The τ-Effective Paradox Revisited: An Extended Analysis of KovacsVolume Recovery Data on Poly (Vinyl Acetate)

Published

October 16, 2008

Author(s)

G B. McKenna, M Vangel, Andrew L. Rukhin, Stefan D. Leigh, B Lotz, C Straupe

Abstract

In 1964 Kovacs (A.J. Kovacs, Transition vitreuse dans les polymeres amorphes. Etude phenomenologique, Fortschr. Hochpolym.-Forsch., 3, 394-507 (1964)) published a paper in which he analyzed structural (volume) recovery data in asymmetry of approach experiments. Kovacs used a parameter referred to as τ-effective (τ_eff) which is defined in terms of the volume departure from equilibrium |δ| as τ_eff^-1 = -1/δ dδ/dt. In plots of the log(1/τ_eff) vs. δ Kovacs observed an apparent paradox in that the values of τ_eff did not coverage to the same point as δ approached zero (i.e., equilibrium). Hence the equilibrium mobility of the structural recovery seemed path dependent. Also, the apparent paradox was accompanied by a spreading of the curves for τ_eff in the up-jump experiments which has come to be known as the expansion gap. While it is currently accepted that the paradox itself does not exist because the curves will converge if the measurements are made closer to δ = 0 (Kovacs' estimates of τ_eff were made for values as small as δ nearly equal} 2.5 x 10 ^-4), the existence of the expansion gap is still a subject of dispute. This is particularly relevant today because recent models of structural recovery have claimed success specifically because the expansion gap was predicted. Here we take the data Kovacs published in 1964, unpublished data from his notebooks taken at the same time, as well as more recent data obtained at the Institut Charles Sadron under his tutelage in the late 1960's and early 1980's. We then examine them using several different statistical analyses to test the following hypothesis: the value of τ_eff as |δ| -> 2.5 x 10^-4 for a temperature jump from T_i to T₀ is significantly different from the value obtained for the temperature jump from T_j to T₀. The temperatures T_i or T_j can be either greater or less than T₀. If the hypothesis is rejected, the τ_eff-paradox and expansion gap need to be rethought. If the hypothesis is accepted, then the argument that reproduction of the expansion gap is an important test of structural recovery models is strengthened. Our analysis leads to the conclusion that the existence of an expansion gap, hence an apparently paradoxical value of τ_eff when |δ| greater than or about equal} 2.5 x 10^-4. However, at smaller values of |δ|it appears that the values of τ_eff are no longer statistically different and, in fact, the data suggest that as |δ| -> 0 all of the τ_eff values converge.

Citation

Plasma Processes and Polymers

Pub Type

Journals

Keywords

assymetry of approach, correlation, expansion gap, glass transition, glassy kinetics, poly(vinyl acetate), structural recovery, volume recovery, τ-effective paradox

Citation

McKenna, G. , Vangel, M. , Rukhin, A. , Leigh, S. , Lotz, B. and Straupe, C. (2008), The τ-Effective Paradox Revisited: An Extended Analysis of KovacsVolume Recovery Data on Poly (Vinyl Acetate), Plasma Processes and Polymers (Accessed April 19, 2024)