Analysis of Elongational Viscosity of Entangled Poly (Propylene Carbonate) Melts by Primitive Chain Network Simulations

Abstract

It has been established that the elongational rheology of polymers depends on their chemistry. However, the analysis of experimental data has been reported for only a few polymers. In this study, we analyzed the elongational viscosity of poly (propylene carbonate) (PPC) melts in terms of monomeric friction via primitive chain network simulations. By incorporating a small polydispersity of materials, the linear viscoelastic response was semi-quantitatively reproduced. Owing to this agreement, we determined units of time and modulus to carry out elongational simulations. The simulation with constant monomeric friction overestimated elongational viscosity, whereas it nicely captured the experimental data if friction decreased with increasing segment orientation. To see the effect of chemistry, we also conducted the simulation for a polystyrene (PS) melt, which has a similar entanglement number per chain and a polydispersity index. The results imply that PPC and PS behave similarly in terms of the reduction of friction under fast deformations.

Primitive Chain Network Simulations for Shear Rheology of Poly(propylene carbonate) Melts

“…The examined systems are shown in Table I. Although the molecular weight distribution is not that large, we observed its effects on the viscoelastic response in the previous study 28) . As such, we took account of the polydispersity assuming log-normal distributions.…”

“…These units were chosen as the average strand length under equilibrium a, the diffusion time of the network node τ 0 , and thermal energy k B T. Here, τ 0 is described as τ 0 = 2n 0 ζ 0 a 2 / 6k B T, where n 0 is the average number of Kuhn segments on the network strand, and ζ 0 is friction of the Kuhn segment under equilibrium. To simulate the PPC melts, we determined units of molecular weight M 0 and modulus G 0 , instead of n 0 and a by the fitting of linear viscoelastic data in the previous study 28) . The obtained values are M 0 = 3.3 (kg/mol), G 0 = 1.6 (MPa), and τ 0 = 8 × 10 −4 (s) at T = 100 °C.…”

“…Here, S is strand orientation defined from the orientation tensor as S = 4 S xy 2 + ( S xx − S yy ) 2 and S c and α are the model parameters, which have been determined as S c = 0.1 and α = 1.25 from the uniaxial data 28) . Note that the definition of S depends on flow geometry 3) , and we adopted the other definition of S for uniaxial deformations to determine S c and α.…”

“…However, their friction model does not excellently work because the data suggest an intensive friction change even at the stretch rates well below the contraction rates of the involved chains. As such, we employed eq 2 that reasonably reproduced the targeted uniaxial data 28) . In the meantime, we note that we do not deny the model by Yaoita et al because a parameter tuning may probably reproduce the uniaxial data even with their model.…”

“…In this study, we performed multi-chain slip-link simulations for poly (propylene carbonate) (PPC) melts under fast shear. For this specific PPC melts, we have determined the friction as a function of segment orientation from the uniaxial data 27) in our previous study 28) . Employing this friction model, we simulated the shear behavior to see its effect on the viscosity growth curve.…”