Microscopic measurement of the pair interaction potential of charge-stabilized colloid.

The past century of research on charge-stabilized colloidal suspensions has been inspired by their intrinsic interest as distinct states of matter [1], by their considerable technological value [2], and more recently by their utility as model condensed matter systems [3, 4]. The standard theory for the interaction between charged colloidal spheres was formulated almost 50 years ago by Derjaguin, Landau, Verwey, and Overbeek (DLVO) [5, 6]. Calculations based on the DLVO theory [7–9] account at least qualitatively for the observed fluid-crystal and fccbcc phase boundaries [10, 11] as well as for many of these phases’ bulk properties [12, 13]. Persistent quantitative discrepancies [10, 11] and anomalous observations including the unaccounted-for monodisperse glassy phase [11] suggest that the theory is not yet complete, however. Differences with the DLVO theory also have been raised on theoretical grounds [14–18]. In light of the fundamental importance of these considerations to the understanding of colloidal systems, we have measured the colloidal pair potential directly, utilizing digital video microscopy and optical trapping techniques. In particular, we extract the twoparticle interaction from the dynamics of isolated pairs of particles moving away from artificially created initial configurations. The colloid in our study consists of commercially available polystyrene sulfate spheres with radius a = 326 nm, monodisperse to within 1 percent (Duke Scientific, No. 5065A). Particles of this size undergo vigorous Brownian motion in water and yet are sufficiently large to be imaged with a conventional light microscope. When such spheres are dispersed in water, the ionic groups bonded to their surfaces dissociate and give rise to a screened electrostatic interaction. For sphere separations large enough that the Debye-Hückel approximation holds, the DLVO theory gives the potential: