EMULSION STABILIZATION 159 rial to know how these parameters change with the environment, rn such aspects as solvency of the medium for the chains and temperature. INTERACTION BETWEEN DROPLETS CONTAINING ADSORBED POLYMER LAYERS (STERIC STABILIZATION) When two droplets containing adsorbed polymer layers (with an adsorbed layer thick- ness, 0) approach a distance of separation, h, whereby these layers begin to overlap, i.e., when h 20, repulsion occurs as a result of two main effects (8). The first repulsive force arises from the unfavorable mixing of the polymer layers when these are present in a good solvent (i.e., the chains are strongly solvated by the medium). The unfavorable mixing of polymer solutions in good solvent conditions was considered by Flory (9), whose theory was applied to the present case of interparticle interaction. A schematic representation of the mixing of polymer layers on close approach is shown in Figure 6, which shows the situation when two droplets with polymer layers are forced to approach a distance, h, that is less than 23, forming an overlap region with a volume element, dV. Before overlap, the chains have a volume fraction, p2, and the solvent has a chemical potential, µ 1 a_ In the overlap region, the volume fraction of the chains is p/, which is higher than p 2 , and the solvent has a chemical potential, µ 1 13, which is lower than µ 1 a. This is equivalent to an increase in the osmotic pressure in the overlap region. As a result, solvent diffuses from the bulk to the overlap region and the two particles or droplets are separated, i.e. this results in strong repulsion. The latter is referred to as mixing or osmotic repulsion. Using the Flory-Krigbaum theory (9), one can calculate the free energy of mixing, G mix ' due to this unfavorable overlap, i.e., 6 G m ix 47T 2 ( 1 ) ( h) 2 ( h) = r1--. N - - X o - - + 23 + - kT 3V 1 �2 av 2 -3R 2 µ� Chemical potential of solvent Fi g ure 6. Schematic representation of the overlap of two polymer layers. (2)

160 JOURNAL OF COSMETIC SCIENCE where k is the Boltzmann constant, T is the absolute temperature, V 1 is the molar volume of the solvent, and N av is the Avogadros's constant. X is a dimensionless quantity that gives a measure of the polymer-solvent interaction, i.e., the solvation of the A chains by the molecules of the medium. It is referred to as the Floury-Huggins inter- action parameter. It is clear from equation 2 that when the Flory-Huggins interaction parameter, X, is less than 0.5, the chains are in good solvent conditions, Gmix is positive, and the interaction is repulsive and increases very rapidly with decreasing h, when the latter is lower than 28. This explains why the hydrophobically modified inulin (HMI) polymeric surfactant is ideal for stabilizing 0/W emulsions. In this case the polyfructose loops are strongly hydrated by water molecules. For stabilization of W /0 emulsions, the stabilizing chains have to be soluble in the oil phase (normally a hydrocarbon). In this case, poly(hydroxy- stearic acid) (PHS) chains are ideal. A polymeric surfactant of PHS-PEO-PHS (Arlacel P135) is an ideal W/0 emulsifier. Equation 2 also shows that when X 0.5, i.e., when the solvency of the medium for the chains becomes poor, Gmix is negative and the interaction becomes attractive. The condition X = 0.5 is referred to as 0-solvent, in which case mixing of the chains with the solvent does not lead to an increase or decrease of the free energy of the system (i.e., polymer mixing behaves as ideal). The 0-condition denotes the onset of change of repulsion to attraction. Thus, to ensure steric stabilization by the above mechanism, one has to ensure that the chains are kept in better than a 0-solvent. The second repulsive force arises from the loss of configurational entropy when the chains overlap. This is schematically illustrated in Figure 7, whereby the polymer chain is represented by a simple rod with one attachment point to the surface. When the two surfaces are separated at infinite distance, each chain will have a number of configura- tions, 000, that are determined by the volume of the hemisphere swept by the rod. When the two surfaces approach a distance, h, that is smaller than the radius of the hemisphere swept by the rod, the volume available to the chains becomes smaller and this results in a reduction in the configurational entropy to a value, D (which is less than 000). This results in strong repulsion, and the effect is referred to as entropic, volume restriction or elastic repulsion, and is given by the following expression (8): - - - - hoo no. of configurations (loo n Gel = 2v ln noo Figure 7. Schematic representation of the entropic, volume restriction or elastic interaction. (3) lost