Ionic Emulsions and Microemulsions

1 Averaging of the Pair Interaction Energy over the Droplet Deformation 

Zn) is the energy of N interacting droplets which may form M films. This configurational integral leads to a pair correlation function of the form 

Further we may assume pairwise additivity of the interaction energy 

The normalising constant is determined by the requirement g z — oo) = 1. For infinitely dilute samples it depends only on the siuface extension and bending properties. In the emulsion case (where the interfacial tension dominates) one obtains const = A(na y/T /4), while in the microemulsion case (where the bending rigidity dominates) the result is const = A i2kc/kT X - /2)].  

Now the pair interaction energy, w(z), as a fimction of the interdroplet distance only, has the following form 

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