Interaction energy sterically stabilized particles

The results of Clayfield and Lumb relate entirely to the loss of configurational entropy of the polymer chains on close approach of the particles, due either to the presence of the impenetrable surface of the opposite particle or the polymer chains that are attached to that particle. In the early papers, the effect of the solvent on the conformation of the macromolecules was ignored but an attempt was made to include the role of solvency in some of the later publications. Notwithstanding this, essentially what Clayfield and Lumb calculated was the elastic contribution to Ae repulsive free energy of interaction between sterically stabilized particles. As such, their results are manifestly unable to explain the observed flocculation of sterically stabilized particles that is induced by decreasing the solvency of the dispersion medium. Even if only for this reason, the assertion by Osmond et al. (1975) that the Clayfield and Lumb theory was the best available at that time is clearly untenable. 

FIGURE 4.34 Schematic energy interaction diagrams for two sterically stabilized particles (a) without electrical double-layer repulsion (b) with electrical double-layer repulsion. 

Many attempts have been made to develop theories to predict the interaction energy between sterically stabilized particles. The details of... 

To determine the steric interaction energy for two parallel plates at a separation, h, the mixing free energy per unit area A, G /A, for the approach of two sterically stabilized particles fi om infinite separation to a separation,... 

FIGURE 10.23 The distance dependence of the steric interaction energy of latex particles stabilized by poly(vinyl alcohol) in water (1) 500 nm, (2) 100 nm, and (3) 10 nm. The elastic modulus is 1.4 x 10 nm . Data from Sonntag [45]. 

Fig. 6.16. Interaction energies versus the mterparticle distances H for sterically stabilized particles (a) without electrical double layer repulsion (AGt = AGd + AGpoi,sO (b) with electrical double layer repulsion (AGj = AGd AGd + AGpoi,sd- For comparison the curves in the absence of AGd are also plotted. (After Pugh, Chap. 4 in Ref. [5].)...

The preceding division of the region of close approach of two sterically stabilized particles into three domains leads quite naturally to a discussion of the steric interaction in terms of two basic components the mixing free energy and the elastic free energy. 

The effect of an applied pressure on the UCFT has been investigated for polymer particles that are sterically stabilized by polyisobutylene and dispersed in 2-methy1-butane. It was observed that the UCFT was shifted to a higher temperature as the hydrostatic pressure applied to the system increased. There was also a qualitative correlation between the UCFT as a function of applied pressure and the 6 conditions of PIB + 2-methylbutane in (P,T) space. These results can be rationalized by considering the effect of pressure on the free volume dissimilarity contribution to the free energy of close approach of interacting particles. Application of corresponding states concepts to the theory of steric stabilization enables a qualitative prediction of the observed stability behaviour as a function of temperature and pressure. 

In a qualitative way, colloids are stable when they are electrically charged (we will not consider here the stability of hydrophilic colloids - gelatine, starch, proteins, macromolecules, biocolloids - where stability may be enhanced by steric arrangements and the affinity of organic functional groups to water). In a physical model of colloid stability particle repulsion due to electrostatic interaction is counteracted by attraction due to van der Waal interaction. The repulsion energy depends on the surface potential and its decrease in the diffuse part of the double layer the decay of the potential with distance is a function of the ionic strength (Fig. 3.2c and Fig. 

FIG. 13.13 Interaction between polymer-coated particles. Overlap of adsorbed polymer layers on close approach of dispersed solid particles (parts a and b). The figure also illustrates the repulsive interaction energy due to the overlap of the polymer layers (dark line in part c). Depending on the nature of the particles, a strong van der Waals attraction and perhaps electrostatic repulsion may exist between the particles in the absence of polymer layers (dashed line in part c), and the steric repulsion stabilizes the dispersion against coagulation in the primary minimum in the interaction potential. 

The second contribution to the steric interaction arises from the loss of configurational entropy of the chains on significant overlap. This effect is referred to as entropic, volume restriction, or elastic interaction, Gei. The latter increases very sharply with a decrease in h when the latter is less than 8. A schematic representation of the variation of Gmix, Gei, G, and Gj =G X + Gei + Ga) is given in Fig. 10. The total energy-distance curve shows only one minimum, at h 25, the depth of which depends on 5, R, and A. At a given R and A, G decreases with an increase in 5. With small particles and thick adsorbed layers (5 > 5 nm), G, becomes very small (approaches thermodynamic stability. This shows the importance of steric stabilization in controlling the flocculation of emulsions and suspensions. 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

The hard sphere interaction energy is an accurate approximation for short-range interactions between particles. This occurs when we have steric stabilization [33,34] due to polymer adsorption and electrostatic stabilization with a thin double layer [35,36] (i.e., high ionic... 

Fig. 13.2. The distance dependence of the steric interaction free energy for polystyrene stabilized particles in cyclohexane at 24 C (a worse than 0-solvent) ( ) experimental points 1, theoretical elastic contribution 2, theoretical mixing contribution 3, total theoretical contribution (after Doroszkowski and Lamboume, 1973).

Both of the diagrams shown in Fig. 14.1 illustrate the strong repulsive interactions that can be generated in heterosteric stabilization by incompatible polymers. Indeed it is evident in this example that the 2-3 particle interactions are stronger than either the 2-2 or 3-3 interactions. In addition. Fig. 14.1b shows the appearance of a —SkT pseudo-secondary minimum in the interactional free energy of polystyrene-coated particles at 5 K below their 0-temperature. This minimum would be sufficient to ensure 2-2 homoflocculation. The 3-3 and 2-3 interactions are clearly repulsive and so the qualitative free energy calculations confirm the possibility, foreshadowed above, of the selective flocculation of one particle type in mixtures of particles sterically stabilized by different polymers. 

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