The Thermodynamics of Colloidal Systems

Consider a liquid droplet in equilibrium with its vapour (see Fig. 3.6). Each molecule is subject to attractive van der Waals forces due to each of its neighbours. Inside, the medium is isotropic (i.e., it has identical properties in all directions) and it can be assumed that the mean global attraction exerted on a molecule inside the droplet by its neighbours is zero. The same is not true for a molecule located near the outer surface of the droplet, which is attracted 

The energy of the droplet is minimised when its surface area is minimised, which implies a spherical shape (assuming there are no external forces) for a given volume of substance. Conversely, in order to deform the droplet and hence increase its surface area by A, energy aE must be supplied, where 

The quantity 7 is called the surface tension of the liquid and it is a physical constant depending on the material under consideration. It is the work required to generate unit area of surface and it is also the reversibly stored energy resulting from an increase of one unit in the surface area. The surface tension characterises the surface free energy and is expressed in [J/m ] or in [N/m]. For example, water has a surface tension 7 = 73 x 10 N/m and benzene a surface tension 7 = 29 x 10 N/m, at room temperature. 

If the air is replaced by a liquid L2, immiscible with the liquid Li constituting the droplet, we find a quite analogous situation. On either side of the interface, the molecules close to the interface are subject to forces which are only partially balanced. In the same way, if we wish to increase the interfacial area, by dispersing Li in L2, for example, the energy 

Let us return to the picture in Fig. 3.6 and break up the droplet we have been talking about. As it becomes more and more divided up, the proportion of atoms at or near to the interfaces will grow. This division (obtained by grinding for a solid) can only occur if we supply energy aE = 7AA to the system, where aA is the increase in area. This energy can be retrieved if the small droplets come back together into a single droplet (coalescence) and, for 

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