A model of moisture‐induced plasticization of crunchy snacks based on fermi' distribution function

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Abstract
The irregular force‐deformation relationships of commerical cheese balls and Zwiebacks at nine levels of water activity in the range 0.11–0.85 were recorded with a computer‐interfaced Universal testing machine. They were characterized by two empirical stiffness parameters, the force at 10 and 20% deformation, and two jaggedness measures, the apparent fractal dimension of the normalized force‐deformation curve and the mean magnitude of its power spectrum. The plots of all four parameters versus the water activity had a stable region followed by a substantial drop at a characteristic water activity level, of the kind expected when a material undergoes a glass transition. The phenomenon over the entire experimental water activity range, could be described by a model whose mathematical formal is a slightly modified version of Fermi' distribution function that is P(aw) = Ps/{1 + exp[(aw — awcp)]/bp} + cp where P(aw) is any of the stiffness or jaggedness parameters, Ps and cp constants whose sum is the magnitude of the parameter when the material is in the dry state (cp is the residual level after plasticization), awcp is a characteristic water activity level representing the region where the major textural changes take place, and bp a constant representing the steepness of the relationship at the transition region.