feos 0.9.5

FeOs - A framework for equations of state and classical density functional theory.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193

use super::{BarkerHenderson, Perturbation, WeeksChandlerAndersen};
use crate::hard_sphere::{HardSphereProperties, MonomerShape};
use feos_core::parameter::Parameters;
use nalgebra::{DMatrix, DVector, SMatrix, matrix, stack, vector};
use num_dual::DualNum;
use serde::{Deserialize, Serialize};

/// uv-theory parameters for a pure substance
#[derive(Debug, Clone, Copy, Serialize, Deserialize)]
pub struct UVTheoryRecord {
    rep: f64,
    att: f64,
    sigma: f64,
    epsilon_k: f64,
}

impl UVTheoryRecord {
    /// Single substance record for uv-theory
    pub fn new(rep: f64, att: f64, sigma: f64, epsilon_k: f64) -> Self {
        Self {
            rep,
            att,
            sigma,
            epsilon_k,
        }
    }
}

/// Constants for BH temperature dependent HS diameter.
const CD_BH: SMatrix<f64, 4, 3> = matrix![
         0.0,                   1.09360455168912E-02, 0.0;
        -2.00897880971934E-01, -1.27074910870683E-02, 0.0;
         1.40422470174053E-02,  7.35946850956932E-02, 1.28463973950737E-02;
         3.71527116894441E-03,  5.05384813757953E-03, 4.91003312452622E-02];

#[inline]
pub fn mie_prefactor<D: DualNum<f64> + Copy>(rep: D, att: D) -> D {
    rep / (rep - att) * (rep / att).powd(att / (rep - att))
}

#[inline]
pub fn mean_field_constant<D: DualNum<f64> + Copy>(rep: D, att: D, x: D) -> D {
    mie_prefactor(rep, att) * (x.powd(-att + 3.0) / (att - 3.0) - x.powd(-rep + 3.0) / (rep - 3.0))
}

/// Parameters for all substances for uv-theory equation of state and Helmholtz energy functional
pub type UVTheoryParameters = Parameters<UVTheoryRecord, f64, ()>;

/// Parameters for all substances for uv-theory equation of state and Helmholtz energy functional
#[derive(Debug, Clone)]
pub struct UVTheoryPars {
    pub perturbation: Perturbation,
    pub rep: DVector<f64>,
    pub att: DVector<f64>,
    pub sigma: DVector<f64>,
    pub epsilon_k: DVector<f64>,
    pub rep_ij: DMatrix<f64>,
    pub att_ij: DMatrix<f64>,
    pub sigma_ij: DMatrix<f64>,
    pub eps_k_ij: DMatrix<f64>,
    pub cd_bh_pure: Vec<[f64; 5]>,
    pub cd_bh_binary: DMatrix<[f64; 5]>,
}

impl UVTheoryPars {
    pub fn new(parameters: &UVTheoryParameters, perturbation: Perturbation) -> Self {
        let n = parameters.pure.len();

        let [rep, att, sigma, epsilon_k] =
            parameters.collate(|pr| [pr.rep, pr.att, pr.sigma, pr.epsilon_k]);

        let mut rep_ij = DMatrix::zeros(n, n);
        let mut att_ij = DMatrix::zeros(n, n);
        let mut sigma_ij = DMatrix::zeros(n, n);
        let mut eps_k_ij = DMatrix::zeros(n, n);
        let [k_ij] = parameters.collate_binary(|&br| [br]);

        for i in 0..n {
            rep_ij[(i, i)] = rep[i];
            att_ij[(i, i)] = att[i];
            sigma_ij[(i, i)] = sigma[i];
            eps_k_ij[(i, i)] = epsilon_k[i];
            for j in i + 1..n {
                rep_ij[(i, j)] = (rep[i] * rep[j]).sqrt();
                rep_ij[(j, i)] = rep_ij[(i, j)];
                att_ij[(i, j)] = (att[i] * att[j]).sqrt();
                att_ij[(j, i)] = att_ij[(i, j)];
                sigma_ij[(i, j)] = 0.5 * (sigma[i] + sigma[j]);
                sigma_ij[(j, i)] = sigma_ij[(i, j)];
                eps_k_ij[(i, j)] = (1.0 - k_ij[(i, j)]) * (epsilon_k[i] * epsilon_k[j]).sqrt();
                eps_k_ij[(j, i)] = eps_k_ij[(i, j)];
            }
        }

        // BH temperature dependent HS diameter, eq. 21
        let cd_bh_pure: Vec<_> = rep.iter().map(|&mi| bh_coefficients(mi, 6.0)).collect();
        let cd_bh_binary = DMatrix::from_fn(n, n, |i, j| bh_coefficients(rep_ij[(i, j)], 6.0));

        Self {
            perturbation,
            rep,
            att,
            sigma,
            epsilon_k,
            rep_ij,
            att_ij,
            sigma_ij,
            eps_k_ij,
            cd_bh_pure,
            cd_bh_binary,
        }
    }
}

#[expect(clippy::toplevel_ref_arg)]
fn bh_coefficients(rep: f64, att: f64) -> [f64; 5] {
    let inv_a76 = 1.0 / mean_field_constant(7.0, att, 1.0);
    let am6 = mean_field_constant(rep, att, 1.0);
    let alpha = 1.0 / am6 - inv_a76;
    let c0 = vector![-2.0 * rep / ((att - rep) * mie_prefactor(rep, att))];
    let x = stack![c0; CD_BH * vector![1.0, alpha, alpha * alpha]];
    x.data.0[0]
}

impl HardSphereProperties for UVTheoryPars {
    fn monomer_shape<D: DualNum<f64> + Copy>(&self, _: D) -> MonomerShape<'_, D> {
        MonomerShape::Spherical(self.sigma.len())
    }

    fn hs_diameter<D: DualNum<f64> + Copy>(&self, temperature: D) -> DVector<D> {
        match self.perturbation {
            Perturbation::BarkerHenderson => BarkerHenderson::diameter_bh(self, temperature),
            Perturbation::WeeksChandlerAndersen => {
                WeeksChandlerAndersen::diameter_wca(self, temperature)
            }
            Perturbation::WeeksChandlerAndersenB3 => {
                WeeksChandlerAndersen::diameter_wca(self, temperature)
            }
        }
    }
}

#[cfg(test)]
pub mod utils {
    use super::*;
    use feos_core::parameter::{Identifier, PureRecord};
    use std::f64;

    pub fn new_simple(rep: f64, att: f64, sigma: f64, epsilon_k: f64) -> UVTheoryParameters {
        UVTheoryParameters::new_pure(PureRecord::new(
            Default::default(),
            0.0,
            UVTheoryRecord::new(rep, att, sigma, epsilon_k),
        ))
        .unwrap()
    }

    pub fn test_parameters(
        rep: f64,
        att: f64,
        sigma: f64,
        epsilon: f64,
        p: Perturbation,
    ) -> UVTheoryPars {
        let identifier = Identifier::new(Some("1"), None, None, None, None, None);
        let model_record = UVTheoryRecord::new(rep, att, sigma, epsilon);
        let pr = PureRecord::new(identifier, 1.0, model_record);
        UVTheoryPars::new(&UVTheoryParameters::new_pure(pr).unwrap(), p)
    }

    pub fn test_parameters_mixture(
        rep: DVector<f64>,
        att: DVector<f64>,
        sigma: DVector<f64>,
        epsilon: DVector<f64>,
    ) -> UVTheoryParameters {
        let identifier = Identifier::new(Some("1"), None, None, None, None, None);
        let model_record = UVTheoryRecord::new(rep[0], att[0], sigma[0], epsilon[0]);
        let pr1 = PureRecord::new(identifier, 1.0, model_record);
        //
        let identifier2 = Identifier::new(Some("1"), None, None, None, None, None);
        let model_record2 = UVTheoryRecord::new(rep[1], att[1], sigma[1], epsilon[1]);
        let pr2 = PureRecord::new(identifier2, 1.0, model_record2);
        UVTheoryParameters::new_binary([pr1, pr2], None, vec![]).unwrap()
    }

    pub fn methane_parameters(rep: f64, att: f64) -> UVTheoryParameters {
        let identifier = Identifier::new(Some("1"), None, None, None, None, None);
        let model_record = UVTheoryRecord::new(rep, att, 3.7039, 150.03);
        let pr = PureRecord::new(identifier, 1.0, model_record);
        UVTheoryParameters::new_pure(pr).unwrap()
    }
}