Ž.Current Opinion in Colloid & Interface Science 6 2001 372᎐382Computer simulations of charge and steric stabilisedcolloidal suspensionsMarjolein DijkstraDebye Institute, Soft Condensed Matter Physics, Utrecht Uni¨ersity, Princetonplein 5, 3584 CC Utrecht, The NetherlandsAbstractComputer simulations of colloidal suspensions are prohibited by slow equilibration as very different length and time scalesare involved for the various species. This is the reason that most simulations involve some degree of coarse-graining, wherebythe degrees of freedom of the microscopic particles are traced out, and the mesoscopic particles interact with an effectivepotential, resulting in a coarse-grained, effective one-component description of the suspension. The focus of this paper is onrecent simulation work of charge and steric stabilised colloidal suspensions. We discuss both direct simulations of the truecolloidal mixture and coarse-grained approaches of the suspension involving effective interactions for the colloids. 䊚 2001Elsevier Science Ltd. All rights reserved.Keywords: Charged colloids; Colloid᎐polymer mixtures; Hard spheres; Phase separation; Effective potentials; Computer simulation1. IntroductionColloidal suspensions are complex fluids that con-sist of mesoscopic particles suspended in a solventŽ.e.g. water . The colloidal particles are significantlylarger than the solvent molecules, but small enoughto show Brownian motion. In the case that the lineardimension R of the colloids is in the regime of 10nm-R-1000 nm, no significant sedimentation oc-curs in the earth’s gravity. Examples of colloidal parti-cles are viruses, proteins, synthetic polymeric particlesŽ.latex, PMMA , micelles, etc. Suspensions of theseparticles play an important role in biology, e.g. blood,but also many industrial products are essentially col-loidal suspensions, e.g. paints, inks, food, detergents,cosmetics.Due to fluctuating dipole moments, an attractive‘dispersion’ force, or Van der Waals force, actsŽ.E-mail address: [email protected] M. Dijkstra .between every pair of atoms separated by a distancer. Summing over all pairs of atoms in two colloidalparticles gives rise to a strong Van der Waals attrac-tion between the colloids, which can be larger byorders of magnitude than the thermal energy kT.BThis may lead to irreversible aggregation of the col-loids. In order to stabilise a colloidal suspensionagainst irreversible aggregation two mechanisms arecommon: charge and steric stabilisation. In the caseof charge stabilisation, the colloidal particles haveionisable groups on their surfaces, which dissociatewhen the particles are suspended in a polar liquid.The colloidal particles then acquire a net surfacecharge Ze, with e the elementary charge and Z the2<<5charge number typically in the range 10 - Z - 10 .The released counterions form a diffuse layer ofthickness around each colloidal particle, where DDis the Debye screening length. The approach of twocharged colloids leads to overlap of these so-calledelectric double layers, and causes a repulsive forcewxthat can stabilise the particles against aggregation 1 .1359-0294r01r$ - see front matter 䊚 2001 Elsevier Science Ltd. All rights reserved.Ž.PII: S 1 3 5 9 - 0 2 9 4 0 1 00106-6()M. Dijkstra r Current Opinion in Colloid & Interface Science 6 2001 372᎐382 373In the case of steric stabilisation the colloidal parti-cles are coated with a polymer layer. When two coatedcolloidal particles approach each other sufficientlyclosely, the polymer layers interpenetrate and overlap,which leads to a reduction of the polymer entropy,and hence to an effective repulsive force between thecolloids. This repulsion leads again to stabilisation ofthe particles against aggregation.Often other components, such as salt ions, poly-mers or smaller colloids, are present in suspension aswell. In the case of charged colloids, the addition ofelectrolyte or salt changes the Debye screening length . On the other hand, the addition of free polymerDcoils or smaller colloids to a steric stabilised colloidalsuspension induces a depletion interaction betweencolloids which is mainly attractive and of a range ofwxthe size of the depletant 2,3 . The concentration ofadded salt, or the size and concentration of addedfree polymers or smaller colloids can therefore, beused as control parameters with which the effectiveinteractions between the colloids can be tailored. Thepossibility of tailoring the effective interactions en-riches the physics of colloidal systems compared toŽ.simple atomic fluids, and leads to a wide range ofpractical applications.The focus of this review is on computer simulationsof steric and charge stabilised colloidal suspensions,with particular emphasis on published research overthe past five years. In Section 2, research on chargestabilised colloidal suspensions is discussed. Thereader is also referred to an excellent review byHansen and Lowen on recent theoretical and experi-¨w䢇䢇xmental advances in charged colloids 4 . Cell modeland hypernetted chain calculations of polyelectrolytesw䢇䢇xare reviewed by Vlachy 5 . In Section 3 a survey onrecent simulation work of steric stabilised suspensionsis presented.2. Charge-stabilised colloidal suspensionsCharge-stabilised colloidal suspensions consist ofŽ.spherical or anisotropic mesoscopic colloidal parti-cles suspended in a polar solvent with co- and counter-ions. The radius of the co- and counterions is compa-rable to that of the solvent molecules, i.e. of the orderof 0.1᎐0.3 nm. A statistical mechanics description ofthese highly asymmetric multicomponent fluids repre-sent a major challenge as very different length andtime scales are involved for the various species. Thisis the reason why attempts to treat the mesoscopiccolloids and the microscopic salt and solvent particleson an equal footing usually fail. It is therefore notsurprising that the present understanding of thesesystems is based on simplified models, in which thedegrees of freedom of the microscopic particles havebeen integrated out, and the mesoscopic particlesŽ.interact with an effective usually pairwise potentialresulting in a coarse-grained effective one-componentdescription of the suspension. The standard and verysuccessful effective one-component description ofcharged colloidal suspensions dates back to the 1940sand is due to Derjaguin, Landau, Verwey, and Over-Ž.wxbeek DLVO 2 . The DLVO theory is the cornerstone of
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