Effect of the molecular mass on the shear and longitudinal viscosity of linear polymers

Abstract

532.135The effect of the molecular mass of a polymer sample on the dependence of the stationary viscosity on the velocity gradient upon simple shear and uniaxial tension is studied. The model of the dynamics of a suspension of noninteracting dumbbells in the anisotropic medium is used. The theoretical results show that the asymptotic behavior of the shear viscosity does not depend on the molecular mass and corresponds to experimental data.The study of the technological processes of polymer processing is an important practical problem whose solution requires a mathematical fornmtation of the behavioral laws of polymer fluids. In mathematical modeling of the flows of linear-polymer solutions and melts, the greatest difficulties are connected with nonlinear effects. For their description it is necessary to obtain a rheological constitutive relation and check its correspondence to the real flows of polymer fluids. The rheological constitutive relation has already been formulated by Altukhov and Pyshnograi [1,2], and Kulicke and Wallbam calculated the simple stationary shear flow and their results agree with experimental data [3]. The indicated relation was derived as a zero approximation of the more general rheological constitutive relation with respect to small parameters related to the reaction of the macromolecular chain and the internal viscosity [4,5]; therefore, this relation needs to be additionally substantiated. AVe now construct a rheological zero-approximation model by a different method and study the effect of the molecular mass and concentration of the polymer on its parameters.Rheological Constitutive Relation. We use the microstructural approach that permits us to establish a relationship between the macro and microeharacteristics of a polymer system [6,7]. In the theory of polymer viscoelasticity, a monolnolecular approximation, in which one inacromolecule moving in an effective medium formed by a solvent and other macromolecules is considered instead of a set of macromolecules in the solvent volume, is the most efficient. To study relatively slow motions, one can use the Kargin-SlonimskiiRouse model. In this model, the macromolecular dynamics is simulated by the motion of N + 1 centers of friction (beads) connected sequentially by elastic forces (springs), and the equations of the dynamics of a macromolecule have the form dwhere m is the mass of a bead, u~ is the velocity of a particle with number a, P/~ is the force of hydrodynamic entrainment, Q~ is the elastic force, and (I)~ is a random (Brownian) force. It is noteworthy that the application of this approach leads to rheological constitutive relations of different complexity (see the review of publications in [6,7]). The simplest rheological model [1, 2] allows one to simulate the stationary viscosimetric flows of linear-polymer solutions and melts qualitatively and quantitatively. We now consider it in more detail. We simulate the dynamics of a macromolecule by an elastic dumbbell that corresponds to the slowest relaxational process of a polymer...

Constitutive equations for weakly entangled linear polymers

“…(43) and (44) are the basic constitutive relations, which allow us to develop a reliable theory of non-linear effects in viscoelasticity of weakly entangled polymer systems [21,[26][27][28][29][30]. To demonstrate that the system of constitutive relations (43) and (44) describe the main observable effects for the flow of polymer melts, we consider below two simple cases of flow: simple shear and simple elongation.…”

“…However, these values do not influence the values 0 and Á 0 resulted in Table 1 because, as shown above, Ä andˇare responsible for the non-linear behaviour of a polymeric liquid (at the big gradients), 0 and Á 0 are initial values of viscosity and relaxation time and are defined at small gradients. The paper [31] contains the results of measurements of the ratio of the second difference of normal stresses to the first one To estimate the value of M e , one has to use indirect arguments, referring to the known dependencies (29) and (31) Fig. 11.…”

Rheological Model for Describing Viscometric Flows of Melts of Branched Polymers

“…Besides the Rauz parameters (drag coeffi cient of beads, equilibrium size of the coiled macromolecule), it is necessary to introduce into the model parameters taking into account the presence of entanglements in the polymer system. For such a model, we use in the present work the modifi ed Vinogradov-Pokrovskii model [21][22][23][24][25]. The specifi c feature of this model is that it takes into account the tensor character of the drag coeffi cient of beads connected with the induced anisotropy of the shear fl ow.…”

Mesoscopic equation of state of polymer systems and description of the dynamic characteristics based on it

“…In [5,6], we calculated flows in a circular pipe, which enables us to refine corrections to the Poiseuille law, and in cylinders with a rotary end and a free surface, which made it possible to describe differences in the motion of Newtonian and polymer fluids. The influence of the molecular weight on shear and longitudinal viscosities was found in [7]. We note that if the condition of independence of the asymptotic behavior of the shear viscosity from the molecular weight is satisfied, there is the following relationship (found in [7]) between the anisotropy parameters introduced into the equations of macromolecular dynamics: κ = 1.2β.…”

“…The influence of the molecular weight on shear and longitudinal viscosities was found in [7]. We note that if the condition of independence of the asymptotic behavior of the shear viscosity from the molecular weight is satisfied, there is the following relationship (found in [7]) between the anisotropy parameters introduced into the equations of macromolecular dynamics: κ = 1.2β.…”