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

Using Molecular-Level Simulations to Determine Diffusivities in the Classroom

We present work describing the practical use of molecular-level simulations to determine diffusivities in a course targeted at the general audience of first-year chemical engineering graduate students. We show how the simulation techniques can be used to directly complement traditional methods for obtaining diffusivities. Our philosophy is to provide a utilitarian tool that can be used in a manner analogous to existing techniques to obtain diffusion coefficients. The advantage of the simulation approach is that it will work in the absence of experimental data and can be easily applied to multicomponent mixtures with an arbitrary number of species. In the implementation of this work, we remain keenly aware of constraints due to time, computational resources, money, and target-audience qualifications, so that the implementation is feasible. We demonstrate that these simulations require only a few minutes to run on a contemporary (AMD Athlon 850 MHz) processor. In our approach we outline the basic steps necessary to obtain a transport diffusivity via molecular-level simulations. We also provide an example problem, where we compare the results of the simulation to the predictions from corresponding states and kinetic theory

Dynamics of Individual Molecules of Linear Polyethylene Liquids under Shear: Atomistic Simulation and Comparison with a Free-draining Bead-rod Chain

Nonequilibrium molecular dynamics (NEMD) simulations of a dense liquid composed of linear polyethylene chains were performed to investigate the chain dynamics under shear. Brownian dynamics (BD) simulations of a freely jointed chain with equivalent contour length were also performed in the case of a dilute solution. This allowed for a close comparison of the chain dynamics of similar molecules for two very different types of liquids. Both simulations exhibited a distribution of the end-to-end vector, |Rete|, with Gaussian behavior at low Weissenberg number (Wi). At high Wi, the NEMD distribution was bimodal, with two peaks associated with rotation and stretching of the individual molecules. BD simulations of a dilute solution did not display a bimodal character; distributions of |Rete| ranged from tightly coiled to fully stretched configurations. The simulations revealed a tumbling behavior of the chains and correlations between the components of Rete exhibited characteristic frequencies of tumbling, which scaled as Wi−0.75. Furthermore, after a critical Wi of approximately 2, another characteristic time scale appeared which scaled as Wi−0.63. Although the free-draining solution is very different than the dense liquid, the BD simulations revealed a similar behavior, with the characteristic time scales mentioned above scaling as Wi−0.68 and Wi−0.66

Atomistic Simulation of Energetic and Entropic Elasticity in Short-chain Polyethylenes

The thermodynamical aspects of polymeric liquids subjected to uniaxial elongational flow are examined using atomistically detailed nonequilibrium Monte Carlo simulations. In particular, attention is paid to the energetic effects, in addition to the entropic ones, which occur under conditions of extreme deformation. Atomistic nonequilibrium Monte Carlo simulations of linear polyethylene systems, ranging in molecular length from C24 to C78 and for temperatures from 300 to 450 K, demonstrate clear contributions of energetic effects to the elasticity of the system. These are manifested in a conformationally dependent heat capacity, which is significant under large deformations. Violations of the hypothesis of purely entropic elasticity are evident in these simulations, in that the free energy of the system is demonstrated to be composed of significant energetic effects under high degrees of orientation. These arise mainly from favorable intermolecular side-to-side interactions developing in the process of elongation due to chain uncoiling and alignment in the direction of extension

Energetic and Entropic Elasticity of Nonisothermal Flowing Polymers: Experiment, Theory, and Simulation

The thermodynamical aspects of polymeric liquids subjected to nonisothermal flow are examined from the complementary perspectives of theory, experiment, and simulation. In particular, attention is paid to the energetic effects, in addition to the entropic ones, that occur under conditions of extreme deformation. Comparisons of experimental measurements of the temperature rise generated under elongational flow at high strain rates with macroscopic finite element simulations offer clear evidence of the persistence and importance of energetic effects under severe deformation. The performance of various forms of the temperature equation are evaluated with regard to experiment, and it is concluded that the standard form of this evolution equation, arising from the concept of purely entropic elasticity, is inadequate for describing nonisothermal flow processes of polymeric liquids under high deformation. Complete temperature equations, in the sense that they possess a direct and explicit dependence on the energetics of the microstructure of the material, provide excellent agreement with experimental data

Energetic and Entropic Elasticity of Nonisothermal Flowing Polymers: Experiment, Theory, and Simulation

The thermodynamical aspects of polymeric liquids subjected to nonisothermal flow are examined from the complementary perspectives of theory, experiment, and simulation. In particular, attention is paid to the energetic effects, in addition to the entropic ones, that occur under conditions of extreme deformation. Comparisons of experimental measurements of the temperature rise generated under elongational flow at high strain rates with macroscopic finite element simulations offer clear evidence of the persistence and importance of energetic effects under severe deformation. The performance of various forms of the temperature equation are evaluated with regard to experiment, and it is concluded that the standard form of this evolution equation, arising from the concept of purely entropic elasticity, is inadequate for describing nonisothermal flow processes of polymeric liquids under high deformation. Complete temperature equations, in the sense that they possess a direct and explicit dependence on the energetics of the microstructure of the material, provide excellent agreement with experimental data

Self-Consistent Multiscale Modeling in the Presence of Inhomogeneous Fields

Molecular dynamics (MD) simulations of a Lennard–Jones fluid in an inhomogeneous external field generate steady-state profiles of density and pressure with nanoscopic heterogeneities. The continuum level of mass, momentum, and energy transport balances is capable of reproducing the MD profiles only when the equation of state for pressure as a function of density is extracted directly from the molecular level of description. We show that the density profile resulting from simulation is consistent with both a molecular-level theoretical prediction from statistical mechanics as well as the solution of the continuum-level set of differential equations describing the conservation of mass and momentum

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. (c) 2005 American Institute of Physics.close161

Absorbing Boundary Conditions for Molecular Dynamics and Multiscale Modeling

We present an application of differential equation based local absorbing boundary conditions to molecular dynamics. The absorbing boundary conditions result in the absorbtion of the majority of waves incident perpendicular to the bounding surface. We demonstrate that boundary conditions developed for the wave equation can be applied to molecular dynamics. Comparisons with damping material boundary conditions are discussed. The concept is extended to the formulation of an atomistic-continuum multiscale scheme with handshaking between the regions based on absorbing boundary conditions. The multiscale model is effective in minimizing spurious reflections at the interface

Eddy heat fluxes from direct current measurements of the Antarctic Polar Front in Shag Rocks Passage

Determining meridional heat flux in the Southern Ocean is critical to the accurate understanding and model simulation of the global ocean. Mesoscale eddies provide a significant but poorly-defined contribution to this transport. An eighteen-month deep-water current meter array deployment in Shag Rocks Passage (53°S, 48°W) between May 2003 and November 2004 provides estimates of the eddy flux of heat across the Polar Front. We calculate a statistically nonzero (99% level), vertically coherent local poleward heat flux of 12.0 ± 5.8 kW m-2 within the eddy frequency band at ~2750 m depth. Exceeding previous deep-water estimates by up to an order of magnitude, this highlights the large spatial variation in flux estimates and illustrates that constriction of circumpolar fronts facilitates large eddy transfers of heat southwards