Mixing Interaction Gmix

In contrast, if 0.5 (i.e., the chains are in a poor solvent condition) then G j will be negative and the mixing interaction will become attractive. G j is always positive, and hence in some cases stable dispersions can be produced in a relatively poor solvent (enhanced steric stabilisation). 

In the overlap region, the chemical potential of the hydrated chains is now higher than in the remainder of the layer (with no overlap). This amounts to an increase in the osmotic pressure in the overlap region, and as a result solvent will diffuse from the bulk to the overlap region this causes the particles to be separated and a strong repulsive energy arises from this effect. Such repulsive energy can be calculated 

The total change in free energy of mixing for the whole interaction zone, V, is obtained by summing over all the elements in V, 

Using the above theory it is possible to derive an expression for the free energy of mixing of two hydrated layers (assuming a uniform segment density distribution in each layer) surrounding two spherical particles as a function of the separation distance h between the particles [3, 4]. 

The sign of G j depends on the value of the Flory-Huggins interaction parameter if 0.5, then G j will be positive and the interaction repulsive, but if 0.5, then will be negative and the interaction attractive. The condition 

When the two surfaces are separated by an infinite distance (00) the number of configurations of the rod is f2(x), which is proportional to the volume of the hemisphere. When a second particle approaches to a distance h such that it cuts the 

Combination of Gmix and Gei with Ga gives the total energy of interaction Gj (assuming there is no contribution from any residual electrostatic interaction) [6], i.e. 

Gmix increases very sharply with decreasing h, when h 23. Gei increases very sharply with decreasing h, when h 3. Gt versus h shows a minimum, Gmin, at separations comparable to 23 when h 23, Gj shows a rapid increase with further decrease in h [32]. 

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The mixing interaction, Gmix, increases very rapidly with a decrease in h when h <26 (and x < 0.5), while Gd also increases very rapidly with decrease of h on further overlap. The Gj-h curve shows a minimum (Gmin) at h 26, but when h <26, Gj increases very rapidly with further decreases in /i. The depth of the minimum depends on the particle size, the Hamaker constant (A) and the adsorbed layer thickness 6. For a given particle size with a Hamaker constant A, Gmin decreases as 6 increases. When 6 reaches values of the order of 5-10 nm, Gmin becomes quite small (particularly when the particle radius is small, say < 1 pm). In this case, the... 

As a result of the unfavourable mixing of the chains, when these are in good solvent, the osmotic pressure in the interaction zone increases - this is described as a free energy of interaction, Gmix, that is given by... 

Table 5.40 Binary interaction parameters for pyroxenes. Parameters refer to an ionic mixing model in which n is the number of sites over which permutability is calculated—i.e., Gmixing = tiRT (Xi In Xj + X2 In X2). Data in J/mole (H), J/(mole X K) (5), and J/(bar X mole) (V), respectively.

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