Fluctuations, mean fields and the order parameters in nematics

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Abstract
We argue that there may be a conceptual difference between calculated (S) and observed (Δ) values of the order parameter in nematics if a mean or molecular field theory is used. Careful definition of the order parameter removes the ambiguity in the case of a Landau approach but a discrepancy remains for molecular field theories. The source of the problem lies in the thermally excited continuum distortions of orientational order which have little thermodynamic effect but may have a large effect on the apparent value of an observable depending on a specific frame of reference. Thus Δ observed by N.M.R., E.S.R. or optical techniques is in fact the S 0 of molecular field theory after renormalization by thermal fluctuations. This renormalization is estimated in terms of the cutoff of distortional modes. The arbitrariness involved in the use of continuum and molecular approaches can be circumvented in an operational way. The coupling between local and continuum modes is introduced via a detailed discussion of depolarized light scattering at high temperatures which could help delineate the validity of continuum theory. Motional narrowing in N.M.R. and E.S.R. is discussed. In fact the extraction from N.M.R. of a cutoff length for the spectrum of thermal fluctuations may further help in the estimation of the renormalization. Experiments indicate that this length is of molecular dimensions, a consequence of which would be the use of S 0 2 (and its associated temperature dependence) instead of Δ2 in scaling the spin lattice relaxation times observed.

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