Regression analysis studies of polymer transitions II. TII from specific heat and other data for polyisobutylene

Linear regression analysis studies with residuals of heat capacity vs. temperature (C_p vs. T) data above the glass transition temperature (T_g) for polyisobutylene (PIB) of molecular weights M¯_v = 1,350,000 and M = 4900 show that the data points can be represented by three straight lines in each case. The lower intersection temperature represents the intermolecular T_ll transition (relaxation); the upper one an intramolecular T_lp process. Both processes are confirmed by ultrasonic velocity data in vulcanized butyl rubber, by zero shear melt viscosity data in PIB (M = 4900); and by isothermal specific volume vs. pressure data in PIB (M¯_v = 36,000). T_ll is confirmed by thermal diffusivity, differential scanning calorimetry (DSC), ¹³C nuclear magnetic resonance (NMR) spectroscopy and the T^* temperature of Lobanov and Frenkel based on Arrhenius-type plots log frequency vs. 1/T_g. A comparison of dynamic mechanical loss data, both old and new, reveal that T_ll follows a Vogel-WLF type relation; log f vs. 1/(T₀ ?1/T_o). PIB samples with number average molecular weights between 7100 to 860,000 have been measured on three types of support systems: glass braid (0.3 Hz), filter paper (11 Hz), brass shim stock (14–16 Hz), and give similar values of T^u. A considerable amount of literature data long neglected from the viewpoint of its bearing on T_ll is reviewed. T_ll has been observed in the same way as T_g by both relaxational and quasi-static methods. Some instructive cross comparisons between these two types of methods emerge. With so many diverse methods yielding evidence for T_ll in PIB, it cannot be dismissed as an artifact. A molecular origin for T_ll is plausible in terms of the Frenkel-Baranov phase dualism mechanism. A complete relaxation map (log f vs. 1/T) has been assembled with frequencies from 10^?2 to 10¹⁰ Hz and temperatures from 150 to 500 K. It shows T_β, T_g, T_ll and methyl group rotation, all based on data in the literature. The molecular weight dependence to T_g and T_ll and the low resiliency of butyl rubber as it relates to T_ll are discussed in the appendices.