Monte Carlo simulation of colloidal membrane filtration: principal issues for modeling

The principal issues involved in developing a Monte Carlo simulation model of colloidal membrane filtration are investigated in this study. An important object for modeling is the physical dynamics responsible for causing particle deposition and accumulation when encountering an open system with continuous outflow. A periodic boundary condition offers a solution to the problem by recirculating continuous flow back through the system. Scaling to full physical dimensions will allow for release of the model from flawed assumptions such as constant cake layer volume fraction and thickness throughout the system. Furthermore, rigorous modeling on a precise scale extends the model to account for random particle collisions with acute accuracy. A major finding of this study proves that forces within the colloidal filtration system are summed and transferred cumulatively through the inter-particle interactions. The force summation and transfer phenomenon only realizes its true value when the model is scaled to full dimensions. The overall strategy for model development, therefore, entails three stages: first, rigorous modeling on a microscopic scale; next, comprehensive inclusion of relevant physical dynamics; and finally, scaling to full physical dimensions.     

Brownian Dynamics, Molecular Dynamics, and Monte Carlo modeling of colloidal systems

This paper serves as an introductory review of Brownian Dynamics (BD), Molecular Dynamics (MD), and Monte Carlo (MC) modeling techniques. These three simulation methods have proven to be exceptional investigative solutions for probing discrete molecular, ionic, and colloidal motions at their basic microscopic levels. The review offers a general study of the classical theories and algorithms that are foundational to Brownian Dynamics, Molecular Dynamics, and Monte Carlo simulations. Important topics of interest include fundamental theories that govern Brownian motion, the Langevin equation, the Verlet algorithm, and the Metropolis method. Brownian Dynamics demonstrates advantages over Molecular Dynamics as pertaining to the issue of time-scale separation. Monte Carlo methods exhibit strengths in terms of ease of implementation. Hybrid techniques that combine these methods and draw from these efficacies are also presented. With their rigorous microscopic approach, Brownian Dynamics, Molecular Dynamics, and Monte Carlo methods prove to be especially viable modeling methods for problems with challenging complexities such as high-level particle concentration and multiple particle interactions. These methods hold promising potential for effective modeling of transport in colloidal systems.     

Reverse Monte Carlo and Voronoi-Delaunay simulation and structure analysis for liquid metals

This paper discusses the applicability of the integrated reverse Monte Carlo and Voronoi-Delaunay approach to local structure analysis and medium-scale structure determination of liquid metals. The advantages of this approach are shown: generation of 3D structural models using experimental diffraction data and subsequent structure determination by atomic coordinate analysis.Original Russian Text Copyright © 2004 by A. S. Roik, V. P. Kazimirov, and V. E. SokolskiiTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 683–691, July–August, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Donnan potential of dilute colloidal dispersions: Monte Carlo simulations

Donnan equilibrium between a salt-free colloidal dispersion and an electrolyte solution has been investigated by Monte Carlo simulations. The Donnan potential is directly calculated by considering two compartments separated by a semipermeable membrane. In order to understand the role played by colloid–ion interactions, the influences of colloidal characteristics, including particle size R, intrinsic particle charge Z, counterion valency z_c, and concentration c_p, on Donnan potential Ψ_D and effective charge Z_eff are examined. Our simulations show that the electroneutrality condition is not followed in both compartments and the Donnan potential arises due to the net charge density. The Donnan potential grows by increasing c_p and Z_eff and by decreasing dielectric constant ε_r, i.e., Ψ_DZ_effc_p/ε_r approximately. Note that the effective charge varies with R,Z,c_p,ε_r and z_c as well. When the salt concentration is increased, the net charge density is lowered and thus the Donnan potential decays accordingly. The validity of the classical theory based on the Nernst equation and the electroneutrality assumption is also examined. In general, the simulation results at high-salt condition can be well represented by such mean-field theory.     

Monte Carlo parametric modeling for predicting biomass calorific value

Due to the nonlinear relationship between the calorific value and the elemental concentration of biomass, methods such as linear regression, widely used in the literature to model this relationship, produce models that fail to provide well-grounded results. In this study, a novel approach, based on Monte Carlo parametric modeling, for calculating the calorific value of biomass from measurements provided by elemental analysis, is presented. Olive husk, a biomass source widely used in the Mediterranean basin, was the subject under investigation. A comprehensive analysis of the thermal properties of olive husk was conducted. The elemental analysis, as well as the calorific value, the moisture content the sampling and the preparation of the examined biomass were performed using the appropriate CEN standards and procedures. Based on the Monte Carlo parametric modeling, the parameters of an exponential model linking the elemental analysis and the calorific value of olive husk were estimated. This study is anticipated to provide further insight to the discussion on models for predicting the calorific value of biomass, by introducing a novel mathematical approach.     

Artificial neural system modeling of Monte Carlo simulations of polymers

In this work, a neural network was used to learn features in potential energy surfaces and relate those features to conformational properties of a series of polymers. Specifically, we modeled Monte Carlo simulations of 20 polymers in which we calculated the characteristic ratio and the temperature coefficient of the characteristic ratio for each polymer. We first created 20 rotational potential energy surfaces using MNDO procedures and then used these energy surfaces to produce 10000 chains, each chain 100 bonds long. From these results we calculated the mean-square end-to-end distance, the characteristic ratio and its corresponding temperature coefficient. A neural network was then used to model the results of these Monte Carlo calculations. We found that artificial neural network simulations were highly accurate in predicting the outcome of the Monte Carlo calculations for polymers for which it was not trained. The overall average error for prediction of the characteristic ratio was 4,82%, and the overall average error for prediction of the temperature coefficient was 0,89%.     

Influence of monovalent ion size on colloidal forces probed by Monte Carlo simulations

The present work studies the role of ionic size in the interactions between the electrical double layers of colloids immersed into electrolyte solutions of monovalent ions. Such interactions are studied by means of Monte Carlo (MC) simulations and the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Despite the omission of the steric effects and some other features of real electrolyte solutions, DLVO theory is known to work qualitatively well for 1:1 electrolyte solutions. However, this affirmation is based on previous tests where an ionic diameter around 0.4 nm was taken for all ionic species. In contrast, some experimental studies suggest that larger hydrated ions should be considered and even specified for each type of ion. In this work, the importance of ionic size is analyzed by applying the primitive model of electrolyte to the intermediate region between a pair of equally charged infinite planar surfaces. The double layer interactions were calculated from the ionic densities at the distance of closest approach to the charged surfaces, this method constitutes an alternative to the traditional calculations at the midplane. Our MC simulations predict the existence of negative net pressures for monovalent electrolytes in the case of zero charge density. In addition, MC simulations reveal some disagreements with theoretical predictions for ionic diameters larger than 0.4 nm. These discrepancies can become significant if surface charge density is large enough due to the restructuration of the double layer. The physical mechanisms for these deviations are also discussed.     

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.     

Molecular modeling of porous carbons using the hybrid reverse Monte Carlo method

We apply a simulation protocol based on the reverse Monte Carlo (RMC) method, which incorporates an energy constraint, to model porous carbons. This method is called hybrid reverse Monte Carlo (HRMC), since it combines the features of the Monte Carlo and reverse Monte Carlo methods. The use of the energy constraint term helps alleviate the problem of the presence of unrealistic features (such as three- and four-membered carbon rings), reported in previous RMC studies of carbons, and also correctly describes the local environment of carbon atoms. The HRMC protocol is used to develop molecular models of saccharose-based porous carbons in which hydrogen atoms are taken into account explicitly in addition to the carbon atoms. We find that the model reproduces the experimental pair correlation function with good accuracy. The local structure differs from that obtained with a previous model (Pikunic, J.; Clinard, C.; Cohaut, N.; Gubbins, K. E.; Guet, J. M.; Pellenq, R. J.-M.; Rannou, I.; Rouzaud, J. N. Langmuir 2003, 19 (20), 8565). We study the local structure by calculating the nearest neighbor distribution, bond angle distribution, and ring statistics.     

Dependence of fragmentation behavior of colloidal aggregates on their fractal structure

The fragmentation dynamics of aggregate of non-Brownian particles in shear flow is investigated numerically. The breakup behaviors of aggregates having the same connectivity but the different space-filling properties are examined. The Lagrangian particle simulation in a linear flow field is performed. The effect of surrounding fluid on the motion of multiple particles is estimated by Stokesian dynamics approach. The inter-particle force is calculated from the retarded van der Waals potential based on the Lifshitz theory. The results obtained in this work indicate that the fragmentation behavior of colloidal aggregates depends on their fractal structure. However, if the resultant aggregate size is smaller than the critical one, the fragmentation behavior shows the universality regardless of their original structure. Furthermore, the restructuring of aggregate in shear flow and its effect on the fragmentation process are also discussed.     

无定形碳的逆向蒙特卡洛法建模

作为一种很有前景的建模方法,逆向蒙特卡洛法（Reverse Monte Carlo 简称RMC 法）在无定形碳结构研究中得到了广泛应用。本文阐述了RMC 法对于无定形碳材料结构识别的意义,简介了该法的基本原理,同时针对使用RMC 法建立无定形碳结构模型时遇到的两大难点：即模拟结构的真实性问题和大尺寸孔网络的建模问题,综述了该方法的改进和发展趋势。几何约束和能量约束的使用,提高了模拟结构的真实性;具有介孔的多孔碳模型的建立,将成为今后研究的热点。     

Attractive interactions in dispersions of identical charged colloidal particles: a Monte Carlo simulation

Using the Debye-Hückel pair potential, the collective interactions between identical charged particles were examined via Monte Carlo simulations. The results have shown that when the number of charges per particle and the particle volume fraction were sufficiently large, the pair long-range electrostatic repulsion generated an effective attractive interaction between identical charged particles because of many-body effects. Disordered liquid-like structures, ordered crystal-like structures, ordered structures dispersed in disordered ones, and disordered structures dispersed in ordered ones have been found. The structures are dependent on the volume fraction and charge of the particles, as well as on the electrolyte concentration.     

Kinetic Monte Carlo modeling of chemical reactions coupled with heat transfer

In this paper, we describe two types of effective events for describing heat transfer in a kinetic Monte Carlo (KMC) simulation that may involve stochastic chemical reactions. Simulations employing these events are referred to as KMC-TBT and KMC-PHE. In KMC-TBT, heat transfer is modeled as the stochastic transfer of "thermal bits" between adjacent grid points. In KMC-PHE, heat transfer is modeled by integrating the Poisson heat equation for a short time. Either approach is capable of capturing the time dependent system behavior exactly. Both KMC-PHE and KMC-TBT are validated by simulating pure heat transfer in a rod and a square and modeling a heated desorption problem where exact numerical results are available. KMC-PHE is much faster than KMC-TBT and is used to study the endothermic desorption of a lattice gas. Interesting findings from this study are reported.     

Inhomogeneous fluids of colloidal hard dumbbells: fundamental measure theory and Monte Carlo simulations

Recently, a density functional theory for hard particles with shape anisotropy was developed, the extended deconvolution fundamental measure theory (edFMT). We apply edFMT to hard dumbbells, arguably the simplest non-convex shape and readily available experimentally in the form of colloids. We obtain good agreement between edFMT and Monte Carlo simulations for fluids of dumbbells in a slit and for the same system under gravity. This indicates that edFMT can be successfully applied to nearly all colloidal shapes, not just for the convex shapes for which edFMT was originally derived. A theory, such as edFMT, that allows a fast and general way of mapping the phase behavior of anisotropic colloids, can act as a useful guide for the design of colloidal shapes for various applications.     

Generalizations for the potential of mean force between two isolated colloidal particles from Monte Carlo simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin-Landau-Verwey-Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Gamma=z(2)l(B)/a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l(B)=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Gamma approximately 0.5 and, second, that onset of attraction occurs at Gamma approximately 1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.     

Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates

In this work we present experimental and simulation analysis of the breakage and restructuring of colloidal aggregates in dilute conditions under shear. In order to cover a broad range of hydrodynamic and interparticle forces, aggregates composed of primary particles with two sizes, d(p) = 90 and 810 nm, were generated. Moreover, to understand the dependence of breakage and restructuring on the cluster structure, aggregates grown under stagnant and turbulent conditions, having substantially different initial internal structures with fractal dimension d(f) equal to 1.7 and 2.7, respectively, were used. The aggregates were broken by exposing them to a well-defined elongational flow produced in a nozzle positioned between two syringes. To investigate the evolution of aggregate size and morphology, respectively, the mean radius of gyration, , and d(f) were monitored during the breakup process using light scattering and confocal laser scanning microscopy. It was found that the evolution of aggregates' fractal dimension during breakage is solely controlled by their initial structure and is independent of the primary particles size. Similarly, the scaling of the steady-state vs the applied hydrodynamic stress is independent of primary particle size, however, depends on the history of aggregate structure. To quantitatively explain these observations, the breakage process was modeled using stokesian dynamics simulations incorporating DLVO and contact interactions among particles. The required flow-field for these simulations was obtained from computational fluid dynamics. The complex flow pattern was simplified by considering a characteristic stream line passing through the zone with the highest hydrodynamic stress inside the nozzle, this being the most critical flow condition experienced by the clusters. As the flow-field along this streamline was found to be neither pure simple shear nor pure extensional flow, the real flow was approximated as an elongational flow followed by a simple shear flow, with a stepwise transition between them. Using this approach, very good agreement between the measured and simulated aggregate size values and structure evolution was obtained. The results of this study show that the process of cluster breakup is very complex and strongly depends on the initial aggregate structure and flow-field conditions.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Monte Carlo free energy calculations using electronic structure methods

The molecular mechanics-based importance sampling function (MMBIF) algorithm [R. Iftimie, D. Salahub, D. Wei, and J. Schofield, J. Chem. Phys. 113, 4852 (2000)] is extended to incorporate semiempirical electronic structure methods in the secondary Markov chain, creating a fully quantum mechanical Monte Carlo sampling method for simulations of reactive chemical systems which, unlike the MMBIF algorithm, does not require the generation of a system-specific force field. The algorithm is applied to calculating the potential of mean force for the isomerization reaction of HCN using thermodynamic integration. Constraints are implemented in the sampling using a modification of the SHAKE algorithm, including that of a fixed, arbitrary reaction coordinate. Simulation results show that sampling efficiency with the semiempirical secondary potential is often comparable in quality to force fields constructed using the methods suggested in the original MMBIF work. The semiempirical based importance sampling method presented here is a useful alternative to MMBIF sampling as it can be applied to systems for which no suitable MM force field can be constructed.