Thermoelasticity of Polymer Networks

Abstract

The thermoelastic properties of polymer networks are of interest owing to the information they provide on κ ) d ln〈R 2 〉0/dT, the temperature coefficient of chain dimensions of the network species. Stress-strain measurements at constant volume provide that information directly, through a determination of the energetic fraction of the restoring force fe/f. Almost always, however, the measurements are conducted under constant-pressure conditions, and a correction is applied to account for the effect of volume change. The correction formula commonly used is known to be inaccurate, and here we present a new one that predicts the volume change and κ quite satisfactorily. Some comparisons of κ obtained from thermoelastic measurements, from small-angle neutron scattering, and from intrinsic viscosity data in athermal solvents are given.

The viscosity-radius relationship for concentrated polymer solutions

“…It can be shown for Gaussian chains that 69,82 :where the thermal expansion coefficient κ is defined;A number of studies have reported experimental values of κ for a range of different polymer and solvent systems. The recent literature is summarized by Graessley and Fetters 59,60 . The κ values reported for the different polymer systems can be either positive or negative indicating that the enthalpic intramolecular thermal expansion deviates from Equation 5 both positively and negatively 75 .…”

“…This equation then demonstrates in physical terms why the values of n vary for different polymers. The values of κ vary for different polymers in both sign and magnitude, and this variation yields differing power law exponents (n) and behavior 59,60 . There has been some discussion in the literature as to the meaning of κ, however it is assumed to be intramolecular in nature and a result of the conformational energies of the network chains.…”

“…Here, scaling arguments and experimental evidence are used to show that chains are predicted to compress in flow, and that variations in the observed power law exponents for shear thinning can be explained by the non-ideality embodied in the thermal compressibility of differing polymers 59,60 . Here the term non-ideality is used to indicate that the chains deviate from random objects and have a degree of chemical interaction resulting in enthalpic effects as observed in their contraction with increasing temperature.…”

“…22,23,25 Here, scaling arguments are used to show that chains are predicted to compress in flow, and that variations in the observed power law exponents for shear thinning can be explained by the non-ideality embodied in the thermal compressibility of differing polymers. 58,59 2. THEORY Adam and Delsanti first used scaling arguments to derive the viscosity-temperature relationship for semi-dilute polymer solutions 60 :…”

“…The recent literature is summarized by Graessley and Fetters. 58,59 The k values reported for the different polymer systems can be either positive or negative indicating that the enthalpic intramolecular thermal expansion deviates from Equation 5 both positively and negatively. 68 Integrating [12] and ignoring the constant terms yields:…”