## Abstract

Optical measurements by one of the authors on two nematogens (5CB and MBBA) under pressure have provided information from which it is possible to deduce (a) how volume varies with pressure and temperature, (b) how the conventional nematic order parameter, here written as $S_{2}$ varies with temperature at constant volume, and (c) how both the nematic-isotropic transition temperature $T_{\text{c}}$ and the order parameter at the transition temperature $S_{2\text{c}}$ change when the specimen is compressed. Comparable, though less extensive, results for a third nematogen, PAA, have previously been published by McColl & Shih. Our values for $\gamma (=-\text{d}\ln T_{\text{c}}/\text{d}\ln V)$ are significantly different from theirs, however, being 6 for 5CB and 2.6 for MBBA, as opposed to 4. We also find that for both 5CB and MBBA $S_{2\text{c}}$ decreases significantly on compression, where McColl & Shih observed no such effect. We compare our results in some detail with predictions based upon a number of mean field theories of nematic order, all of them elaborations of the well-known theory of Maier & Saupe; they are summarized in $\text{section}5$ of the paper. None of these theories is in satisfactory agreement with all the data, despite the extra adjustable parameters which they contain. However successful they may appear to be when compared with data for $S_{2}$ obtained at constant (atmospheric) pressure, they cannot be fitted to our curves for $(S_{2}^{\text{M.S.}}-S_{2})$, the deviation of $S_{2}$ from the Maier-Saupe value, at constant volume, though it is at constant volume that one would expect the theories to work best. It is also difficult to reconcile the theories with the fact that if the nematic-isotropic transition could be constrained to take place at constant volume the molar entropy, for both 5CB and MBBA, would increase by only about 0.09 $N_{\text{A}}k_{\text{B}}$, this may be deduced from the slope of the transition line, $\text{d}T_{\text{c}}/\text{d}p$, taken in conjunction with some of our volumetric data. Most mean field theories imply that the only order-dependent term in the entropy is the entropy of misalignment and that this should increase at the transition by more than 2.27 $S_{2\text{c}}^{2}$, which is two or three times larger than 0.09 $N_{\text{A}}k_{\text{B}}$. The discrepancy can only be removed by the introduction of yet another ad hoc adjustable parameter, such as the cluster size in the cluster model which some authors have advocated. The paper includes, in an appendix, a comparison between different methods which have been suggested for calculating the local field in a nematic.