1. Introduction

Nonequilibrium molecular dynamics (NEMD) simulations play a significant role in our understanding of rheological and structural behaviors of polymeric materials in flowing systems, which is important not only in practical polymer processing, but also in advancing our knowledge of fundamental characteristics of chain molecules, i.e., viscoelasticity.¹ In our previous paper², we have developed so-called proper-SLLOD (or p-SLLOD) algorithm. Furthermore, more recently using the p-SLLOD algorithm, we have recently performed NEMD simulations of short-chain alkanes, such as C₁₀H₂₂ (decane), C₁₆H₃₄ (hexadecane) and C₂₄H₅₀ (tetracosane) under planar elongation flow (PEF) ³ extending work done by Cui et al. for steady-state shear flow to steady-state PEF⁴. Many interesting results have been observed there. We also extended our NEMD simulations of PEF from the short-chain alkanes performed in the previous paper⁵ to the more complex linear polyethylene melts of C₅₀H₁₀₂ up to C₁₂₈H₂₅₈. In this study, we perform NEMD simulations of complex linear polyethylene melt of C₅₀H₁₀₂, C₇₈H₁₅₈ and C₁₂₈H₂₅₈ under PCF and compare it to our previous results of short-chain and long-chain alkanes in both PCF and PEF.  

2. Technical approach

In the present work, the same temperature, T=450 K, was used for all the systems. A different density, however, was employed for each system: r=0.7426 g/cm³ for C₅₀H₁₀₂, r=0.7640 g/cm³ for C₇₈H₁₅₈, and r=0.7754 g/cm³ for C₁₂₈H₂₅₈. Specifically, we employed 120 molecules for C₅₀H₁₀₂ (total 6000 interaction sites), 160 molecules for C₇₈H₁₅₈ (total 12480 interaction sites), and 256 molecules for C₁₂₈H₂₅₈ (total 32768 interaction sites). The reduced shear rate employed in this study ranges from =0.0002 to 1.0. The box dimensions (x•y•z in unit of Å) of 93.02•45•45 were employed for C₅₀H_102, 130.5•54•54 for C₇₈H_158, and 212.7•68•68 for C₁₂₈H_258.

  3. Results and Discussion

The longest relaxation times, the so-called Rouse time t_Rouse, were determined by the time correlation function of the end-to-end vector of chains using equilibrium molecular dynamics simulations: t_Rouse=500 ps for C₅₀H₁₀₂, t_Rouse =1.4 ns for C₇₈H₁₅₈, and t_Rouse =5.5 ns for C₁₂₈H₂₅₈. The corresponding reduced critical elongation rates are found to be =0.0047 for C₅₀H₁₀₂, =0.0016 for C₇₈H₁₅₈, and =0.00043 for C₁₂₈H₁₅₈. Approximately, above the critical shear rate for each system, the shear viscosity, h, showed shear-thinning behavior as shear rate increased for all the systems in this study. In our previous study of short-chain alkanes under PCF and PEF, we observed tension-thinning behavior. Linear polyethylene melts under PEF also showed this behavior. The minimum behavior in the hydrostatic pressure was observed for all the systems. In the linear polymer melt under PEF, this behavior appeared to originate from the change in the intermolecular LJ potential energy with shear rate through the two competing factors of chain alignment (static factor) and intermolecular collision (dynamic factor). As for two important structural quantities, the mean square end-to-end distance of chains, <R_ete²>, and the mean square radius of gyration of chains, <R_g²>, it was observed and compared with other systems. Further details of chain conformation have been represented well by investigating the conformation tensor, which is considered an important physical quantity in polymer rheology.   Several interesting differences between the polyethylene molecules under shear and elongational flows will also be discussed.  

4. References

¹F. A. Morrison, Understanding Rheology (Oxford University Press, New York, 2001).

²C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005).

³C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 184906 (2005).

⁴S. T. Cui, S. A. Gupta, and P. T. Cummings, J. Chem. Phys. 105, 1214 (1996).

⁵C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. in press.