This thesis presents an experimental study of the influence of an external field and alignment upon a colloid of a liquid crystal (octycyanobiphenyl denoted 8CB) and a silica gel of aerosil nano-particles. The first techniques used was an AC-calorimetry (alternating current heating) and the systems under investigation were firstly put under the influence of a magnetic field at John Hopkins University in Baltimore by professor Leheny's group. The experiments revealed changes in transition temperatures, nematic range and critical coefficient that could account for what we called a 'memory' of the above mentioned structures. The second technique, dielectric spectroscopy, was applied to the same very densities of mixture s mentioned in the first paragraph. The samples were applied in one procedure an increasingly higher alternating electric field. An overall increase of the capacitance of the sample was measured. The second experiment was to reproduce the application of the magnetic field from the AC-calorimetry experiment now with an electric field. In dielectric spectroscopy case, an increase in transition temperature after the application of the procedure was revealed.

This thesis presents a series of studies of quenched random disorder (QRD) on liquid crystals. We have used high-resolution AC-Calorimetry, high-resolution X-Ray Diffraction (XRD), X-Ray Intensity Fluctuation Spectroscopy (XIFS), Turbidity, Integrated Low-Angle Light Scattering (ILALS), as well as Polarizing Microscopy to characterize the effects of a nano-colloidal dispersions of aerosils in the phase transitions of several liquid crystals. The aerosil ($SIL$) is made of 70~AA~ diameter SiO$_{2}$ particles coated with hydroxyl (-OH) groups. The coating allows the $SIL$ particles to hydrogen-bond together, to form a very low density gel in an organic solvent. This provides the quenched random disorder. The liquid crystals of interest are: octyloxycyanobiphenyl ($8OCB$), 4-extit{n}-pentylphenylthiol-4'-extit{n}-octyloxybenzoate (ar{8}$S5), 4'-transbutyl-4-cyano-4-heptyl-bicyclohexane ($CCN47$), and octylcyanobiphenyl ($8CB$). Studies have been carried out as a function of aerosil concentration and temperature spanning the following phase transitions, Isotropic to Nematic (emph{I-N}), nematic to smectic-emph{A} (emph{N-SmA}), smectic-emph{A} to smectic-emph{C} (emph{SmA-SmC}), and crystallization.

We have developed a new modulation calorimetry technique using RF-Field heating. This technique eliminates temperature gradients across the sample leading to a higher precision in evaluating the heat capacity compared to the previous techniques. A frequency scan was carried out on a 8CB+aerosil sample showing a wide plateau indicating the region of frequency independent heat capacity. A temperature scan was then performed through the first-order nematic to isotropic and second order smectic-A to nematic transitions and was shown to be consistent with the previous work. The amplitude of the RF heating power applied to the sample depends on the permittivity and the loss factor of the sample. Since the permittivity of a dielectric material has a strong temperature dependence in liquid crystals, new information is obtained. The heat capacity measurements have a relative resolution of better than 0.06%, and the phase shift a resolution of 0.03%, were shown to be significant improvements over traditional heating methods. We then applied this new RF calorimetry on bulk and aerosil 8CB dispersions. For the bulk 8CB, the step-like character of smectic-A to nematic transition, and first order nematic to isotropic transitions indicated the strong dominance of the permittivity and the loss factor of the material. For the 8CB+aerosil samples at different silica density, our data were consistent with the previous work and provides clear evidence for the coupling between the smectic-A and nematic phases. We have undertaken a combined T-dependent optical and calorimetric investigation of CCN47+aerosil samples through the I-N transition over a range of silica densities displaying the double I-N transition peak. This work offers compelling evidence that the I-N transition with weak quenched random disorder proceeds via a two-step process in which random-dilution is followed by random-field interactions on cooling from the isotropic phase, a previously unrecognized phenomena.