Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method

A finite element particle transport model, consisting of Navier-Stokes and continuity equations defined in arbitrary Lagrangian-Eulerian (ALE) kinematics, is employed to describe the motion of a rigid uncharged spherical particle in a cylindrical channel of uniform cross-section. The wall correction factors for the spherical particle moving with a fluid confined in an infinitely long cylindrical channel, as well as in finite length channels are presented. Two finite channel effects are considered, namely, motion of the particle at the entrance and exit of an open channel, and the motion of a particle toward the capped end of the channel. The numerical model demonstrates good agreement with many existing analytical results for infinite channels in the Stokes flow regime. Simple correlations for the hindrance factors are presented.     

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

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.     

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

On the role of scattering resonances in the F+HD reaction dynamics

We study scattering resonances in the F+HD-->HF+D reaction using a new method for direct evaluation of the lifetime Q-matrix [Aquilanti et al., J. Chem. Phys. 2005, 123, 054314]. We show that most of the resonances are due to van der Waals states in the entrance and exit reaction channels. The metastable states observed in the product reaction channel are assigned by calculating the energy levels and wave functions of the HF...D van der Waals complex. The behavior of resonance energies, widths, and decay branching ratios as functions of total angular momentum is analyzed. The effect of isotopic substitution on resonance energies and lifetimes is elucidated by comparison with previous results for the F+H2 reaction. It is demonstrated that HF(v'=3) products near threshold are formed by decay of the narrow resonances supported by van der Waals wells in the exit channel. State-to-state differential cross sections in the HF(v'=3) channel exhibit characteristic forward-backward peaks due to the formation of a long-lived metastable complex. The role of the exit-channel resonances in the interpretation of molecular beam experiments is discussed.     

Comparative study between continuum and atomistic approaches of liquid flow through a finite length cylindrical nanopore

Steady state pressure driven flow of liquid argon through a finite length cylindrical nanopore was investigated numerically by classical Navier-Stokes (NS) hydrodynamic models and nonequilibrium molecular dynamics (MD) simulations. In both approaches, the nanopore was nominally 2.2 nm in diameter and 6 nm long. For the MD simulations, the intermolecular properties of the walls were specified independently from the liquid. Comparisons between the approaches were made in terms of the gross feature of total flow rate through the nanopore, as well as the more refined considerations of the spatial distributions of pressure, density, and velocity. The results showed that for the NS equations to predict the same trends in total flow rate with increasing pressure difference as the MD simulation, submodels for variations in density and viscosity with pressure are needed to be included. The classical NS boundary conditions quantitatively agreed with the flow rate predictions from MD simulations only under the condition of having a neutral-like solid-liquid interaction. Under these conditions, the NS and MD models also agreed well in streamwise distributions of pressure, density, and velocity, but not in the radial direction.     

An improved potential energy surface for the F+H2 reaction

A new ground state potential energy surface has been developed for the F+H₂ reaction. Using the UCCSD(T) method, ab initio calculations were performed for 786 geometries located mainly in the exit channel of the reaction. The new data was used to correct exit channel errors that have become apparent in the potential energy surface of Stark and Werner [J. Chem. Phys. 104 (1996) 6515]. While the entrance channel and saddlepoint properties of the Stark–Werner surface are unchanged on the new potential, the exit channel behavior is more satisfactory. The exothermicity on the new surface is much closer to the experimental value. The new surface also greatly diminishes the exit channel van der Waals well that was too pronounced on the Stark–Werner surface. Several preliminary dynamical scattering calculations were carried out using the new surface for total angular momentum equal to zero for F+H₂ and F+HD. It is found that gross features of the reaction dynamics are quite similar to those predicted by the Stark–Werner surface, in particular the reactive resonance for F+HD and F+H₂ survive. However, the most of the exit channel van der Waals resonances disappear on the new surface. It is predicted that the differential cross-sections at low collision energy for the F+H₂ reaction may be drastically modified from the predictions based on the Stark–Werner surface.     

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.     

Simulation Study on Translocation of Confined Chain Through Interacting Nanopore

The translocation of a confined polymer chain through an interacting nanopore has been studied using two-dimensional bond fluctuation model with Monte Carlo dynamics. For different pore-polymer interaction, the average escaping time〈Τesc〉of the polymer chain through the nanopore, increases roughly linearly with the chain length and the nanopore length, respectively. However, the large repulsive and attractive pore-polymer interaction adds the difficulty of the monomers of the chain entering and leaving the nanopore, respec-tively, leading to the nonmonotonical dependence of〈Τesc〉on the pore-polymer interaction. The detailed translocation dynamics of the chain through the interacting nanopore is inves-tigated too.     

Cavitation of polyethylene during extrusion processing instabilities

We present observations of cavitation that occur inside a capillary die during extrusion of polyethylene. This phenomenon was observed over the last 1.5 mm of the capillary tube immediately upstream of the exit. We observed spontaneous formation of voids near the wall that grew to a typical length and width of 150 μm, and then shrank and disappeared over a time frame of approximately 20 ms. From velocity measurements of these structures, we concluded that their width in the radial direction was smaller than in the axial and lateral directions, and they were near the wall. The shape of the cavities was highly irregular. We assessed the roles of extensional stress and shear stress at the exit region and concluded that they were not the direct cause of cavitation. Rather, cavitation occurs in conjunction with an upstream rupture of the polymer that occurs in the contraction region leading into the capillary tube (gross melt fracture). We argue that the exit region does, however, serve as the initiation point of the cavitation because of a combination of the reduced pressure and extensional stress. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2791–2799, 2002     

Quasi-classical trajectories study of Ne79Br2(B) vibrational predissociation

A full-dimensional quasi-classical trajectories study on the vibrational predissociation (VP) of the Ne79Br2(B) complex is presented. Following the most recent experiments, the Br2(B) vibrational levels v'=16-29 were explored. The total angular momentum, J, was taken to be zero, and a semiclassical Franck-Condon model to compute initial conditions from quantum distributions was employed. Predissociation lifetimes were extracted from Ne79Br2 population decay by using two different exponential laws. Predicted lifetimes are in excellent agreement with the last experimental results [J. A. Cabrera, C. R. Bieler, B. C. Olbricht, W. E. van der Veer and K. C. Janda, J. Chem. Phys., 2005, 123, 054311]. The Br2 fragment ro-vibrational distributions resulting from the VP of the molecule were obtained from the statistics of classical magnitudes using the standard binning procedure. Computed rotational distributions (for the Deltav'=-1, -2 channels) are also in very good agreement with the experimental results [M. Nejad-Sattari and T. A. Stephenson, J. Chem. Phys., 1997, 106 5454]. The influence of two quantum effects-the closing of the Deltav'=-1 dissociation channel and the intramolecular vibrational relaxation (IVR) mechanism-on the agreement with experimental rotational distributions, is discussed. Due to the classical character of our calculations and the binning procedure we used, the agreement of computed vibrational distributions with experimental and quantum theoretical is qualitative. For instance, for v'=28-for which the Deltav'=-1 channel is experimentally found to be closed-the Deltav'=-2 channel becomes statistically more significant. A discussion on the viability of similar quasi-classical methods to model the VP dynamics of analogous clusters is presented.     

Analytical method for the representation of atoms-in-molecules densities

We present analytic refinements and applications of the deformed atomic densities method [Fernández Rico, J.; López, R.; Ramírez, G. J Chem Phys 1999, 110, 4213-4220]. In this method the molecular electron density is partitioned into atomic contributions, using a minimal deformation criterion for every two-center distributions, and the atomic contributions are expanded in spherical harmonics times radial factors. Recurrence relations are introduced for the partition of the two-center distributions, and the final radial factors are expressed in terms of exponential functions multiplied by polynomials. Algorithms for the practical implementation are developed and tested, showing excellent performances. The usefulness of the present approach is illustrated by examining its ability to describe the deformation of atoms in different molecular environments and the relationship between these atomic densities and some chemical properties of molecules.     

Phase space analysis of formaldehyde dissociation branching and comparison with quasiclassical trajectory calculations

We investigate the dependence of the branching ratio of formaldehyde dissociation to molecular and radical products on the total energy and angular momentum and the HCO rotational state distributions by using a combination of transition state/Rice-Ramsperger-Kassel-Marcus theory and phase space theory. Comparisons are made with recent quasiclassical trajectory (QCT) calculations [Farnum, J. D.; Zhang, X.; Bowman, J. M. J. Chem. Phys. 2007, 126, 134305]. The combined phase-space analysis is in semiquantitative agreement with the QCT results for the rotational distributions of HCO but is only in qualitative agreement for the branching ratio. Nevertheless, that level of agreement serves to provide insight into the QCT results, which showed suppression of the radical channel with increasing total angular momentum for a fixed total energy.     

Diffusion model of solute dynamics in a membrane channel: mapping onto the two-site model and optimizing the flux

The steady-state flux through a singly occupied membrane channel is found for both discrete and continuum models of the solute dynamics in the channel. The former describes the dynamics as nearest-neighbor jumps between N sites, while the latter assumes that the molecule diffuses in a one-dimensional potential of mean force. For both models it is shown that the flux is the same as that for a simple two-site model with appropriately chosen rate constants, which contain all the relevant information about the more detailed dynamics. An interesting consequence of single occupancy is that the flux has a maximum as a function of the channel-solute interaction. If this interaction is too attractive, the molecule will never leave the channel, thus blocking it for the passage of other molecules. If it is too repulsive, the solute molecule will never enter the channel. Thus the flux vanishes in the two limits and, hence, has a maximum somewhere in-between. In the framework of the diffusion model, we find the optimal intrachannel potential of mean force that maximizes the flux using the calculus of variations. For a symmetric channel this potential is flat and occupies the entire channel. In the general case of an asymmetric channel, the optimal potential is obtained by tilting the optimal flat potential for the corresponding symmetric channel around the channel center, so that the solute is driven towards the reservoir with the lower solute concentration by a constant force. This implies that the flux is higher when the solute binding near the channel exit is stronger than that near the entrance.     

Modeling electrochemical deposition inside nanotubes to obtain metal-semiconductor multiscale nanocables or conical nanopores

Nanocables with a radial metal-semiconductor heterostructure have recently been prepared by electrochemical deposition inside metal nanotubes. First, a bare nanoporous polycarbonate track-etched membrane is coated uniformly with a metal film by electroless deposition. The film forms a working electrode for further deposition of a semiconductor layer that grows radially inside the nanopore when the deposition rate is slow. We propose a new physical model for the nanocable synthesis and study the effects of the deposited species concentration, potential-dependent reaction rate, and nanopore dimensions on the electrochemical deposition. The problem involves both axial diffusion through the nanopore and radial transport to the nanopore surface, with a surface reaction rate that depends on the axial position and the time. This is so because the radial potential drop across the deposited semiconductor layer changes with the layer thickness through the nanopore. Since axially uniform nanocables are needed for most applications, we consider the relative role of reaction and axial diffusion rates on the deposition process. However, in those cases where partial, empty-core deposition should be desirable (e.g., for producing conical nanopores to be used in single nanoparticle detection), we give conditions where asymmetric geometries can be experimentally realized.     

Effect of Interaction upon Translocation of Confined Polymer Chain Through Nanopore

The effect of the interaction between nanopore and chain monomer on the translocation of a single polymer chain confined in a finite size square through an interacting nanopore to a large space has been studied by two-dimensional bond fluctuation model with Monte Carlo simulation. Results indicate that the free energy barrier before the successful translocation of the chain depends linearly on the chain length as well as the nanopore length for different pore-polymer interaction, and the attractive interaction reduces the free energy barrier, leading to the reduction of the average trapping time.     

State-to-state chemiluminescence in reactions of Mn atoms with S2Cl2

A combined experimental and time-dependent density functional theory (TDDFT) investigation of the title reaction is presented. Both 'hot' and 'cold' laser-ablated Mn atom beams have been employed to determine the translational excitation functions for production of MnCl*(c(5)Σ(+), d(5)Π, e(5)Δ, e(5)Σ(+), A(7)Π). Analysis in terms of the multiple line-of-centres approach shows that the 'hot' results are dominated by reactions of the second metastable state of Mn, z(8)P(J), all with very low thresholds; while the first metastable state, a(6)D(J), and the ground state, a(6)S, are the precursors in the 'cold' results, all with significant excess barriers. The post-threshold behaviour of most z(8)P(J) and a(6)D(J) reaction channels implies that the transition states shift forward with increasing collision energy. The TDDFT calculations suggest that, while Mn*(z(8)P(J), a(6)D(J)) insertion into the S-Cl bond is facile, the observed chemiluminescence channels mostly derive from abstraction in a preferred linear Mn-Cl-S configuration, and that the low z(8)P(J) thresholds originate from attractive but excited reagent potentials which either reach a seam of interactions in the product valley or (in the c(5)Σ(+) case) lead to an octet potential very close in energy to the product sextet. The excess barriers in the Mn*(a(6)D(J)) and Mn(a(6)S) reactions appear for the most part to derive from exit channel mixing with lower-lying product potentials. The observed transition state shifts are consistent with the system being forced to ride up the repulsive wall of the entrance valley as collision energy increases, the location of that wall being different for the z(8)P(J) and a(6)D(J) cases.     

Simulation study on the translocation of a partially charged polymer through a nanopore

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.     

Prediction of viscosity for molecular fluids at experimentally accessible shear rates using the transient time correlation function formalism

Nonequilibrium molecular dynamics (NEMD) simulations were performed and the transient time correlation function (TTCF) method applied to calculate the shear viscosity of n-decane. Using the TTCF method we were able to calculate the viscosity at shear rate orders of magnitude lower than is possible by direct NEMD simulation alone. For the first time for a molecular fluid, we were able to simulate shear rates accessible by experimental measurements, which are typically performed at shear rates well below those accessible by NEMD simulation. The TTCF method allows us to close the gap between the lowest shear rates accessible by MD simulation and the highest shear rates possible in experimental studies. Additionally a multiple time step method for Gaussian thermostatted SLLOD equations of motion was developed following earlier work [G. A. Pan et al., J. Chem. Phys. 122, 4114 (2005)] for atomic fluids.     

Single-file diffusion near channel boundaries

Molecular transport under the conditions of single-file diffusion was investigated near the channel boundaries by using dynamic Monte Carlo and molecular dynamics simulations of tracer exchange between single-file channels and their surroundings. The boundary effect reported in our recent papers (Vasenkov S.; K?rger, J. Phys. Rev. E 2002, 66, 052601. Schüring, A.; Vasenkov S.; Fritzsche, S. J. Phys. Chem. B 2005, 109, 16711) was studied in detail. This boundary effect is characterized by deviations of the intrachannel concentration profiles of tracer molecules observed in the case of single-file diffusion near the channel boundaries from the corresponding profiles typical for normal diffusion. It has been shown in our previous studies that these deviations occur under the conditions when the potential-energy difference inside and outside of single-file channels was both comparable and much larger than the activation energy of intrachannel diffusion. Here, we report a quantitative model describing the boundary effect. According to this model, an occurrence of the boundary effect is related to a complex character of diffusion in finite single-file systems. Such diffusion can be described by the following two types of movements occurring in parallel: (i) correlated displacements of all molecules in any particular channel and (ii) fast displacements of single molecules, which are uncorrelated with the displacements of all other molecules in the same channel. The latter displacements are restricted to a certain length interval that depends on the channel length and the channel occupancy. This length interval is shown to determine the extensions of the channel margins where the boundary effect is observed.