MOLECULAR WEIGHT DEPENDENCE OF RELAXATION SPECTRA OF AMORPHOUS POLYMERS IN THE RUBBERY REGION

PART VI RELATIONSHIP BETWEEN RELAXATION SPECTRUM AND MOLECULAR WEIGHT DISTRIBUTION ESTIMATED FROM THE EMPIRICAL BLENDING LAW IN TWO-COMPONENT SYSTEMS

Abstract

An empirical blending law for the relaxation moduli of two different molecular weight samples found in various amorphous polymers was generalized to give the relaxation spectrum, H(lnθ) in the rubbery region as a function of the molecular weight distribution (differential), f(M) in the form,
H(lnθ) =∫₀^∞f(M)H_M(ln [θ/λ_M])dM,
where θ and M are the independent variables representing the relaxation time and the molecular weight, respectively. H_M and λ_M are the relaxation spectrum of a monodisperse sample and the shift factor, respectively, and both of them are dependent on M.
The molecular weight dependences of both H_M and λ_M were then estimated from various sources of experimental data. After the substitutions of those into the above equation and appropriate approximations the following simple relationship was obtained.
H(lnθ_M)/G₀=Mnf/3.4,
G₀θ_M/K=_M^3.4
Here M_n denotes the number average molecular weight of the sample and G₀ and K represent the pseudoequilibrium modulus at the rubbery plateau and the proportionality constant in the 3.4 th power law, respectively.