Per Linse

Electrical double layer forces. A Monte Carlo study

Using a novel method the force between two charged surfaces with an intervening electrolyte solution has been determined from Monte Carlo simulations. We find large deviations from the standard Poisson–Boltzmann treatment of the so called double layer force for divalent counterions at high surface charge densities and at short separations. The deviations have two causes: (i) Due to the inclusion of the effect of ion–ion correlations the counterions concentrate more towards the charged wall reducing the overlap between the double layers; and (ii) correlated fluctuations in the ion clouds of the two surfaces lead to an attractive interaction of a van der Waals type. For some realistic values of the parameters the attraction overcomes the repulsive part and there is a net attractive force between similarly charged surfaces. This finding leads to a modification of our conceptual understanding of the interaction between charged particles and it shows that the DLVO theory is qualitatively deficient under some, ...

The cell model for polyelectrolyte systems. Exact statistical mechanical relations, Monte Carlo simulations, and the Poisson–Boltzmann approximation

Some exact statistical mechanical relations have been derived for polyelectrolyte systems within the primitive model. Using the cell model, the osmotic pressure is determined through an explicit evaluation of the derivative of the partition function. Planar, cylindrical, and spherical systems are considered and for a planar charged wall the contact value theorem [Henderson and Blum, J. Chem. Phys. 69, 5441 (1978)] is obtained as a special case. Analogous relations are derived for the cylindrical and spherical geometries. It is argued that the exact relations can be used as consistency tests for analytical approximations. It is pointed out that one merit of the Poisson–Boltzmann approximation is that the validity of the exact equations is retained. Finally, a simple method is devised for determining the osmotic pressure from Monte Carlo simulations. Results from such simulations are used to assess the accuracy of the osmotic pressure calculated using the Poisson–Boltzmann equation. For monovalent ions, the...

Self-diffusion of small molecules in colloidal systems

The self-diffusion of small molecules in colloidal systems is calculated using the cell model to describe the effect of varying concentration of colloidal particles. The relevant boundary conditions are found using arguments from the thermodynamics of irreversible processes. From a general description of the self-diffusion in systems with spherically symmetrical particles we derive expressions for the concentration dependence of the effective self-diffusion coefficientDeff for several cases of practical importance. It is shown that when the molecule studied is strongly attracted to the particle a minimum inDeff is expected around volume fractionΦ=0.35. It is also shown that the often made distinction between free and bound molecules is often problematic and a more general description is proposed. The obstruction effect generated by the excluded volume is discussed both for spherical and spheroidal systems. It is pointed out that the often used formula due to Wang ((1954) J Amer Chem Soc 76:4755) is incorrect for self-diffusion and for the obstruction factor for spheres we obtain (1+0.5Φ)−1. This expresion is tested both by experiments on water diffusion in systems containing latex particles and through computer simulations and it is found valid over a wide concentration range. For prolate ellipsoids the obstruction factor is not greatly different from that for spheres, while for oblate aggregates the limiting obstruction factor of 2/3 can be obtained at low concentrations. It is demonstrated that this effect can be used to distinguish between different aggregate shapes. It is also shown that the disorder present in a solution of colloidal particles leads to a decrease in the obstruction effect.

Monte Carlo simulation of liquid–liquid benzene–water interface

A Monte Carlo simulation of liquid–liquid benzene–water interface is reported. Molecular pair potentials obtained from quantum mechanical calculations have been used. The two phases remain stable over 70 000 configurations/molecule and the interior of each phase is shown to have bulk properties. The intrinsic interface is molecularly sharp, but the interfacial region is broadened by capillary waves. The preferential water–benzene orientation at the interface is similar to that in a dilute aqueous solution of benzene. There is no longitudinal water ordering induced by the interface. The presence of the nonpolar phase gives an alignment of water dipoles parallel to the surface and a reduced probability of parallel orientation of adjacent dipoles. The hydrogen bonds between water neighbors are reinforced at the interface.

Ewald summation and reaction field methods for potentials with atomic charges, dipoles, and polarizabilities

The Ewald summation technique and the reaction field method have been generalized to potentials with atomic charges, dipole moments, and anisotropic polarizabilities. These are two common methods to treat long-range interactions in molecular simulations. Expressions for the potential energy, the electrostatic potential, the electrostatic field, the electrostatic field gradient, the force, and the virial are given, allowing for the calculation of long-range contributions to these properties within the Ewald summation or reaction field methods. We have compared numerical results using the Ewald summation under vacuum conditions with those from direct summations for a number of simple systems and found a complete agreement within the numerical precision with the exception of trivial shifts of the potential. The expressions given will facilitate the use of polarizable models in molecular simulations and hence improving our understanding of condensed matter.

Electrostatic attraction and phase separation in solutions of like-charged colloidal particles

Asymmetric electrolytes consisting of highly charged spherical macroions and small ions representing an aqueous solution of ionic surfactant micelles have been studied at different macroion concentrations by means of Monte Carlo simulations. The model system comprises macroions with 60 elementary charges and either monovalent, divalent, or trivalent counterions interacting solely through hard-core and Coulomb forces. Thermodynamic and structural properties are examined, and the effects of the counterion valency are discussed. For the lowest electrostatic macroion–counterion coupling (monovalent counterions), the macroions are well separated and an effective repulsive potential is acting between them. At stronger electrostatic coupling (divalent counterions), the double-layer repulsion between the macroions is strongly reduced and at short separations the attractive force becomes comparable to the double-layer repulsion. At even stronger coupling (trivalent counterions), the attractive correlation force be...

Monte Carlo simulations of oppositely charged macroions in solution

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed.

Polyelectrolyte–macroion complexation. I. Effect of linear charge density, chain length, and macroion charge

The complexation between a linear flexible polyelectrolyte and one or several oppositely charged macroions was examined by employing a simple model system with focus on the electrostatic interactions. The composition and the structure of the complex as well as conformational data of the polyelectrolyte were obtained by using Monte Carlo simulations. These properties were investigated at different linear charge densities of the polyelectrolyte, different chain lengths of the polyelectrolyte, and different macroion charges, all at different numbers of macroions at constant volume. The binding isotherms obtained are Langmuir type, and in excess of macroions the polyelectrolyte–macroion complex displays a charge reversal. Upon complexation, the polyelectrolyte extension first reduces and thereafter increases as the number of complexed macroions increases, the minimal extension appearing for a neutral complex. Macroions prefer to complex to central polyelectrolyte segments, but for a neutral or an overcharged ...

Polyelectrolyte–macroion complexation. II. Effect of chain flexibility

A simple model with focus on the electrostatic interaction has been used to examine the complexation of a linear polyelectrolyte possessing variable flexibility with one or several oppositely charged macroions. Composition, structure, and thermodynamic properties of the complexes were obtained by using Monte Carlo simulations. Binding isotherms obtained were Langmuir-type with a quantitative binding up to a neutral complex with a plateau value corresponding to ∼50% overcharging, the largest overcharging appearing for the stiffest chain. Free energy calculations demonstrated that the complexation of the first macroion becomes less favorable as the chain stiffness is increased, whereas the opposite was found for a complexation of a macroion to a neutral complex. For a neutral complex and with a flexible chain, the repulsion between complexed macroions is strongly screened and the complexed macroions are located near each other. However, for a very stiff chain, the macroions are sequentially positioned along...

Structure, phase stability, and thermodynamics in charged colloidal solutions

Model systems of charged spherical macroions and point counterions interacting solely through hard-sphere and Coulomb interaction were investigated by means of extensive Monte Carlo simulations. The macroion-charge to counterion-charge ratio was varied from 10 to 80, the macroion volume fraction from 0.001 25 to 0.08, and the reduced parameter that remained, an electrostatic coupling parameter, over a range of two orders in magnitude. The part of the parameter space investigated includes nearly all experimental colloidal solutions (in the salt-free limit) in which the colloids are carrying up 80 (monovalent counterions) or 160 (divalent counterions) elementary charges. The effects on the structure of varying the counterion charge, the macroion charge, the macroion size, the temperature, the dielectric permittivity, and the macroion volume fraction are presented. At a low charge ratio, a low volume fraction, and/or a low electrostatic coupling, the counterion distribution is only weakly perturbed by the ma...