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 ( T 1 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 T 1 avg . There is no clear correlation of the average entropy of activation ( Δ ‡ S ̄ ) and enthalpy of activation ( Δ ‡ H ̄ ) with MW, but there is a clear correlation between Δ ‡ S ̄ and Δ ‡ H ̄ , i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, Δ ‡ G ̄ , being approximately independent of MW. Measurements of the temperature dependence of T 1 avg as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to Δ ‡ H ̄ = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in Δ ‡ G ̄ 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 / T 1 avg in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature. [ABSTRACT FROM AUTHOR]