Pretransitional behavior of the density of the nematic phase

Volume and temperature studies on pentylcyanobiphenyl, in a single-capillary dilatometer capable of a sensitivity in density of 2 × ${10}^{-6\mathrm{}}$ g/${\mathrm{cm}}^3$ in a constant-temperature bath stable to ±0.2 mK, are reported. The data in the nematic-phase pretransitional region have been fit by an equation of the form $V=a+bT+c{|1-\frac{T}{T_{\mathrm{SP}}}|}^e$, where $T_{\mathrm{SP}}$ represents the limit of mechanical stability of the nematic phase (where $\frac{\mathrm{dp}}{dV=0\mathrm{}}$), and the "pretransition exponent" $e=0.50\mathrm{}\pm 0.01$. To this accuracy, the nematic volume near the transition has the square-root behavior also suggested earlier by experimental results on $N-(p-\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{x}\mathrm{y}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{y}\mathrm{l}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{e})-p-\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{y}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}$ (MBBA) and other compounds. A new thermodynamic mean-field understanding of this behavior is presented and discussed. Tricriticality of a particular kind is also discussed.