Reference

isosteric_heat(model::IsothermModel, Vᵍ, p, T; Vᵃ = zero(eltype(model))) -> Qₛₜ

Calculate the isosteric heat of adsorption for a given isotherm model.

Arguments

• model::IsothermModel: The isotherm model used to describe the adsorption process.
• Vᵍ: The molar volume of the gas phase.
• Vᵃ: The molar volume of the adsorbed phase (typically Vᵃ << Vᵍ; default is zero).
• p: Pressure at which the isosteric heat is evaluated.
• T: Temperature at which the isosteric heat is evaluated.

Returns

• Qₛₜ: The estimated isosteric heat of adsorption.

Description

The function estimates the isosteric heat of adsorption Qₛₜ for a single component using its isotherm and the Clausius-Clapeyron equation:

Qₛₜ = -T * (Vᵍ - Vᵃ) * (∂n/∂T)ₚ / (∂n/∂p)ₜ

where:

• n is the loading,
• Vᵍ is the molar volume of the gas phase,
• Vᵃ is the molar volume of the adsorbed phase,
• T is the temperature,
• p is the pressure.

This equation is derived based on the Clausius-Clapeyron relation, which relates the temperature dependence of the loading to the isosteric heat.

References:

1. Pan, H., Ritter, J. A., & Balbuena, P. B. (1998). Examination of the approximations used in determining the isosteric heat of adsorption from the Clausius−Clapeyron equation. Langmuir: The ACS Journal of Surfaces and Colloids, 14(21), 6323–6327. doi:10.1021/la9803373

pressure(model::IsothermModel, x, T, f; approx = :exact)

given an isotherm::IsothermModel and x = f(model,p,T), find p such that f(model,p,T) = x. There are two options for f and x:

• when f is sp_res, then x = sp_res(model, p, T)
• when f is loading, then x = loading(model, p, T)

By default, it performs a root-finding over the isotherm. but custom implementations can be done by overloading pressure_impl(model::MyModel,x,T,f::typeof(f),approx) The approx::Symbol argument indicates if the procedure is exact or approximate. by default a henry coefficient aproximation is used when approx =:henry is used.

saturated_loading(model::IsothermModel, T)

Returns the loading of of an adsorption isotherm when the pressure tends to infinity. by default it is evaluated at 1/√eps(eltype(model)) (6.7108864e7 for Float64 inputs.).

Inputs

• model::IsothermModel: the isotherm model
• T: temperature.

loading(model::IsothermModel, p, T) -> q

Calculate the loading q based on the provided isotherm model, pressure p, and temperature T.

Arguments

• model::IsothermModel: An instance of IsothermModel, representing the isotherm model to be used for the calculation.
• p: The pressure at which the loading is to be calculated.
• T: The temperature at which the loading is to be calculated.

Returns

• q: The calculated loading based on the isotherm model, pressure, and temperature.

Description

This function computes the loading q based on the given isotherm model, pressure p, and temperature T.

henry_coefficient(model::IsothermModel, T) -> H

Calculate the Henry's coefficient for a single component system using the specified isotherm model and temperature T.

Arguments

• model::IsothermModel: An instance of IsothermModel, representing the isotherm model to be used for the calculation.
• T: The temperature at which the Henry's coefficient is to be calculated.

Returns

• H: The Henry's coefficient in the default units of [mol/kg].

Description

This function returns the Henry's coefficient, which is a measure of the initial slope of the adsorption isotherm at low pressures. It is defined as the derivative of the loading q with respect to pressure p at p = 0:

H = (∂q/∂p) at p = 0 at a given T.

sp_res(model::IsothermModel, p, T) -> Π

Calculate the reduced spreading pressure for a given isotherm model at a specific pressure p and temperature T.

Arguments

• model::IsothermModel: An instance of IsothermModel, representing the isotherm model used for the calculation.
• p: The pressure at which the reduced spreading pressure is to be calculated.
• T: The temperature at which the reduced spreading pressure is to be calculated.

Returns

• Π: The reduced spreading pressure

Description

The reduced spreading pressure is a key quantity in Ideal Adsorbed Solution Theory (IAST), used to describe the adsorption behavior of mixtures. This function calculates the reduced spreading pressure Π by integrating the isotherm equation over the pressure range from 0 to p.

The reduced spreading pressure is often calculated numerically as:

Π = ∫ (q(p') / p') dp' from 0 to p

where:

• q(p') is the loading at pressure p'.