Charge Regulation of Colloidal Particles: Theory and Simulations

Abstract

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...

Osmotic stress and pore nucleation in charged biological nanoshells and capsids

“…Here we shall assume fixed surface charges, so that charge regulation effects are not taken into account at this level of approximation. Although such mechanisms are known to have a non-trivial influence on both the ionic diffusion and structure across the double layers [82][83][84][85][86][87][88], our current aim is rather to highlight the effects of salt addition on the mechanical shell properties at fixed surface charges. Ions are free to move throughout the system, and are allowed to diffuse through the semi-permeable membrane, just like the solvent molecules.…”

Charge-, salt- and flexoelectricity-driven anchoring effects in nematics

“…III. Therefore, charge regulation is of major interest in soft matter applications, from the charging behaviour of colloidal particles [47,[58][59][60][61][62], to the effect on interaction potentials [63], to phase (a)…”

“…Furthermore, recently it was shown within a minimal sticky hard-sphere model that the equilibrium constant of a surface group on a chargeable surface does not equal the equilibrium constant of the same functional group in single molecules, see for details Ref. [62].…”

Equilibrium conformations and surface charge regulation of spherical polymer brushes in stretched regimes

“…Electrostatic interactions are usually of great relevance for driving (and further stabilizing) these processes [57][58][59][60][61][62][63] . They are one of the main driven forces that controls the so-called charge-regulation mechanisms, responsible for the binding/dissociation of ions into/from surface functional groups in an aqueous environment containing acidic/basic dissociated ions [64][65][66][67][68][69][70][71][72] .…”

“…One traditional approach for modeling the CR process in bulk solutions is the Ninham and Parsegian 73 (NP) theory of ionic dissociation. However, since this theoretical framework relies on the use of bulk association constants, its extension to the (highly inhomogeneous) environment in the vicinity of curved surfaces is not straightforward 69 . Quite recently, a charge regulation approach has been proposed which overcomes this drawback of NP theory by allowing for the calculation of surface association constants in the case in which functional groups are randomly arranged into lattice sites over the nanoparticle's surface 68,69 .…”