Colloid-atom analogy

In this chapter we discuss the basics of the phase behaviour of hard spheres plus depletants. Phase transitions are the result of physical properties of a collection of particles depending on many-body interactions. In Chap. 2 we focused on two-body interactions. As we shall see, depletion elfects are commonly not pair-wise additive. Therefore, the prediction of phase transitions of particles with depletion interaction is not straightforward. As a starting point a description is required for the thermodynamic properties of the pure colloidal dispersion. Here the colloid-atom analogy, recognized by Einstein and exploited by Perrin in his classical experiments, is very useful. Subsequently, we explain the basics of the free volume theory for the phase behaviour of colloids -I- depletants. In this chapter we treat only simplest type of depletant, the penetrable hard sphere. 

The colloid-atom analogy can also be applied to interacting systems. The direct interaction potentials between atoms then have to be replaced by the potential of mean force between the dispersed colloidal particles. In the calculation of the... 

Colloidal crystal A close-packed structure formed from colloidal particles analogous to an atomic crystal. 

In the recent literature the terms nanoparticles and nanosystems are used, in analogy to colloid and colloidal systems. The prefix nano indicates dimensions in the 1 to 100 nm range. This is above the atomic scale and, unless highly refined methods are used, below the resolution of a light microscope and thus also below the accuracy of optical microstructuring techniques. 

Up to date, besides the SFA, several non-interferometric techniques have been developed for direct measurements of surface forces between solid surfaces. The most popular and widespread is atomic force microscopy, AFM [14]. This technique has been refined for surface forces measurements by introducing the colloidal probe technique [15,16], The AFM colloidal probe method is, compared to the SFA, rapid and allows for considerable flexibility with respect to the used substrates, taken into account that there is no requirement for the surfaces to be neither transparent, nor atomically smooth over macroscopic areas. However, it suffers an inherent drawback as compared to the SFA It is not possible to determine the absolute distance between the surfaces, which is a serious limitation, especially in studies of soft interfaces, such as, e.g., polymer adsorption layers. Another interesting surface forces technique that deserves attention is measurement and analysis of surface and interaction forces (MASIF), developed by Parker [17]. This technique allows measurement of interaction between two macroscopic surfaces and uses a bimorph as a force sensor. In analogy to the AFM, this technique allows for rapid measurements and expands flexibility with respect to substrate choice however, it fails if the absolute distance resolution is required. 

Equation 10.26 would be valid if colloidal diffusion processes were exactly analogous to those for individual molecules. However, the interactions between particles in colloidal systems tend to extend over distances much greater than those involved in the formation of atomic or molecular activated complexes (say, 10-100 run vs. O.l-l.O nm). As a result, the effects of those interactions will begin to be felt by the particles well before they approach to the critical distance r. Their mutual diffusion rate will therefore be reduced and the collision frequency will drop accordingly. The collision frequency will also be reduced by the hydrostatic effect mentioned above for rapid coagulation. 

Fig. 12 shows an experiment [31], analogous to nanoindentation of atomic crystals, in which an indenter is driven into a colloidal single crystal, grown on a (100) template, to observe the resulting dislocation dynamics by both confocal and laser diffraction microscopies. The indenter is simply a commercial sewing needle, which is produced with a hemispherical tip with a diameter of 40 pm. The ratio of the tip and particle radii is similar to that in nanoindentation experiments. The needle is attached to a piezoelectric drive and is moved at a rate of 3.4 pm/h. 

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