Mixed equilibrium/nonequilibrium effects govern surface mobility in polymer glasses

Using angle-resolved X-ray photoelectron spectroscopy, sum-frequency generation vibrational spectroscopy, contact angle measurements, and molecular dynamics simulations, we verify that the glass transition temperature (T_g) of polymer glass is lower near the free surface. However, the experimental T_g-gradients showed a linear variation with depth (z) from the free surface, while the simulated equilibrium T_g-gradients exhibited a double exponential z-dependence. In typical simulations, T_g is determined based on the relaxation time of the system reaching a prescribed threshold value at equilibrium. Conversely, the experiments determined T_g by observing the unfreezing of molecular mobility during heating from a kinetically arrested, nonequilibrium glassy state. To investigate the impact of nonequilibrium effects on the T_g-gradient, we reduced the thermal annealing time in simulations, allowing the system to fall out of equilibrium. We observe a decrease in the relaxation time and the emergence of a modified z-dependence consistent with a linear T_g-gradient near the free surface. We further validate the impact of nonequilibrium effects by studying the dependence of the T_g on the heating/cooling rate for polymer films of varying thickness (h). Our experimental results reveal significant variations in the T_g-heating/cooling rate dependence with h below the bulk T_g, which are also observed in simulation when the simulated system is not equilibrated. We explain our findings by the reduction in mass density within the inner region of the system under nonequilibrium conditions, as observed in simulation, and recent research indicating a decrease in the local T_g of a polymer when placed next to a softer material.