Extended correlated disorder model

It is not clear whether in the centered rectangular lattice gas of section 3.2 such a Kosterlitz-Thouless transition occurs, or whether the disordered phase extends, though being incommensurate, down to the commensurate (3x1) phase (then this transition is believed to belong to a new chiral universality class ), or whether there is another disorder line for (3 x 1) correlations. However, Kosterlitz-Thouless type transitions have been found for various two-dimensional models the XY ferromagnet , the Coulomb gas . ... 

The polarization model is extended to account for the ion-ion and ion-surface interactions, not included in the mean field electrical potential. The role of the disorder on the dipole correlation length A, is modeled through an empirical relation, and it is shown that the polarization model reduces to the traditional Poisson Boltzmann formalism (modified to account for additional interactions) when X, becomes sufficiently small. 

Blackwell and coworkers [19] have extensively studied the case of liquid crystalline main-chain copolymers produced by the random polymerization of two or three different monomers. The X-ray scattering patterns of these materials usually display a set of non-periodic diffuse streaks. These diffuse streaks were analyzed by extending the model of disorder of Hosemann to take into account chemical disorder. The description of the data by this model gave the correlation length of the ordering, information on the conformations of the repeat units and proved the random sequence of the copolymers. Subsequent molecular modelling studies revealed the detailed conformation of the repeat units. 

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