Dielectric Relaxations in Ultra-Thin Films of PMMA: Assessing the Length Scale of Cooperativity in the Dynamic Glass Transition

The local and cooperative dynamics of supported ultra-thin films $(L=4-170\ {\rm nm})$ of poly(methyl methacrylate) was investigated by dielectric spectroscopy at frequencies from 0.1 Hz to 106 Hz and temperatures from 250–423 K. To assess the effect of stereoregularity, three tacticities ($i, a$ and $s$-PMMA) of similar molecular weight $M_{n}=120-140\times 10^{3}\ {\rm g}\ {\rm mol}^{ -1}$ were studied. A second $M_{n}$ value for $s$-PMMA was also studied. For i-PMMA, a decrease of the glass transition temperature $T_{{\rm g}}$ by up to 10K was observed for a film thickness $L< 25\ {\rm mn}$ (which is comparable to $R_{EE}$), indicated by a down-shift of the peak temperature $T_{\alpha}$ in the loss $\varepsilon^{\prime \prime}(T)$ at low and high frequencies and by a shift of the maximum in the apparent activation energy $E_{a}(T)$ of the $\alpha$-process. Changes in the relaxation strength and the peak shape are apparent for $L\leq 50\ {\rm nm}$. In addition, the $\beta$-relaxation probing the local mobility was investigated for $i-, a$- and $s$-PMMA. Interestingly, all polymers revealed a systematic speedup in the local dynamics for $L< 25 \ {\rm nm}$ which is accompanied by systematic changes in the relaxation strength. For i-PMMA, a clear relation between the thickness dependence of $\tau_{\beta}$ and $\tau_{\alpha}$ was found indicating that thickness dependences in the cooperative dynamics are predominantly induced by changes in the local mobility. These findings are consistent with the idea of confinement induced changes in the orientation and conformation statistics for thicknesses below $R_{{\rm EE}}$.