Brian J. Edwards

Comparison of the Hydration and Diffusion of Protons in Perfluorosulfonic Acid Membranes with Molecular Dynamics Simulations

Classical molecular dynamics (MD) simulations were performed to determine the hydrated morphology and hydronium ion diffusion coefficients in two different perfluorosulfonic acid (PFSA) membranes as functions of water content. The structural and transport properties of 1143 equivalent weight (EW) Nafion, with its relatively long perfluoroether side chains, are compared to the short-side-chain (SSC) PFSA ionomer at an EW of 977. The separation of the side chains was kept uniform in both ionomers consisting of -(CF 2) 15- units in the backbone, and the degree of hydration was varied from 5 to 20 weight % water. The MD simulations indicated that the distribution of water clusters is more dispersed in the SSC ionomer, which leads to a more connected water-channel network at the low water contents. This suggests that the SSC ionomer may be more inclined to form sample-spanning aqueous domains through which transport of water and protons may occur. The diffusion coefficients for both hydronium ions and water molecules were calculated at hydration levels of 4.4, 6.4, 9.6, and 12.8 H 2O/SO 3H for each ionomer. When compared to experimental proton diffusion coefficients, this suggests that as the water content is increased the contribution of proton hopping to the overall proton diffusion increases.

Poisson bracket formulation of viscoelastic flow equations of differential type: A unified approach

The Hamiltonian formulation of equations in continuum mechanics through a generalized bracket operation is shown here to reproduce a variety of incompressible viscoelastic fluid models, including the Giesekus model (with particular cases the upper‐convected Maxwell and the Oldroyd‐B models), the FENE–P dumbbell, the Phan‐Thien/Tanner, the Leonov, the Bird/DeAguiar, and the bead–spring chain models. The analysis allows comparison of the differential models on a more fundamental level than previously possible by reformulating the equations in terms of the Hamiltonian (system energy) and the dissipation of the system expressed as functionals involving the velocity vector and structural parameter(s). In fact, all of these models involve only slight variations of the same general Hamiltonian and the dissipation tensor. An advantage of this formulation is the establishment of thermodynamic admissibility criteria which in complex flows can shed light on the range of validity and/or faithfulness of the numerical ...

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.

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.

An Analysis of Single and Double Generator Thermodynamic Formalisms for the Macroscopic Description of Complex Fluids

Several seemingly distinct formalisms have been developed recently as an alternative to the modern conventional approach (based on balance equations) for describing the mechanics and thermodynamics of complex fluids under dynamical conditions. Two of these approaches for isolated thermodynamic systems are the single generator Bracket Formalism and the more recent GENERIC Formalism incorporating a second generating functional. The interrelationships between these two alternate approaches are examined on an abstract level and direct connections are determined for some specific examples of fluid systems: a compressible, nonisothermal, isotropic fluid, an arbitrary fluid with an unspecified internal variable, and a chemically reactive fluid system. In so doing, new physical insight is obtained regarding the thermodynamic origins of key elements of each formalism. For purely macroscopic systems, it is shown that the GENERIC degeneracy condition on the dissipative metric matrix ensures global energy conservation, produces a symmetric metric matrix, and allows this matrix to be split into purely thermodynamic and kinematical components for systems with linear dissipation. The last realization leads to the natural driving forces expressed in bracket form being constrained Volterra derivatives of the entropy functional with respect to the system variables. The use of this concept in the Bracket Formalism provides a symmetric, bilinear dissipation bracket without the need for an explicit energy correction term.

Individual chain dynamics of a polyethylene melt undergoing steady shear flow

Synopsis Individual molecule dynamics have been shown to influence significantly the bulk rheological and microstructural properties of short-chain, unentangled, linear polyethylene liquids undergoing high strain-rate flows. The objective of this work was to extend this analysis to a linear polyethylene composed of macromolecules of a much greater length and entanglement density; i.e., a liquid consisting of C400H802 molecules, with approximately ten kinks per chain at equilibrium, as calculated by the Z1 code of Kr€ [Comput. Phys. Commun. 168, 209‐232 (2005)]. To achieve this, we performed nonequilibrium molecular dynamics (NEMD) simulations of a model system using the well-established potential model of Siepmann et al. [Nature 365, 330‐332 (1993)] for a wide range of Weissenberg numbers (Wi) under steady shear flow. A recent study by Baig et al. [Macromolecules 43, 6886‐6902 (2010)] examined this same system using NEMD simulations, but focused on the bulk rheological and microstructural properties as calculated from ensemble averages of the chains comprising the macromolecular liquids. In so doing, some key features of the system dynamics were not fully elucidated, which this article aims to highlight. Specifically, it was found that this polyethylene liquid displays multiple timescales associated with not only the decorrelation of the end-to-end vector (commonly related to the Rouse time or disengagement time, depending on the entanglement density of the liquid), but also ones associated with the retraction and rotation cycles of the individual molecules. Furthermore, when accounting for these individual chain dynamics, the “longest” relaxation time of the system was higher by a factor of 1.7, independent of shear rate, when calculated self-consistently due to the coupling of relaxation modes. Brownian dynamics (BD) simulations were also performed on an analogous free-draining bead-rod chain model to compare the rotation and retraction dynamics of a single chain in dilute solution with individual molecular motions in the melt. These BD simulations revealed that the dynamics of the free-draining chain are qualitatively and quantitatively similar to those of the individual chains comprising the polyethylene melt at strain rates in excess of Wi � 50, implying a possible breakdown of reptation theory in the high shear limit. An examination of the bulk-average properties revealed the effects of the chain rotation and retraction cycles upon commonly modeled microstructural properties, such as the distribution function of the chain end-to-end vector and the entanglement number density. V C 2015 The Society of Rheology.

A validation of the p-SLLOD equations of motion for homogeneous steady-state flows

A validation of the p-SLLOD equations of motion for nonequilibrium molecular dynamics simulation under homogeneous steady-state flow is presented. We demonstrate that these equations generate the correct center-of-mass trajectory of the system, are completely compatible with (and derivable from) Hamiltonian dynamics, satisfy an appropriate energy balance, and require no fictitious external force to generate the required homogeneous flow. It is also shown that no rigorous derivation of the SLLOD equations exists to date.

An Examination of the Validity of Nonequilibrium Molecular-dynamics Simulation Algorithms for Arbitrary Steady-state Flows

Nonlinear-response theory of nonequilibrium molecular-dynamics simulation algorithms is considered under the imposition of an arbitrary steady-state flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow [D. J. Evans and E. P. Morriss, Phys. Rev. A 30, 1528 (1984)], it is demonstrated that the p-SLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.

A comparison of simple rheological models and simulation data of n-hexadecane under shear and elongational flows

The microscopic origins of five rheological models are investigated by comparing their predictions for the conformation tensor and stress tensor with the same tensors obtained via nonequilibrium molecular dynamics simulations for n-hexadecane. Steady-state simulations were performed under both planar Couette and planar elongational flows, and the results of each are compared with rheological model predictions in the same flows, without any fitting parameters where possible. The use of the conformation tensor for comparisons between theory and experiment/simulation, rather than just the stress tensor, allows additional information to be obtained regarding the physical basis of each model examined herein. The character of the relationship between stress and conformation is examined using model predictions and simulation data.