A New Monte Carlo Method for the Titration of Molecules and Minerals (original) (raw)

Reactive Monte Carlo simulations for charge regulation of colloidal particles

Journal of Chemical Physics, 2022

We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.

Grand-canonical Monte-Carlo simulation of solutions of salt mixtures: theory and implementation

2017

A Grand-canonical Monte-Carlo simulation method extended to simulate a mixture of salts is presented. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. This leads to some complications compared to regular Grand Canonical simulation. Here, a recipe for simulation of electrolyte solution of salt mixture is presented. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts or their mixtures at different concentrations using the primitive ion model. The osmotic pressures of the electrolyte solutions are calculated and shown to depend linearly on the salt concentrations within the concentration range simulated. We also show that at the same concentration of divalent anions, the presence of divalent cations make it easier to insert monovalent cations into the system. This can explain some quantitative differences observed in experiments of the MgCl2 salt mixture and MgSO4 salt mixture.

A Multi-scale Monte Carlo Method for Electrolytes

2015

Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside the cavity, arising due to the fluctuations of ions outside. We find that these effective interactions consist of two types: 1) a constant cavity potential due to the asymmetry of the electrolyte, and 2) a reaction potential that depends on the positions of all ions inside. Combining the Grand Canonical Monte Carlo (GCMC) with a recently developed fast algorithm based of image charge method, we perform a multi-scale Monte Carlo simulation of symmetric electrolytes, and compare it with other simulation methods, including PBC+GCMC method, as well as large scale Monte Carlo simulation. We demonstrate that our multi-scale MC method is capable of capturing the correct physics of a large system using a small scale simulation.

Statistics versus dynamics: two methods for calculating the effective charge of colloidal particles

Journal of Physics: Condensed Matter, 2005

Two methods for calculating the effective charge of colloidal particles inside a salt free suspension are presented and analysed using Monte Carlo simulations. The first method is based on the Alexander prescription, in which the exact electrostatic potential is matched asymptomatically to the solution of the linearized Poisson-Boltzmann equation. The second method relies on a dynamical criterion, which defines the condensed counterions through a bound on their total energy. Although the two methods appear to be quite different, they lead to identical values of the effective colloidal charge, even for suspensions with multivalent counterions for which the Poisson-Boltzmann equation fails.

Monte Carlo method in the theory of solutions

Computer Physics Reports, 1990

The development of computer technology has allowed simulation methods to take the still vacant place of a strict theory of liquid phase. The Monte Carlo (MC) method is one such method. Though the basic ideas of MC are simple, the concrete realization requires solution of a number of problems which are due to inevitable limitations on the number of particles as well as on the number of generated states and also because of the necessity to simplify the form of intermolecular interaction potentials. These problems are divided in our review into five main groups: (1) the problem of ergodicity, (2) convergence of the results, (3) boundary conditions, (4) the specificity of free energy computation, (5) analytical approximation of intermolecular interaction energies. The emphasis in the review will be given mainly to those aspects which have been insufficiently discussed in literature. The conclusions drawn in this review may be applied not only when using MC but also in computations of equilibrium characteristics by means of the molecular dynamics (MD) method.

Effective charge of colloidal particles

The Journal of Chemical Physics, 2004

A new dynamical definition of the effective colloidal charge, especially suitable for the Monte Carlo and Molecular-dynamics simulations, is proposed. It is shown that for aqueous colloidal suspensions containing monovalent counterions the ''dynamical'' effective charge agrees perfectly with the ''statistical'' effective charge calculated using the Alexander prescription. In the case of multivalent ions, the effective charge behaves in a qualitatively different way from the predictions of the Poisson-Boltzmann theory.

Multiple ``time step'' Monte Carlo simulations: Application to charged systems with Ewald summation

Chemical Physics, 2004

Recently, we have proposed an efficient scheme for Monte Carlo simulations, the multiple ''time step'' Monte Carlo ͑MTS-MC͒ ͓J. Chem. Phys. 117, 8203 ͑2002͔͒ based on the separation of the potential interactions into two additive parts. In this paper, the structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of the Ewald summation and the common Metropolis Monte Carlo method. We report a number of observables as a function of CPU time calculated using MC and MTS-MC. The correlation functions indicate that speedups on the order of 4.5-7.5 can be obtained for systems of 108 -500 waters for nϭ10 splitting parameter.