The results have demonstrated unexpectedly long-range attractive forces between colloidal entities. Whereas currently prevailing theory posits electrostatic forces over spans on the order of nanometers — and perhaps micrometers under extreme circumstances — the results obtained here show attractive behaviors over distances that are several orders of magnitude larger. Further, these attractive forces were observed not only between unlike-charged entities, but also between like-charged entities, thereby compounding the apparent anomaly.
4.1 The existence of long-range attractions
To test for potential artifacts, various control experiments were carried out. First, the seemingly attractive forces might have been observed merely because some fortuitous plane was investigated, a plane that happened to show attractive movements secondary to displacements elsewhere arising from phenomena such as thermally induced movements. In other words, the attractive movements may not have been primary. To test for this trivial explanation, representative planes were investigated throughout the chamber volume, both for the positively charged bead case (like-unlike) and the negatively charged bead case (like-like). In both situations, attractive movements toward the central bead from all directions were recorded throughout. Further, when the bead was removed from the chamber after some time, a dense residue of microspheres was always observed to have collected beneath the bead, reaffirming the primary movement of microspheres toward the bead. This was seen irrespective of microsphere concentration.
Other control experiments were carried out to determine whether the results might have been specific to the unique types of specimens studied. For example, some unknown substance might have been released into the suspension by the microsphere or the bead, which then induced attractive movements. To test this possibility, we replaced the gel bead with a grain of Nafion and found essentially similar results. Substituting the sulfate microspheres for carboxylate microspheres produced essentially similar results as well, as did replacing the glass-bottomed chamber with an all-polycarbonate chamber.
Hence, the long-range attractions found here seem to exist over a range of materials and situations. The fact that microspheres always — without exception — accumulated in time near or on the bead, reinforces the notion that what has been observed is indeed a long-range attraction.
4.2 Origin of long-range attractive forces
While short-range interactions have abundant theoretical underpinning,38–42
long-range interactions remain poorly understood. When like-charged colloidal particles are suspended in aqueous solution, they ordinarily attract one another.5,34
As the particles draw close enough, the attractive forces become balanced by repulsive forces between the like-charged entities. At that point, particles occupy quasi-stable sites and form colloid crystals, in which the surface-to-surface distance between particles is on the order of particle size.5, 23, 26
Although appreciable effort has been devoted to such attractive forces, there is still no common agreement on the mechanism. Following an early suggestion by Langmuir,9
Feynman suggested that the reason for such unexpected long-range attractions was an intermediate of unlike charges.20
In other words, long-range attraction between negatively charged entities arose because of positively charged intermediates: “like-likes-like because of an intermediate of unlikes.” This idea was extended in detail by Sogami and Ise et al.,10–16
who experimentally demonstrated many features of the attraction that were consistent with this concept.
Recent results from this laboratory have provided understanding of the source of the required “unlikes.” Adjacent to many hydrophilic surfaces such as those studied here, extensive regions of water with altered characteristics are observed.36, 37
These regions can extend up to hundreds of micrometers from the respective surface, and because they exclude solutes, they have been referred to as “exclusion zones.” Exclusion zones next to most hydrophilic surfaces are negatively charged, apparently through expulsion of positively charged entities, which then lie in the regions beyond.43
Thus, abundant positively charged entities may well constitute Feynman’s “unlikes.”
Additional experiments from this laboratory confirm not only the presence of unlikes, but also that pairwise attractions can occur over macroscopic separations.34
In this recent report, pairs of like-charged gel beads were placed in a chamber at initial surface-to-surface separations up to 0.5 mm. When gently dislodged from the chamber floor, the beads consistently approached one another and eventually wound up touching. These studies also used microelectrodes and pH-sensitive dyes to demonstrate the presence of unlike charges lying in between the charged beads, and this was true whether the beads were positively charged or negatively charged.
The key to explaining the long-range attraction could lie in the abundance of exclusion-zone-generated unlikes. In both types of experiment reported here, like-like and like-unlike, the microspheres themselves are of uniform charge polarity. Each microsphere is expected to have its own exclusion zone, with positive cloud beyond. Because of the abundance of these positive unlikes, microspheres may be perpetually attracted toward one another, conferring a cohesion on the microsphere array. The array then effectively acts as a unit. Hence, any attractive force applied to array microspheres closest to the bead may be felt as well by array microspheres extremely distant. Indeed, microspheres 2-mm distant from the bead moved toward the bead at velocities similar to those much less distant (; and , flat portion), confirming the cohesion — the underlying basis of which must be attractive interactions.
If the like-likes-like concept is correct, then one might expect that like-charged microspheres might ultimately aggregate. However, that is neither expected nor found. As particles approach one another, repulsive forces between particles will increase; once attractive and repulsive forces are in balance, the system remains stable.23
This feature is amply evidenced in studies of colloid crystals.5,26
Thus, the like-likes-like mechanism does not necessarily anticipate aggregation.
On the other hand, the extreme distance over which such attractive interactions can apparently act was unexpected. When microsphere concentration was reduced so that microspheres were as far as 200 μm apart, the attraction was maintained; microspheres continued to move toward the bead as a unit. The velocities were indeed lower than normal (), but at a far enough distance from the bead, microspheres still translated toward the bead at a consistent velocity irrespective of distance from the bead. Hence, the attractive forces necessary to maintain cohesion persisted even at these extreme inter-microsphere separations.
In sum, attractive interactions could be detected at distances up to 2 mm. In part, the extreme range stems from the fact that the colloidal particles that are being attracted act as a unit, held by cohesive forces.
4.3 Attractive forces near the bead
In the discussion above, we considered the microsphere array, focusing on the reason why velocities could be independent of distance from the bead. On the other hand, at distances closer than ~200 μm from the bead in the like-unlike situation, microspheres translated toward the bead with higher velocity — the magnitude increasing with increasing proximity. An important question arises from this observation: If microspheres acted as a cohesive unit, why should the velocity be higher closer to the bead and lower farther away?
A possibility is that the attractive force very close to the bead is indeed high. This is not surprising with positive bead attracting negative microspheres. If such attractive force exceeds the cohesive force holding together the microspheres, then microspheres of the array will pull progressively apart. This is observed: microspheres farther away do not move toward the bead as rapidly as those closer. The primary attractive force should then diminish with radial spread — ultimately falling to the point at which it equals the inter-microsphere force holding together the array. At that point, the array will translate as a unit, the velocity at the near edge equaling the velocity at the far edge. Hence, the observed velocity distribution is not entirely surprising.
4.4 Exclusion zones: an additional source of long-range forces
Results obtained with a negative bead and negative microspheres were essentially similar to the results with positive bead and negative microspheres with one notable difference: the presence of a 300-μm exclusion zone surrounding the bead. This zone contained no microspheres at all. Microspheres nevertheless moved consistently toward the bead, right up to the exclusion zone’s far edge. It is as though an attractive force between like-charged entities projected across this large empty zone from the bead to the microsphere array.
The explanation may once again follow from the like-likes-like phenomenon. Around the bead, the exclusion zone is negatively charged37
whereas the region beyond has low pH, indicating excess protons and positive charge.43
These proton unlikes will attract negatively charged microspheres, which will then confer the attractive movements onto the entire microsphere array, as observed.
One may notice that when the microspheres approached the edge of the exclusion zone, they did not speed up as they did in the positively charged bead case. The situation here is quite different. In the case of the positively charged bead, the primary attraction was from the bead surface — a well-defined positively charged feature. In the present case the attractor is diffuse; it is a cloud of protons, which may be spread diffusely over the solution. Hence, the situation is quite different, and the force vs. distance relation is not necessarily expected to be the same.
A point of perhaps secondary significance is that microsphere velocity appeared to decrease somewhat as microspheres approached the edge of the exclusion zone. The diminution could be a real effect; however, it almost certainly stems at least in part from an asymmetry — the fact that the bead rests on the bottom of the chamber. The exclusion zone is thus somewhat egg-shaped and microspheres translating into its vicinity moved in a partially downward direction, resulting in the sediment patterns shown in . Hence, the velocity as viewed from above will be a vector component of the actual velocity, and thus lower than that measured farther away where no downward component existed.
4.5 Mechanistic Considerations
Overall, the results reported in this paper appear counter-intuitive on a number of counts. First, only nanometer-scale interactions are predicted by standard DLVO theory (although micrometer-scale interactions have been amply observed; see citations above). Much of conventional physical chemistry is based on interactional limits extending over relatively short ranges. By contrast, the attractive interactions reported here extend to distances on the sub-millimeter scale, orders of magnitude larger than anticipated. A second and perhaps even more counter-intuitive point is that the attraction exists even when the protagonists have the same charge. As demonstrated, the explanation of these counterintuitive observations appears to be the like-likes-like mechanism.
A potential alternative explanation is that of an electrophoretic cell, wherein an electrical potential draws microspheres toward the bead. Thus, the central bead might generate a potential difference around itself, attracting the microspheres toward it. However, such potential differences have been directly measured; they extend over a span of only about 200 μm, 37
whereas the attractive force extends an order of magnitude farther. Moreover, the attractive movement was seen even when bead and microspheres were of the same polarity.