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pure_pets_functional.rs
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164 lines (144 loc) · 5.45 KB
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use crate::hard_sphere::{FMTVersion, HardSphereProperties};
use crate::pets::Pets;
use crate::pets::eos::dispersion::{A, B};
use feos_core::{FeosError, FeosResult};
use feos_dft::{FunctionalContribution, WeightFunction, WeightFunctionInfo, WeightFunctionShape};
use nalgebra::dvector;
use ndarray::*;
use num_dual::*;
use std::f64::consts::{FRAC_PI_6, PI};
const PI36M1: f64 = 1.0 / (36.0 * PI);
const N3_CUTOFF: f64 = 1e-5;
#[derive(Clone)]
pub struct PureFMTFunctional<'a> {
parameters: &'a Pets,
version: FMTVersion,
}
impl<'a> PureFMTFunctional<'a> {
pub fn new(parameters: &'a Pets, version: FMTVersion) -> Self {
Self {
parameters,
version,
}
}
}
impl<'a> FunctionalContribution for PureFMTFunctional<'a> {
fn name(&self) -> &'static str {
"Pure FMT"
}
fn weight_functions<N: DualNum<f64> + Copy>(&self, temperature: N) -> WeightFunctionInfo<N> {
let r = self.parameters.hs_diameter(temperature) * N::from(0.5);
WeightFunctionInfo::new(dvector![0], false).extend(
vec![
WeightFunctionShape::Delta,
WeightFunctionShape::Theta,
WeightFunctionShape::DeltaVec,
]
.into_iter()
.map(|s| WeightFunction::new_unscaled(r.clone(), s))
.collect(),
false,
)
}
fn helmholtz_energy_density<N: DualNum<f64> + Copy>(
&self,
temperature: N,
weighted_densities: ArrayView2<N>,
) -> FeosResult<Array1<N>> {
// 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(FeosError::IterationFailed(String::from(
"PureFMTFunctional",
)));
}
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));
// Different FMT versions
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 phi = -(&n0 * &ln31) + n1n2 * &n3m1rec + n2n2 * n2 * PI36M1 * f3;
Ok(phi)
}
}
#[derive(Clone)]
pub struct PureAttFunctional<'a> {
parameters: &'a Pets,
}
impl<'a> PureAttFunctional<'a> {
pub fn new(parameters: &'a Pets) -> Self {
Self { parameters }
}
}
impl<'a> FunctionalContribution for PureAttFunctional<'a> {
fn name(&self) -> &'static str {
"Pure attractive"
}
fn weight_functions<N: DualNum<f64> + Copy>(&self, temperature: N) -> WeightFunctionInfo<N> {
let d = self.parameters.hs_diameter(temperature);
const PSI: f64 = 1.21; // Homosegmented DFT (Heier2018)
WeightFunctionInfo::new(dvector![0], false).add(
WeightFunction::new_scaled(d * N::from(PSI), WeightFunctionShape::Theta),
false,
)
}
fn helmholtz_energy_density<N: DualNum<f64> + Copy>(
&self,
temperature: N,
weighted_densities: ArrayView2<N>,
) -> Result<Array1<N>, FeosError> {
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 * d.powi(3));
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) * A[i]);
i2 = i2 + eta.mapv(|eta| eta.powi(i as i32) * B[i]);
}
let c1 =
eta.mapv(|eta| ((eta * 8.0 - eta.powi(2) * 2.0) / (eta - 1.0).powi(4) + 1.0).recip());
let phi =
rho.mapv(|rho| -(rho).powi(2) * e * s3 * PI) * (i1 * 2.0 + c1 * i2.mapv(|i2| i2 * e));
Ok(phi)
}
}