Flow-Induced Orientation and Stretching of Entangled Polymers in the Framework of Nonequilibrium Thermodynamics

Abstract

We provide a description of the Marrucci–Ianniruberto constitutive equation [Philos. Trans. R. Soc. London, A2003361677688] for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics and we properly extend it to account for a second normal stress difference by introducing a second order term in the relaxation tensor in terms of the conformation tensor. The modified model incorporates one additional parameter, the anisotropic mobility parameter α, which allows for nonvanishing predictions of the second normal stress coefficient. Application of the second law of thermodynamics and the requirement that the evolution equation must preserve the positive-definite nature of the conformation tensor between successive entanglement points along the chain for all times and all flow fields constrain the convective constraint release (CCR) parameter β ccr to values strictly greater than one (β ccr > 1) and the new parameter α to values in the interval 0 ≤ α ≤ 1 − β ccr –1. The modified model provides a satisfactory description of available experimental data for the transient and steady-state shear rheology of entangled polystyrene melts [ Schweizer Schweizer J. Rheol.20044813451363] and for the elongational steady-state stress of an entangled polystyrene solution [ Ye Ye J. Rheol.200347443468] over the entire range of shear and elongation rates covered in the rheological measurements.

From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions

“…By properly introducing more refinements, such as contour length fluctuations, by considering a σ-dependent curvilinear segment diffusion along the polymer's contour (see, e.g., Refs. 6, 52, and 53 and references therein), uplifting the IAA by introducing a first-order derivative with respect to s and a term proportional to the single-link distribution function, 2,25,54 CCR by allowing for flow-induced relaxation times, [10][11][12]55 flow-induced alignment of chain ends 32,56 via a modification of the boundary conditions for the single-link distribution function, and chain stretch, 8,57 could further improve the tumbling-snake's model capacity to favorably predict the rheological response of entangled polymer melts and concentrated polymer solutions. Especially, the latter is particularly important for strong elongation flows.…”

“…Invoking such a concept while deriving a rheological constitutive model for entangled polymer melts in the context of non-equilibrium thermodynamics, has shown promising. 10 Thus, in this work, we revisit the contradiction between the rheological data for the extensional viscosity of polymer melts solutions and show that the link tension coefficient, given as ε = ε 0 S 2 2 , is able to predict this behavior in a qualitative manner, while the coefficient ε 0 decreases as the polymer concentration increases. The structure of this manuscript is as follows: In Sec.…”

“…The incorporation of additional mechanisms that were originally omitted, like contour length fluctuations accounting for the dynamical evolution of the primitive path contour length, and constraint release (CR) accounting for the dynamical release of entanglements, 2,4,5 allowed for the precise description of linear viscoelastic (LVE) properties. [4][5][6][7] However, and despite the persevering efforts of polymer scientists to improve upon it in the non-linear regime, by incorporating, e.g., chain stretch due to elongation of the tube by the flow, 8 finite extensibility, 9,10 and convective constraint release (CCR) accounting for a flow-induced release of entanglements, [10][11][12][13] it still lacks consistency with available rheological data. In spite of the overall accepted effectiveness, and partial success, of the tube/reptation model, it is not the sole formalism that aims addressing the molecular origins of high molecular weight polymeric systems.…”

A nonequilibrium thermodynamics perspective of thixotropy

“…It should be noted that in the present approach the polymeric segments are assumed to be below the entanglement threshold; however, there are available free energy expressions that can be used beyond this threshold. 23 The first integral in Eq. 5expresses the sum of the elastic energy of the Hookean springs, wherein all segments are deformed due to the imposed flow.…”

“…[17][18][19] NET laws provide the means to impose restrictions to the model parameters. Up to date, several micro-structured systems, such as liquid crystals, [20][21][22] polymer melts and solutions, [17][18][19][22][23][24] immiscible complex fluids, [17][18][19][25][26][27] polymer nanocomposites, [28][29][30][31][32][33] drilling fluids, 34 blood, 35 ionomers, 36 and micellar systems, 37 have been addressed through NET, a fact that attests to its usefulness and applicability. To the best of our knowledge, only the model proposed by Beris et al 38 for concentrated star polymer suspensions, a system exhibiting a yield stress, was derived via the use of NET principles.…”