Revisiting the influence of chain length on the α- and β-relaxations in oligomeric glass formers.

Dielectric relaxation measurements of a series of oligo(propylene glycol) dimethyl ethers, CH3-O-[CH2-CH(CH3)-O]N-CH3, including samples with the number of PG units N = 1, 2, 3, 7, 17, 34, and 69, were made by Mattsson et al. [Phys. Rev. Lett. 94, 165701 (2005)] at ambient pressure. The objective of the study was to relate the change of properties of the glass transition dynamics to the number of monomer units N in the chain. Not examined in the previous publication is how the change of the width of the frequency dispersion of the α-relaxation with N is related to the observed change in the α-β bifurcation characterized by the ratio, τ(α)(T(g))/τ(β)(T(g)). In this paper, the frequency dispersion of the dimer, trimer, and heptamer are fitted by the Fourier transform of the Kohlrausch stretched exponential function, φ(t) = exp[-(t/τ(α))(1-n)]. Determined from experimental data, both τ(α)(T(g))/τ(β)(T(g)) and n increase with N. More interestingly, we find τ(α)(T(g))/τ(β)(T(g)) has approximately the same value as [τ(α)(T(g))/t(c)](n) with t(c) = 2 ps, in accordance with the prediction of the Coupling Model of approximate relation between τ(α) and τ(β) given by τ(β) ≈ (t(c))(n)(τ(α))(1-n). Considered also are previously unpublished dielectric loss spectra of the heptamer taken at different combinations of T and P with τ(α)(T,P) fixed by Roland et al. [Phys. Rev. B 77, 012201 (2008)]. The dielectric loss data show not only the α-loss peaks superpose but also the high frequency flank including the barely resolved JG β-relaxation superposes approximately. This is again consistent with the approximate relation between τ(α) and τ(β) from the Coupling Model because n is unchanged on varying P and T with τ(α)(T,P) kept constant, and t(c) is a constant. The additional advance made herein has the benefit of enhancing the impact of the earlier experimental studies of the oligo(propylene glycol) dimethyl ethers on current understanding of the dynamics of glass transition.