Pressure−Temperature Dependence of Polymer Segmental Dynamics. Comparison between the Adam−Gibbs Approach and Density Scalings

Abstract

By means of dielectric spectroscopy, the segmental dynamics (R-relaxation) of four different polymers (poly(vinyl acetate), poly(vinyl methyl ether), poly(vinyl chloride) and poly( o-chlorostyrene)) was mea- sured over a broad range of frequencies (10-1-107 Hz), pressures (0-300 MPa), and temperatures (240-460 K). Two different approaches were used to analyze the temperature-pressure dependence of the relaxation time: a pressure-extended Adam-Gibbs equation (U(T,P) ) U0 exp(C/(TSc(T,P)))) and a particular density scaling (log(U) ∝ f (TV A )), both recently proposed. Both approaches give an excellent description of the experimental data; however, an inconsistency between them was found. We show that other scaling laws can give an equally good description of the experimental data, being therefore possible to improve the consistency between the density scaling and the AG framework. The problem of the glass transition has been in the focus of the debate for decades, and it is an important open question in condensed matter physics in general and of polymer science in particular. Historically, the study of the molecular dynamics approaching the glassy state was restricted to mainly analyze the effect of temperature. Thus, measurements of the relaxation time (at atmospheric pressure) as a function of temperature were performed in order to get information about molecular motions. Although much has been learned from these studies, it is not possible to separate thermal and density effects only by varying the temperature. However, the glass transition can also be approached by applying high enough pressure to a supercooled liquid. Both the increase of pressure and the decrease of temperature result in slower molecular motions. These two different ways of approaching the glass transition allow decou- pling thermal and volumetric effects. Some of the seminal works in the study of the pressure effects on molecular dynamics of glass-formers were done in the 1960s, 1-3 and a renewed interest has arisen during the past years. 4-10 The improvement of the experimental techniques has made possible to obtain large amount of accurate data over broader ranges of pressure, temperature, and frequency and therefore contributes to the better understanding of the involved processes. In the past years mainly two different approaches have been used to analyze the pressure-temperature dependence of the relaxation times of glass-forming systems. One is based on the Adam-Gibbs (AG) theory 11 and was developed by Casalini et al. 5 They have recently proposed an extended AG equation to describe the behavior of the structural relaxation time, U ,a s a function of both pressure and temperature. This equation was derived from the AG theory by writing the configurational entropy, Sc, in terms of the excess of both thermal heat capacity and thermal expansion. The second approach is based on a density scaling 12,13 (log(U) ∝ f (TV A ), A being a material constant) which superposes into a single master curve the experimental data measured at different pressures and temperatures. The material specific constant (A) has been empirically determined for several glass-formers, including a few polymers, and has also been related to the ratio of the activation enthalpy at constant volume to that at constant pressure. 12 More recently, Roland et al. 14 have proposed a way to calculate the parameter A only from equation-of-state (EOS) data, without performing any relaxation measurement. Since both approaches have given so far an excellent description of the experimental data, there could be some connection between them. This is a point that has not been yet explored and which could suggest new hints for the mechanisms of the glass transition. In this work the R-relaxation of four polymers was studied using broad-band dielectric spectroscopy (10 -2 -10 7 Hz) over a wide temperature range and pressures up to 300 MPa. The temperature-pressure dependence of the experimental relaxation times was found to be very well described using both the extended AG equation, with thermal and expansion coefficients determined from calorimetric and PVT data, respectively, and the previously mentioned density scaling. A connection between both approaches has been explored, showing that the proposed scaling (TV A ) and the AG frame are not completely consistent within the ranges of pressures and temperatures here explored. We show that a new density scaling provides not only an equivalent excellent description of the experimental data but also a better consistency between both approaches. 2. Theoretical Background