No abstract

The local elastic strength κ, segmental friction coefficient ζ, and the Brownian force intensity B of polymer chains in a melt are expected to change under fast flow. This study examined the effects of those changes on rheological and structural properties of the Rouse model, the most frequently utilized model for unentangled melts. Specifically, the Langevin equation of the Rouse model was solved with the decoupling and preaveraging approximations to derive analytical expressions of nonlinear rheological properties and the end-to-end stretch ratio under steady shear and extension. The expressions explicitly included nonequilibrium parameters r κ , r ζ , and r B defined as the ratios of κ, ζ, and B under flow to those at equilibrium, thereby offering a method of evaluating each of r κ , r ζ , and r B from rheological and structural data under flow within the framework of those approximations. Data of extensional viscosity η E and the relaxation rate of the tensile stress decay coefficient η̇E − reported for the unentangled polystyrene melt (PS-27k; M = 27.1 × 10 3 ) and data of shear viscosity η and the first normal stress difference coefficient Ψ 1 reported for the PS-14k melt (M = 13.7 × 10 3 ) were analyzed with this method to evaluate the r ζ /r κ ratio under respective flow conditions. The r ζ /r κ ratios thus obtained under extension and shear were found to exhibit the same dependence on the Weissenberg number Wi, given that Wi was reduced to an iso-local stretch state wherein the local elastic unit of the chain (Rouse spring) is stretched to the same extent under extension and shear. The analytical expressions of the rheological properties also enabled a preliminary test of the behavior of r B . This test, made for the η E , ηĖ − , η, and Ψ 1 data mentioned above, posed a serious question about the relationships under fast flow often assumed in molecular models, r B = r ζ (proportionality between B and ζ not affected by flow) and r B = 1 (no flow effect on B).

For a type-A Rouse chain, a recent study derived an analytical expression of its dielectric loss εʺ under steady shear in terms of the basic Rouse parameters, the spring strength κ, the friction coefficient ζ, and the mean-square Brownian force intensity B, all being allowed to arbitrarily change with the Weissenberg number Wi (= shear rate multiplied by the longest relaxation time at equilibrium) and the latter two having a tensorial form; see Sato et al., Nihon Reoroji Gakkaishi, 50, 253 (2022). As a follow up, we have conducted a rheo-dielectric test for a type-A unentangled melt, poly(butylene oxide) with the molecular weight of 16 × 10 3 , to measure ε y ʺ in the velocity gradient (y) direction as well as the viscosity η and the first normal stress difference coefficient Ψ 1 . Both dielectric relaxation time and intensity were found to decrease on an increase of Wi up to the onset of rheological nonlinearity (Wi ~ 1) where η and Ψ 1 exhibited moderate thinning, but the dielectric relaxation mode distribution was not affected by this increase of Wi. Analyzing those ε y ʺ, η, and Ψ 1 data on the basis of the above expressions, we found that κ increases moderately (by ~ 40 %) but the off-diagonal components of ζ remains negligibly small on that increase of Wi. We also found that the diagonal components ζ xx (with x being the velocity direction) and B yy hardly change but ζ yy decreases moderately (by ~ 20 %). These results, suggesting the onset of the finite extensive nonlinear elasticity as well as a violation of a relationship B yy ∝ ζ yy (naively expected from the fluctuation-dissipation theorem), serves as a good starting point for deeper investigation of κ, ζ, and B.