Isotherms for Expedited Moisture Sorption

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This Demonstration explores data fitting with two to six experimental equilibrium moisture sorption isotherm values within a selected water activity range. You can choose from four 2-parameter models (Halsey, Oswin, Smith or Henderson) or three 3-parameter models (GAB, hybrid or double power-law). To facilitate the fit, you can match the entered data points visually with a curve generated by adjusting the sliders within the chosen model's parameters prior to the nonlinear regression. The emphasis is on estimating the equilibrium moisture sorption isotherm curve in any particular water activity range from the lowest possible number of experimental data points obtained by either the static or dynamic (gravimetric) method.

Contributed by: Mark D. Normand and Micha Peleg (December 2020)
Open content licensed under CC BY-NC-SA



Snapshot 1: the six sorption isotherm data points from the thumbnail image spanned over a large range fitted with the 3-parameter double power-law model

Snapshot 2: three sorption isotherm data points spanned over a large range fitted with the 3-parameter GAB model

Snapshot 3: three sorption isotherm data points taken over a small high range fitted with the 3-parameter hybrid model

Snapshot 4: three sorption isotherm data points taken over a small low range fitted with the 3-parameter double power-law model

Snapshot 5: three sorption isotherm data points spanned over a large range fitted with the 2-parameter Henderson model

Snapshot 6: three sorption isotherm data points spanned over an intermediate range fitted with the 2-parameter Oswin model

The 3-parameter Guggenheim, Anderson and de Boer (GAB) sorption model, which is an expanded version of a variant of the more famous two-parameter Brunauer, Emmett and Teller (BET) model, has been commonly written in the form , where is the equilibrium moisture content in percent on a dry basis (g water/100g dry matter) that corresponds to a water activity level and , and are adjustable parameters obtained by curve fitting [1–3]. However, the validity of the "water monolayer" concept can be challenged on several grounds [4], so two alternative 3-parameter models are also offered, namely, the hybrid model and the double power-law model where and .

The 2-parameter models are

Halsey, , for ;

Henderson, ;

Oswin, , for ; and

Smith, , for .

By definition, the fitted curves of all seven models pass through the origin, that is, .

This Demonstration lets you enter from two to six experimental data points with sliders, after choosing one of the seven given models. The default initial settings of all six points' coordinates may be restored by clicking the purple "default data values" setter. To facilitate the fit and assure convergence during the regression, where appropriate, you can adjust the gray curve given by the guessed initial parameter value sliders to match the entered data visually.

When done, click the green "fit selected model to data and plot results" setter to fit the selected model to the entered data using the current slider settings as the initial guesses of the model's parameters. Once the entered initial guesses of the parameters enable a successful fit, the Demonstration will calculate and display the best-fit parameters and show the fit's correlation coefficient in blue. It will also superimpose a plot of the fitted curve on the entered data, which is plotted as black dots. The color of the fitted curve matches the color of the setter bar text of the currently selected model. If the fit appears to need improvement, you can click either the red "default parameter values" or the blue "last fitted parameter values" setter to start from those initial parameter guesses, then optionally further adjust their values and repeat the regression until a higher is obtained. "Fit failed!" appears in red if the fit attempt was not successful.

The number of entered experimental points cannot be smaller than the number of sought model parameters and not all allowed entries and corresponding calculated model equations have real-life counterparts.


[1] H. A. Iglesias and J. Chirife, Handbook of Food Isotherms: Water Sorption Parameters for Food and Food Components, New York: Academic Press, 1982.

[2] W. Wolf, W. E. L. Spiess and G. Jung, Sorption Isotherms and Water Activity of Food Materials, New York: Elsevier, 1985.

[3] R. D. Andrade P., R. Lemus M. and C. E. Pérez C., "Models of Sorption Isotherms for Food: Uses and Limitations," Vitae, 18(3), 2011 pp. 325–334.

[4] M. Peleg, "Models of Sigmoid Equilibrium Moisture Sorption Isotherms with and without the Monolayer Hypothesis," Food Engineering Reviews, 12(1), 2020 pp. 1–13. doi:10.1007/s12393-019-09207-x.

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