A simple model for cooperative and non-exponential processes in non-crystalline polymers

A quite simple Markov chain model is presented in an attempt to understand several characteristic properties of the structural relaxation in glass-former materials. A second order Markov model is proposed for a small region of the material. Only a few parameters are necessary for the definition of the material in the model equations namely the energy levels accessible to that small region and the transition probabilities between them. The later are considered dependent on the energy levels and the potential barrier heights between them, on temperature, on a reference transition rate parameter and on a cooperativity or memory parameter related to the interaction with the neighbour regions. Isothermal relaxations at different temperatures were simulated with selected values of the model parameters. As a result, non-exponentiality of energy relaxations and its temperature dependence appears directly related to the cooperativity parameter. Markov chain model shows also non-linearity and memory effects, and a transition between two different regimes in the dependence of the relaxation times with temperature.