GLASS TRANSITION IN RUBBERY MATERIALS
When the perturbation frequency imposed on a rubber falls within the glass transition zone of its viscoelastic spectrum, energy absorption is maximized. This phenomenon is the operative mechanism for various applications of elastomers requiring large energy dissipation. Nevertheless, a fundamental understanding of the glass transition is lacking. The diversity of properties that depend both on chemical structure and thermodynamic conditions makes modeling difficult and a first principles theory perhaps unachievable; indeed, the number of models for the glass transition seems to be inversely proportional to their ability to accurately describe the myriad behaviors. The progress made at quantifying the role of the thermodynamic variables temperature, T, and density, ρ, on the dynamics is described. An important aspect of the work was the discovery that relaxation times and viscosities of molecular liquids and polymers superpose when plotted against the scaling variable T/ργ, with the scaling exponent γ a material constant sensibly related to the nature of the intermolecular repulsive potential; thus, dynamic spectroscopy measurements can be used to quantify the forces between molecules. Other properties derive from the scaling behavior, including the Boyer-Spencer rule and the correlation of fluctuations in the potential energy with fluctuations in the virial pressure.ABSTRACT
Local segmental relaxation times measured dielectrically for two polybutadienes having the indicated molecular weights. The dynamics change by more than five orders of magnitude over a 30° temperature range. The arrows denote Tg measured from the change in thermal expansivity.
Local segmental relaxation times for polyisoprene (upper panel) as a function of inverse temperature at ambient pressure and (lower panel) versus pressure at various temperatures.
Local segmental relaxation times from Figure 2, plotted versus density at constant pressure with varying temperature (squares) and at fixed temperature with varying pressure (circles and diamonds).
Activation energy ratio for polypropylene glycol versus molecular weight. With decreasing number of chain ends, the hydrogen bond concentration decreases, which enhances the effect density has on the segmental dynamics.
Lennard-Jones potential (Eq. 4). Note that the total potential is steeper for small interparticle distances than the repulsive term alone because of the contribution of the attractive component.
Scaling of molecular liquids. OTP/OPP: blend of 67% o-terphenyl and 33% o-phenylphenol; BMPC: 1,1′-bis(p-methoxyphenyl)cyclohexane; BMMPC: 1,1′-di(4-methoxy-5-methylphenyl)cyclohexane; PDE: phenolphthaleindimethylether; KDE: cresolphthalein-dimethylether. The scaling exponents are as indicated.
Scaling of polymers. PCHMA: polycyclohexylmethacrylate; PI: 1,4-polyisoprene; PVE: polyvinylethylene; PVME: polyvinylmethylether; PVAc: polyvinylacetate; PPG: polypropylene glycol; POB: polyoxybutylene; DGEBA: diglycidyl ether of bisphenol A; PPGE: poly[(phenyl glycidy ether)-co-formaldehyde]; PMPS: polymethylphenylsiloxane; PCGE: poly[(o-cresyl glycidyl ether)–co-formaldehyde]; PMTS: polytmethyltolylsiloxane. The scaling exponents are as indicated.
Scaling of the diffusion constants for LJ particles having the indicated exponent for the repulsive term in Eq. 5. Pressures are in LJ units, and the quantity plotted on the ordinate is the reduced D* = (ρ1/3/T1/2)D (see ref. 56).
Fluctuations in the virial pressure versus fluctuation in the potential energy for LJ particles with m = 8. The line through the data is the linear least squares fit, the slope of which is mIPL = 11. The inset, showing resentative fluctuations in the two quantities over time, illustrates the correlations of the two quantities.
The relationship between the activation energy ratio and the scaling exponent. The solid line is the fit of Eq. 12, yielding αPTg = 0.19 ± 0.01. The value of γ for H-bonded materials is approximate because density scaling breaks down due to the dependence of hydrogen bond concentration on state temperature and pressure.
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