Dilation Models

fit_model(model, pressures_mpa, fractional_dilations, [uncertainty_method])

Fit a dilation model to a set of pressures and fractional dilations.

Any keyword arguments get passed on to the specific model.

uncertainty_method can be any supported method of propagating uncertainty within the model.

predict_dilation(model::SorptionModel, args...)

Predict fractional dilation with a dilation model. Predictions are generally returned in the format of a vector of values corresponding to an input of a vector of pressures.

Get the derivative of a dilation vs pressure curve at a given pressure.

fit_model(::DualModeDilation, pressures_mpa, frac_dilations, uncertainty_method=nothing; kwargs...)

Fit the dilation data to an dual mode dilation model, using a dual mode model previoulsy fit to concentration and pressure data.

Dilation is described by two additional parameters, $V_D$ and $f$ using the following model:

${\Delta}{V} / V_0 = V_D (k_D \cdot p + \frac{f C_{H}^{'}bp}{1+bp})$

• $V_D$ represents the effective condensed penetrant molar volume.
• $f$ represents an empirical fit describing how much the langmuir mode participates in dilation.

J.D. Moon, M. Galizia, H. Borjigin, R. Liu, J.S. Riffle, B.D. Freeman, D.R. Paul, Water Vapor Sorption, Diffusion, and Dilation in Polybenzimidazoles, Macromolecules. 51 (2018) 7197–7208. https://doi.org/10.1021/acs.macromol.8b01659.

fit_model(::EmpiricalDilation, pressures_mpa, frac_dilations, uncertainty_method=nothing; n_params=3, kwargs...)

Fit the dilation data to an empirical dilation model with no physical meaning. This model is intended to fit any dilation curve given enough parameters. The user may specify up to 4 empirical paramteres. Loosely, the use of each parameter is as follows:

• n_params = 1: Linear dilation
• n_params = 2-3: Unscaled(2) dual mode like (3) dilation (3=default)
• n_params = 4-5: Dual mode like dilation with concave up (4) or tapering behavior permitted with scaling (5)

If using uncertainty_method (:JackKnife or :Hessian implemented), each extra parameter will greatly increase the resulting uncertainty, as this model is completely empirical.