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Copy pathpure_saft_functional.rs
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319 lines (283 loc) · 10.9 KB
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use super::polar::{pair_integral_ij, triplet_integral_ijk};
use super::PcSaftParameters;
use crate::association::Association;
use crate::hard_sphere::{FMTVersion, HardSphereProperties};
use crate::pcsaft::eos::dispersion::{A0, A1, A2, B0, B1, B2};
use crate::pcsaft::eos::polar::{AD, AQ, BD, BQ, CD, CQ, PI_SQ_43};
use feos_core::{EosError, EosResult};
use feos_dft::{
FunctionalContributionDual, WeightFunction, WeightFunctionInfo, WeightFunctionShape,
};
use ndarray::*;
use num_dual::*;
use std::f64::consts::{FRAC_PI_6, PI};
use std::fmt;
use std::sync::Arc;
const PI36M1: f64 = 1.0 / (36.0 * PI);
const N3_CUTOFF: f64 = 1e-5;
const N0_CUTOFF: f64 = 1e-9;
pub struct PureFMTAssocFunctional {
parameters: Arc<PcSaftParameters>,
association: Association<PcSaftParameters>,
version: FMTVersion,
}
impl PureFMTAssocFunctional {
pub fn new(parameters: Arc<PcSaftParameters>, version: FMTVersion) -> Self {
let association = Association::new(¶meters, ¶meters.association, 50, 1e-10);
Self {
parameters,
association,
version,
}
}
}
impl<N: DualNum<f64> + Copy + ScalarOperand> FunctionalContributionDual<N>
for PureFMTAssocFunctional
{
fn weight_functions(&self, temperature: N) -> WeightFunctionInfo<N> {
let r = self.parameters.hs_diameter(temperature) * 0.5;
WeightFunctionInfo::new(arr1(&[0]), false).extend(
vec![
WeightFunctionShape::Delta,
WeightFunctionShape::Theta,
WeightFunctionShape::DeltaVec,
]
.into_iter()
.map(|s| WeightFunction {
prefactor: self.parameters.m.mapv(|m| m.into()),
kernel_radius: r.clone(),
shape: s,
})
.collect(),
false,
)
}
fn calculate_helmholtz_energy_density(
&self,
temperature: N,
weighted_densities: ArrayView2<N>,
) -> EosResult<Array1<N>> {
let p = &self.parameters;
// weighted densities
let n2 = weighted_densities.index_axis(Axis(0), 0);
let n3 = weighted_densities.index_axis(Axis(0), 1);
let n2v = weighted_densities.slice_axis(Axis(0), Slice::new(2, None, 1));
// temperature dependent segment radius
let r = self.parameters.hs_diameter(temperature)[0] * 0.5;
// auxiliary variables
if n3.iter().any(|n3| n3.re() > 1.0) {
return Err(EosError::IterationFailed(String::from(
"PureFMTAssocFunctional",
)));
}
let ln31 = n3.mapv(|n3| (-n3).ln_1p());
let n3rec = n3.mapv(|n3| n3.recip());
let n3m1 = n3.mapv(|n3| -n3 + 1.0);
let n3m1rec = n3m1.mapv(|n3m1| n3m1.recip());
let n1 = n2.mapv(|n2| n2 / (r * 4.0 * PI));
let n0 = n2.mapv(|n2| n2 / (r * r * 4.0 * PI));
let n1v = n2v.mapv(|n2v| n2v / (r * 4.0 * PI));
let (n1n2, n2n2) = match self.version {
FMTVersion::WhiteBear => (
&n1 * &n2 - (&n1v * &n2v).sum_axis(Axis(0)),
&n2 * &n2 - (&n2v * &n2v).sum_axis(Axis(0)) * 3.0,
),
FMTVersion::AntiSymWhiteBear => {
let mut xi2 = (&n2v * &n2v).sum_axis(Axis(0)) / n2.map(|n| n.powi(2));
xi2.iter_mut().for_each(|x| {
if x.re() > 1.0 {
*x = N::one()
}
});
(
&n1 * &n2 - (&n1v * &n2v).sum_axis(Axis(0)),
&n2 * &n2 * xi2.mapv(|x| (-x + 1.0).powi(3)),
)
}
_ => unreachable!(),
};
// The f3 term contains a 0/0, therefore a taylor expansion is used for small values of n3
let mut f3 = (&n3m1 * &n3m1 * &ln31 + n3) * &n3rec * n3rec * &n3m1rec * &n3m1rec;
f3.iter_mut().zip(n3).for_each(|(f3, &n3)| {
if n3.re() < N3_CUTOFF {
*f3 = (((n3 * 35.0 / 6.0 + 4.8) * n3 + 3.75) * n3 + 8.0 / 3.0) * n3 + 1.5;
}
});
let mut phi = -(&n0 * &ln31) + n1n2 * &n3m1rec + n2n2 * n2 * PI36M1 * f3;
// association
let a = &p.association;
if !a.is_empty() {
let mut xi = -(&n2v * &n2v).sum_axis(Axis(0)) / (&n2 * &n2) + 1.0;
xi.iter_mut().zip(&n2).for_each(|(xi, &n2)| {
if n2.re() < N0_CUTOFF * 4.0 * PI * p.m[0] * r.re().powi(2) {
*xi = N::one();
}
});
let rho0 = (&n0 / p.m[0] * &xi).insert_axis(Axis(0));
phi += &(self.association.calculate_helmholtz_energy_density(
temperature,
&rho0,
&n2,
&n3m1rec,
&xi,
))?;
}
Ok(phi)
}
}
impl fmt::Display for PureFMTAssocFunctional {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(f, "Pure FMT+association")
}
}
#[derive(Clone)]
pub struct PureChainFunctional {
parameters: Arc<PcSaftParameters>,
}
impl PureChainFunctional {
pub fn new(parameters: Arc<PcSaftParameters>) -> Self {
Self { parameters }
}
}
impl<N: DualNum<f64> + Copy + ScalarOperand> FunctionalContributionDual<N> for PureChainFunctional {
fn weight_functions(&self, temperature: N) -> WeightFunctionInfo<N> {
let d = self.parameters.hs_diameter(temperature);
WeightFunctionInfo::new(arr1(&[0]), true)
.add(
WeightFunction::new_scaled(d.clone(), WeightFunctionShape::Delta),
false,
)
.add(
WeightFunction {
prefactor: (&self.parameters.m / 8.0).mapv(|x| x.into()),
kernel_radius: d,
shape: WeightFunctionShape::Theta,
},
false,
)
}
fn calculate_helmholtz_energy_density(
&self,
_: N,
weighted_densities: ArrayView2<N>,
) -> EosResult<Array1<N>> {
let rho = weighted_densities.index_axis(Axis(0), 0);
// negative lambdas lead to nan, therefore the absolute value is used
let lambda = weighted_densities
.index_axis(Axis(0), 1)
.map(|&l| if l.re() < 0.0 { -l } else { l } + N::from(f64::EPSILON));
let eta = weighted_densities.index_axis(Axis(0), 2);
let y = eta.mapv(|eta| (eta * 0.5 - 1.0) / (eta - 1.0).powi(3));
Ok(-(y * lambda).mapv(|x| (x.ln() - 1.0) * (self.parameters.m[0] - 1.0)) * rho)
}
}
impl fmt::Display for PureChainFunctional {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(f, "Pure chain")
}
}
#[derive(Clone)]
pub struct PureAttFunctional {
parameters: Arc<PcSaftParameters>,
}
impl PureAttFunctional {
pub fn new(parameters: Arc<PcSaftParameters>) -> Self {
Self { parameters }
}
}
impl<N: DualNum<f64> + Copy + ScalarOperand> FunctionalContributionDual<N> for PureAttFunctional {
fn weight_functions(&self, temperature: N) -> WeightFunctionInfo<N> {
let d = self.parameters.hs_diameter(temperature);
const PSI: f64 = 1.3862; // Homosegmented DFT (Sauer2017)
WeightFunctionInfo::new(arr1(&[0]), false).add(
WeightFunction::new_scaled(d * PSI, WeightFunctionShape::Theta),
false,
)
}
fn weight_functions_pdgt(&self, temperature: N) -> WeightFunctionInfo<N> {
let d = self.parameters.hs_diameter(temperature);
const PSI: f64 = 1.3286; // pDGT (Rehner2018)
WeightFunctionInfo::new(arr1(&[0]), false).add(
WeightFunction::new_scaled(d * PSI, WeightFunctionShape::Theta),
false,
)
}
fn calculate_helmholtz_energy_density(
&self,
temperature: N,
weighted_densities: ArrayView2<N>,
) -> EosResult<Array1<N>> {
let p = &self.parameters;
let rho = weighted_densities.index_axis(Axis(0), 0);
// temperature dependent segment radius
let d = p.hs_diameter(temperature)[0];
let eta = rho.mapv(|rho| rho * FRAC_PI_6 * p.m[0] * d.powi(3));
let m1 = (p.m[0] - 1.0) / p.m[0];
let m2 = m1 * (p.m[0] - 2.0) / p.m[0];
let e = temperature.recip() * p.epsilon_k[0];
let s3 = p.sigma[0].powi(3);
// I1, I2 and C1
let mut i1: Array1<N> = Array::zeros(eta.raw_dim());
let mut i2: Array1<N> = Array::zeros(eta.raw_dim());
for i in 0..=6 {
i1 = i1 + eta.mapv(|eta| eta.powi(i as i32) * (A0[i] + m1 * A1[i] + m2 * A2[i]));
i2 = i2 + eta.mapv(|eta| eta.powi(i as i32) * (B0[i] + m1 * B1[i] + m2 * B2[i]));
}
let c1 = eta.mapv(|eta| {
((eta * 8.0 - eta.powi(2) * 2.0) / (eta - 1.0).powi(4) * p.m[0]
+ (eta * 20.0 - eta.powi(2) * 27.0 + eta.powi(3) * 12.0 - eta.powi(4) * 2.0)
/ ((eta - 1.0) * (eta - 2.0)).powi(2)
* (1.0 - p.m[0])
+ 1.0)
.recip()
});
let mut phi = rho.mapv(|rho| -(rho * p.m[0]).powi(2) * e * s3 * PI)
* (i1 * 2.0 + c1 * i2.mapv(|i2| i2 * p.m[0] * e));
// dipoles
if p.ndipole > 0 {
let mu2_term = e * s3 * p.mu2[0];
let m = p.m[0].min(2.0);
let m1 = (m - 1.0) / m;
let m2 = m1 * (m - 2.0) / m;
let phi2 = -(&rho * &rho)
* pair_integral_ij(m1, m2, &eta, &AD, &BD, e)
* (mu2_term * mu2_term / s3 * PI);
let phi3 = -(&rho * &rho * rho)
* triplet_integral_ijk(m1, m2, &eta, &CD)
* (mu2_term * mu2_term * mu2_term / s3 * PI_SQ_43);
let mut phi_d = &phi2 * &phi2 / (&phi2 - &phi3);
phi_d.iter_mut().zip(phi2.iter()).for_each(|(p, &p2)| {
if p.re().is_nan() {
*p = p2;
}
});
phi += &phi_d;
}
// quadrupoles
if p.nquadpole > 0 {
let q2_term = e * p.sigma[0].powi(5) * p.q2[0];
let m = p.m[0].min(2.0);
let m1 = (m - 1.0) / m;
let m2 = m1 * (m - 2.0) / m;
let phi2 = -(&rho * &rho)
* pair_integral_ij(m1, m2, &eta, &AQ, &BQ, e)
* (q2_term * q2_term / p.sigma[0].powi(7) * PI * 0.5625);
let phi3 = (&rho * &rho * rho)
* triplet_integral_ijk(m1, m2, &eta, &CQ)
* (q2_term * q2_term * q2_term / s3.powi(3) * PI * PI * 0.5625);
let mut phi_q = &phi2 * &phi2 / (&phi2 - &phi3);
phi_q.iter_mut().zip(phi2.iter()).for_each(|(p, &p2)| {
if p.re().is_nan() {
*p = p2;
}
});
phi += &phi_q;
}
Ok(phi)
}
}
impl fmt::Display for PureAttFunctional {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
write!(f, "Pure attractive")
}
}