Conformation of liquid crystal side chain polymers in the smectic phase : models for anisotropic random walks

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Abstract
Three models are proposed in order to explain the observed temperature dependent anisotropy of the radii of gyration of liquid crystal side chain polymers in the smectic phase. In these models it is assumed that the conformation of the backbone in the planes between the smectic lamellae can be described by a random walk, by a self-avoiding walk, or by a straight path respectively. In each model crossings of the side chain polymer through the lamellae are allowed and weighted by a suitable Boltzmann-factor. The first and the third model are the extremes which may occur with respect to the degrees of freedom the backbone has in the planes. Every other, probably more realistic, model will show an anisotropy intermediate between these two models. It is shown that the results derived with the use of these models differ little with regard to large scale properties of the systems which are examined in small angle scattering experiments. Excluded volume effects the consideration of which casts some doubt on existing theories and non-equilibrium effects which make the interpretation of existing experiments difficult are discussed