Rheological and structural studies of linear polyethylene melts under planar elongational flow using nonequilibrium molecular dynamics simulations.

We present various rheological and structural properties of three polyethylene liquids, C50H102, C78H158, and C128H258, using nonequilibrium molecular dynamics simulations of planar elongational flow. All three melts display tension-thinning behavior of both elongational viscosities, eta1 and eta2. This tension thinning appears to follow the power law with respect to the elongation rate, i.e., eta approximately epsilon(b), where the exponent b is shown to be approximately -0.4 for eta1 and eta2. More specifically, b of eta1 is shown to be slightly larger than that of eta2 and to increase in magnitude with the chain length, while b of eta2 appeared to be independent of the chain length. We also investigated separately the contribution of each mode to the two elongational viscosities. For all three liquids, the intermolecular Lennard-Jones (LJ), intramolecular LJ, and bond-stretching modes make positive contributions to both eta1 and eta2, while the bond-torsional and bond-bending modes make negative contributions to both eta1 and eta2. The contribution of each of the five modes decreases in magnitude with increasing elongation rate. The hydrostatic pressure shows a clear minimum at a certain elongation rate for each liquid, and the elongation rate at which the minimum occurs appears to increase with the chain length. The behavior of the hydrostatic pressure with respect to the elongation rate is shown to correlate with the intermolecular LJ energy from a microscopic viewpoint. On the other hand, R(ete)2 and R(g)2 appear to be correlated with the intramolecular LJ energy. The study of the effect of the elongational field on the conformation tensor c shows that the degree of increase of tr(c)-3 with the elongation rate becomes stronger as the chain length increases. Also, the well-known linear reaction between sigma and c does not seem to be satisfactory. It seems that a simple relation between sigma and c would not be valid, in general, for arbitrary flows.

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations.

We report for the first time rheological and structural properties of liquid decane, hexadecane, and tetracosane using nonequilibrium molecular-dynamics (NEMD) simulations under planar elongational flow (PEF). The underlying NEMD algorithm employed is the so-called p-SLLOD algorithm [C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005)]. Two elongational viscosities are measured, and they are shown not to be equal to each other, indicating two independent viscometric functions in PEF. With an appropriate definition, it is observed that the two elongational viscosities converge to each other at very low elongation rates, i.e., in the Newtonian regime. For all three alkanes, tension-thinning behavior is observed. At high elongation rates, chains appear to be fully stretched. This is supported by the result of the mean-square end-to-end distance of chains (R(ete2)) and the mean-square radius of gyration of chains (R(g2)), and further supported by the result of the intramolecular Lennard-Jones (LJ) potential energy. It is also observed that (R(ete2)) and (R(g2)) show a different trend as a function of strain rate from those in shear flow: after reaching a plateau value, (R(ete2)) and (R(g2)) are found to increase further as elongation rate increases. A minimum in the hydrostatic pressure is observed for hexadecane and tetracosane at about epsilon(msigma2/epsilon)1/2=0.02. This phenomenon is shown to be associated with the intermolecular LJ potential energy. The bond-bending and torsional energies display similar trends, but a different behavior is observed for the bond-stretching energy. An important observation common in these three bonded-intramolecular interactions is that all three modes are suppressed to a small value at high elongation rates. We conjecture that a liquid-crystal-like, nematic structure is present in these systems at high elongation rates, which is characterized by a strong chain alignment with a fully stretched conformation.

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow.

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.

Structure of a sheared soft-disk fluid from a nonequilibrium potential.

The distortion of structure of a simple, inverse-12, soft-disk fluid undergoing two-dimensional plane Couette flow was studied by nonequilibrium molecular dynamics (NEMD) simulation and by equilibrium Monte Carlo (MC) simulation with a nonequilibrium potential, under which the equilibrium structure of the fluid is that of the nonequilibrium fluid. Extension of the iterative predictor-corrector method of [Phys. Rev. A 33, 3451 (1986)]] was used to extract the nonequilibrium potential with the structure input from the NEMD simulation. Very good agreement for the structural properties and pressure tensor generated by the NEMD and MC simulation methods was found, thus providing the evidence that nonequilibrium liquid structure can be accurately reproduced via simple equilibrium simulations or theories using a properly chosen nonequilibrium potential. The method developed in the present study and numerical results presented here can be used to guide and test theoretical developments, providing them with the "experimental" results for the nonequilibrium potential.

Distribution functions of a simple fluid under shear. II. High shear rates.

The distortion of structure of a simple, inverse 12 soft-sphere fluid undergoing plane Couette flow is studied by nonequilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) with a high-shear-rate version of the nonequilibrium (NE) potential obtained recently from the NE distribution function theory of Gan and Eu [Phys. Rev. A 45, 3670; 46, 6344 (1992)]. The theory suggests a NE potential under which the equilibrium structure of the fluid is that of a NE fluid, and also suggests a corresponding Ornstein-Zernike equation with its closure relations. As in the low-shear-rate case [Yu. V. Kalyuzhnyi, S. T. Cui, P. T. Cummings, and H. D. Cochran, Phys. Rev. E 60, 1716 (1999)] the agreement between EMD and the modified hypernetted chain version of the theory is good. Although the high-shear-rate version of the NE potential improves the agreement between NEMD and EMD results (in comparison with the low-shear-rate version), its predictions are still unsatisfactory. With the high-shear-rate NE potential, EMD gives qualitatively correct predictions only for the shift of the position of the first maximum of the NE distribution function. The corresponding changes in the magnitude of the first maximum predicted by EMD have an opposite direction in comparison with those predicted by NEMD. It is concluded that the NE potential used is not very successful, and more accurate models for the potential are needed.

Distribution functions of a simple fluid under shear: low shear rates.

Anisotropic pair distribution functions for a simple, soft sphere fluid at moderate and high density under shear have been calculated by nonequilibrium molecular dynamics, by equilibrium molecular dynamics with a nonequilibrium potential, and by a nonequilibrium distribution function theory [H. H. Gan and B. C. Eu, Phys. Rev. A 45, 3670 (1992)] and some variants. The nonequilibrium distribution function theory consists of a nonequilibrium Ornstein-Zernike relation, a closure relation, and a nonequilibrium potential and is solved in spherical harmonics. The distortion of the fluid structure due to shear is presented as the difference between the nonequilibrium and equilibrium pair distribution functions. From comparison of the results of theory against results of equilibrium molecular dynamics with the nonequilibrium potential at low shear rates, it is concluded that, for a given nonequilibrium potential, the theory is reasonably accurate, especially with the modified hypernetted chain closure. The equilibrium molecular-dynamics results with the nonequilibrium potential are also compared against the results of nonequilibrium molecular dynamics and suggest that the nonequilibrium potential used is not very accurate. In continuing work, a nonequilibrium potential better suited to high shear rates [H. H. Gan and B. C. Eu, Phys. Rev. A 46, 6344 (1992)] is being tested.

Transient rheology of a polyethylene melt under shear.

Using nonequilibrium molecular dynamics simulation, we have studied the response of a C100 model polymer melt to a step change from equilibrium to a constant, high shear rate flow. The transient shear stress of the model polymer melt exhibits pronounced overshoot at the strain value predicted by the reptation model, in striking similarity to melts of longer, entangled polymer governed by reptation motion. At the maximum of shear stress overshoot, the molecular orientational order and the alignment angle are found to be midway between those characteristic of Newtonian flow and full alignment with the flow. The Doi-Edwards theory is found to be applicable but only by taking into account the shear-rate-dependence of the terminal relaxation time. We further analyze the molecular origins of such behavior in short polymer chains by decomposing the total stress into the contributions from various molecular interactions.