Long-range Repulsive Systems

Rheological properties, Russel argues, are most interesting when the pair interaction potential between the particles dominates the flow 

This volume fraction represents an increase in the effective particle size to give a collision diameter Reff 

This new particle diameter represents the separation at which the hydrodynamic stress balances with the thermal and thermodynamic stresses  

As we have seen in the previous chapter, strongly interacting colloidal systems are characterised by a very rapid increase in the low shear 

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Double-layer forces are commonly used to induce repulsive interactions in colloidal systems. However, the range of electrostatic forces is strongly reduced by increasing the ionic strength of the continuous phase. Also, electrostatic effects are strong only in polar solvents, which is a severe restriction. An alternative way to create long-range repulsion is to adsorb macromolecules at the interface between the dispersed and the continuous phase. Polymer chains may be densely adsorbed on surfaces where they form loops and tails with a very broad distribution of sizes... 

Recently Klein and Leyvraz considered nonclassical nucleation near a spinodal using a model with weak long-range repulsive potentials, and showed that it differed substantially from the classical picture, as expected from the considerations of Harrowell and Oxtoby. However, it is unclear whether real systems behave in such a way as to show the influence of a metastability limit for the undercooled liquid. 

If we want to create a colloidally stable system, some type of interparticle repulsion needs to be introduced to overcome the van der Waals attraction. In a stable system, the maximum attractive interparticle energy should be less than 1 -2 kT to allow thermal motion to readily break all particle-particle bonds. Since the magnitude and range of the attractive van der Waals interaction scales with the effective Hamaker constant, a relatively long-range repulsion is needed to stabilize suspensions of ceramic powders such as alumina and silicon carbide silica, however, is stabilized by a very short-range repulsion. 

The experimental systems are not a one-component system and contain, in particular, water, salt, and polymers. It is the effective interaction resulting from the contributions of the other components that provide the combination of short-range attraction and long-range repulsion. For now, we will not worry about how long-range repulsion can appear and we shall focus on the shape of the structure factor when particles aggregate into domains. 

The corresponding potential of mean force (pmf) displays a similar functional form (Fig. 5b). In Systems II and IV, the mean force has not approached zero at the longest separation considered, and hence should be considerably more repulsive (shifted upward) than shown to match the conventional limit U (r) 0 as r oo. For System I, the pmf at contact (r = 2Ru) is reduced to 7kT. Regarding System III, only a weak long-range repulsion remains, a barrier of IkT appears at r 2.4Rm> and a global minimum of - 2kT occurs at macroion contact. 

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