Interactions and Dynamics in Charge-Stabilized Colloids
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to show that the conventional theory works remarkably well—even beyond its nominal domain of applicability. We then discuss experimental evidence for attractive interactions among like-charged colloidal spheres and introduce new techniques that make such measurements possible. Finally we address some of the most recent theoretical advances that promise to explain the still-anomalous observations and also to suggest in what contexts the newly recognized effects should be apparent. Colloidal Electrostatic Interactions The electrostatic coupling among charged colloidal particles results from a hierarchy of many-body interactions. In general, charged colloidal particles interact not only with each other but also with a sea of surrounding ions—some with the same charge called coions and others with opposite charge called counterions, as shown schematically in Figure 1. Charge-stabilized colloidal particles tend to carry much larger charges than the counterions and coions, and also tend to be physically much larger. Often they are referred to as macroions, a class that includes charged polymer strands (polyelectrolytes and polyampholytes) and their aggregates such as membranes and vesicles. Steric exclusion of simple ions from the macroions' interiors adds complexity to an already busy picture. Macroions influence the distribution of simple ions. These in turn mediate and moderate the interactions between the macroions. To make matters even more complicated, macroions and simple ions also interact with molecules in the
suspending fluid. When viewed in this way, the availability of any analytical theory for colloidal interactions is remarkable. That such a theory can accurately describe the behavior of richly complex suspensions is extraordinary. Despite everything the conventional theory of colloidal electrostatic interactions is quite straightforward to formulate. We treat the suspending fluid with its simple ions as an ordinary electrolyte. The local electric potential (r) depends on the concentration n,(r) of ions of type /, each with charge z,e, through Poisson's equation V24>(r) = - — % ten
(1)
where e is the fluid's dielectric constant. Unfortunately the ionic concentrations themselves depend on the local electric potential in an intrinsically nonlinear manner described in the meanfield approximation by the Boltzmann distribution n,(r) =
K,(0)
exp
Z/e(r) kRT
(2)
wherefcBis Boltzmann's constant and T is the system's temperature. The ionic concentration for species i far from the spheres is n,-
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