Nonlinear reptation in molecular based hysteresis models for polymers

Abstract

Abstract.We extend the linear "stick-slip" models of Doi-Edwards and JohnsonStacer to nonlinear tube reptation models. We then show that such models, when combined with probabilistic formulations allowing distributions of relaxation times, provide a good description of dynamic experiments with highly filled rubber in tensile deformations. A connection to other applications including dielectric polarization and reptation in other viscoelastic materials (e.g., living tissue) is noted. Introduction.This note is prompted by several thrusts in our research efforts. The first is to extend linear reptation models for polymeric materials to models incorporating nonlinearities and to use the resulting systems to explain molecular based hysteresis (e.g., via internal variable formulations).A second direction involves exploration

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

“…The models, based on a linear stick-slip assumption, while capturing some of the hysteresis in several types of materials, do not capture especially well the shapes of the nonlinearities in the hysteresis loops. While these models are a useful initial effort, further development along the lines of the nonlinear stick-slip assumptions of [6,7] is needed.…”

“…This new model, in which polymer chains are treated as strings of interconnected beads, permits the incorporation of many important physical parameters (such as temperature, segment bond length, internal friction, and segment density) in the overall hysteretic constitutive relationship. Our goal here is to present development of this model based upon physical considerations at the molecular level; its form is similar to that developed in [6,7] and does have the general form (1) of Boltzmann type, even though the kernel is not of convolution type,.…”

“…We recall that our model is based on the linear Rouse model (4) (which is linear due to the assumptions on the underlying potentials) and the linearization assumption (15). Moreover, both (24) and (28) are assumptions that are linear in nature (as opposed to the nonlinear Johnson-Stacer type ratio assumptions of [6,7] which led to full nonlinear models for hysteretic constitutive laws there). To provide a better fit to the carbon-black filled polyisoprene data, one may require nonlinear assumptions in the model development similar to those in [6,7], or the more appropriate assumption in (2) of a Lennard-Jones type higher order potential [28,30] which permits repulsive forces as "beads" in the molecular chain become close.…”

“…Previous efforts summarized in [6] have shown, through comparison with experimental data, that the best fit to filled elastomer data occurs when g e and g v are cubic, along with Y as a distribution of exponentials. Banks, et al, [7,2] subsequently developed nonlinear models based on stick-slip "molecular" ideas of Johnson and Stacer [26] and Doi and Edwards [10] which resulted in a . WORK UNIT NUMBER…”

A Brief Review of Some Approaches to Hysteresis in Viscoelastic Polymers

“…Our previous efforts as summarized in [20,21] have shown, through comparison with experimental data, that the best fit to filled elastomer data occurs when g e and g v are cubic, along with Y as a distribution of decaying exponentials. We subsequently [18,19,20,21] developed nonlinear models based on stick-slip "molecular" ideas of Johnson and Stacer [43] and Doi and Edwards [34] which resulted in a form for g e , g v and Y in (1) that matched the empirical findings reported in [20,24,25]. These models allow for multiple relaxation times present in polymer strands of composite materials within a virtual compartmental model of entangled chemically cross-linked/physically constrained system of long chain "molecules".…”