Transport in a disordered medium: Analysis and Monte Carlo simulation

We consider a classical stochastic model describing particle transport on a lattice with randomly distributed nearest-neighbor transition rates. Applying an effective medium theory to the model, we determine average properties related to the particle's dynamics ind-dimensions. In particular, we calculate the mean-square displacement, and the fourth moment of the displacement in one-, two- and three dimensions. The results compare favorably with Monte Carlo simulations of the model. We also present preliminary results for the velocity autocorrelation function.An aspect of the bond percolation problem, which is a special case of the stochastic model is investigated; the average inverse cluster size, <N _c ^–1>, is calculated. In one dimension the expression for this quantity is exact and in higher dimensions our results are very accurate not too close to the percolation concentration.     

The grand canonical ensemble Monte Carlo method applied to electrolyte solutions

A grand canonical ensemble Monte Carlo method is developed for application to electrolyte solutions.

The method proves to be of comparable accuracy and speed to the conventional NVT Monte Carlo method for electrolytes but has the added advantage of being able to fix the chemical potential. This latter point is vital for the study of surface phenomena. Application of the method to 1:1 and 2:2 primitive model electrolytes is made as is a comparison with the results of approximate statistical mechanical treatments.     

Equilibrium partitioning of a simple fluid in a matrix-filled cylindrical pores with adsorbing walls: A grand canonical Monte Carlo study

We have studied a model of a hard sphere fluid adsorbed in a cylindrical pore filled with quenched disordered matrix of hard sphere particles using Grand canonical Monte Carlo simulations. The interactions between matrix species and pore walls are assumed of a hard sphere type. However, the pore walls exert a short-range attraction upon adsorbed fluid particles. We discuss the adsorption isotherms and the density profiles of fluid particles in pores with different microporosity for several values of the pore radius. We have observed that like in homogeneous microporous media the adsorption increases with increasing porosity. However, trends of behavior of the isotherms also reflect layering of adsorbed fluid. The data obtained in this study may serve as a benchmark for the development of the theory of confined quenched-annealed systems and for computer simulation investigation of models permitting phase transitions in pores. This project has been supported in parts by DGAPA of the UNAM under research grant IN111597, by the National Council for Science and Technology (CONACyT), grant No. 25301-E.     

Improvement of the grand canonical quantum Monte Carlo method at low temperatures

We introduce an improvement of the algorithm for the simulation of correlated fermi systems in the grand canonical ensemble. Using this new method the computer time grows no more with the square but essentially linearly with the inverse temperature. At low temperatures the number of operations is diminished by a factor typically between 5 and 20. We present results for correlation functions of the one-dimensional Hubbard model at various band fillings.     

Capillary condensation in a fractal porous medium

Small-angle x-ray and neutron scattering are used to characterize the surface roughness and porosity of a natural rock which are described over three decades in length scales and over nine decades in scattered intensities by a surface fractal dimension D = 2.68+/-0.03. When this porous medium is exposed to a vapor of a contrast-matched water, neutron scattering reveals that surface roughness disappears at small scales, where a Porod behavior typical of smooth interfaces is observed instead. Water-sorption measurements confirm that such interface smoothing is due predominantly to the water condensing in the most strongly curved asperities rather than covering the surface with a wetting film of uniform thickness.     

Influence of unlike dispersive interactions on methane adsorption in graphite: a grand canonical Monte Carlo simulation and classical density functional theory study

Activated carbons are popular adsorbents due to their large micro- and mesoporous volumes and high specific surface areas. Modeling adsorption behaviour using molecular computations is frequently undertaken, but the influence of the unlike intermolecular interactions on adsorption behaviour is often not well understood. This study employed grand canonical Monte Carlo simulations, and classical density functional theory coupled with a simple lattice gas model to study the influence of unlike intermolecular interactions on adsorption behaviour, with a focus on the dispersive interactions. Both approaches yielded qualitative agreement with experimental data from the literature, although only a fitted classical density functional theory approach agreed quantitatively. Changing the potential energy well depth of the methane-carbon interaction did not change the Langmuir-type adsorption behaviour observed, however, there was some dependence of the adsorption behaviour on the unlike interactions, depending on the thermodynamic conditions.     

Monte Carlo study of percolation on disordered triangular lattices

A simple model for amorphous solids, consisting of a mixed bond triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is studied here by using computational simulation. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of regular [attenuated] bonds ρ [1−ρ] (0≤ρ≤1) and (2) the factor r, which is defined as the ratio between the value of the conductivity associated to an attenuated bond and that corresponding to a regular bond (0≤r≤1). The results obtained show how the percolation properties of the disordered system are modified with respect to the standard random bond percolation problem (r=0).     

Thermodynamics of the uniform electron gas: Fermionic path integral Monte Carlo simulations in the restricted grand canonical ensemble

The uniform electron gas (UEG) is one of the key models for the understanding of warm dense matter—an exotic, highly compressed state of matter between solid and plasma phases. The difficulty in modelling the UEG arises from the need to simultaneously account for Coulomb correlations, quantum effects, and exchange effects, as well as finite temperature. The most accurate results so far were obtained from quantum Monte Carlo (QMC) simulations with a variety of representations. However, QMC for electrons is hampered by the fermion sign problem. Here, we present results from a novel fermionic propagator path integral Monte Carlo in the restricted grand canonical ensemble. The ab initio simulation results for the spin-resolved pair distribution functions and static structure factor are reported for two isotherms (T in the units of the Fermi temperature). Furthermore, we combine the results from the linear response theory in the Singwi-Tosi-Land-Sjölander scheme with the QMC data to remove finite-size errors in the interaction energy. We present a new corrected parametrization for the interaction energy and the exchange–correlation free energy in the thermodynamic limit, and benchmark our results against the restricted path integral Monte Carlo by Brown et al. [Phys. Rev. Lett. 110 , 146405 (2013)] and configuration path integral Monte Carlo/permutation-blocking path integral Monte Carlo by Dornheim et al. [Phys. Rev. Lett. 117 , 115701 (2016)].     

A grand ensemble Monte Carlo study of krypton adsorbed on graphite

Computer simulations have been carried out along the 90·2 K isotherm for the adsorption of Kr on graphite. The grand ensemble Monte Carlo technique was used and the adsorbate and adsorbent were represented by widely accepted two body potentials. Additional runs were also carried out in which the third body force, due to the adsorbent substrate was introduced into the Kr-Kr potential. In agreement with earlier work, no stable commensurate phase could be found, and it is concluded that a further development of intermolecular potentials is required in order to achieve agreement between simulation and experiment.

The analysis of the data from MC runs employed conventional examination of distribution functions, the use of free energies as in earlier work, and also new methods, developed in the course of this work, for the examination of lateral distributions and snapshots.     

A biased grand canonical Monte Carlo method for simulating adsorption using all-atom and branched united atom models

Configurational-bias Monte Carlo sampling techniques have been developed which overcome the difficulties of sampling configuration space efficiently for all-atom molecular models and for branched species represented with united atom models. Implementation details of this sampling scheme are discussed. The accuracy of a united atom forcefield with non-bond parameters optimized for zeolite adsorption and a widely used all-atom forcefield are evaluated by comparison with experimental sorption isotherms of linear and branched hydrocarbons.     

Linear scaling of computer time with the inverse temperature for the grand canonical quantum Monte Carlo method

Using a new method of storing and updating one particle Green's functions the computer time for the simulation of correlated fermi systems in the grand canonical ensemble scales linearly with the inverse temperature. This reduces the number of operations by a factor of typically 20 and more at low temperatures compared with the standard algorithm.     

A core-softened fluid model in disordered porous media. Grand canonical Monte Carlo simulation and integral equations

We have studied the microscopic structure and thermodynamic properties of a core-softened fluid model in disordered matrices of Lennard-Jones particles by using grand canonical Monte Carlo simulation. The dependence of density on the applied chemical potential (adsorption isotherms), pair distribution functions, as well as the heat capacity in different matrices are discussed. The microscopic structure of the model in matrices changes with density similar to the bulk model. Thus one should expect that the structural anomaly persists at least in dilute matrices. The region of densities for the heat capacity anomaly shrinks with increasing matrix density. This behavior is also observed for the diffusion coefficient on density from independent molecular dynamics simulation. Theoretical results for the model have been obtained by using replica Ornstein-Zernike integral equations with hypernetted chain closure. Predictions of the theory generally are in good agreement with simulation data, except for the heat capacity on fluid density. However, possible anomalies of thermodynamic properties for the model in disordered matrices are not captured adequately by the present theory. It seems necessary to develop and apply more elaborated, thermodynamically self-consistent closures to capture these features.     

Exchange bias in a magnetic ordered/disordered nanoparticle system: A Monte Carlo simulation study

We have employed the Monte Carlo (MC) simulation method to gain information on the exchange bias (EB) effect in nanoparticles composed of a ferromagnetic core and a disordered ferrimagnetic shell. The magnetic disorder of the shell affects the EB properties to the extent that they exhibit aging and training effects. The results of our MC simulations are in very good agreement with the experimental findings in a granular system composed of Fe nanoparticles (mean size ∼6 nm) embedded in a Fe oxide matrix confirming that the glassy nature of the shell is responsible for the observed aging and training effects.     

Structural and thermodynamic properties of the restricted primitive model electrolyte in a mixture with uncharged hard spheres: a grand canonical Monte Carlo simulation and integral equation study

A restricted primitive model electrolyte in a mixture with uncharged hard spheres was studied at room temperature using grand canonical Monte Carlo computer simulation and Ornstein–Zernike integral equation theory in the hypernetted chain approximation (HNC). The mean spherical approximation results are also presented for a few cases. We obtained the pair distribution functions of species of the system, the dependencies of the total fluid density and the ionic fraction on the chemical potentials, the excess internal energy and the heat capacity at constant volume for a wide range of chemical potentials of the species from the simulations and HNC theory. In the majority of cases, good agreement between the theoretical predictions and simulation data is obtained. The composition of the mixture is determined by the chemical potentials of both species. The pair distribution functions have a Debye-like shape at low densities for various values of the ion fraction. By increasing the chemical potential of the uncharged component, weak trends for structuring of the solution are observed with the formation of ion-hard sphere-ion complexes. At high densities, a tendency for in-phase oscillations of ion–ion functions is observed similar to the pure electrolyte in the restricted primitive model. We analysed the chemical potential–density and the chemical potential–ion fraction projections of the equation of state in detail. Also, the heat capacity at constant volume has been calculated for the first time. The model and the results are useful for the development of the theory of inhomogeneous fluid mixtures.     

The phase diagrams of a finite superlattice with disordered interface: A Monte Carlo study

Monte Carlo Simulation (MCS) has been used to study critical and compensation behavior of a ferrimagnetic superlattice on a simple cubic lattice. The superlattice consists of k unit cells, where the unit cell contains L layers of spin −1/2 A atoms, L layers of spin −1 B atoms and a disordered interface in between that is characterized by a random arrangement of A and B atoms of A_pB_1−p type and a negative A-B coupling. We investigate the finite and the infinite superlattices and we found that the existence and the number of the compensation points depend strongly on the thickness of the superlattice (number of unit cells).     

Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior

We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, and thermodynamic consistency is not satisfied along the hysteresis loop.     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001