Highly anisotropic rigidity of `ribbon-like' polymers: II. Nematic phases in systems between two and three dimensions

Various extensions of Onsager theory based on the second virial approximation are constructed in order to describe nematic P-phases in ribbon polymer solutions. If the average coil shape is anisotropic and the concentration is not too high, the coils can be considered as anisotropic solid objects and an ordinary expansion over the coil concentration can be performed. This first approach can be applied to study pancake nematic ordering. At-higher concentrations and when the polymer chains are rather long, the polymer solution can be considered as a solution of short fragments connected into chains with a particular statistics reflecting the polymer structure with two rigidities: a similar virial expansion can be constructed. This last approach allows the consideration of the various symmetries of the nematic phases simultaneously. We also take into account the correlation correction to the mean field result which provides an essential additional angular dependence to the interaction free energy. Scaling arguments are applied in the case where the intra-coil correlations are very strong, or if the coils interact as opaque objects. The methods developed here will be used in further publications to study liquid crystalline ordering in solutions of ribbon chains.