Arkady I. Leonov

Nonequilibrium thermodynamics and rheology of viscoelastic polymer media

SummaryNonlinear constitutive equations for viscoelastic polymer media have been derived with the help of irreversible thermodynamical methods. These equations contain a small number of constants which have obvious physical meaning. The work is based on the hypothesis that the high-elasticity state characterized by large elastic strains is the local equilibrium thermodynamical state of these media. A theoretical description is given to explain the kinetic transition of fluid polymer media into high-elasticity state at temperatures above the flow temperature.ZusammenfassungMit Hilfe der Methoden der Thermodynamik irreversibler Prozesse werden nichtlineare rheologische Stoffgleichungen für viskoelastische Polymere abgeleitet. Diese Gleichungen enthalten nur wenige Konstanten, die eine klare physikalische Bedeutung haben. Die Untersuchung ist auf die Hypothese gegründet, daß der hochelastische Zustand, der durch große elastische Dehnungen gekennzeichnet ist, der Zustand des lokalen thermodynamischen Gleichgewichts dieser Stoffe ist. Es wird eine theoretische Erklärung des kinetischen Übergangs von flüssigen Polymeren in den hochelastischen Zustand bei Temperaturen oberhalb der Fließtemperatur gegeben.

On the theory of the adhesive friction of elastomers

Abstract The process of adhesive friction of an elastomer body sliding over a smooth rigid surface has been considered as a stationary stochastic process that consists in the formation and breakage of adhesive linking chains which bind the polymer body to the surface. The breaking off is believed to be due to either thermal excitations or stress in the link arising from its elongation because of the external force applied to the body. The friction force is calculated as the sum of the stresses in the individual linking chains. We utilized the well-known strain-stress dependence for a polymeric macromolecule, the transition probability for the link to pass from a bound to a free state depending on the stress. We have developed a general theory of the stochastic process of elastomer-wall interaction with arbitrary transition probabilities and, making use of a linear strain-stress dependence, also obtained simple and explicit expressions for the friction force.

A Kinetic-Model for Sulfur Accelerated Vulcanization of a Natural-Rubber Compound

Vulcanization kinetics for a natural rubber compound were studied by a kinetic approach using the cure meter and DSC methods. A simplified but realistic model reaction scheme was used to simulate induction, curing, and overcure periods continuously. Physically significant parameters of the model were extracted from isothermal experimental data using a cure meter. The calculation demonstrated a good correspondence with isothermal cure meter data over the temperature range studied. The length of induction time, variation of maximum modulus with temperature, and the reversion phenomena observed from cure curves can be predicted. DSC data were found to be incompatible with the cure meter test, because the complex vulcanization reaction system is multiexothermal and it is difficult to isolate the heat due to crosslinking. Hence, the cure meter technique is suggested for the study of crosslink formation. The kinetic approach provides a way to incorporate vulcanization kinetics into simulation of reactive processing operations.

Analysis of simple constitutive equations for viscoelastic liquids

To construct viscoelastic constitutive equations properly one needs to know, apart from their predictability, how robust they are and what possible underwater reefs one may meet that could ruin a weak rheological ship in the course of its difficult route through the ocean of solving complicated problems.

Modeling spurt and stress oscillations in flows of molten polymers

The paper presents an approach for modeling polymer flows with non-slip, slip and changing non-slip — slip boundary conditions at the wall. The model consists of a viscoelastic constitutive equation for polymer flows in the bulk, prediction of the transition from non-slip to sliding boundary conditions, a wall slip model, and a model for the compressibility effects in capillary polymer flows. The bulk viscoelastic constitutive equation contains a hardening parameter which is solely determined by the polymer molecular characteristics. It delimits the conditions for the onset of solid, rubber-like behavior. The non-monotone wall slip model introduced for polymer melts, modifies a slip model derived from a simple stochastic model of interface molecular dynamics for cross-linked elastomers. The predictions for the onset of spurt, as well as the numerical simulations of hysteresis, spurt, and stress oscillations are demonstrated. They are also compared with available data for a high molecular weight, narrow distributed polyisoprene. By using this model beyond the critical conditions, many of the qualitative features of the spurt and oscillations observed in capillary and Couette flows of molten polymers, are described.

ON THE DEPENDENCE OF FRICTION FORCE ON SLIDING VELOCITY IN THE THEORY OF ADHESIVE FRICTION OF ELASTOMERS

Abstract An improvement of a recent statistical theory of the adhesive friction of elastomers is proposed taking into account the delay in breaking polymeric chains off the wall owing to Brownian oscillations of the terminal segment attached to the wall. This results in the appearance of an S-shape dependence in the curve relating friction force to sliding velocity. The general formulae of the theory are then revised and when the force acting on a single chain depends linearly on its extension, a simple and explicit expression for friction force on sliding velocity is obtained. The applications of the sliding friction dependence to the stick-slip phenomena in flow of molten polymers are also discussed.

A theory of necking in semi-crystalline polymers

Abstract Necking or cold drawing is a smoothed jump in cross-sectional area of long and thin bars (filaments or films) propagating with a constant speed. The necks in polymers, first observed about seventy years ago, are now commonly used in modern processing of polymer films and fibers. Yet till recently there was a lack in fundamental understanding of necking mechanism(s). For semi-crystalline polymers with co-existing amorphous and crystalline phases, recent experiments revealed that such a mechanism is related to unfolding crystalline blocks. Using this idea, this paper develops a theoretical model and includes it in a general continuum framework. Additionally, the paper explains the “forced” (reversible) elasticity observed in slowly propagating polymeric necks, and also briefly analyses the viscoelastic effects and dissipative heat generation when polymer necks propagate fast enough.

On the conditions of potentiality in finite elasticity and hypo-elasticity

Abstract Thermodynamic approaches to finite elasticity are almost generally accepted. Nevertheless, there is still a lack of proof for the necessity of potential strain-stress relations in generally defined elasticity and hypo-elasticity. This situation has resulted in ambiguous applications of the general concept of elasticity to the description of irreversible phenomena in viscoelastic solids and liquids. This paper makes a brief review of the general concepts of elasticity and hypo-elasticity, with most of the attention paid to the Eulerian description, employed in viscoelastic theories. Then it is demonstrated that all hypothetical materials with non-potential finite elastic or hypo-elastic constitutive relations can create an energy from nothing, i.e. work as perpetual motion machines. This gives a ‘physical’ proof of necessity of potential conditions in general finite elasticity and hypo-elasticity and their extensions to finite viscoelasticity.

A linear model of the stick-slip phenomena in polymer flow in rheometers

A linear approach was employed for the qualitative theoretical study of the stick-slip phenomena in polymer flows in rheometers. For this purpose, the familiar three-constant rheological equation and a linear wall friction law (i.e. wall stress — slip velocity dependence) were used with some additional hypotheses about the onset of the stick-slip behaviour. The friction law used was derived from a crude molecular approach. On the basis of these equations the inertialess stickslip behaviour of a viscoelastic liquid flowing through a capillary at a constant flow rate was considered. To be able to describe some transient phenomena in this problem, inertial effects (as an example) were taken into account. Furthermore, the distortions on the extrudate surface due to the slip phenomena inside the capillary were described theoretically within the framework of a linear approximation. In the final part of the study the possibility of rapid stochastization was discussed for rotational stick-slip flow of polymers in a cone-plate rheometer.

On flows of viscoelastic liquids in long channels and dies

Abstract General non-existence of steady rectilinear viscoelastic flows in long tubes results in occurring secondary flows. The early analytical and experimental studies of dilute polymer solutions as well as recent experiments and direct numerical simulations of polymer melts found the secondary flows to be very weak. It suggests that for many applications to polymer processing the secondary flows can either be neglected or when necessary, treated as small disturbances relative to rectilinear flow component. The paper develops and justifies an approach based on partitioning flow in the main, quasi-rectilinear part and small disturbances. The formulated quasi-rectilinear flow problem is described by a second order non-linear elliptic PDE that is close to simple shearing. The calculations of main axial velocity profiles employing this approach are successfully compared with recent experimental data. Using a perturbance procedure a forth order linear PDE for secondary flows is then derived. In contrast to the quasi-rectilinear flows whose description needs only knowledge of three shear viscometric functions, computations of secondary flows depend on features of viscoelastic constitutive equations. Scaling evaluations and calculations of two secondary flow problems for simple geometry confirm that these flows are very weak.