On the statistics of dense,disordered assemblies: Equilibrium and dynamics

We consider implications of a lattice model which operates with a vacancy fraction h as a measure of structural disorder. Consequences for the configurational thermodynamics of one- and multicomponent systems and their phase equilibria are briefly indicated. The principal topic is the glassy state under steady state conditions, as well as the kinetics of relaxational processes toward equilibrium. The central role of the h-function in its dependence on variables of state is made evident among others by the connection between equation of state and thermo-elastic properties. Moreover, a dynamics of volume relaxation can be treated by means of a corresponding theory for the h-function. Applications of this theory to isothermal annealing below the glass temperature T_g, the response to a constant cooling rate of the melt through the transition zone, and the computation of a complex compression modulus are reviewed. The implications of vacancy cluster distributions for the analysis of positron spectroscopy are pointed out. Finally we indicate the basis for the development of correlations between T_g and structural parameters.     

Depletion potential in the infinite dilution limit

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the rational function approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are found.     

Molecular dynamics simulation of dense carbon dioxide fluid on amorphous silica surfaces

Molecular dynamics (MD) simulations of dense carbon dioxide on the amorphous dehydroxylated silica surfaces have been carried out. The adsorption potential surfaces of the silica solids have been obtained in order to evaluate the characteristics of the amorphous surfaces. The atom density profiles, adsorption free energy profiles, surface orientation order parameters, and radial distribution functions for the CO2 molecules have been presented in order to study the effect of the amorphous surfaces on the microscopic interfacial structure properties of the CO2 molecules. The translational diffusion and orientation rotation at silica surfaces have also been investigated. It was observed that there is marked hindrance of the translational diffusion and orientation rotation of CO2 molecules near amorphous silica surfaces.     

The vanishing limit of the square-well fluid: the adhesive hard-sphere model as a reference system

We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature Tc is estimated via a constant B2*c assumption, due to the highly nonlinear transformation between B2*c and Tc. This explains the previously observed validity of the law of corresponding states. The critical density rho c is also found to be constant when measured in units of the cube of the average distance between two bonded particles (1+0.5 delta)sigma. The possibility of describing the delta-->0 dependence with precise functional forms provides improved accurate estimates of the critical parameters of the adhesive hard-sphere model.     

A graph-based toy model of chemistry

Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the "look-and-feel" of chemistry: Molecules are represented as labeled graphs, i.e., by their structural formulas; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulas; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks: Diels-Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.     

A toy model of polymer stretching

We present an extremely simplified model of multiple-domain polymer stretching in an atomic force microscopy experiment. We portray each module as a binary set of contacts and decompose the system energy into a harmonic term (the cantilever) and long-range interaction terms inside each domain. Exact equilibrium computations and Monte Carlo simulations qualitatively reproduce the experimental sawtooth pattern of force-extension profiles, corresponding (in our model) to first-order phase transitions. We study the influence of the coupling induced by the cantilever and the pulling speed on the relative heights of the force peaks. The results suggest that the increasing height of the critical force for subsequent unfolding events is an out-of-equilibrium effect due to a finite pulling speed. The dependence of the average unfolding force on the pulling speed is shown to reproduce the experimental logarithmic law.     

Microchannel emulsification: from computational fluid dynamics to predictive analytical model

Emulsion droplet formation was investigated in terrace-based microchannel systems that generate droplets through spontaneous Laplace pressure driven snap-off. The droplet formation mechanism was investigated through high-speed imaging and computational fluid dynamics (CFD) simulation, and we found good agreement in the overall shape of the phases during droplet formation. An analytical model was derived from the insights that were gained from the CFD simulations, which describes the droplet diameter as a function of applied pressure. The analytical model covers the influence of both process parameters and geometry of the terrace well and can be used for fast optimization and evaluation studies.     

Water at a hydrophilic solid surface probed by ab initio molecular dynamics: inhomogeneous thin layers of dense fluid

We present a microscopic model of the interface between liquid water and a hydrophilic, solid surface, as obtained from ab initio molecular dynamics simulations. In particular, we focused on the (100) surface of cubic SiC, a leading semiconductor candidate for biocompatible devices. Our results show that in the liquid in contact with the clean substrate, molecular dissociation occurs in a manner unexpectedly similar to that observed in the gas phase. After full hydroxylation takes place, the formation of a thin (approximately 3 A) interfacial layer is observed, which has higher density than bulk water and forms stable hydrogen bonds with the substrate. The presence of this thin layer points at rather weak effects on the structural properties of water induced by a one-dimensional confinement between approximately 1.3 nm hydrophilic substrates. In addition, our results show that the liquid does not uniformly wet the surface, but molecules preferably bind along directions parallel to the Si dimer rows.     

Self-consistent fluid variational theory for the dissociation of dense nitrogen

The self-consistent fluid variational theory is used to calculate the pressure dissociation of dense nitrogen at high temperatures. The accurate high-pressure and high-temperature effective pair potentials are adopted to describe the intermolecular interactions, which are made to consider molecular dissociation. This paper focuses on a mixture of nitrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperature. The equation of state and dissociation degree are calculated from the free-energy functions in the range of temperature of 2000-15 000 K and density of 0.2-3.0 gcm(3), which can be compared with other approaches and experiments.     

Adiabatic transfer of population in a dense fluid: the role of dephasing statistics

We report the results of simulation studies of the statistics of vibrational dephasing of a YCl (Y=H, D, T, and I) diatom in dense fluid Ar at two temperatures, including the effect of strong field driving on the energy level modulation statistics. The distribution of energy level modulations is found to be non-Gaussian with a high energy tail. Aspects of stimulated Raman adiabatic passage (STIRAP) between the vibrational levels of HCl in dense fluid Ar have been investigated. For HCl with nearly degenerate v=0-->v=1 and v=1-->v=2 transitions, the combined effect of modulation and power broadening reduces the STIRAP efficiency for population transfer from v=0 to v=2 of the order of 30%. However, if the transitions used have very different frequencies, as in the original model studied by Demirplak and Rice [J. Chem. Phys. 116, 8028 (2002)], the STIRAP efficiency for population transfer remains high, of the order of 80%, even with non-Gaussian modulation of energy levels.     

Equilibrium structure of the multi-component screened charged hard-sphere fluid

The generalized mean spherical approximation of the structural properties of the binary charge-symmetric fluid of screened charged hard-spheres of the same diameter, i.e., the screened restricted primitive model, is extended to include binary charge-asymmetric and multi-component fluids. Molecular dynamics simulation data are generated to assess the accuracy of the corresponding theoretical predictions.     

Anharmonic nuclear dynamics in the mixed quantum-classical limit

This study employs mixed quantum-classical dynamics (MQCD) formalism to evaluate the linear electronic dipole moment time correlation function (DMTCF) in which a Morse oscillator serves to model the associated vibrations in a mixed quantum-classical (MQC) environment. While the main purpose of this work is to study the applicability of MQCD formalism to anharmonic systems in condensed phase, approximate schemes to physically evaluate the mathematically divergent integrals have been developed in order to deal with the essential singularities that arise while evaluating the Morse oscillator canonical partition function and the DMTCF in MQC systems in the classical limit. The motivation for numerically and analytically evaluating these divergent integrals is that a partition function of any system should lead to a finite value at any temperature and therefore this divergence is unphysical. Additionally, since a partition function is to signify the number of accessible states to the system at hand, divergent results are not physically acceptable. As such, straightforward approximate analytic expressions, at different levels of rigor, for both the classical Morse oscillator partition function and the DMTCF in MQC systems are derived, for the first time. Calculations of Morse oscillator partition function values using different approaches at various temperatures for CO, HCl, and I(2) molecules, showing good results, are presented to test the expressions derived herein. It is found that this divergence, due to singularity, diminishes upon lowering the temperature and only arises at high temperatures. The gradual diminishing of the singularity upon lowering the temperature is sensible since the Morse potential fits the parabolic potential at low temperatures. Model calculations and discussion of the DMTCF and linear absorption spectra in MQC systems using the molecular constants of CO molecule are provided. The linear absorption lineshape is derived by two methods, one of which is asymptotic expansion.     

On the short-time limit of ring polymer molecular dynamics

We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.     

Stochastic entangled chain dynamics of dense polymer solutions

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.     

Equilibrium polymerization: towards a numerical description of the dynamics of wormlike micelles

The self‐diffusion of surfactant in a system of cylindrical, polymer‐like micelles is studied for high concentrations in the framework of the equilibrium polymerization model. The different types of coarse grained dynamic equilibrium‐polymers algorithms are first briefly reviewed and commented. The results suggest that the self‐diffusion is dominated by the smallest species, in marked contrast with rheological experiments showing the behaviour of the slowest (i. e. longest) chains. The self‐diffusion coefficient D is described using Phillies' formalism. An analysis of the experimental and simulational results suggests that the dependence D ˜ ϕ^–1.5 is found without the ansatz of the presence of entanglements.     

Thermodynamic properties in the molecular dynamics ensemble applied to the gaussian core model fluid

The thermodynamic properties of pressure, energy, isothermal pressure coefficient, thermal expansion coefficient, isothermal and adiabatic compressibilities, isobaric and isochoric heat capacities, Joule-Thomson coefficient, and speed of sound are considered in a classical molecular dynamics ensemble. These properties were obtained using the treatment of Lustig [J. Chem. Phys. 100, 3048 (1994)] and Meier and Kabelac [J. Chem. Phys. 124, 064104 (2006)], whereby thermodynamic state variables are expressible in terms of phase-space functions determined directly from molecular dynamics simulations. The complete thermodynamic information about an equilibrium system can be obtained from this general formalism. We apply this method to the gaussian core model fluid because the complex phase behavior of this simple model provides a severe test for this treatment. Waterlike and other anomalies are observed for some of the thermodynamic properties of the gaussian core model fluid.     

Nucleation simulations using the fluid dynamics software FLUENT with the fine particle model FPM

This work is an assessment of the capabilities of the FLUENT-FPM software package to simulate actual nucleation experiments. In the first step, we verified the FPM condensation routine with the NEWALC code. Next, homogeneous nucleation of n-butanol, n-pentanol, and n-hexanol in a laminar flow diffusion chamber (LFDC) was simulated and the results were compared to experimental data and an earlier model, which was described by Lihavainen and Viisanen (2001) and will be called femtube2 in the following. Models based on classical nucleation theory typically give too small nucleation rates for alcohol vapors. Also, the FPM underestimates particle production by several orders of magnitude, the factor being a constant for each nucleation isotherm (i.e., at constant nucleation temperature). However, experimental observations beyond exact particle concentrations can be reproduced. We found a behavior similar to the experiment for the dependence of the concentration of nucleated particles N on the flow rate. After correcting the FPM nucleation rate by a constant factor, experimentally found vapor depletion effects could be simulated. Comparing the FPM and femtube2, we observed that the FPM systematically predicts lower saturation ratio values. Further investigation of vapor depletion showed significant differences between the FPM and the femtube2 model. Furthermore, FPM simulations confirm the earlier found carrier gas effect (Lihavainen and Viisanen, 2001).     

Early chemistry in hot and dense nitromethane: molecular dynamics simulations

We report density functional molecular dynamic simulations to determine the early chemical events of hot (T=3000 K) and dense (rho=1.97 g/cm(3), V/V(0)=0.68) nitromethane (CH(3)NO(2)). The first step in the decomposition process is an intermolecular proton abstraction mechanism that leads to the formation of CH(3)NO(2)H(+) and the aci ion H(2)CNO(2) (-). This event is also confirmed to occur in a fast annealing simulation to a final temperature of 4000 K at rho=2.20 g/cm(3). An intramolecular hydrogen transfer that transforms nitromethane into the aci acid form, CH(2)NO(2)H, accompanies this event. To our knowledge, this is the first confirmation of chemical reactivity with bond selectivity for an energetic material near the Chapman-Jouget state of the fully reacted material. We also report the decomposition mechanism followed up to the formation of H(2)O as the first stable product. We note that similarities in the global features of reactants, intermediates, and products of the reacting fluid seem to indicate a threshold for similar chemistry in the range of high densities and temperatures reported herein.     

Equilibrium properties of dense hydrogen isotope gases based on the theory of simple fluids

We present a new method for the prediction of the equilibrium properties of dense gases containing hydrogen isotopes. The proposed approach combines the Feynman-Hibbs effective potential method and a deconvolution scheme introduced by Weeks et al. The resulting equations of state and the chemical potentials as functions of pressure for each of the hydrogen isotope gases depend on a single set of Lennard-Jones parameters. In addition to its simplicity, the proposed method with optimized Lennard-Jones potential parameters accurately describes the equilibrium properties of hydrogen isotope fluids in the regime of moderate temperatures and pressures. The present approach should find applications in the nonlocal density functional theory of inhomogeneous quantum fluids and should also be of particular relevance to hydrogen (clean energy) storage and to the separation of quantum isotopes by novel nanomaterials.