A MODEL OF MOISTURE-INDUCED PLASTICIZATION OF CRUNCHY SNACKS BASED ON FERMIS DISTRIBUTION FUNCTION

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 format is a slightly modified version of Fermi's distribution function that is P(a(w)) = P-s/{1 + exp[(a(w) - a(wcp))]/b(P)} + c(P) where P(a(w)) is any of the stiffness or jaggedness parameters, P-s and c(P) constants whose sum is the magnitude of the parameter when the material is in the dry state (c(P) is the residual level after plasticization), a(wcp) is a characteristic water activity level representing the region where the major textural changes take place, and b(P) a constant representing the steepness of the relationship at the transition region.