A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy-enthalpy compensation and dynamic gradients near the free surface.

We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin-lattice relaxation time (T1 avg) was measured near the free surface and in the bulk. Spin-lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence T1 avg. There is no clear correlation of the average entropy of activation (Δ‡S̄) and enthalpy of activation (Δ‡H̄) with MW, but there is a clear correlation between Δ‡S̄ and Δ‡H̄, i.e., entropy-enthalpy compensation. This results in the average Gibbs energy of activation, Δ‡Ḡ, being approximately independent of MW. Measurements of the temperature dependence of T1 avg as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to Δ‡H̄ = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in Δ‡Ḡ near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a "double-exponential" depth dependence. This model can explain the depth dependence of 1/T1 avg in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.