Correlated and cooperative motions in segmental relaxation: Influence of constitutive unit weight and intermolecular interactions

This work clarifies the notion of correlated and cooperative motions appearing during the α-relaxation process through the role of the molecular weight of the constitutive units and of the interchain dipolar interactions. By studying amorphous copolymers of poly(ethylene-co-vinyl acetate) with different vinyl acetate contents, we show that the correlated motions are not sensitive to the interchain dipolar interactions, in contrast to the cooperative motions, which increase with a strengthening of the intermolecular interactions for this sample family. Concerning the influence of the molecular weight $m_0$, the notion of “correlated motions” seems to be equivalent to the notion of “cooperative motions” only for low $m_0$ systems.

Figure 1

EVA80 sample: (a) The real ($C$′) and the imaginary ($C$″) parts of the complex heat capacity vs temperature; (b) dielectric loss ε″ vs frequency on the whole temperature range investigated.

Figure 2

Dielectric relaxation strength (Δε) at $\tau =0.01\mathrm{s}$ as a function of VAc content (wt %). The estimated uncertainty in the amount of Δε is ±10%.

Figure 3

Number of dynamically correlated segments $N_C$ for EVA copolymers as a function of $\mathrm{lo}{\mathrm{g}}_{10}(\tau /{\tau }_0)$ (where ${\tau }_0={10}^{-15}\mathrm{s}$). The red dashed line corresponds to the fit of all the experimental points plotted using Eq. (3) with $A=4.62,N_0=4.0,z=1.0,\psi =0.51$. Gray squares correspond to the data in Refs. [7, 11, 26]. The estimated uncertainty in the amount of $N_c$ is ±10%.

Figure 4

$N_{\alpha }$ as a function of $\mathrm{lo}{\mathrm{g}}_{10}(\tau /{\tau }_0)$ (where ${\tau }_0={10}^{-15}\mathrm{s}$) for EVA copolymers. Hollow symbols are from combined BDS and MTDSC experiments, and filled symbols are from only MTDSC experiments corresponding to the calorimetric $T_g(\tau \sim 10\mathrm{s})$. The red dashed line corresponds to the fit shown in Fig. 3. The solid red line corresponds to the fit of all the experimental points plotted using Eq. (3), with $A=5.62,N_0=3.75,z=1.1,\psi =0.45$. The inset shows the $N_{\alpha }$ variations as a function of the VAc content (wt %) at four different relaxation times. The estimated uncertainty in the amount of $N_{\alpha }$ is ±10%.

Figure 5

$N_C/N_{\alpha }$ ratio as a function of the relaxation time τ for EVA copolymers. The gray symbols correspond to the data taken from Ref. [7]. The numbers indicate the molecular weight of the constitutive unit for each sample in $\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$.