A non-Markov chain model of heterogeneous polymer dynamics for exploring relaxation and creep behavior

Abstract The viscoelastic responses of polymers, such as relaxation and creep, are substantially influenced by their mechanical and rheological behaviors, which are governed by the dynamics of polymer chains. Soft polymers, distinguished by their complex and nonlinear mechanical characteristics, offer a broad spectrum of potential applications across diverse sectors. To address these complexities, this paper introduces the Rouse-Bueche-Zimm bead-spring model, predicated on an internal viscosity framework, to dissect the heterogeneous and non-Markovian dynamics of polymers. This model conceptualizes polymer chains as a series of beads and springs, utilizing a three-dimensional force balance equation in conjunction with the generalized Langevin equation. The analysis of internal viscosity enables an investigation into non-Markovian effects. The model incorporates heterogeneity by assigning different friction coefficients and potential functions to different beads. Employing scaling theory, non-affine behavior, and mode-coupling theory, analytical solutions are derived to encompass both heterogeneity and non-Markovian dynamics. Additionally, the study introduces a novel relaxation function, expressed as a hyperbolic cosine, to supersede the traditional exponential function. Comparative numerical analyses with experimental data from extant literature substantiate the enhanced adaptability of the proposed hyperbolic cosine relaxation function in comparison to its classical exponential predecessor.