Activity & group contribution¶

Excess-Gibbs / activity-coefficient models (Margules, van Laar, Wilson, NRTL, UNIQUAC, regular-solution and Flory-Huggins), available both as plain functions and as differentiable ActivityModel objects, plus the predictive group contribution methods (UNIFAC, modified UNIFAC/Dortmund, and Joback).

Activity-coefficient models¶

activity ¶

Activity-coefficient models for non-ideal liquid mixtures.

The package collects excess-Gibbs / activity-coefficient models that share a common, differentiable jax.numpy implementation:

margules and vanlaar: two-parameter binary models;
wilson, nrtl and uniquac: multicomponent local-composition models;
regular_solution: Scatchard-Hildebrand regular-solution and Flory-Huggins models from pure-component descriptors.

Each model exposes *_ln_gamma and *_gamma functions; the local- composition models additionally provide builders that assemble their interaction matrices from temperature and physical parameters.

For a uniform, object-oriented interface (used by the gamma-phi equilibrium engine and the parameter regressor), models wraps each kernel in a differentiable model object implementing ActivityModel.

Modules:

Name	Description
`margules`	Two-parameter Margules activity-coefficient model for binary mixtures.
`models`	Object-oriented activity-coefficient models with a uniform, differentiable API.
`nrtl`	Multicomponent NRTL (non-random two-liquid) activity-coefficient model.
`regular_solution`	Regular-solution and Flory-Huggins activity-coefficient models.
`uniquac`	Multicomponent UNIQUAC activity-coefficient model.
`vanlaar`	Van Laar activity-coefficient model for binary mixtures.
`wilson`	Multicomponent Wilson activity-coefficient model.

Classes:

Name	Description
`NRTL`	NRTL model with the standard `tau_ij = a_ij + b_ij/T + e_ij ln T` law.
`UNIQUAC`	UNIQUAC model with `tau_ij = exp(a_ij + b_ij/T)`.
`ActivityModel`	Structural type for a liquid activity-coefficient model.
`FloryHuggins`	Athermal Flory-Huggins size-asymmetry model.
`Hildebrand`	Flory-Huggins-Hildebrand model: regular-solution enthalpy + FH entropy.
`Margules`	Two-parameter Margules binary model with `A = a + b/T`.
`RegularSolution`	Scatchard-Hildebrand regular-solution model (cohesive-energy descriptors).
`VanLaar`	Two-parameter van Laar binary model with `A = a + b/T`.
`Wilson`	Wilson model built from molar volumes and interaction energies.

Functions:

Name	Description
`margules_excess_gibbs`	Dimensionless excess Gibbs energy `g^E / (R T)` of a binary mixture.
`margules_gamma`	Activity coefficients `(gamma_1, gamma_2)` for a binary Margules mixture.
`margules_ln_gamma`	Natural log of the activity coefficients for a binary Margules mixture.
`excess_gibbs`	Dimensionless excess Gibbs energy `g^E/(RT) = sum_i x_i ln(gamma_i)`.
`gamma`	Activity coefficients `gamma_i` from any `ActivityModel`.
`nrtl_from_energies`	Build a temperature-independent `NRTL` from energies `dg_ij` (J/mol).
`uniquac_from_energies`	Build a temperature-dependent `UNIQUAC` from energies `du_ij` (J/mol).
`van_laar`	Build a `VanLaar` binary model (constant `A` unless `b` given).
`nrtl_excess_gibbs`	Dimensionless excess Gibbs energy `g^E / (R T)` for an NRTL mixture.
`nrtl_g`	Compute `G_ij = exp(-alpha_ij * tau_ij)` from `tau` and `alpha`.
`nrtl_gamma`	Activity coefficients `gamma_i` for a multicomponent NRTL mixture.
`nrtl_ln_gamma`	Log activity coefficients `ln(gamma_i)` for a multicomponent NRTL mixture.
`nrtl_tau`	Build the `tau` matrix from the common temperature correlation.
`flory_huggins_gamma`	Activity coefficients from the athermal Flory-Huggins model.
`flory_huggins_ln_gamma`	Athermal Flory-Huggins (size-asymmetry) log activity coefficients.
`hildebrand_ln_gamma`	Flory-Huggins-Hildebrand `ln(gamma)`: regular-solution enthalpy + FH entropy.
`regular_solution_gamma`	Activity coefficients from regular-solution theory.
`regular_solution_ln_gamma`	Log activity coefficients from Scatchard-Hildebrand regular-solution theory.
`volume_fractions`	Volume (segment) fractions `phi_i = x_i v_i / sum_j x_j v_j`.
`uniquac_gamma`	Activity coefficients for a multicomponent UNIQUAC mixture.
`uniquac_ln_gamma`	Log activity coefficients for a multicomponent UNIQUAC mixture.
`uniquac_tau`	Build `tau_ij = exp(-Delta u_ij / (R T))` from interaction energies (J/mol).
`van_laar_gamma`	Activity coefficients `(gamma_1, gamma_2)` for a binary van Laar mixture.
`van_laar_ln_gamma`	Natural log of the activity coefficients for a binary van Laar mixture.
`wilson_excess_gibbs`	Dimensionless excess Gibbs energy `g^E / (R T)` for a Wilson mixture.
`wilson_gamma`	Activity coefficients for a multicomponent Wilson mixture.
`wilson_lambda`	Build the Wilson `Lambda` matrix from molar volumes and energy parameters.
`wilson_ln_gamma`	Log activity coefficients for a multicomponent Wilson mixture.

NRTL `dataclass` ¶

NRTL(a: Array, b: Array, alpha: Array, e: Array)

NRTL model with the standard tau_ij = a_ij + b_ij/T + e_ij ln T law.

Attributes:

Name	Type	Description
`a`	`Array`	Constant part of `tau` (dimensionless), shape `(n, n)`.
`b`	`Array`	`1/T` part of `tau` (K), shape `(n, n)`.
`alpha`	`Array`	Non-randomness factors `alpha_ij = alpha_ji`, shape `(n, n)`.
`e`	`Array`	`ln T` part of `tau` (dimensionless), shape `(n, n)`; usually zero.

Methods:

Name	Description
`tau`	Temperature-dependent `tau` matrix.
`ln_gamma`	Log activity coefficients `ln(gamma_i)`.

tau ¶

tau(t: ArrayLike) -> Array

Temperature-dependent tau matrix.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i).

UNIQUAC `dataclass` ¶

UNIQUAC(r: Array, q: Array, a: Array, b: Array)

UNIQUAC model with tau_ij = exp(a_ij + b_ij/T).

Attributes:

Name	Type	Description
`r`	`Array`	Volume (size) parameters `r_i`, shape `(n,)`.
`q`	`Array`	Surface-area parameters `q_i`, shape `(n,)`.
`a`	`Array`	Constant part of `ln(tau)` (dimensionless), shape `(n, n)`.
`b`	`Array`	`1/T` part of `ln(tau)` (K), shape `(n, n)`.

Methods:

Name	Description
`tau`	Temperature-dependent `tau` matrix (`exp(a + b/T)`).
`ln_gamma`	Log activity coefficients `ln(gamma_i)`.

tau ¶

tau(t: ArrayLike) -> Array

Temperature-dependent tau matrix (exp(a + b/T)).

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i).

ActivityModel ¶

Bases: Protocol

Structural type for a liquid activity-coefficient model.

A model maps a liquid composition and temperature to the vector of log activity coefficients ln(gamma_i). That single method is all the equilibrium engines require.

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `ln(gamma_i)` at composition `x`, temperature `t`.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i) at composition x, temperature t.

FloryHuggins `dataclass` ¶

FloryHuggins(volume: Array)

Athermal Flory-Huggins size-asymmetry model.

Attributes:

Name	Type	Description
`volume`	`Array`	Molecular size descriptors `v_i` (only ratios matter), shape `(n,)`.

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `ln(gamma_i)` (the combinatorial part).

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i) (the combinatorial part).

Hildebrand `dataclass` ¶

Hildebrand(volume: Array, delta: Array)

Flory-Huggins-Hildebrand model: regular-solution enthalpy + FH entropy.

Attributes:

Name	Type	Description
`volume`	`Array`	Liquid molar volumes `v_i` (m^3/mol), shape `(n,)`.
`delta`	`Array`	Solubility parameters `delta_i` (Pa**0.5), shape `(n,)`.

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `ln(gamma_i)`.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i).

Margules `dataclass` ¶

Margules(a12: Array, b12: Array, a21: Array, b21: Array)

Two-parameter Margules binary model with A = a + b/T.

Attributes:

Name	Type	Description
`a12`	`Array`	Constant part of `A12`; `b12`: its `1/T` part (K).
`a21`	`Array`	Constant part of `A21`; `b21`: its `1/T` part (K).

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `[ln(gamma_1), ln(gamma_2)]` for the binary.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients [ln(gamma_1), ln(gamma_2)] for the binary.

RegularSolution `dataclass` ¶

RegularSolution(volume: Array, delta: Array)

Scatchard-Hildebrand regular-solution model (cohesive-energy descriptors).

Attributes:

Name	Type	Description
`volume`	`Array`	Liquid molar volumes `v_i` (m^3/mol), shape `(n,)`.
`delta`	`Array`	Solubility parameters `delta_i` (Pa**0.5), shape `(n,)`.

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `ln(gamma_i)` (all non-negative).

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i) (all non-negative).

VanLaar `dataclass` ¶

VanLaar(a12: Array, b12: Array, a21: Array, b21: Array)

Two-parameter van Laar binary model with A = a + b/T.

Attributes:

Name	Type	Description
`a12`	`Array`	Constant part of `A12`; `b12`: its `1/T` part (K).
`a21`	`Array`	Constant part of `A21`; `b21`: its `1/T` part (K).

Methods:

Name	Description
`ln_gamma`	Log activity coefficients `[ln(gamma_1), ln(gamma_2)]` for the binary.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients [ln(gamma_1), ln(gamma_2)] for the binary.

Wilson `dataclass` ¶

Wilson(volume: Array, energy: Array)

Wilson model built from molar volumes and interaction energies.

Attributes:

Name	Type	Description
`volume`	`Array`	Liquid molar volumes `v_i` (any consistent unit), shape `(n,)`.
`energy`	`Array`	Energy differences `(lambda_ij - lambda_ii)` (J/mol), shape `(n, n)`.

Methods:

Name	Description
`lam`	Temperature-dependent Wilson `Lambda` matrix.
`ln_gamma`	Log activity coefficients `ln(gamma_i)` (cannot predict an LLE split).

lam ¶

lam(t: ArrayLike) -> Array

Temperature-dependent Wilson Lambda matrix.

ln_gamma ¶

ln_gamma(x: Array, t: ArrayLike) -> Array

Log activity coefficients ln(gamma_i) (cannot predict an LLE split).

margules_excess_gibbs ¶

margules_excess_gibbs(
    x1: ArrayLike, a12: ArrayLike, a21: ArrayLike
) -> Array

Dimensionless excess Gibbs energy g^E / (R T) of a binary mixture.

Parameters:

Name	Type	Description	Default
`x1`	`ArrayLike`	Mole fraction of component 1, in `[0, 1]`.	required
`a12`	`ArrayLike`	Margules parameter `A12` (equals `ln(gamma_1)` at infinite dilution).	required
`a21`	`ArrayLike`	Margules parameter `A21` (equals `ln(gamma_2)` at infinite dilution).	required

Returns:

Type	Description
`Array`	The dimensionless excess Gibbs energy.

margules_gamma ¶

margules_gamma(
    x1: ArrayLike, a12: ArrayLike, a21: ArrayLike
) -> tuple[Array, Array]

Activity coefficients (gamma_1, gamma_2) for a binary Margules mixture.

margules_ln_gamma ¶

margules_ln_gamma(
    x1: ArrayLike, a12: ArrayLike, a21: ArrayLike
) -> tuple[Array, Array]

Natural log of the activity coefficients for a binary Margules mixture.

Parameters:

Name	Type	Description	Default
`x1`	`ArrayLike`	Mole fraction of component 1, in `[0, 1]`.	required
`a12`	`ArrayLike`	Margules parameter `A12`.	required
`a21`	`ArrayLike`	Margules parameter `A21`.	required

Returns:

Type	Description
`tuple[Array, Array]`	A tuple `(ln_gamma1, ln_gamma2)`.

excess_gibbs ¶

excess_gibbs(
    model: ActivityModel, x: Array, t: ArrayLike
) -> Array

Dimensionless excess Gibbs energy g^E/(RT) = sum_i x_i ln(gamma_i).

This identity holds for every activity model (the log activity coefficients are the partial molar excess Gibbs energies), so it gives a single, exact, model-independent g^E, handy for plotting and for stability tests.

gamma ¶

gamma(
    model: ActivityModel, x: Array, t: ArrayLike
) -> Array

Activity coefficients gamma_i from any ActivityModel.

nrtl_from_energies ¶

nrtl_from_energies(dg: Array, alpha: Array) -> NRTL

Build a temperature-independent NRTL from energies dg_ij (J/mol).

Uses tau_ij = dg_ij / (R T) (i.e. a = 0, b = dg / R), the common "g_ij - g_jj" parameterisation.

uniquac_from_energies ¶

uniquac_from_energies(
    r: Array, q: Array, du: Array
) -> UNIQUAC

Build a temperature-dependent UNIQUAC from energies du_ij (J/mol).

Uses tau_ij = exp(-du_ij / (R T)) (a = 0, b = -du / R).

van_laar ¶

van_laar(
    a12: ArrayLike,
    a21: ArrayLike,
    b12: ArrayLike = 0.0,
    b21: ArrayLike = 0.0,
) -> VanLaar

Build a VanLaar binary model (constant A unless b given).

nrtl_excess_gibbs ¶

nrtl_excess_gibbs(
    x: Array, tau: Array, alpha: Array
) -> Array

Dimensionless excess Gibbs energy g^E / (R T) for an NRTL mixture.

nrtl_g ¶

nrtl_g(tau: Array, alpha: Array) -> Array

Compute G_ij = exp(-alpha_ij * tau_ij) from tau and alpha.

nrtl_gamma ¶

nrtl_gamma(x: Array, tau: Array, alpha: Array) -> Array

Activity coefficients gamma_i for a multicomponent NRTL mixture.

nrtl_ln_gamma ¶

nrtl_ln_gamma(x: Array, tau: Array, alpha: Array) -> Array

Log activity coefficients ln(gamma_i) for a multicomponent NRTL mixture.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`tau`	`Array`	Interaction parameter matrix `tau_ij`, shape `(n, n)`, diagonal 0.	required
`alpha`	`Array`	Non-randomness matrix `alpha_ij = alpha_ji`, shape `(n, n)`.	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(n,)`.

nrtl_tau ¶

nrtl_tau(
    t: ArrayLike, a: Array, b: Array, c: ArrayLike = 0.0
) -> Array

Build the tau matrix from the common temperature correlation.

tau_ij = a_ij + b_ij / T + c_ij * ln(T). Pass arrays of shape (n, n) for a and b (and optionally c); the diagonal should be zero.

flory_huggins_gamma ¶

flory_huggins_gamma(x: Array, volume: Array) -> Array

Activity coefficients from the athermal Flory-Huggins model.

flory_huggins_ln_gamma ¶

flory_huggins_ln_gamma(x: Array, volume: Array) -> Array

Athermal Flory-Huggins (size-asymmetry) log activity coefficients.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`volume`	`Array`	Molecular size descriptors `v_i` (molar volume or van der Waals volume; only ratios matter), shape `(n,)`.	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(n,)` (the combinatorial part, non-positive).

hildebrand_ln_gamma ¶

hildebrand_ln_gamma(
    x: Array, volume: Array, delta: Array, t: ArrayLike
) -> Array

Flory-Huggins-Hildebrand ln(gamma): regular-solution enthalpy + FH entropy.

The sum of regular_solution_ln_gamma (enthalpic) and flory_huggins_ln_gamma (combinatorial/entropic), giving a model that handles both energetic and size-asymmetry effects with pure-component data.

regular_solution_gamma ¶

regular_solution_gamma(
    x: Array, volume: Array, delta: Array, t: ArrayLike
) -> Array

Activity coefficients from regular-solution theory.

regular_solution_ln_gamma ¶

regular_solution_ln_gamma(
    x: Array, volume: Array, delta: Array, t: ArrayLike
) -> Array

Log activity coefficients from Scatchard-Hildebrand regular-solution theory.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`volume`	`Array`	Liquid molar volumes `v_i` (m^3/mol), shape `(n,)`.	required
`delta`	`Array`	Solubility parameters `delta_i` (Pa0.5 = J0.5/m**1.5), shape `(n,)`.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(n,)` (all non-negative).

volume_fractions ¶

volume_fractions(x: Array, volume: Array) -> Array

Volume (segment) fractions phi_i = x_i v_i / sum_j x_j v_j.

uniquac_gamma ¶

uniquac_gamma(
    x: Array, r: Array, q: Array, tau: Array
) -> Array

Activity coefficients for a multicomponent UNIQUAC mixture.

uniquac_ln_gamma ¶

uniquac_ln_gamma(
    x: Array, r: Array, q: Array, tau: Array
) -> Array

Log activity coefficients for a multicomponent UNIQUAC mixture.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`r`	`Array`	Volume (size) parameters `r_i`, shape `(n,)`.	required
`q`	`Array`	Surface-area parameters `q_i`, shape `(n,)`.	required
`tau`	`Array`	Interaction matrix `tau_ij`, shape `(n, n)`, diagonal 1.	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(n,)`.

uniquac_tau ¶

uniquac_tau(t: ArrayLike, du: Array) -> Array

Build tau_ij = exp(-Delta u_ij / (R T)) from interaction energies (J/mol).

van_laar_gamma ¶

van_laar_gamma(
    x1: ArrayLike, a12: ArrayLike, a21: ArrayLike
) -> tuple[Array, Array]

Activity coefficients (gamma_1, gamma_2) for a binary van Laar mixture.

van_laar_ln_gamma ¶

van_laar_ln_gamma(
    x1: ArrayLike, a12: ArrayLike, a21: ArrayLike
) -> tuple[Array, Array]

Natural log of the activity coefficients for a binary van Laar mixture.

Parameters:

Name	Type	Description	Default
`x1`	`ArrayLike`	Mole fraction of component 1, in `[0, 1]`.	required
`a12`	`ArrayLike`	Infinite-dilution value `ln(gamma_1^inf)`.	required
`a21`	`ArrayLike`	Infinite-dilution value `ln(gamma_2^inf)`.	required

Returns:

Type	Description
`tuple[Array, Array]`	A tuple `(ln_gamma1, ln_gamma2)`.

wilson_excess_gibbs ¶

wilson_excess_gibbs(x: Array, lam: Array) -> Array

Dimensionless excess Gibbs energy g^E / (R T) for a Wilson mixture.

wilson_gamma ¶

wilson_gamma(x: Array, lam: Array) -> Array

Activity coefficients for a multicomponent Wilson mixture.

wilson_lambda ¶

wilson_lambda(
    t: ArrayLike, volume: Array, energy: Array
) -> Array

Build the Wilson Lambda matrix from molar volumes and energy parameters.

Parameters:

Name	Type	Description	Default
`t`	`ArrayLike`	Temperature (K).	required
`volume`	`Array`	Liquid molar volumes `v_i`, shape `(n,)` (any consistent unit).	required
`energy`	`Array`	Energy differences `(lambda_ij - lambda_ii)` in J/mol, shape `(n, n)`.	required

Returns:

Type	Description
`Array`	`Lambda` matrix of shape `(n, n)`.

wilson_ln_gamma ¶

wilson_ln_gamma(x: Array, lam: Array) -> Array

Log activity coefficients for a multicomponent Wilson mixture.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(n,)`.	required
`lam`	`Array`	Wilson interaction matrix `Lambda_ij`, shape `(n, n)`, diagonal 1.	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(n,)`.

Group contribution¶

groupcontrib ¶

Group-contribution methods for parameter-free property prediction.

unifac predicts liquid-phase activity coefficients from functional-group interactions.
joback estimates pure-component constants (critical properties, boiling point, formation properties, ideal-gas Cp) from a count of functional groups.

These let Fugacio cover mixtures and species for which curated, fitted parameters are unavailable, the role the project README assigns to group contribution.

Modules:

Name	Description
`dortmund`	Modified UNIFAC (Dortmund): predictive activity coefficients with T-dependence.
`joback`	Joback group-contribution estimation of pure-component constants.
`unifac`	UNIFAC group-contribution model for predictive activity coefficients.

Classes:

Name	Description
`JobackGroup`	A single Joback functional-group contribution row.

Functions:

Name	Description
`modified_unifac_activity`	Predict `ln(gamma)` for named database components with modified UNIFAC.
`modified_unifac_ln_gamma`	Log activity coefficients from modified UNIFAC (Dortmund), given group tables.
`joback_estimate`	Estimate pure-component constants from Joback groups and return a Component.
`unifac_activity`	Predict `ln(gamma)` for named database components using bundled tables.
`unifac_ln_gamma`	Log activity coefficients from UNIFAC, given explicit group tables.

JobackGroup `dataclass` ¶

JobackGroup(
    tc: float,
    pc: float,
    vc: float,
    tb: float,
    tm: float,
    hform: float,
    gform: float,
    cpa: float,
    cpb: float,
    cpc: float,
    cpd: float,
)

A single Joback functional-group contribution row.

modified_unifac_activity ¶

modified_unifac_activity(
    components: list[str], x: Array, t: ArrayLike
) -> Array

Predict ln(gamma) for named database components with modified UNIFAC.

Parameters:

Name	Type	Description	Default
`components`	`list[str]`	Component names with assignments in `DO_COMPONENT_GROUPS`.	required
`x`	`Array`	Mole fractions aligned with `components`.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(len(components),)`.

modified_unifac_ln_gamma ¶

modified_unifac_ln_gamma(
    x: Array,
    nu: Array,
    r: Array,
    q: Array,
    main_index: Array,
    a_main: Array,
    b_main: Array,
    c_main: Array,
    t: ArrayLike,
) -> Array

Log activity coefficients from modified UNIFAC (Dortmund), given group tables.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(ncomp,)`.	required
`nu`	`Array`	Subgroup counts, shape `(ncomp, ngroup)`.	required
`r`	`Array`	Subgroup `R_k` values, shape `(ngroup,)`.	required
`q`	`Array`	Subgroup `Q_k` values, shape `(ngroup,)`.	required
`main_index`	`Array`	Each subgroup's main-group index, shape `(ngroup,)`.	required
`a_main`	`Array`	Constant interaction-coefficient matrix, shape `(nmain, nmain)`.	required
`b_main`	`Array`	Linear-in-`T` interaction-coefficient matrix, shape `(nmain, nmain)`.	required
`c_main`	`Array`	Quadratic-in-`T` interaction-coefficient matrix, shape `(nmain, nmain)`.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(ncomp,)`.

joback_estimate ¶

joback_estimate(
    groups: dict[str, int],
    n_atoms: int,
    *,
    name: str = "estimated",
    formula: str = "",
    mw: float = 0.0,
) -> Component

Estimate pure-component constants from Joback groups and return a Component.

Parameters:

Name	Type	Description	Default
`groups`	`dict[str, int]`	Mapping of group label (see `GROUPS`) to occurrence count.	required
`n_atoms`	`int`	Total number of atoms in the molecule (hydrogens included), required by the critical-pressure correlation.	required
`name`	`str`	Name to assign to the resulting component.	`'estimated'`
`formula`	`str`	Optional molecular formula.	`''`
`mw`	`float`	Optional molar mass (g/mol); Joback does not estimate it.	`0.0`

Returns:

Type	Description
`Component`	A `Component` with estimated `tc`
`Component`	(K), `pc` (Pa), `vc` (m^3/mol), `tb` (K), formation properties
`Component`	(J/mol), and an ideal-gas `cp_ig` correlation.

Raises:

Type	Description
`KeyError`	if any group label is not in `GROUPS`.

unifac_activity ¶

unifac_activity(
    components: list[str], x: Array, t: ArrayLike
) -> Array

Predict ln(gamma) for named database components using bundled tables.

Parameters:

Name	Type	Description	Default
`components`	`list[str]`	Component names with UNIFAC assignments in `COMPONENT_GROUPS`.	required
`x`	`Array`	Mole fractions aligned with `components`.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(len(components),)`.

unifac_ln_gamma ¶

unifac_ln_gamma(
    x: Array,
    nu: Array,
    r: Array,
    q: Array,
    main_index: Array,
    a_main: Array,
    t: ArrayLike,
) -> Array

Log activity coefficients from UNIFAC, given explicit group tables.

Parameters:

Name	Type	Description	Default
`x`	`Array`	Mole fractions, shape `(ncomp,)`.	required
`nu`	`Array`	Subgroup counts, integer-valued array of shape `(ncomp, ngroup)`.	required
`r`	`Array`	Subgroup `R_k` values, shape `(ngroup,)`.	required
`q`	`Array`	Subgroup `Q_k` values, shape `(ngroup,)`.	required
`main_index`	`Array`	Index of each subgroup's main group into `a_main`, shape `(ngroup,)`.	required
`a_main`	`Array`	Main-group interaction matrix `a_mn` (K), shape `(nmain, nmain)`.	required
`t`	`ArrayLike`	Temperature (K).	required

Returns:

Type	Description
`Array`	`ln(gamma)` of shape `(ncomp,)`.

Activity & group contribution¶

Activity-coefficient models¶

activity ¶

NRTL dataclass ¶

tau ¶

ln_gamma ¶

UNIQUAC dataclass ¶

tau ¶

ln_gamma ¶

ActivityModel ¶

ln_gamma ¶

FloryHuggins dataclass ¶

ln_gamma ¶

Hildebrand dataclass ¶

ln_gamma ¶

Margules dataclass ¶

ln_gamma ¶

RegularSolution dataclass ¶

ln_gamma ¶

VanLaar dataclass ¶

ln_gamma ¶

Wilson dataclass ¶

lam ¶

ln_gamma ¶

margules_excess_gibbs ¶

margules_gamma ¶

margules_ln_gamma ¶

excess_gibbs ¶

gamma ¶

nrtl_from_energies ¶

uniquac_from_energies ¶

van_laar ¶

nrtl_excess_gibbs ¶

nrtl_g ¶

nrtl_gamma ¶

nrtl_ln_gamma ¶

nrtl_tau ¶

flory_huggins_gamma ¶

flory_huggins_ln_gamma ¶

hildebrand_ln_gamma ¶

regular_solution_gamma ¶

regular_solution_ln_gamma ¶

volume_fractions ¶

uniquac_gamma ¶

uniquac_ln_gamma ¶

uniquac_tau ¶

van_laar_gamma ¶

van_laar_ln_gamma ¶

wilson_excess_gibbs ¶

wilson_gamma ¶

wilson_lambda ¶

wilson_ln_gamma ¶

Group contribution¶

groupcontrib ¶

JobackGroup dataclass ¶

modified_unifac_activity ¶

modified_unifac_ln_gamma ¶

joback_estimate ¶

unifac_activity ¶

unifac_ln_gamma ¶

NRTL `dataclass` ¶

UNIQUAC `dataclass` ¶

FloryHuggins `dataclass` ¶

Hildebrand `dataclass` ¶

Margules `dataclass` ¶

RegularSolution `dataclass` ¶

VanLaar `dataclass` ¶

Wilson `dataclass` ¶

JobackGroup `dataclass` ¶