Low-Temperature Heat Capacity, Glass-Transition Cooperativity, and Glass-Structure Vault Breakdown in a Series of Poly(n-alkyl methacrylate)s

Abstract

Heat capacity in the 1 K range and close to Tg was studied in a series of poly(n-alkyl methacrylate)s, PnAMA, including some random copolymers. We report on two findings: (i) The glass transition temperature Tg and the cooperativity of the R process that freezes-in at Tg, NR(Tg), decrease smoothly between methyl (PMMA) and hexyl member (PnHMA); the cooperativity from NR(Tg) ) 35 to NR(Tg) ≈ 1. (ii) The tunnel density measured in the 1 K range as c1 constant of the heat capacity function increases between PMMA and the ethyl member (PEMA), shows, after a maximum near PEMA, a sharp drop (factor of 6) to the butyl member (PnBMA), and remains constant at a low level up to the octyl member (PnOMA). The cooperativity of the R process near Tg and the tunnel density will be correlated assuming that freezing-in (vitrification) fixes the dynamic heterogeneity in the self-organized equilibrium liquid near Tg. We try to explain how freezing of dynamic heterogeneities in the PnAMA series is responsible for the trend in the tunnel density including the sharp drop: Freezing-in of cooperativity shells around Glarum defects forms some vaults that enlarge the free volume near these defects in comparison to a situation without vaults. The maximum in c1 is promoted by this additional free volume; the drop in c1 is caused by a vault breakdown effect if the cooperativity shell is too small for vault formation, NR(Tg) < 15.

Relaxation in Poly(alkyl methacrylate)s: Crossover Region and Nanophase Separation

“…[91] The discussed results of the 3 x method measurements in a wide frequency range are independently confirmed by an analysis of conventional DSC data for different poly(alkyl methacrylate)s using a modified [92,93] Narayanaswamy Moynihan (MNM) model and temperaturemodulated DSC measurements ( Figure 8). [92,94] A systematic compilation of the cooperativity at T g is presented in the literature [94] (Figure 9 a and Table 1). Cooperativity is large (N a L 40) for PMMA, having the shortest sidechain and the largest T on -T g difference.…”

“…[92,94] The reasons for this systematic differences are mainly the strong temperature dependence of cooperativity and the temperature differences between DSC and dynamic glass transition temperature, T g -T x , of the order of a few kelvin (see Table 1). However, for both DSC and TMDSC data, cooperativity depends on the side-chain length (C number) in a similar way.…”

“…DSC cooling curves (dT/dt = -10 K/min, thin solid line) and real and imaginary parts of dynamic heat capacity (9) from temperature modulated DSC (t p = 60 s) for (a) PEMA and (b) PPeMA. [94] The methods to determine Dc p from a tangent construction and dT and T x from a fit to the c99 p (T) data with a Gaussian function are indicated.…”

“…(a) Square root of cooperativity versus side-chain length (C number) as calculated from conventional DSC at T g (0) and temperature-modulated DSC at T x (9) using the fluctuation formula (Equation (1)). [94] The calorimetric parameters (T g ; Dc p ; dT) were determined applying a modified Narayanaswamy Moynihan model in the case of DSC data and according to the procedure shown in Figure 8 in the case of TMDSC. The difference between N a from DSC and TMDSC is mainly due to the differences in the (effective) measurement frequency, i. e. the T g À T x difference of a few K. The a and a ranges are indicated by labels.…”

“…(b) Fragility m for the a and a processes from dielectric (g) and shear (F) data as a function of the number of C atoms in the alkyl part of the side-chain. [33,94] The relaxation temperature for a frequency x = 0.01 rad/s (s = 100 s) is used as T g in Equation (4) in the case of dielectric data. Analogously, the relaxation temperature for x = 10 rad/s was used formally as T g in the case of shear data.…”