Randall S. Dumont

Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at low pressurea)

Nonequilibrium molecular dynamics (NEMD) simulations are used to investigate pressure-driven water flow passing through carbon nanotube (CNT) membranes at low pressures (5.0 MPa) typical of real nanofiltration (NF) systems. The CNT membrane is modeled as a simplified NF membrane with smooth surfaces, and uniform straight pores of typical NF pore sizes. A NEMD simulation system is constructed to study the effects of the membrane structure (pores size and membrane thickness) on the pure water transport properties. All simulations are run under operating conditions (temperature and pressure difference) similar to a real NF processes. Simulation results are analyzed to obtain water flux, density, and velocity distributions along both the flow and radial directions. Results show that water flow through a CNT membrane under a pressure difference has the unique transport properties of very fast flow and a non-parabolic radial distribution of velocities which cannot be represented by the Hagen-Poiseuille or Navier-Stokes equations. Density distributions along radial and flow directions show that water molecules in the CNT form layers with an oscillatory density profile, and have a lower average density than in the bulk flow. The NEMD simulations provide direct access to dynamic aspects of water flow through a CNT membrane and give a view of the pressure-driven transport phenomena on a molecular scale.

Simulation of many-spin system dynamics via sparse matrix methodology

A sparse-matrix-based numerical method is constructed to simulate NMR spectra of many-spin systems, including the effects of chemical exchange and/or relaxation. The associated computational demands are predicted to scale like O(22n), as the number of spins n increases. This is vastly superior to the inevitable O(26n) scaling of conventional Householder-based methodology. The improved scaling is verified via numerical computations of simple isomerization systems with four to nine spins. The new method is based on splitting the propagator and use of Chebyshev polynomial expansion of the exponential function.

Nonequilibrium molecular dynamics simulation of pressure-driven water transport through modified CNT membranes.

Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effect of water-membrane interactions on the transport properties of pressure-driven water flow passing through carbon nanotube (CNT) membranes. The CNT membrane is modified with different physical properties to alter the van der Waals interactions or the electrostatic interactions between water molecules and the CNT membranes. The unmodified and modified CNT membranes are models of simplified nanofiltration (NF) membranes at operating conditions consistent with real NF systems. All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K), constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The water flow rate, density, and velocity (in flow direction) distributions are obtained by analyzing the NEMD simulation results to compare transport through the modified and unmodified CNT membranes. The pressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted by the Navier-Stokes equations. For water passing through the modified membrane with stronger van der Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities. These investigations show the effect of water-CNT membrane interactions on water transport under NF operating conditions. This work can help provide and improve the understanding of how these membrane characteristics affect membrane performance for real NF processes.

Argon cluster evaporation dynamics

Expansion of argon clusters in a vacuum is simulated via molecular dynamics computations. The resulting evaporation dynamics is investigated with observations of temperature and pV energy loss curves. Observed cooling curves (T vs n) and collapse curves (pV/n vs n) are found to depend on final cluster size but not the initial cluster ensemble. The evaporation mechanism consists of an initial rapid cooling‐and‐collapse stage of a preliquid dense‐gas‐like cluster, followed by ‘‘equilibrium’’ evaporation, and then another cooling stage of the resulting relatively incompressible liquidlike subcluster. Elements of this dynamics evaporation mechanism are tested by examination of finite n phase diagrams constructed using Metropolis Monte Carlo simulations of the fixed T and p ensemble.

Dual Lanczos simulation of dynamic nuclear magnetic resonance spectra for systems with many spins or exchange sites

A stable formulation of dual Lanczos tridiagonalization of non-Hermitian matrices, along with solution of tridiagonal systems of equations, is used to simulate liquid nuclear magnetic resonance (NMR) spectra for systems with chemical exchange. The method provides computer storage and performance advantages over our previously developed sparse-matrix methodology [Dumont, Jain, and Bain, J. Chem. Phys. 106, 5928 (1997)], in addition to the incorporation of full blocking of the system Liouvillian with respect to the conservation of z magnetization. Convergence with respect to number of Lanczos iterations is investigated in some detail in order to achieve optimal performance.

Monte Carlo sampling for atomic and molecular clusters with fixed energy and angular momentum

This paper presents a Monte Carlo method for sampling atomic and molecular cluster states according to the fixed energy and angular momentum ensemble, i.e., the EJ ensemble. Features of the methodology include the avoidance of numerical problems inherent in a straightforward implementation of Monte Carlo to EJ‐ensemble averaging. In addition, qualitative characteristics of atomic momentum distribution within a cluster are extracted from exact analytic formulas, and illustrated numerically for argon clusters.

Statistical dynamics and kinetics of unimolecular processes

The statistical theory of arbitrary unimolecular reactions is developed with an ergodic theoretic basis. In the process, unimolecular kinetics is derived from dynamics, in terms of well‐defined mixing and time‐scale assumptions. The statistical theory is then taken beyond kinetics via the new ‘‘generalized flux renewal model’’ which incorporates ‘‘nonstatistical effects’’ due to nonzero relaxation time and direct components. Effects of direct component delays and nonzero relaxation times are examined closely. In particular, an estimate of the longest reaction time scale accounting for these effects is provided.

Statistical dynamical theory of isomerization

An ergodic theoretic basis for the statistical theory of isomerization is provided. A strong mixing assumption is used to derive the absorbing boundary method of computing isomerization dynamics. In addition, the absorbing boundary method is shown to fail in systems exhibiting certain long‐time correlations. In order to account for these correlations, we construct a new statistical theory termed the ‘‘flux renewal model.’’ The new model is based on the consistent application of strong mixing, with the incorporation of nonzero relaxation time. It utilizes statistical calculations to eliminate the explicit computation of long‐time trajectories exhibiting characteristics of chaos. The flux renewal model is tested and compared with the absorbing boundary method via numerical computations of the isomerization dynamics of the chaotic siamese stadium billiard. The flux renewal model is shown to give the best approximation to the isomerization flux–flux correlation. It does this by simultaneously handling nonstat...

Nonstatistical inversion dynamics of T‐shaped Ar3

Numerical computations reveal nonstatistical characteristics of microcanonical T‐shaped Ar3 inversion at energies associated with strongly chaotic dynamics. Nonstatisticality is most pronounced at higher energies where internal relaxation time scales are comparable to the inversion time. At such energies, population decay curves exhibit damped oscillations about the equilibrium population. At energies just above the inversion threshold, where inversion is very slow, near statistical nonoscillatory behavior is observed. The ‘‘absorbing barrier method’’ of Straub and Berne [J. Chem. Phys. 83, 1138 (1985)] is shown to provide a reasonable model for observed population decays. Characteristics of corresponding gap distributions are described in terms of an adapted ‘‘delayed lifetime gap model.’’ Analysis of the model which combines the absorbing barrier method and the adapted delayed lifetime gap model provides insight into the observation of both oscillatory and nonoscillatory population decays. Specifically,...

EJ ensemble momentum sampling

The ‘‘EJ’’ ensemble (i.e., ensemble with fixed total energy and angular momentum) momentum sampling algorithm recently proposed by Nyman et al. [J. Chem. Phys. 93, 6767 (1990)] is verified to give correctly distributed atomic momenta. The proof is based on explicit analytic determination of the atomic momentum distribution generated by the algorithm. The simpler case of microcanonical momentum sampling is also treated using similar methodology.