We have developed a new, extremely sensitive real-space technique (intensity fluctuation microscopy) to probe the order of the nematic–smectic-$A$ $\mathrm{}\left(\mathrm{NA}\right)\mathrm{}$ transition. Using this technique, we show that the $\mathrm{NA}$ transition in $4^{\prime }-n$-octyl-4-cyanobiphenyl (8CB) is clearly first order, contrary to calorimetric studies but in agreement with conclusions drawn from front-velocity measurements. We characterize the strength of the discontinuity at the first-order transition by the dimensionless quantity $t_0{=(T}_{\mathrm{NA}}-T^{*}{)/T}^{*}.$ By precisely measuring $t_0,$ we have made the first detailed tests of predictions based on the Halperin-Lubensky-Ma (HLM) theory of fluctuation-induced, first-order phase transitions. First, we explore the effect of an external magnetic field on the $\mathrm{NA}$ transition. Although modest fields (of order 10 T) are predicted to drive the weakly first-order transition in pure 8CB second order, we observe no such effect; we establish instead that the lower bound on this critical field is $\approx 30\mathrm{T}.$ Likewise, we observe no effect in mixtures of 8CB with its longer chemical homolog $4^{\prime }-n$-decyl-4-cyanobiphenyl (10CB). Second, we examine the dependence of $t_0$ as a function of 8CB–10CB mixture concentration and find that the data in mixtures with small nematic temperature range are well-fit by the parameters derived by Anisimov et al. based on calorimetric measurements. As we increase the nematic range (by using concentrations closer to pure 8CB), the measured $t_0$ deviates more and more from the HLM predictions. Smectic fluctuations, which are neglected in the HLM calculation, are an obvious candidate to explain such a discrepancy, but one’s naive expectation is that they would reduce $t_0$ below the HLM levels, whereas the observed values are too large. However, a recent renormalization-group calculation concludes that smectic fluctuations, surprisingly, should indeed increase $t_0,$ explaining the observations presented here.

• Received 1 August 2001

DOI:https://doi.org/10.1103/PhysRevE.65.021702