Dynamical arrest into a frozen glassy state occurs at a temperature $T_{\mathrm{dyn}}$ near $T_g$, with a lower $T_{\mathrm{dyn}}$ for a slower cooling rate.

${\xi }_{\mathrm{DH}}$ has been shown to correlate with the activation volume for structural relaxation [defined through the pressure dependence of ${\tau }_{\alpha }(T)$], the volumetric contribution to the dynamic fragility, and the properties of the excess in the vibrational density of states compared with the Debye prediction, i.e., the Boson peak [15, 25].

Bond stretching and bond bending account for the two DOF “lost” upon polymerization, but these DOF do not participate in molecular motions for polymers with high dihedral barriers and large bending energies.

Note that regions of correlated motion are often referred to in the literature as cooperatively rearranging regions, even though different definitions are often used [22, 31, 86].

Ortlieb et al. [22] defined excitations following the approach used by Keys et al. [23].

Since $C_p=C_V+TV{\lambda }^2/{\kappa }_T$, where $\lambda$ is the thermal expansion coefficient and ${\kappa }_T$ is the isothermal bulk modulus, the approximation $C_V\simeq c_p$ will slightly overestimate the number of the correlated monomers from Eq. (a1). Hempel et al. [7] calculated a correction factor based on data for both small molecular and polymeric glass formers, which if applied would increase the determined correlation volume values by $\approx 3\%$. However, since (i) the correction factor is small, (ii) we do not know how the correction varies for the different chemistries, or $M$, investigated here, and (iii) a correction will not affect the conclusions of this Letter, we follow the approach normally used in literature and approximate $c_V\approx c_p$.

The amplitude-renormalized $c_p^{\prime \prime }(T)$ peaks (inset to Fig. 4) show a broadening $\delta T$ with increasing $M$. The asymmetry for longer PMMA chains is due to vitrification effects below $T_g$ [45], so the temperature range of the Gaussian fit was limited to $T\gtrsim T_g$. Qualitatively similar trends ($T_{\alpha }$ and $\delta T$ increasing with $M$) are observed for PS and PDMS (see Fig. S3 in [43]). The increase in $\delta T$ is more prominent in PMMA and PS than in the more flexible PPG-DME and PDMS.

The excess wing has commonly been attributed to a “hidden” $\beta$ relaxation [12, 62, 92] or, alternatively, to an intrinsic feature of the $\alpha$ relaxation [93].