The Logistic Function in Glass Transition Models of Amorphous Polymers: II. A Theoretical Framework for Isothermal Compression Processes

Recently, a methodology to derive an exactly‐solvable Riccati equation that approximates the macroscopic‐phenomenological behavior of amorphous polymers at glass transition during isobaric cooling was introduced [C. Corbisieri, Macromol. Theory Simul . 33 (2024): 2400052]. In the present work, this methodology is applied to derive a closed‐form expression in terms of mathematical functions that describes the pressure derivative of the specific volume during isothermal compression. For this purpose, a relation between the compression rate and relaxation time at glass transition pressure, , formally identical to the Frenkel–Kobeko–Reiner equation, is postulated. The closed‐form expression contains the logistic function, thus featuring a continuous transition region centered around the temperature and compression‐rate dependent glass transition pressure. The resulting constitutive model well‐fits the pressure‐volume‐temperature data of polycarbonate in the equilibrium state, the vitreous state, and at glass transition, collected in the standard isothermal mode in the pressure range at temperatures . This work thus confirms the validity of the logistic function in glass transition models of amorphous polymers and establishes a theoretical framework to assess the glass transition during isothermal compression.