Work of dispersion

The work of dispersion, Wd, involved in wetting a unit area of the solid substrate is given by the difference between the interfacial tension of the solid/liquid interface, ysL, and that of the solid/vapor interface, ySv,... 

Thus, the work of dispersion depends on yLV and 0, both of which are reduced by the addition of surfactant. 

In general, for liquids, which are normally smooth, the value of i is equal to 1. For solids, i is always greater than 1. The effect of surface roughness on adhesion, penetration and spreading for a rough cube is shown in Table 9.3. The total work for the sum of all of these steps is referred to as the work of dispersion. When the work of dispersion is negative, dispersion is spontaneous. 

Thus, wetting of the external surface of the powder depends on the liquid surface tension and the contact angle. i 9 < 90°, cos9 is positive and the work of dispersion is negative - that is, wetting will be spontaneous. 

Wcr hom work of homogeneous formation of critical nucleus Wi work of dispersion... 

The conditions of stability of colloidal particles with respect to further dispersion down to molecular sizes can be found by analyzing the A (d) dependence at d - b. If the value of a does not change with the decrease in d down to the molecular dimensions, and if a can be used to describe the work of dispersing, further dispersion of particles down to molecular sizes is thermodynamically favorable. In a real polydisperse system the dispersed particles of colloidal range with some defined particle size distribution may, however, also fluctuationally form at a = const. 

The conditions needed for a spontaneous dispersion of the condensed phase and the formation of a lyophilic colloidal system were analyzed by Rehbinder and Shchukin back in 1958, and a quantitative description of this problem was proposed. That original analysis was based on the estimation of the changes in the free energy, AF, upon dispersing a condensed phase in a given dispersion medium [62]. Let s assume that, as a result of dispersion, n particles have separated from the condensed phase. Due to the participation of these separated particles in Brownian motion, the work of dispersion, wa5 o, is balanced by the gain in entropy, AS... 

Expressions 4.3, 4.5, 4.6, and 4.9 in the C = v/V scheme are represented by a single equation, namely. Equation 4.8, and in the C = n/N scheme by Equation 4.11. In the latter scheme, the competition between the work of dispersion needed to isolate spherical particles from a macroscopic phase and the entropy gain dne to the participation of the released particles in Brownian motion can be represented by the following relation ... 

This rather crude estimate reveals substantial differences in the energy of dispersion of a compact phase and that of agglomerate consisting of aggregated particles. In the latter case, the work of dispersion is r//io times lower than in the former case, and the difference increases with an increase in particle size. Consequently, for a particle aggregate, the conditions under which spontaneous dispersion takes place are quantitatively different from those for a compact phase (Figure 4.37). 

Similar to the AF(r) behavior at v = const, the AF n) analysis at r = const may reveal significant differences between the C = v/F and C = nIN schemes. In this case, these differences are also quantitative the positions of and, correspondingly, of (i.e.. In are shifted. In both of these schemes, the dependence of AF on the relation between the work of dispersion in an individual act of particle isolation, w, and the entropy factor is similar. It is worth emphasizing here that this potential barrier, w, is a true and universal physical characteristic of the described systems, differing from a virtual maximum in the AF(r) function at v =const. 

Within a restriction to the case of dilute monodisperse systems, the analysis of the ratio between the elementary work of dispersion, w, conceived as the work of particle isolation from a compact phase or disperse strnctnre, and the entropy factor, kT ln [l/C]-i-l, represents a general, universal approach to the evaluation of the possibility of the spontaneous dispersion of a macroscopic phase into colloid size particles (Figure 4,39), In the analysis of the behavior of the AF function, while setting the various variables, r, a, C, T, v, and n constant, the function is determined by the work of the dispersion factor, which is equal to the entropy factor, The transition in the dispersion process from positive values for the system free energy to negative ones determines the possibility of the formation of a thermodynamically stable system. 

FIGURE 4.39 The relationship between a change in the system free energy, AF/kT, for a monodisperse system and the particle concentration for varions valnes of the work of dispersion, w (in kF units), needed to isolate an individual particle from a macroscopic phase, which is either a compact phase (w = a8 a) or a globular structure composed of identical particles (w = 1/2zM]). The characteristic steep transitions from positive values of AF to negative ones and negative minima at larger dilutions are clearly visible. (Redrawn from Shchukin, E.D., J. Dispers. Sci. Technol., 25, 875, 2004.)... 

Let us consider an agrochemical powder with surface euea A. Before the powder is dispersed in the liquid it has a surface tension y and after immersion in the liquid it has a surface tension Ysl. The work of dispersion W i is simply given by the difference in adhesion or wetting tension of the SL and SV,... 

---