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prehner committed Mar 4, 2024
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"cells": [
{
"cell_type": "markdown",
"id": "e68c660a",
"id": "da49f9b5",
"metadata": {},
"source": [
"# Surface tension using PC-SAFT Helmholtz energy functionals\n",
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{
"cell_type": "code",
"execution_count": 1,
"id": "aec9f4a6",
"id": "94396ac3",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "9c0bda0d",
"id": "a11cda3a",
"metadata": {},
"source": [
"### Water parameters for PC-SAFT \n",
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{
"cell_type": "code",
"execution_count": 2,
"id": "1cebc474",
"id": "dc2d6991",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "6a8558a0",
"id": "bd417eb1",
"metadata": {},
"source": [
"Let's first compute the critical point. We will make use of the critical temperature later."
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{
"cell_type": "code",
"execution_count": 3,
"id": "ca8309b3",
"id": "62080689",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "15f7d7ce",
"id": "97af8edc",
"metadata": {},
"source": [
"As you can see, the model overestimates the critical temperature."
]
},
{
"cell_type": "markdown",
"id": "a0c359e1",
"id": "306ec78f",
"metadata": {},
"source": [
"## Surface tension for single VLE\n",
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},
{
"cell_type": "markdown",
"id": "a8b0cd08",
"id": "986c0b75",
"metadata": {},
"source": [
"For the VLE, we use the `PhaseEquilibrium.pure` method. Here for $T = 300$ Kelvin."
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{
"cell_type": "code",
"execution_count": 4,
"id": "71a10a1a",
"id": "a51dc479",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "25a60f64",
"id": "f18ba1b7",
"metadata": {},
"source": [
"Next, we initialize the density profile. For the surface tension, a 1D DFT calculation in Cartesian coordinates is conducted. Thus, the density profile will be an 1D array (we have a single substance). \n",
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{
"cell_type": "code",
"execution_count": 5,
"id": "f8893b0c",
"id": "157ad243",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "95488c7a",
"id": "961c6405",
"metadata": {},
"source": [
"The above method does not yet run a calculation. If we try to extract the surface tension, it will return `None`. Let's store the initial density profile for a later comparison."
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{
"cell_type": "code",
"execution_count": 6,
"id": "1c0c8cfd",
"id": "378ad857",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "6ab83e40",
"id": "741d217b",
"metadata": {},
"source": [
"To calculate the equilibrium density profile, we have to call the `solve()` method:"
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{
"cell_type": "code",
"execution_count": 7,
"id": "78780ff5",
"id": "42774e6e",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "d717bb99",
"id": "43343b55",
"metadata": {},
"source": [
"`solve()` calculates the equilibrium density profile and returns the `PlanarInterface` object so that we can readily extract the `surface_tension`.\n",
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{
"cell_type": "code",
"execution_count": 8,
"id": "8c5b6598",
"id": "f7400976",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "392c8210",
"id": "b4a64981",
"metadata": {},
"source": [
"## Comparison to NIST data using `SurfaceTensionDiagram`\n",
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{
"cell_type": "code",
"execution_count": 9,
"id": "b3b6f81e",
"id": "c1793ee7",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "1eb01b17",
"id": "26fddb5a",
"metadata": {},
"source": [
"For the `SurfaceTensionDiagram`, we need to provide the VLE's. We compute those using the `PhaseDiagram` object (here for 50 temperatures between 275 Kelvin and the critical temperature) from which we get a list of `PhaseEquilibrium`s via the `states` filed. The `SurfaceTensionDiagram` is nice, because we can reuse equilibrium density profiles from prior iterations as input for the next iteration. It's therefore typically faster and more stable than an \"naive\" implementation by hand.\n",
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{
"cell_type": "code",
"execution_count": 10,
"id": "263c4cdc",
"id": "2fbce44a",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "887ee03e",
"id": "d7f3c4e0",
"metadata": {},
"source": [
"We now can extract all surface tensions via `surface_tension` as well as the liquid and vapor states via the `liquid` and `vapor` getters, respectively. Let's store the results in a pandas `DataFrame` to make plotting easier."
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{
"cell_type": "code",
"execution_count": 11,
"id": "509fcbab",
"id": "0043c952",
"metadata": {},
"outputs": [],
"source": [
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{
"cell_type": "code",
"execution_count": 12,
"id": "3eeff4c6",
"id": "e54859fa",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "6dd31eb7",
"id": "85c84336",
"metadata": {},
"source": [
"## Concluding remkars\n",
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"cells": [
{
"cell_type": "markdown",
"id": "2ecc222c",
"id": "37d6f894",
"metadata": {},
"source": [
"# Entropy scaling of pure substances\n",
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{
"cell_type": "code",
"execution_count": 1,
"id": "bddac7b3",
"id": "9ebdf14f",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "895a97e1",
"id": "ccad8dfc",
"metadata": {},
"source": [
"## PC-SAFT (individual component parameters)\n",
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{
"cell_type": "code",
"execution_count": 2,
"id": "779857cc",
"id": "c5c99382",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "3749415d",
"id": "c14501f4",
"metadata": {},
"source": [
"## PC-SAFT homo-GC\n",
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{
"cell_type": "code",
"execution_count": 3,
"id": "2c47b21e",
"id": "d04045e7",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "bd5bdf9b",
"id": "4d9bc741",
"metadata": {},
"source": [
"### Build equations of state\n",
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{
"cell_type": "code",
"execution_count": 4,
"id": "de424915",
"id": "10424a72",
"metadata": {},
"outputs": [],
"source": [
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},
{
"cell_type": "markdown",
"id": "541cd829",
"id": "0a780c8c",
"metadata": {},
"source": [
"### Compare parameters"
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{
"cell_type": "code",
"execution_count": 5,
"id": "daee3073",
"id": "54e84f54",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "ba2e5844",
"id": "dd8f7520",
"metadata": {},
"source": [
"## Compare methods to NIST data (T = 450 K)\n",
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{
"cell_type": "code",
"execution_count": 6,
"id": "03890e24",
"id": "7d25ee92",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "markdown",
"id": "2a723b1a",
"id": "7bbea8b1",
"metadata": {},
"source": [
"We loop through experimental data, read temperature, pressure and the phase (liquid or vapor) and generate `State` objects for the experimental conditions. Then, we compute the residual molar entropy and the logarithmic reduced viscosity."
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{
"cell_type": "code",
"execution_count": 7,
"id": "66826843",
"id": "31d78635",
"metadata": {},
"outputs": [
{
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{
"cell_type": "code",
"execution_count": 8,
"id": "a7088286",
"id": "acd653ef",
"metadata": {},
"outputs": [
{
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{
"cell_type": "code",
"execution_count": 9,
"id": "6668cacf",
"id": "4fc23eba",
"metadata": {},
"outputs": [
{
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.. raw:: html

</div>
<div class=col-md-9 content>

feos.dft.State.chemical\_potential\_contributions
=================================================

.. currentmodule:: feos.dft

.. automethod:: State.chemical_potential_contributions
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