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.

Keywords: coarse-graining; entangled polymers; molecular simulations; rheology; viscoelasticity.

Figure 1

Typical snapshot of a chain with $Z=88$ involved in Zw48 under elongation with the elongation rate of $\dot{\epsilon }{\tau }_0=4.4\times {10}^{-5}$, taken at the elongational strain of 1.76. Thin black lines are the other chains, and thick green lines are segments entangled to the test chain. The yellow frame shows the simulation box for periodic boundary conditions.

Figure 2

Linear viscoelasticity at $T=70 °\mathrm{C}$ from experiments [31] (shown by symbols and plotted against the bottom and left axes) and simulations (indicated by curves and plotted against the top and right axes) for Zw47 (PPC158k), Zw34 (PPC111k), and Zw21 (PPC69k) from left to right.

Figure 3

Viscosity growth curves under uniaxial elongation at $T=70 °\mathrm{C}$ for Zw47 (PPC158k, panel (a)), Zw34 (PPC111k, panel (b)), and Zw21 (PPC69k, panel (c)) from top to bottom. Experimental data [32] are shown by circles. Simulation results with and without the change of friction (according to Euqation (2)) are indicated by red solid and black broken curves. Red broken curves show the linear viscoelastic envelopes. The strain rates are $2.8\times {10}^{-1}, 8.5\times {10}^{-2}, 2.8\times {10}^{-2}, 5.6\times {10}^{-3}, 1.8\times {10}^{-3}, 5.6\times {10}^{-4}, \mathrm{and} 1.8\times {10}^{-4}$ s⁻¹ for Zw47 (PPC158k), $3\times {10}^{-3}, 1\times {10}^{-2}, 3\times {10}^{-2}, 1\times {10}^{-1}, \mathrm{and} 3\times {10}^{-1}$ s⁻¹ for Zw34 (PPC111k), and $4\times {10}^{-3}, 6.1\times {10}^{-3}, 4\times {10}^{-2}, 6.1\times {10}^{-2}, 4\times {10}^{-1}, \mathrm{and} 6.1\times {10}^{-1}$ s⁻¹ for Zw21 (PPC69k), respectively.

Figure 4

Steady-state elongational viscosity (a) and the friction (b) at $T=70 °\mathrm{C}$ as a function of the strain rate for Zw47 (PPC158k, black), Zw34 (PPC111k, red), and Zw21 (PPC69k, blue). Experimental data [32] are shown by unfilled circles. In the top panel (a), simulation results with and without the friction change (according to Equation (2)) are drawn by solid and broken curves, respectively.

Figure 5

Simulation results for a polystyrene melt with $M_w=520 \mathrm{k}$ and $M_w/M_n=$ 1.3 for linear viscoelasticity (a), elongational growth curve (b), and steady-state elongational viscosity (c) at $T=130 °\mathrm{C}$. Circles and curves are experimental and simulation results, respectively. Solid and broken curves in the panel (b) exhibit the simulation results with the friction change and the linear viscoelastic envelope. The strain rates are $2.8\times {10}^{-4}$, $8.4\times {10}^{-4}$, and $2.8\times {10}^{-3}$ s⁻¹, from left to right. In the panel (c), solid and broken curves correspond to the simulation with and without the friction change.

Figure 6

Comparison between Zw47 (the polydispersity index of 1.3, black curves) and Z47 (monodisperse, red curves) for linear viscoelasticity (a) and steady-state elongational viscosity plotted against strain rate (b). The experimental data for PPC158 k are also shown by symbols.