    "cnt_diameter = 1.7 # nm\n",
    "act_cnt_pack_density = 1.9*10**12 # paths/cm^2\n",
    "theor_cnt_pack_density = 1 / np.pi / (cnt_diameter/2)**2 # paths/nm^2\n",
    "theor_cnt_pack_density *= (10**9 / 10**2)**2 # paths/cm^2\n",
    "\n",
    "act_theor_ratio = act_cnt_pack_density / theor_cnt_pack_density\n",
    "print(f'{act_theor_ratio:.4f} : ratio of actual/theoretical CNT packing density')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1964e+13 paths/cm^2\n",
      "0.2196 paths/nm^2 : actual CNT packing density for CNTs with diameter 0.5 nm\n"
     ]
    }
   ],
   "source": [
    "# calculate theoretical packing density for 0.5 nm diameter CNT and scale for actual packing\n",
    "\n",
    "cnt_diameter = 0.5 # nm\n",
    "theor_cnt_pack_density = 1 / np.pi / (cnt_diameter/2)**2 # paths/nm^2\n",
    "theor_cnt_pack_density *= (10**9 / 10**2)**2 # paths/cm^2\n",
    "\n",
    "act_cnt_pack_density = theor_cnt_pack_density * act_theor_ratio # paths/cm^2\n",
    "print(f'{act_cnt_pack_density:.4e} paths/cm^2')\n",
    "act_cnt_pack_density *= (10**2 / 10**9)**2 # paths/nm^2\n",
    "print(f'{act_cnt_pack_density:.4f} paths/nm^2 : actual CNT packing density for CNTs with diameter 0.5 nm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0220 paths/nm^2 : calculated actual PA packing density for pores with diameter 0.5 nm\n"
     ]
    }
   ],
   "source": [
    "# assume an order of magnitude worse packing density for PA membrane with pore diameter 0.5 nm\n",
    "\n",
    "act_PA_pack_density = act_cnt_pack_density / 10\n",
    "print(f'{act_PA_pack_density:.4f} paths/nm^2 : calculated actual PA packing density for pores with diameter 0.5 nm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2196 : number of paths in 100,000.00 nm^2\n"
     ]
    }
   ],
   "source": [
    "# let unit area be 0.1 micrometer squared\n",
    "\n",
    "unit_area = 0.1 * (10**9 / 10**6)**2 # um^2 to nm^2\n",
    "n_paths = round(act_PA_pack_density*unit_area)\n",
    "print(f'{n_paths} : number of paths in {unit_area:,.2f} nm^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.6350 Angstroms^2 : area for a single path\n",
      "\n",
      "39269.9082 Angstroms^2 : total available area for transport\n",
      "\n",
      "1.0000e+07 Angstroms^2 : total membrane area\n",
      "\n",
      "0.003926990816987242 Angstroms^2 : available fraction of total area\n"
     ]
    }
   ],
   "source": [
    "# calculate area of one path (Angstroms^2)\n",
    "\n",
    "A_i = np.pi*2.5**2\n",
    "print(f'{A_i:.4f} Angstroms^2 : area for a single path')\n",
    "\n",
    "print(f'\\n{A_i*2000:.4f} Angstroms^2 : total available area for transport')\n",
    "\n",
    "print(f'\\n{unit_area * (10 / 1)**2:.4e} Angstroms^2 : total membrane area')\n",
    "\n",
    "print(f'\\n{A_i*2000 / (unit_area * (10 / 1)**2)} Angstroms^2 : available fraction of total area')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropic shift for 2000 paths : 3.3005 kcal/mol/K\n"
     ]
    }
   ],
   "source": [
    "# calculate the entropic shift for 2000 paths of equal area A_i across 1e7 Angstroms^2 total area\n",
    "\n",
    "n_paths_list = np.arange(1, 2001, 1)\n",
    "dS = np.zeros(len(n_paths_list))\n",
    "for i,n in enumerate(n_paths_list):\n",
    "    dS[i] = -R*300*np.log(n*A_i/(unit_area * (10 / 1)**2))\n",
    "\n",
    "print(f'Entropic shift for {n_paths_list[-1]} paths : {dS[-1]:.4f} kcal/mol/K')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_paths_list, dS)\n",
    "plt.xlabel('number of paths')\n",
    "plt.ylabel('$-RT \\ln{\\sum_i^n A_i / A}$')\n",
    "plt.title(f'Entropic shift for paths with equal area {A_i:.4f} $\\AA^2$ and total membrane area {unit_area * (10 / 1)**2:,.0f} $\\AA^2$')\n",
    "plt.savefig('figs/entropic_shift.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21964 : number of paths in 1,000,000.00 nm^2\n"
     ]
    }
   ],
   "source": [
    "# let unit area be 0.2 micrometer squared\n",
    "\n",
    "unit_area = 1 * (10**9 / 10**6)**2 # um^2 to nm^2\n",
    "n_paths = round(act_PA_pack_density*unit_area)\n",
    "print(f'{n_paths} : number of paths in {unit_area:,.2f} nm^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.6350 Angstroms^2 : area for a single path\n",
      "\n",
      "431262.1315 Angstroms^2 : total available area for transport\n",
      "\n",
      "1.0000e+08 Angstroms^2 : total membrane area\n",
      "\n",
      "0.0043126213152153885 Angstroms^2 : available fraction of total area\n"
     ]
    }
   ],
   "source": [
    "# calculate area of one path (Angstroms^2)\n",
    "\n",
    "A_i = np.pi*2.5**2\n",
    "print(f'{A_i:.4f} Angstroms^2 : area for a single path')\n",
    "\n",
    "print(f'\\n{A_i*n_paths:.4f} Angstroms^2 : total available area for transport')\n",
    "\n",
    "print(f'\\n{unit_area * (10 / 1)**2:.4e} Angstroms^2 : total membrane area')\n",
    "\n",
    "print(f'\\n{A_i*n_paths / (unit_area * (10 / 1)**2)} Angstroms^2 : available fraction of total area')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropic shift for 21963 paths : 3.2447 kcal/mol/K\n"
     ]
    }
   ],
   "source": [
    "# calculate the entropic shift for n_paths of equal area A_i across 1e7 Angstroms^2 total area\n",
    "\n",
    "n_paths_list = np.arange(1, n_paths, 1)\n",
    "dS = np.zeros(len(n_paths_list))\n",
    "for i,n in enumerate(n_paths_list):\n",
    "    dS[i] = -R*300*np.log(n*A_i/(unit_area * (10 / 1)**2))\n",
    "\n",
    "print(f'Entropic shift for {n_paths_list[-1]} paths : {dS[-1]:.4f} kcal/mol/K')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Entropic shift for paths with equal area 19.6350 $\\\\AA^2$ and total membrane area 100,000,000 $\\\\AA^2$')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_paths_list, dS)\n",
    "plt.xlabel('number of paths')\n",
    "plt.ylabel('$-RT \\ln{\\sum_i^n A_i / A}$')\n",
    "plt.title(f'Entropic shift for paths with equal area {A_i:.4f} $\\AA^2$ and total membrane area {unit_area * (10 / 1)**2:,.0f} $\\AA^2$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.8.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}