{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "940cc903",
   "metadata": {},
   "source": [
    "# Model Potentials\n",
    "\n",
    "These EOS for model potentials are useful for understanding theory, and capture some (but perhaps not all) of the physics of \"real\" fluids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f5463428",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-15T22:40:52.217143Z",
     "iopub.status.busy": "2024-03-15T22:40:52.216980Z",
     "iopub.status.idle": "2024-03-15T22:40:52.231043Z",
     "shell.execute_reply": "2024-03-15T22:40:52.230591Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.19.1'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import teqp\n",
    "teqp.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf22ac3d",
   "metadata": {},
   "source": [
    "## Square-well\n",
    "\n",
    "The potential is defined by\n",
    "\n",
    "$$\n",
    "V(r) = \\left\\lbrace \\begin{array}{cc}\n",
    "         \\infty & r < \\sigma \\\\\n",
    "         -\\varepsilon & \\sigma < r < \\lambda\\sigma \\\\\n",
    "         0 & r > \\lambda \\sigma\n",
    "         \\end{array}\\right.        \n",
    "$$\n",
    "\n",
    "from which an EOS can be developed by correlating results from molecular simulation. The EOS is from:\n",
    "\n",
    " Rodolfo Espíndola-Heredia, Fernando del Río and Anatol Malijevsky\n",
    " Optimized equation of the state of the\n",
    " square-well fluid of variable range based on\n",
    " a fourth-order free-energy expansion\n",
    " J. Chem. Phys. 130, 024509 (2009); https://doi.org/10.1063/1.3054361\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "435a84a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-15T22:40:52.233061Z",
     "iopub.status.busy": "2024-03-15T22:40:52.232897Z",
     "iopub.status.idle": "2024-03-15T22:40:52.235488Z",
     "shell.execute_reply": "2024-03-15T22:40:52.235094Z"
    }
   },
   "outputs": [],
   "source": [
    "model = teqp.make_model({  \n",
    "  \"kind\": \"SW_EspindolaHeredia2009\", \n",
    "  \"model\": {\n",
    "      \"lambda\": 1.3\n",
    "  }\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0caf9ea",
   "metadata": {},
   "source": [
    "## EXP-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dc38b705",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-15T22:40:52.237416Z",
     "iopub.status.busy": "2024-03-15T22:40:52.237257Z",
     "iopub.status.idle": "2024-03-15T22:40:52.239795Z",
     "shell.execute_reply": "2024-03-15T22:40:52.239384Z"
    }
   },
   "outputs": [],
   "source": [
    "model = teqp.make_model({  \n",
    "  \"kind\": \"EXP6_Kataoka1992\", \n",
    "  \"model\": {\n",
    "      \"alpha\": 12\n",
    "  }\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b87cbd05",
   "metadata": {},
   "source": [
    "## Lennard-Jones Fluid\n",
    "\n",
    "The Lennard-Jones potential is given by\n",
    "$$\n",
    "V(r) = 4\\varepsilon\\left((\\sigma/r)^{12}-(\\sigma/r)^{6}\\right)\n",
    "$$\n",
    "\n",
    "and EOS are available from many authors. teqp includes the EOS from Thol, Kolafa-Nezbeda, and Johnson."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "739e3e2b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-15T22:40:52.241560Z",
     "iopub.status.busy": "2024-03-15T22:40:52.241406Z",
     "iopub.status.idle": "2024-03-15T22:40:52.246065Z",
     "shell.execute_reply": "2024-03-15T22:40:52.245648Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LJ126_TholJPCRD2016 (1.3035125549100017, 0.3103860327864468) (1.32, 0.31)\n",
      "LJ126_KolafaNezbeda1994 (1.3396478193468193, 0.3108038977722935) (1.3396, 0.3108)\n",
      "LJ126_Johnson1993 (1.3130000571792173, 0.3099999768607838) (1.313, 0.31)\n"
     ]
    }
   ],
   "source": [
    "for kind, crit in [\n",
    "    [\"LJ126_TholJPCRD2016\", (1.32, 0.31)], # Note the true critical point was not used\n",
    "    [\"LJ126_KolafaNezbeda1994\", (1.3396, 0.3108)],\n",
    "    [\"LJ126_Johnson1993\", (1.313, 0.310)]]:\n",
    "    \n",
    "    j = { \"kind\": kind, \"model\": {} }\n",
    "    model = teqp.make_model(j)\n",
    "    print(kind, model.solve_pure_critical(1.3, 0.3), crit)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fad87158",
   "metadata": {},
   "source": [
    "## Two-Center Lennard-Jones Fluid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ae5646de",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-03-15T22:40:52.247834Z",
     "iopub.status.busy": "2024-03-15T22:40:52.247679Z",
     "iopub.status.idle": "2024-03-15T22:40:52.252722Z",
     "shell.execute_reply": "2024-03-15T22:40:52.252268Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2.8282972062188056, 0.2005046666634018)\n",
      "(2.832574303561834, 0.2003194655463274)\n"
     ]
    }
   ],
   "source": [
    "model = teqp.make_model({  \n",
    "  'kind': '2CLJF-Dipole', \n",
    "  'model': {\n",
    "      \"author\": \"2CLJF_Lisal\",\n",
    "      'L^*': 0.5,\n",
    "      '(mu^*)^2': 0.1\n",
    "  }\n",
    "})\n",
    "print(model.solve_pure_critical(1.3, 0.3))\n",
    "\n",
    "model = teqp.make_model({  \n",
    "  'kind': '2CLJF-Quadrupole', \n",
    "  'model': {\n",
    "      \"author\": \"2CLJF_Lisal\",\n",
    "      'L^*': 0.5,\n",
    "      '(Q^*)^2': 0.1\n",
    "  }\n",
    "})\n",
    "print(model.solve_pure_critical(1.3, 0.3))"
   ]
  }
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