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A complete thermodynamic description has been given for the case of circular LC islands embeddedin a contiguous LE phase based upon the formulation of the Gibbs energy of the monolayer, definedas 2 G mono = µsN s − ΠA (2)where N s is the number of amphiphile molecules and µs their chemical potential. If contributions toG mono due to irregularities at the colloidal level are considered separately, a more detailed breakdowngives 2,3 (3)A m is the area occupied by the LE phase, N m, Πm and λ ∗ s,m are the number of amphiphiles, localspreading pressure and chemical potential for a uniform LE phase, respectively. The sum ∑ is takenover different categories of domains, defined according to the number of molecules j) ( they contain,n dj = number of islands in that category, R j = their radius, Λj = line tension, f edge el,j = electrostaticenergy of the fringe field of a domain due to polar head groups, λ ∗ s,j = molecular chemical potentialin a LC island of type j. The last term, G mix, is the free energy of mixing and contains the effects ofelectrostatic repulsion between domains, kinetic energy and polydispersity via a term –TS poly with T= absolute temperature and S poly = entropy of polydispersity.In equilibrium, G mono has its minimum value and the above expression can be shown to lead to threeequilibrium conditions: (i) mechanical equilibrium across every domain boundary, ii) ( uniformity ofmolecular chemical potential (µs) and (iii) the law of mass action: chemical potential per domain µd,j= jµs.Combination of these conditions yields the equilibrium distribution of domain sizes2 :(4)intwhere N d = total number of domains, δ= average distance between molecules in LC phase, f el =electrostatic work of inserting a domain of radius R into the film, k = Boltzmann’s constant. C is anormalisation constant.With G mix written as N dg mix, a m = A m/N m and n d = N d/A the expression for an arbitrary isothermpassing through the main transition region (thequation of state) follows from this treatment as 3(5)46
Here, we have assumed all islands to have equal sizes. This is based on numerical results obtainedwith eq 4 which imply a low degree of polydispersity (~ 10%) in most practical cases. From astability analysis of the solution to problem (i-iii) it has been concluded that even for this relativelysimple model system an instability may occur in the form of a negative lateral compressibility κ =−[A(∂Π/∂A) T] -1 . This strongly suggests that shape transitions (e.g. to more elongated domains) maybecome inevitable in order to restore monolayer stability.References1. Knobler, C.M. (1990). Adv. Chem.Phys. 77: 397.2. Mulder, W.H. (1997). J. Phys.Chem.B 101: 7744.3. Mulder, W.H. (1998) J. Phys.Chem.B 102: 5460.O-28ELECTROCATALYTIC DECHLORINATION OF CHLORORGANICCOMPOUNDS IN AQUEOUS MEDIAS. KulikovDepartment of Biological and Chemical Sciences, Cave HillHalogenated organic compounds are being considered among the most widely spread pollutants inwater. Some of them are very dangerous even in small, on the border of analytical detectionconcentrations. These compounds can be separated from water (liquid-liquid extraction, absorption,permeative technology .....) and then detoxified with known techniques.47
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