Self-Assembly as Phase Separation

Aggregation of amphiphilic molecules may be regarded as a (micro)phase separation between a polar (water) and an apolar (oil) phase. In the two-phase system, each of the phases contains a fraction of the other component their compositions are determined by the solubility of oil in water and vice versa. In equilibrium, the chemical potential p of the oil in the oil phase equals that of the oil in the aqueous phase  

PoiKoily phase) cau be approximated by p , the chemical potential of pure oil, and the solubility of oil in water is so low that the solution can be assumed to behave ideally. Hence, Equation 11.1 becomes 

Doii is the chemical potential of pure oil (Y = 1) as derived by extrapolation from the ideal solution regime 

We now discuss the energetic and entropic contributions that are involved in phase separation, that is, the reverse of mixing. Consider a mixture of components A and B in which the interactions A-A, A-B, and B-B are energetically eqnal. Snch a mixture is called ideal. Mixtures are entropically favorable mixing increases the configurational entropies of each component. Per mole of ideal mixture the entropy of mixing is 

FIGURE 11.2 Phase diagram for an oil-water mixture. The stable areas indicate the conditions at which one phase exists, whereas in the unstable area two phases occur. 4 refers to the volume fraction of the oil. 

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