A <i>β</i>-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

Abstract

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.