Nonlinear rheology of polydisperse blends of entangled linear polymers: Rolie-Double-Poly models

Abstract

While there has been much success in modeling the linear and nonlinear rheology of monodisperse entangled linear polymers, progress in the constitutive modeling of polymeric materials continues to lag behind the needs of industry. Industrially sourced polymers are typically polydisperse (comprising a broad distribution of molecular weights), making their rheology more suitable for processing but also more difficult to predict. To date, there are no molecular-based constitutive models that are practically suitable for describing industrially relevant polymers in industrially relevant flows. In this article, we extend but strongly simplify the model of Read et al. [J. Rheol. 56, 823-873 (2012)], which is able to predict the linear and nonlinear rheology of bidisperse blends but is prohibitively complex for industrial use. We propose a pair of simplified tube models for polydisperse melts of entangled linear polymers that combine the success of the double reptation approximation [des Cloizeaux, Europhys. Lett. 5, 437-442 (1988)] in the linear regime with the success of the Rolie-Poly constitutive equation [Likhtman et al., J. Non Newtonian Fluid Mech. 114, 1-12 (2003)] in the nonlinear regime. We first review the key concepts of the double reptation approximation and the original (monodisperse) Rolie-Poly constitutive model. Subsequently, we provide the details of our approximate models for the particular case of a bidisperse blend and show that these models naturally identify the effects from couplings between constraint release and chain retraction (i.e., the so-called "enhanced stretch relaxation time"). Finally, we generalize to a multicomponent (polydisperse) model, based on the same underlying principles. Along the way, we also show that both of our models are in qualitative, and largely quantitative, agreement with experimental data for bidisperse and polydisperse melts of entangled linear polymers.

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

“…For example, the Rolie-Double-Poly [13] and BoB models do not make exactly the same prediction for linear rheology of polydisperse linears, and both differ from the Likhtman-McLeish theory [14] in prediction for monodisperse linear polymers. Such variations are inevitable where different theories make different assumptions or approximations.…”

“…Once an LVE mastercurve has been constructed, a range of options already exist within RepTate to compare the mastercurve with theory. These include fitting Maxwell modes to the curve; Dynamic Tube Dilution theory for stars [2]; the linear rheology version of the Rolie-Double-Poly [13] model; the BoB model for polydisperse linear or branched polymers [10][11][12]. Different theories may apply to different materials, and may involve different levels of approximation.…”

“…C. Polydisperse linear entangled polymers, Rolie-Double-Poly model [13] In Ref [13], a range of experimental nonlinear shear and extensional rheology data of bidisperse or polydisperse linear entangled polystyrene and polyisoprene material, together with predictions using the proposed "Rolie-Double-Poly" (RDP) model, were discussed. In particular, the molecular weight distribution of a polydisperse linear entangled polystyrene "PSIV", described in Ref.…”

“…This requires two tube parameter values for polystyrene: i) the average molecular weight between entanglements, which we choose to be M e = 16.6 kg/mol, and ii) the entanglement relaxation time, which we choose to be τ e = 3.4 × 10 −3 s at 160 • C. These parameters are as used in Ref. [13].…”

“…This allows the software to calculate the reptation and stretch relaxation times. This calculation accounts for both static dilution (due to the unentangled chains) and dynamic dilution (shorter entangled chains release their entanglements on longer chains, acting as solvent for the longer chains) as described in [13]. We set the entanglement plateau modulus G 0 N = 0.2 MPa.…”