Critical behavior of a smectic- A to nematic phase transition imbedded in a random network of voids

We present the results of a systematic ac calorimetric study on the smectic-A to nematic (Sm-A--N) phase transition for the alkylcyanobiphenyl liquid crystals, 8CB and 9CB, imbedded in the randomly interconnected voids of Millipore cellulose membranes. The confining void size ranged from 5 to 0.025 {μ}m, which, although large, introduces substantial changes compared to the bulk behavior. The heat capacity peak at the Sm-A--N transition temperature changes from sharp and prominent to broad and small with increased confinement. Concomitant with the heat capacity peak shape change, critical behavior analysis reveals that the random confinement drives the heat capacity critical exponent from its bulk value towards zero, approaching the three-dimensional XY universality class value prediction of -0.007. This change in the critical exponent is liquid-crystal material and voids size dependent, and is equivalent to what occurs with increasing nematic range that weakens the coupling between smectic and nematic order parameters. The Millipore confinement does not alter the nematic range; it is the randomness it introduces that changes the nature of the coupling. In addition, but in a manner not fully consistent with finite size effects, transition temperatures are shifted down from bulk and the transition enthalpy is suppressed. Supporting results are found in a study of binary mixtures of 9CB and 10CB.