Application of the Weibull distribution function for modeling the kinetics of isothermal dehydration of equilibrium swollen poly (acrylic acid) hydrogel

Abstract

A theoretical procedure for evaluating the density distribution function ( p( E a )) of apparent activation energies ( E a ), based on modeling of the experimental isothermal conversion curves by Weibull probability function of reacting times was established. This procedure was applied on isothermal dehydration of poly (acrylic acid) hydrogel (PAAH) at four different operating temperatures (306, 324, 345 and 361 K). It was established that: (a) the experimental conversion curves at all temperatures can be described by the Weibull probability distribution function of reacting times in a wide range of the degree of conversion (0.14 ⩽ α ⩽ 0.95); (b) the Weibull distribution parameters ( β and η) show functional dependences on the operating temperature, and (c) the apparent activation energy ( E a ) varies with the degree of conversion ( α). It was shown that the density distribution function of activation energies is independent on the temperature, and because of this fact, the considered function is an Eigen characteristic of the dehydration studied. The calculated p( E a ) function is in good agreement with the experimental p( E a ) function ( p( E a ) exp), obtained by the Miura procedure.