Correlation of Cooperatively Localized Rearrangement on the “Fluidized Domain" of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Compliance with K-W-W Stretched Exponential Function

Abstract

Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation" model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain" has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free energy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitutive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush–Williams–Watts (K-W-W) stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.