Dynamic scaling in entangled mean-field gelation polymers

Abstract

We present a simple reaction kinetics model to describe the polymer synthesis used by Lusignan et al.[1] to produce randomly branched polymers in the vulcanization class. Numerical solution of the rate equations gives probabilities for different connections in the final product, which we use to generate a numerical ensemble of representative molecules. All structural quantities probed in ref. [1] are in quantitative agreement with our results for the entire range of molecular weights considered. However, with detailed topological information available in our calculations, our estimate of the 'rheologically relevant' linear segment length is smaller than that estimated in ref [1]. We use a numerical method [2] based on tube model of polymer melts to calculate the rheological properties of such molecules. Results are in good agreement with experiment, except that in the case of the largest molecular weight samples our estimate of the zero-shear viscosity is significantly lower than the experimental findings. Using acid concentration as an indicator for closeness to the gelation transition, we show that the high-molecular-weight polymers considered are at the limit of meanfield behavior -which possibly is the reason for this disagreement. For a truly mean-field gelation class of model polymers, we numerically calculate the rheological properties for a range of segment lengths. Our calculations show that the tube theory with dynamical dilation predicts that, very close to the gelation limit, contribution to viscosity for this class of polymers is dominated by the contribution from constraint-release Rouse motion and the final viscosity exponent approaches Rouse-like value.

From reactor to rheology in industrial polymers

“…The crossover molecular weight between these two regimes is obviously inversely proportional to the branching density, but it is not clear what the proportionality constant is. Das et al investigated this same series of resins, using a Monte‐Carlo algorithm based on reaction rate equations to generate a representative set of molecules. As a proxy for intrinsic viscosity (which they could not calculate) they examined the scaling behavior of the ideal radius of gyration as a function of molecular weight, concluding that the crossover molecular weight between scaling regimes may be 10 times larger than the typical strand length between cross‐links.…”

reptate rheology software: Toolkit for the analysis of theories and experiments

“…More recently, Larson's Hierarchical model [4][5][6] and the "Branch-on-Branch" (BoB) model [10][11][12] have been released as freely-available software for predicting rheology of entangled branched polymers, using tube model concepts. Despite powerful predictive capability, these are command-line driven codes with no built-in capacity for viewing or analysing experimental data.…”

Numerical prediction of nonlinear rheology of branched polymer melts

“…A number of articles already cover the methodology used in calculating the rheological response of branched polymers in the linear regime in BoB [Das et al (2006a); Das et al (2006b);Wang et al (2010)]. We only summarize the main ideas here, chiefly to introduce the variables that are required in the calculation of the nonlinear rheology.…”