IranWe introduce a new method for simulating colloidal suspensions with spherical colloidal particles of dielectric constant different from the surrounding medium. The method uses exact calculation of the Green function to obtain the ion-ion interaction potential in the presence of a dielectric discontinuity at the surface of the colloidal particle. The new method is orders of magnitude faster than the traditional approaches based on series expansions of the interaction potential.
To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem of NP approach is traced back to the use of bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is non-trivially related with the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.Electrostatic interactions play a fundamental role in physics, chemistry, and biology. The long-range nature of the Coulomb force, however, makes it very difficult to study theoretically 1 . In aqueous systems ions are usually hydrated by water molecules. On the other hand, acids lose proton, which associates with the water molecule forming a hydronium ion 2 . There are many reactions that are controlled by pH, and the acid-base equilibrium directly influences the functionality of biomolecules. Although pH can be easily tuned in experiments, it is much more difficult to account for the chemical equilibrium in theoretical and simulation studies 3 .Colloidal particles often have organic functional groups on their surfaces. In aqueous systems these groups dissociate, loosing a proton, resulting in a colloidal surface charge 4-7 . The amount of surface charge strongly depends on the pH of the environment 8,9 and is controlled by the chemical equilibrium between hydronium ions and the functional groups. This process is known as charge regulation (CR) 10-16 . The concept of charge regulation was first described by Linderstrøm-Lang 17-19 and studied theoretically by Ninham and Parsegian. 20 . CR is of fundamental importance in colloidal science 10,21-32 and biophysics 33-39 . It has been applied to explore the stability of electrical double layers 9,40-45 and is of great technological importance in fields as diverse as mineral preparation, agriculture, ceramics, and surface coating 46 .Consider a weak acid HA in equilibrium with bulk water, HA+H 2 O ⇄ H 3 O + +A -. For dilute solutions the concentration of all species is controlled by the law of mass action, K eq = c HA /c A -c H +,where K eq is the equilibrium constant and c indicates the concentration of each specie. Ninham and Parsegian (NP) supposed that the same equilibrium relation will hold for the reactive (acidic) sites on the colloidal surface with the local concentration of hydronium determined by the Boltzmann distribution, c surfq is the proto...
A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nano-particles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far-field. All the results are compared with the Monte Carlo simulations, showing an excellent agreement between the theory and the simulations.PACS numbers: 64.70.pv, 61.20.Qg, 82.45.Gj Colloidal suspensions are of great practical interest for biology, chemistry, and physics. The subject has a long history going back more than a hundred years. In spite of the intense effort, many interesting phenomena which are found in colloidal science have not been fully elucidated. For example, it is well known that the stability of a hydrophobic colloidal suspension depends specifically on the electrolyte present in suspension. Addition of multivalent counterions results in a rapid precipitation of colloidal particles. What is more surprising is that even for monovalent counterions, stability of colloidal suspensions depend strongly on the precise nature of the counterions. Thus, as one goes along the halogen series, the critical coagulation concentrations of positive colloidal particles can decrease by as much as an order of magnitude, when anion is changed from fluoride to iodide [1]. Another interesting phenomenon found in suspensions with multivalent ions is the reversal of electrophoretic mobility [2,3], or equivalently charge reversal [4][5][6][7]. Under some conditions, it is also possible to observe like-charge attraction between the colloidal particles of the same sign of charge [8][9][10][11][12]. Many of these interesting phenomena are the consequence of strong electrostatic correlations between the counterions. The role of electrostatic correlations has been studied using simple models of colloidal suspensions which neglect particle polarizability. The standard Poisson-Boltzmann equation (PB) -used extensively in colloidal science -fails to account for the induced charge at the particle-solvent interface, predicting that the counterion density should remain unaffected by the colloidal polarizability. In this Letter, we will show that the induced colloidal charge significantly modifies the ionic density distribution even for monovalent counterions. The theory developed in this Letter allows us to accurately predict the counterion density distribution both in the weak (monovalent counterions) and strong (multivalent counterions) coupling limits.We will use the primitive model of colloidal suspension in which colloidal particles are represented by hard spheres of radius a and dielectric constant ǫ c with the ...
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