Interaction between like-charged colloidal spheres in electrolyte solutions

Abstract

How colloidal particles interact with each other is one of the key issues that determines our ability to interpret experimental results for phase transitions in colloidal dispersions and our ability to apply colloid science to various industrial processes. The long-accepted theories for answering this question have been challenged by results from recent experiments. Herein we show from Monte-Carlo simulations that there is a short-range attractive force between identical macroions in electrolyte solutions containing divalent counterions. Complementing some recent and related results by others, we present strong evidence of attraction between a pair of spherical macroions in the presence of added salt ions for the conditions where the interacting macroion pair is not affected by any other macroions that may be in the solution. This attractive force follows from the internal-energy contribution of counterion mediation. Contrary to conventional expectations, for charged macroions in an electrolyte solution, the entropic force is repulsive at most solution conditions because of localization of small ions in the vicinity of macroions. Both Derjaguin-Landau-Verwey-Overbeek theory and Sogami-Ise theory fail to describe the attractive interactions found in our simulations; the former predicts only repulsive interaction and the latter predicts a long-range attraction that is too weak and occurs at macroion separations that are too large. Our simulations provide fundamental ''data'' toward an improved theory for the potential of mean force as required for optimum design of new materials including those containing nanoparticles.The potential of mean force between colloidal particles in electrolyte solutions plays a central role in describing the phase behavior and the kinetics of agglomeration in colloidal dispersions (1, 2). It is of fundamental importance for understanding the properties of inorganic materials (e.g., ceramics composed of nanoparticles), foods such as milk, and solutions of biomacromolecules including globular proteins (3-5). After decades of theoretical and experimental efforts, some aspects of colloidal interactions remain puzzling, in particular the issue of attractive electrostatic forces between like-charged colloidal particles in an electrolyte solution. Experimental evidence for such attraction has been indirect and largely complicated by boundary or polydispersity effects (6-8). Classical theories are not satisfactory because they are based on the mean-field approximation that neglects the effects of excluded volume and Coulombic correlations among small ions. Depending on simplifying assumptions, these theories have led to qualitatively different results. For example, theories based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) approximation describe the electrostatic interaction between macroions of the same charge as screened repulsion (9-10, 12, 13), and others, represented by Sogami-Ise (SI) theory, predict a universal long-range attractive interaction (11,14). Likewise, the possibil...

Electrostatic interactions in strongly coupled soft matter

“…As already seen from Eq. (4), the coupling strength grows quite rapidly with the counterion valency (Ξ ∼ q 3 ), which agrees with experimental and numerical evidence indicating highly growing correlation effects for increasing counterion valency [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. In fact as known from these studies, typical coupling strength of Ξ ∼ 10 2 (or larger) already reflects strong-coupling regime and a value of Ξ ∼ 1 (or smaller) typically corresponds to the weak-coupling regime.…”

“…For instance, the DNA condensation process, in which long DNA molecules condense into a tightly packed, circumferentially wound torus, is observed in experiments where multivalent counterions (such as trivalent spermidine ions) are introduced [10]. A similar trend has also been found in numerous numerical simulations of like-charged membranes, colloids and polymers [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42], where highly charged macroions are found to form closely-packed bound states due to attractive forces of electrostatic origin. These attractive forces are of typically large strength compared to the usual van-der-Waals attraction and may have significant practical implications where, for instance, multivalent counterions are present.…”

“…The main scenarios which are put forward to explain the phenomenon of like-charge attraction have gone beyond the mean-field level by demonstrating that this phenomenon can be reproduced quantitatively by inclusion of electrostatic correlations [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,…”

“…Counterions form electrostatically-bound clouds in the proximity of macroions and in many cases, predominantly determine the electric properties of charged solutions [3]. In particular, counterions can alter the effective interaction between like-charged macroions, and may generate a dominant electrostatic attraction between them in certain physical conditions [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,…”

Ionic Effects in Collapse of Polyelectrolyte Brushes

“…The attraction is magnified as the valence of counterions increases. 3,4,8,14 According to a previous Monte Carlo simulation, 47 electrostatic attraction between like-charged macroions is most significant at an intermediate concentration of counterions. A similar effect can be identified in a polyelectrolyte brush.…”