(543b) Rheological And Entanglement Characteristics Of Polyethylene Liquids And Visualization Of Conformational Changes In Shear And Elongational Flows

Abstract

In this work, we have performed nonequilibrium molecular dynamics simulations and investigated entanglement characteristics of a series of linear-chain polyethylene liquids C₂₄H₅₀, C₅₀H₁₀₂, C₇₈H₁₅₈, and C₁₂₈H₂₅₈under both planar Couette and planar elongational flow. We also presented visualizations of the molecular structure of these linear polyethylene liquids in the two types of flow and compare them with their equilibrium static structures.   

Technical approach

The NVT NEMD simulations were carried out using the p-SLLOD equations of motion [1] with the Nosé-Hoover thermostat [2] for arbitrary homogeneous flows. In planar Couette flow, the p-SLLOD equations of motion are same as the SLLOD equations of motion [1]. The p-SLLOD equations of motion with Nosé-Hoover thermostat were integrated using the reversible Reference System Propagator Algorithm (r-RESPA) with two time scales, as developed by Tuckerman et al. [3] and applied by Cui. et al. [4]. The long time scale was 2.35fs under PCF and 2.26fs under PEF and the short time scale was 0.452 under PCF and 0.226fs under PEF. We applied the Siepmann-Karaboni-Smit (SKS) united-atom model for linear alkanes [5] to both types of flow. For PEF, the Kraynik-Reinelt Boundary Condition (KRBC) [6] was adopted.

            The densities of each alkane are r = 0.7728 g/cm³ for C₂₄H₅₀, r = 0.7426 g/cm³ for C₅₀H₁₀₂, r = 0.7640 g/cm³ for C₇₈H₁₅₈, and r = 0.7754 g/cm³ for C₁₂₈H₂₅₈.  The simulations were conducted at the temperature of 450K, with the exception of C₂₄H₅₀, which was conducted at 333K under both PCF and PEF. For PCF, the simulated ranges for dimensionless shear rates r*=rt_ref  were 0.0005 °Âr* °Â1.0 for C₂₄H₅₀, 0.001°Â r* °Â1.0 for C₅₀H₁₀₂, 0.0002°Â r* °Â1.0 for C₇₈H₁₅₈, and 0.0001°Â r* °Â1.0 for C₁₂₈H₂₅₈.  For PEF, the equivalent ranges for ¥å*= ¥å t_ref were 0.0005°Â ¥å* °Â1.0 for C₂₄H₅₀, 0.001°Â ¥å* °Â0.2 for C₅₀H₁₀₂, 0.0002°Â ¥å* °Â0.2 for C₇₈H₁₅₈, and 0.0001°Â ¥å* °Â0.2 for C₁₂₈H₂₅₈.

We obtained both steady-state and transient system configurations at various strain rates and time values in order to investigate the entanglement properties. For steady-state properties, we collected 1037 configurational data points separated by Rouse time. For transient properties, 114 configurational data points are gathered. We also explored entanglement properties as functions of chain length. With these data, the Z-code [7,8] was applied for quantities characterizing the entanglement network. When applied to a polymeric configuration, it returns the instantaneous configuration of the complete entanglement network, from which various quantities, such as network anisotropy, contour length, stiffness, mesh size, number of knots, and further characteristics, can be evaluated.

Results

The viscosities for both flow fields became larger as the chain length increased.  We observed thinning behavior with strain rate in these liquids under both PCF and PEF.  The zero shear-rate viscosity for these polyethylenes was approximately equal to the zero elongation-rate viscosity.  All viscosities followed the power-law model.  Although the power-law index of first elongational viscosity under PEF increased as the chain length increased, it was independent of chain length under PCF. The behavior observed for the mean pressure and the intermolecular LJ potential displayed a distinct correlation for all polyethylene melts.  Similarly, the behavior of <R_ete²> and<R_g²> was related to the intramolecular LJ potential energy for all liquids.  The global and local chain flexibilities were examined by investigating the bond-torsional, bond-bending, and bond-stretching energies per mode. As might be expected, the chains are highly flexible at low strain rates, but become fairly stiff at the very highest strain rates simulated. 

The primitive path, L_pp, exhibits an overshoot during the onset of shear flow, and a monotonic increase toward its steady-state value under elongational flow. The variations of L_pp and tube diameter, a_pp, with strain rate are similar, and mirror the behavior of the intramolecular LJ energy and <R_ete²>. The number of entanglements monotonically decreases with strain rate in both PCF and PEF. The contour length and a_pp increase monotonically with chain length. These data provide first impressions about the dynamical behavior of the flow-induced network structure. To visualize of conformational changes, we made snapshots of the linear polyethylene liquids for analysis. The figure below displays some sample configurations from the simulations of C₁₂₈H₂₅₈ under equilibrium, PCF, and PEF, the latter two at the highest strain rate values simulated.  The upper simulation boxes display the entire number of chains in the systems and the lower boxes display the corresponding network entanglement structures.

References

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[2] D.J. Evans and G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids. Academic Press, New York, 1990.

[3] M. Tuckerman, B.J. Berne, and G.J. Martyna,  J. Chem. Phys. 97 (1992) 1990-2001.

[4] S.T. Cui, P.T. Cummings, and H.D. Cochran,  J. Chem. Phys. 104 (1996) 225-262.

[5] J.I. Siepmann, S. Karaboni, and B. Smit, Nature 365 (1993) 330-332.

[6] A.M. Kraynik and D.A. Reinelt, Int. J. Multiphase Flow 18 (1992) 1045-1059.

[7] M. Vladkov and J.L. Barrat,  Macromol. Theory Simul. 15 (2006) 252-262.

[8] M. Kröger, Comput. Phys. Commun. 168 (2005) 209-232.