Georgios C. Boulougouris

On the calculation of the chemical potential using the particle deletion scheme

A new formulation is presented for the calculation of the chemical potential from molecular simulation based on a test particle removal (inverse Widom) scheme. The new formulation introduces an intermediate stage in the calculation where the test particle to be removed is substituted by a hard particle. Chemical potential calculations at high densities from NVT and NPT Monte Carlo simulations, using a fast analytical algorithm for the computation of volume accessible to the hard core particle, are presented for the pure Lennard-Jones fluid and found to be in excellent agreement with predictions from an accurate equation of state and from simulations using the test particle insertion scheme (Widom insertion scheme). Binary mixture simulations are presented also and the new scheme is applied in the Gibbs ensemble. In all cases where the system is highly dense, the new inverse Widom scheme affords a significant reduction in CPU time compared with the widely used test particle insertion method of Widom. In ad...

Dynamical integration of a Markovian web: A first passage time approach

In this work we address the dynamics of Markovian systems by tracking the evolution of the probability distribution, utilizing mean first passage time theory to augment the set of states considered. The method is validated on a lattice system and is applied, in conjunction with landscape analysis (saddle point searches) and multidimensional transition-state theory, to an atomistic model of glassy atactic polystyrene, in order to follow its time evolution over more than ten orders of magnitude on the time scale, from less than 10(-15) up to 10(-5) s. Frequencies extracted from the eigenvalues of the rate constant matrix are in favorable agreement with experimental measurements of subglass relaxation transitions at 250 K.

Calculation of the chemical potential of chain molecules using the staged particle deletion scheme

A formulation is presented for the calculation of the chemical potential of chain molecules from molecular simulation based on the staged deletion of a test molecule. This formulation is an extension of a formulation presented recently [Boulougouris et al., Mol. Phys. 96, 905 (1999)] for the case of spherical molecules. An analytical method for the calculation of the volume accessible to a hard-sphere chain molecule is used together with the excluded volume map sampling technique. The new method is applied to a fluid of tangent sphere dimers and to ethane under various conditions. NPT, NVT, and Gibbs ensemble Monte Carlo simulation results are presented. Extensive comparison is made against calculations with the Widom test particle insertion method. In all cases, the new method results in considerable savings in CPU time.

Monte Carlo Sampling of a Markov Web.

The efficiency of Markov-Chain Monte Carlo simulations can be enhanced by exploiting information about trial moves that would normally be rejected. The original presentation of this approach was limited to a specific MC sampling scheme. Here we present a general derivation of a method to improve the sampling efficiency of Monte Carlo simulations by collecting information about the microstates that can be linked directly to the sampled point via an independent Markov transition matrix. As an illustration, we show that our approach greatly enhances the efficiency of a scheme to compute the density of states of a square-well fluid.

Monte Carlo simulation of carbon monoxide, carbon dioxide and methane adsorption on activated carbon

In this study, the adsorption capacity of pure and activated carbon with regard to carbon monoxide (CO), carbon dioxide (CO2) and methane (CH4) gases at 298 K and pressure from 0.01 up to 2.0 MPa has been investigated computationally. Computational work refers to Monte Carlo (MC) simulation of each adsorbed gas on a graphite model with varying density of activation sites. The Grand Canonical Monte Carlo (GCMC) simulation technique was employed to obtain the uptake of each adsorbed gas by considering a graphite model of parallel sheets activated by carboxyl and hydroxyl groups, as observed experimentally. The simulation adsorption data for these gases within the examined carbon pore material are presented and discussed in terms of the adsorbate fluid molecular characteristics and corresponding interactions between adsorbate species and adsorbent material. We found that the simulated adsorption uptake of the examined graphite model under these conditions with regard to the aforementioned fluids increases in the order CO < CH4 < CO2.

On the role of inherent structures in glass-forming materials: I. The vitrification process.

In this work, we investigate the role of inherent structures in the vitrification process of glass-forming materials by using a two-component Lennard-Jones mixture. We start with a simplified model that describes the dynamics of the atomistic system as a Poisson process consisting of a series of transitions from one potential energy minimum (inherent structure) to another, the rate of individual transitions being described by a first-order kinetic law. We investigate the validity of this model by comparing the mean square displacement resulting from atomistic molecular dynamics (MD) trajectories with the corresponding mean square displacement based on inherent structures. Furthermore, in the case of vitrification via stepwise cooling, we identify the role of the potential energy landscape in determining the properties of the resulting glass. Interestingly, the cooling rate is not sufficient to define the resulting glass in a stepwise cooling process, because the time spent by the system at different temperatures (length of the steps) has a highly nonlinear impact on the properties of the resulting glass. In contrast to previous investigations of supercooled liquids, we focus on a range of temperatures close to and below the glass transition temperature, where the use of MD is incapable of producing equilibrated samples of the metastable supercooled state. Our aim is to develop a methodology that enables mapping the dynamics under these conditions to a coarse-grained first-order kinetic model based on the Poisson process approximation. This model can be used in order to extend our dynamical sampling ability to much broader time scales and therefore allow us to create computer glasses with cooling rates closer to those used experimentally. In a continuation to this work, we provide the mathematical formulation for lifting the coarse-grained Poisson process model and reproducing the full dynamics of the atomistic system.

Novel Monte Carlo scheme for systems with short-ranged interactions

We propose a Monte Carlo (MC) sampling algorithm to simulate systems of particles interacting via very short-ranged discontinuous potentials. Such models are often used to describe protein solutions or colloidal suspensions. Most normal MC algorithms fail for such systems because, at low temperatures, they tend to get trapped in local potential-energy local minima due to the short range of the pair potential. To circumvent this problem, we have devised a scheme that changes the construction of trial moves in such a way that the potential-energy difference between initial and final states drops out of the acceptance rule for the Monte Carlo trial moves. This approach allows us to simulate systems with short-ranged attraction under conditions that were unreachable up to now.

Probing subglass relaxation in polymers via a geometric representation of probabilities, observables, and relaxation modes for discrete stochastic systems

The dynamics of many physical, chemical, and biological systems can be reduced to a succession of infrequent transitions in a network of discrete states representing low energy regions in configuration space. This enables accessing long-time dynamics and predicting macroscopic properties. Here we develop a new, perfectly general statistical mechanical/geometric formulation that expresses both state probabilities and all observables in the same Euclidean space, spanned by the eigenvectors of the symmetrized time evolution operator. Our formalism leads to simple expressions for nonequilibrium and equilibrium ensemble averages, variances, and time correlation functions of any observable and allows a rigorous decomposition of the dynamics into relaxation modes. Applying it to subglass segmental relaxation in atactic polystyrene up to times on the order of 10 micros, we probe the molecular mechanism of the gamma and delta processes and unequivocally identify the delta process with rotation of a single phenyl group around its stem.

Tracking a glassy polymer on its energy landscape in the course of elastic deformation

The response to deformation of a detailed computer model of glassy atactic polystyrene, represented as a collection of basins on its potential energy landscape, has been investigated. The volumetric behaviour of the polymer is calculated via ‘brute force’ molecular dynamics quenching simulations. Results are compared with corresponding estimates obtained by invoking the quasi-harmonic approximation (QHA) for a variety of temperatures below the glass temperature and with experimental data. The stress-controlled uniaxial deformations fall in the linear elastic regime and the resulting strains are calculated as ensemble averages of QHA estimates over 200 uncorrelated inherent structures of the potential energy landscape. The elastic constants (Youngs modulus and Poisson ratio) and their temperature dependence are in very good agreement with experiments for glassy atactic polystyrene. Additionally, a classification of the deformed inherent structures in respect to the geometry and general shape of their energy minima is undertaken. A distortion of the potential energy basins upon mechanical deformation in the elastic regime is observed in all cases.

Thermodynamic interpolation for the simulation of two-phase flow of non-ideal mixtures

This paper describes the development and application of a technique for the rapid interpolation of thermodynamic properties of mixtures for the purposes of simulating two-phase flow. The technique is based on adaptive inverse interpolation and can be applied to any Equation of State and multicomponent mixture. Following analysis of its accuracy, the method is coupled with a two-phase flow model, based on the homogeneous equilibrium mixture assumption, and applied to the simulation of flows of carbon dioxide (CO2) rich mixtures. This coupled flow model is used to simulate the experimental decompression of binary and quinternary mixtures. It is found that the predictions are in good agreement with the experimental data and that the interpolation approach provides a flexible, robust means of obtaining thermodynamic properties for use in flow models.