How the free volume reduction freezes bulk amorphous lattice polymers

The classical free volume theory of polymer glass transition assumed that the reduction of free volume would stop at a critical fraction around 0.025 upon glass transition in bulk amorphous polymers. The well-known WLF equation for the non-Arrhenius temperature-dependent viscosity above the glass transition temperature was thus derived. It is so far not yet clear whether there exists such an intrinsic frozen transition upon the reduction of only free volume. We hereby performed dynamic Monte Carlo simulations of bulk lattice polymers under athermal conditions, in which single vacant lattice sites serve as free-volume elements in the micro-relaxation model for mimicking the Brownian motions of polymers in the lattice space. We observed that the averaged diffusion constants of polymers linearly decay into zero upon the gradual reduction of free volume fractions down to zero. No sudden frozen transition occurs around the free volume fraction 0.025 as commonly observed in the practical experiments and the free volume theories, which implies other frozen mechanisms beyond the present case. Here the free-volume fraction was treated as a fixed geometric parameter, and volume relaxation was not included. The linear dependence could be attributed to the thermal fluctuation theorem of simple liquids, as evidenced by the linear dependence of diffusion constants on the reciprocal chain lengths under constant free volume fractions. Our observations demonstrated that, in this athermal lattice model, free-volume reduction alone does not generate an intrinsic frozen transition in bulk amorphous polymers.