7852
J. Phys. Chem. B 2000, 104, 7852-7857
Charged Colloidal Solutions with Short Flexible Counterions Jurij Resˇcˇ icˇ † and Per Linse* Physical Chemisty 1, Center for Chemistry and Chemical Engineering, Lund UniVersity, P.O. Box 124, S-221 00 Lund, Sweden ReceiVed: February 29, 2000; In Final Form: May 2, 2000
Micellar-like solutions consisting of macroions with 60 negative elementary charges with short flexible counterions were studied by Monte Carlo simulations. The structure of the systems was considered as a function of the properties of the flexible counterions and the macroion density. At increasing charge of the flexible counterions, a reduced macroion-macroion repulsion is observed and eventually the system phase separates. The effects are similar to that found for simple multivalent counterions, but weaker, originating from spatial correlations between counterions residing on different macroions. Another type of reduced phase stability appears as the separation between the charges in a flexible dimer increases; now the reduced stability is induced by counterions bridging pairs of macrions.
1. Introduction The function of charged colloids is essential not only in modern technological processes, but it is also vital in nearly all biological systems. Despite their ubiquity, colloidal systems are still not yet fully understood. For a half century the DLVO1,2 theory has dominated the description of the interactions between charged colloidal particles in solution. Since the mid-80s, however, severe disagreements between experiments and the DLVO theory have been reported,3-5 which have renewed theoretical interest in this area. Recently, fundamental progress in understanding of the behavior of highly asymmetric electrolytes has been made. At sufficiently strong electrostatic coupling, a net attractive force between like-charged colloidal particles in simple model systems has been demonstrated using Monte Carlo (MC) simulations6-11 (for a review, see ref 12), in contradiction to the DLVO theory, which always predicts repulsive interactions. In the presence of trivalent counterions in aqueous solution, the electrostatic forces can cause a clustering of the colloidal particles9 or even a phase separation.10 In many important colloidal systems, multivalent counterions are of a molecular nature usually having more than one charged site. It has been experimentally demonstrated that multivalent ions like ATP, short polyamines, and oligopeptides play a crucial role in determining higher-order DNA structure.13-15 Understanding the mechanisms of biological molecules like DNA and proteins are very important in, e.g., the rapidly growing research field of human gene therapy. Flocculation is another well-known phenomenon in colloid chemistry, widely used in numerous engineering applications. Here, high-mass polyelectrolytes (e.g., polyacrylamide and its derivatives) have been found to be very efficient flocculants.16 Nevertheless, short polyelectrolytes like polyamines are also expected to exhibit similar bridging effects, which is the first step leading to a phase separation. In comparison to simple multivalent ions, one can, however, expect the electrostatic screening and correlation appearing in systems with short * To whom correspondence should be addressed. † Permanent address: Faculty of Chemistry and Chemical Technology, University of Ljubljana, P.O. Box 537, 1000 Ljubljana, Slovenia.
flexible counterions to be inferior to that in systems with simple counterions of the same total charge. Moreover, one anticipates that the effects will decrease with increasing distance between the charged sites. It is therefore also of principle interest to examine the influence of counterions possesing more than one charged site on both thermodynamical and structural properties of charged colloidal systems. In the following, we will refer to these ions as flexible counterions in contrast to the simple ones. The aim of this work is to study models representing solutions of spherical and charged colloidal particles with short flexible counterions. In particular, our focus is to examine the influence of the number of charges residing in the flexible counterions and of the separation of these charges on both thermodynamic and structural properties and relate these results to properties of systems with simple counterions. Previous and related simulation studies have involved investigations of short flexible polyelectrolytes at oppositely charged planar surfaces17 and the force between two charged colloidal particles with flexible counterions.18 2. Model and Method 2.A. Model. The model system contains two types of spherical and charged particles: (i) macroions of diameter σM ) 40 Å and charge ZM ) -60, representing charged colloidal particles, and (ii) small ions of diameter σI ) 4 Å and charge ZI ) +1, representing the oppositely charged counterions. The small ions are bonded to each other to form linear oligomers (dimers to tetramers). The solvent enters the model only by its dielectric permittivity r. The total potential energy of the system can be expressed as
Utot )
el bond uhs ∑ ij + ∑ uij + ∑ uij i
