Rheological Model for Describing Viscometric Flows of Melts of Branched Polymers

Abstract

The present paper considers the problem of constructing a rheological constitutive relation for melts of branched polymers with the use of a modifi ed Vinogradov-Pokrovskii rheological model generalized to the case of several noninteracting models, each of which corresponds to the account in the stress tensor of the contribution of a particular polymer fraction and is characterized by its own relaxation time and viscosity. Since the number of model parameters markedly increases thereby, simple dependences of its parameters on the mode number are proposed. On the basis of the obtained model, the nonlinear nonstationary effects at simple shear and uniaxial tensor have been considered.Keywords: rheology, polymer melts, mesoscopic approach, rheological equation of state, viscometric fl ows.Introduction. Experimental investigations of various polymer fl uids point to their linear viscoelastic behavior. To investigate such effects, a large number of models describing the rheological behavior of polymer fl uids at both qualitative and quantitative levels were proposed. It should be noted thereby that two radically different classes of models exist: models of the fi rst class use the phenomenological approach, and in models of the second class the microscopic approach is used. In the phenomenological approach, the dynamics of macroscopic bodies is constructed on the basis of the general laws determined experimentally. This class of models includes the Maxwell, Oldroyd [1], and ProkuninLeonov [2] phenomenological models. The other class of models is based on the mesoscopic approach. In such models, the macromolecular dynamics is described on the basis of model notions and, consequently, takes into account, in some approximation, both the structure of the polymer molecule and the processes of intermolecular interaction. Such models often use the one-molecule approximation in which instead of the whole aggregate of macromolecules, one chosen macromolecule moving in some "effective" medium is considered. In some of the models of this class the macromolecule is represented as a series of beads and springs (elastic force) connecting them. For example, one of the fi rst of such models is the Kargin-Slonimskii-Rauz model. Thus, the mesoscopic approach, as opposed to the phenomenological one, makes it possible to follow the relationship between the micro-and macroscopic characteristics of polymer systems and, consequently, explain various phenomena in polymer melts, for example, the diffusion, viscoelasticity, and other phenomena. However, this approach requires the introduction of additional mesoscopic parameters, which should also be determined experimentally. Among the above models are also the Doi-Edwards [3], De Gennes [4], and Curtiss-Bird [5] models. In these models, each macromolecule is considered as a fl exible chain moving inside some tube formed by other macromolecules; and at short observation times the molecule can move only along the tube. However, the initial Doi-Edwards model did not take into account the elongat...

Modeling of nonlinear viscoelastic polymeric materials at their large periodic deformation

“…(1) which considers only one relaxation process complies so greatly to the experimental data. When describing the non-linear dependence of shift viscosity and normal stresses of the firstorder difference, this model shows only qualitative compliance of calculated dependences and the experimental data [4,8,9].…”

“…The numeric calculations are based on the equations written down on the basis of the mVP rheological model [4]. The model is unique since it considers the tensor nature of the friction coefficient for beads which is defined by the induced anisotropy of a shift flow.…”

“…Here σ ik -a stress tensor; p -hydrostatic pressure; η o and τ 0 -initial values of shear viscosity and relaxation time for a polymeric component; v ik -velocity gradients tensor; a ik -the symmetric second rank tensor of anisotropy; I = a jj -first invariant of anisotropy tensor; γ ik = (v ik + v ki )/2 -symmetrized tensor of velocity gradients; κ, β -phenomenological parameters of the model considering the sizes and the form of a macromolecular ball in macromolecule dynamical equations and which are connected by a ratio: κ=1.2•β, that corresponds with condition of independence of asymptotical behavior of stationary shear viscosity of the polymer molecular weight [4].…”

“…A number of rheological models [1][2][3][4] are often applied to describe rheological features of polymeric materials at quite small periodic or stationary deformations. However, when processing solutions and melts of polymers we have to face with deformation of higher orders.…”

“…Nowadays there are a lot of rheological models some of which are still developing whereas others have already lost their relevance. The most prominent are: Gizekus model [1], Leonov-Prokunin model [2], the extended pom-pom model [3], the modified Vinogradov-Pokrovsky (mVP) model [4]. All of them describe well the linear effects at small periodic deformations and non-linear effects at large stationary deformations.…”