arXiv:cond-mat/0510238v1 [cond-mat.soft] 10 Oct 2005 Calorimetric study of the nematic to smectic-A and smectic-A to smectic-C phase transitions in liquid-crystal+aerosil dispersions A. Roshi and G. S. Iannacchione ∗ Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA. P. S. Clegg Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom. R. J. Birgeneau Department of Physics, University of California, Berkeley, California, 94720, USA. M. E. Neubert Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA. (Dated: December 17, 2013) A high-resolution calorimetric study has been carried out on nano-colloidal dispersions of aerosils in the liquid crystal 4-n -pentylphenylthiol-4’-n -octyloxybenzoate ( ¯ 8S5) as a function of aerosil con- centration and temperature spanning the smectic-C to nematic phases. Over this temperature range, this liquid crystal possesses two continuous XY phase transitions: a fluctuation dominated nematic to smectic-A transition with α ≈ αXY = -0.013 and a mean-field smectic-A to smectic-C transition. The effective critical character of the N -SmA transition remains unchanged over the entire range of introduced quenched random disorder while the peak height and enthalpy can be well described by considering a cut-off length scale to the quasi-critical fluctuations. The robust nature of the N -SmA transition in this system contrasts with cyanobiphenyl-aerosil systems and may be due to the mesogens being non-polar and having a long nematic range. The character of the SmA-SmC transition changes gradually with increasing disorder but remains mean-field-like. The heat capacity maximum at the SmA-SmC transition scales as ρ -0.5 S with an apparent evolution from tricritical to a simple mean-field step behavior. These results may be generally understood as a stiffening of the liquid crystal (both the nematic elasticity as well as the smectic layer compression modulus B) with silica density. PACS numbers: 64.70.Md, 61.30.Eb, 65.40.Ba I. INTRODUCTION The study of quenched random disorder effects ad- dresses many fundamental issues of current interest in statistical mechanics. Recent experimental advances have shed considerable light onto the random-field theo- retic approach, believed to be underlying the physics of quenched random disorder (QRD). In particular, these efforts have led to the systematic study of the random- field model for transitions that break a continuous sym- metry [1]. This model is applicable to a terrific range of phenomena: This include unique assemblies of colloids, complex fluids, charge density waves, spin glasses, and doped semiconductors, to name a few. The experimental efforts to date have focussed on idealized physical systems in order to isolate the essential features of quenched ran- dom disorder. Considerable research has been carried out on the superfluid transition of 4 He and 4 He- 3 He mixtures in a variety of porous media [2, 3] as well as doped mag- netic systems [4] but many questions remain due to the quantum nature of the former and the glass-like behavior * Electronic address: gsiannac@wpi.edu of the latter [1]. In the random-field approach, the effect of the disor- der is mapped onto a local field,  h(  r), directly coupled to the order parameter. This local field varies randomly through the system on length scales smaller than the length scales of the ordered phase such that 〈  h〉  r =0 while 〈  h ·  h〉  r = 0. Because the nature of the imposed disorder is modelled as a dilute (or weak) random-field, the effect of QRD may be understood statistically. By studying in detail good realizations of particular univer- sality classes, the results can be applied more generally to a wide variety of physical systems. A particularly fruitful physical system to explore QRD effects in general and the random-field model in particular, have been nano- colloidal dispersions of an aerosil gel in a liquid crystal (LC) host (LC+sil) [1, 5]. The most well studied LC+sil phase transition has been the continuous nematic to smectic-A (N -SmA) phase transition. This transition involves the break- ing of a continuous symmetry and belongs, though not simply, to the 3D-XY universality class [6]. In gen- eral, high-resolution x-ray [7, 8, 9, 10] and calorime- try [5, 11, 12, 13, 14, 15] studies on the N -SmA+sil tran- sition have found that the (quasi-) long-range ordered smectic phase is destroyed for all densities of aerosil.