Renat N. Khaliullin

Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions

The discrete slip-link model (DSM) was developed to describe the dynamics of flexible polymer melts. The model is able to predict linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. The model also shows good agreement with dielectric relaxation experiments, except for the single data set available for bidisperse linear systems with a small volume fraction of long chains. In this work, both shear and elongational flow predictions obtained using the DSM without parameter adjustment are shown. Model predictions for shear flow agree very well with experimental results. The DSM is able to capture the transient response as well as the steady-state viscosity. However, for elongational flow, agreement is unsatisfactory at large strains. The DSM captures the onset of strain hardening, but after a Hencky strain between 2 and 3, it predicts transient strain softening, whereas experiments show only monotonic growth. We explore a number of assumptions and approximations of the model and their effect on flow predictions. The approximations are related to the neglect of these phenomena, which are expected to be more sensitive in elongational flow: finite extensibility, convective constraint

Calculation of the Helmholtz potential of an elastic strand in an external electric field

We derive from statistical mechanics the Gibbs free energy of an elastic random-walk chain affected by the presence of an external electric field. Intrachain charge interactions are ignored. In addition, we find two approximations of the Helmholtz potential for this system analogous to the gaussian and Cohen-Padé approximations for an elastic strand without the presence of an electric field. Our expressions agree well with exact numerical calculations of the potential in a wide range of conditions. Our analog of the gaussian approximation exhibits distortion of the monomer density due to the presence of the electric field, and our analog of the Cohen-Padé approximation additionally includes finite chain extensibility effects. The Helmholtz potential may be used in modeling the dynamics of electrophoresis experiments.

Self‐Consistent Modeling of Constraint Release in a Single‐Chain Mean‐Field Slip‐Link Model

In slip‐link models, entanglements are discrete objects along the chain. As a result, it is not necessary to assume that constraint release is Rouse‐like motion of the primitive path. Instead, entanglements can be created or destroyed anywhere along the chain by the motion of surrounding chains. We call this motion “constraint dynamics,” since the imposition of constraints must occur, as well as their release. Also, since we deal with a stochastic model including full fluctuations, stress relaxation follows rigorously from the dynamics, and it is not necessary to assume that the relaxation modulus is a product of two simultaneous processes, as is typically done in tube models. We propose an efficient and self‐consistent method method for the implementation of constraint dynamics in a mean‐field slip‐link model. If binary interactions are assumed for entanglements, the implementation is mathematically equivalent to the algorithm employed by Takimoto and Doi. Unlike that work, however, the dynamics do not r...

Unified Mathematical Model for Linear Viscoelastic Predictions of Linear and Branched Polymers

Application of the slip‐link model to entangled star‐branched polymers is considered. Relaxation of each arm by primitive‐path length fluctuations occurs, as well as destruction and creation of entanglements by ‘constraint dynamics’. Rouse dynamics to mimic constraint release is completely avoided. In addition, the branch point position can fluctuate and, in contrast to tube models, even pass through slip‐links without stretching; all dynamics are determined by the chain free energy and Brownian forces. All adjustable parameters are determined from linear chain LVE comparisons. The proposed model is compared with the tube model, which contains certain limitations in premetive path relaxation that not found in the slip‐link model. The proposed formulation can be applied to more complicated branches and to cross‐linked networks as well.