These three experimental observations suggest that the metastable colloidal crystallites are bound together by a strong long-range attraction not accounted for by the DLVO theory. Recent direct measurements of the pairwise colloidal interaction potential [16, 17, 18] demonstrate that no such attraction appears for isolated pairs of spheres. Attractions are observed, however, when spheres are rigidly confined to the plane by closely spaced parallel glass surfaces [18, 28, 29], although the mechanism for this attraction is not yet understood. Since the metastable crystals form at glass walls, a wall-mediated interaction might explain our observations.
Two considerations stand in the way of this interpretation. First, the wall separation in the present experiments is ten times larger than in the experiments for which pair attractions were measured, and the ability of a single wall to induce attractive interactions has not been demonstrated. Second, the walls' measured influence on colloidal interactions falls off with distance, h, from the wall . Consequently, the effect might not extend far enough to stabilize the crystalline layers farthest from the wall.
To examine the range and magnitude of intersphere attractions mediated by a single glass wall, we performed direct interaction measurements in the same sample cell used to study the metastable crystals. The measurement technique is described in detail in Ref. . Its salient features are quite straightforward. Two optical tweezers are used to position a pair of spheres at fixed separations in the focal plane of the microscope. When the laser powering the traps is interrupted, the spheres move under the combined influence of random thermal forces and their mutual interaction. Blinking the traps on and off in synchrony with the video camera's shutter allows us to sample experimentally the Markovian propagator for the master equation whose steady-state solution is the equilibrium pair distribution function for the spheres, g(r). The pair distribution function is related to the pair interaction potential through Boltzmann's equation:
Approximately 20,000 images of sphere pairs taken at 1/30 sec intervals suffice to measure an interaction potential with 60 nm spatial resolution and energy sensitivity over a range of and , respectively. To avoid many-body contributions to the measurements, we diluted the suspension so that no other spheres wandered within 25 of the test pair.
The lower trace in Fig. 4 was obtained with the optical tweezers focused from the sample cell's upper glass wall. At this distance from the wall, the measured interaction potential has a strongly attractive minimum at a center-to-center separation of . This confirms that a single wall can induce an attraction between like-charged colloidal spheres comparable to that deduced from structural analysis of the metastable crystals. The range and strength of the attraction are too great to be accounted for by van der Waals attraction. Image charges in the nearby glass walls similarly would exert too weak an influence. The attraction's dependence on distance from the wall suggests instead a counterion-mediated mechanism .
No attraction is evident in the upper trace of Fig. 4 which was measured from the lower wall. As has been observed for spheres confined by a pair of closely spaced glass walls , attractive interactions only appear when the spheres' ion clouds interact strongly with the glass wall's screening charge. These conditions are not considered in the formulation of the DLVO theory [14, 15]. The DLVO theory should apply, however, for isolated pairs of spheres far from the walls. The dashed curve in Fig. 4 is a three parameter fit to Eq. (1) for the effective charge, Z= 7300, the Debye-Hückel screening length, , and an additive offset.
The absence of an attractive minimum at suggests that the wall-induced attractive interaction alone cannot stabilize the fourth and fifth layers of crystals such as those in Fig. 1 which are at least from the wall. Furthermore, diluting the suspension for the interaction measurements probably reduced the electrolyte's ionic strength and increased not only the screening length but also the range of the wall-induced interaction. This seems likely because the center-to-center separation of both the attractive minimum and the repulsive core in U(r) exceed the crystals' nearest neighbor spacing of . In the higher ionic concentrations at which the metastable crystals were studied, the influence of the wall is likely to extend even less far than is indicated in Fig. 4. Interaction measurements in the confined geometry by Kepler and Fraden  also show that the range and strength of the wall-induced interaction depend strongly on the electrolyte's ionic concentration. They confirm, in particular, that higher ionic strengths lead to shorter-ranged attractions.