Fundamental Interparticle Forces

Given the relationships for interactions between molecules described above, how can we convert that information into interactions between large groups of molecules, specifically, colloidal particles Mathematically, the simplest situation to analyze is that involving two hard, flat, nonpolar, effectively incite surfaces separated by a distance H in a vacuum. Hamaker showed that the free energy of attraction per unit area in such a case is given by 

In most practical instances, it is safe to neglect all of the higher terms. 

A comparison of Equations (10.4) and (10.10) shows that the free energy of attraction between two surfaces falls off much more slowly than that between individual molecules. This extended range of bulk interactions plays an important role in determining the properties of systems involving surfaces and interfaces. 

Due to the fact that interactions between surfaces fall off much more slowly with distance than those for individual atoms or molecules, a significant comphcating factor enters into the quantum mechanical evaluation of the attractive forces. The quantum-mechanical effects leading to the London-van der Waals interactions occur close to the speed of light, yet even at the short distances involved in colloids, relativistic effects can be significant. 

One must keep in mind that the preceding discussion was couched in terms of interactions in a vacuum or other inert environment, which is not a very practical situation for most applications. In order to understand real colloidal systems, one must take into consideration the effects of an intervening medium, the continuous phase, on the above interactions. 

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In this chapter, we described the fundamentals of suspension iheol-ogy from dilute suspensions to concentrated suspensions. Attention has been paid to interparticle forces and the structure of the suspension because these things drastically influence suspension iheology. In addition, visco-elastic properties of concentrated suspensions including ceramic pastes have been discussed. Finally, the mechanical properties of dry ceramic powders have been discussed in terms of the dJoulomb yield criterion, which gives the stress necessary for flow (or deformation) of the powder. These mechanical prc rties will be used in the next chapter to predict the ease with vdiich dry powders, pastes, and suspensions can be made into green bodies by various techniques. 

Theories of interparticle forces play a fundamental part in many theoretical aspects of colloidal behaviour. It is therefore of great importance to have experimental evidence for the validity of these theories. One approach to this is to study the forces between macroscopic objects, to which the same theoretical equations should apply. Since these forces arc exceedingly small until the bodies come into very close proximity, work in this area has faced considerable experimental difficulties. Experiments on the force between two plates and between a plate and a lens have been of limited validity because of the difficulty in achieving adequate surface smoothness and in completely eliminating dust. The... 

Fundamentally, the rheological properties of concentrated colloidal suspensions are determined by the interplay of thermodynamic and fluid mechanical interactions. This means that there exists an intimate relationship between the particle interactions, including Brownian motion, the suspension structure (i.e. the spatial particle distribution in the liquid), and the rheological response. With particles in the colloidal size range (at least one dimension <1 pm), the range and magnitude of the interparticle forces will have a profound influence on the suspension structure and hence, the rheological behaviour (4, 7). Both the fluid mechanical interactions and the interparticle forces are... 

Different techniques are suitable for different tasks. For example, BD focuses on molecules and particles in solution where the solvent is implicitly lumped into a friction force. On the other hand, DSMC and LB are typically applied to various fluid-related problems. MD is the only fundamental, first principles tool where the equations of motion are solved using as input an interparticle potential. MC methods map the system description into a stochastic Markov-based framework. MD and MC are often thought of as molecular modeling tools, whereas the rest are mesoscopic tools (lattice MC is also a mesoscopic tool). 

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