Phases of Thin Colloidal Layers
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The Phase Diagram of 3D Monodisperse Colloidal Systems Monodisperse suspensions of 0.1-1micrometer-diameter colloidal spheres can serve as powerful model systems for investigating collective phenomena in
MRS BULLETIN/OCTOBER 1998
condensed-matter physics4 as the length and time scales of spheres suspended in a fluid such as water are observable with ordinary optical video microscopy. Two types of spheres have been studied extensively: highly charged polystyrene (PS) spheres with up to 105 surface charge groups, and silica or polyfmethyl methacrylate) (PMMA) spheres with much less surface charge that are often coated with thin polymer overlayers to avoid aggregation. These are sometimes called "charge-stabilized" and "sterically stabilized" colloids, respectively.5 As is discussed in detail in the article by Crocker and Grier in this issue,6 despite four decades of research on colloids, the interparticle interactions of micrometersized highly charged colloidal spheres are not yet perfectly understood. This system remains theoretically intractable because of the many-body, nonadditive nature of the interionic electrostatic coupling—particularly when the spheres
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Figure 1. The pair potential UfrJ between a pair of spheres, each of radius a = 150 nm and carrying a charge of 1,000-electron equivalents separated by a center-to-center distance r. The potentials are calculated for spheres dispersed in aqueous salt solutions—the screening lengths of which, K ', range from «-a = 8 to «a = 1. Potentials are plotted in units of the thermal-energy scale ksT.
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are comparable in size to the range of their interaction. Sterically stabilized PMMA or silica spheres interact with simpler hard-sphere or soft-sphere repulsions, especially when they are suspended in a solvent that minimizes their electrostatic interactions. For the sake of clarity, I will assume that "charge-stabilized" spheres interact through a screened-Coulomb — or Yukawa—repulsion. This component of the Derjagin, Landau, Verwey, and Overbeek theory 6 for colloidal electrostatic interactions dominates for highly charged spheres in a weakly screening electrolyte and is shown computed for various values of the electrostatic screening length in Figure 1. The Yukawa repulsion is derived through the linearization of the Poisson-Boltzmann equation describing the distribution of screening charges around a spherical macroion. This approximation is not justifiable for spheres with high surface-charge densities. Nevertheless the measured potentials appear to follow the form well'1—at least under some conditions—provided that the spheres' actual charge is replaced with a much smaller effective charge. One can see from the plots in Figure 1 that the shape of the effective Yukawa potential changes from something that looks like a hard-sphere (HS) repulsion to something much more closely resembling a long-range Coulomb potential as the screening length K ' increases. This can be accomplished in practice by reducing the concentration of ions dissolved in the electrolyte. The
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