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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.

This thesis presents the investigation of the liquid crystal (LC) - particle suspensions. Particles from nano- to micro-size, spherical to two-dimensional shapes, with different functionality are dispersed into nematic and smectic phases. The aim is to create ordered nanoparticle (NP) assemblies and thereby modify the common properties of the liquid crystal, such as dielectric anisotropy and electro-optical, revealing any interaction between particles and LC properties. It is found that for concentrations (>0.5vol%), the ferroelectric NPs have increased the sensitivity of the nematic liquid crystal to the electric field through electro-optical responses, which is seen by an enhancement in the dielectric anisotropy. This could be induced by the coupling of the electrical dipole moments in the spherical NPs with the LC director field. The electro-optical properties of the chiral smectic (SmC*) phase (tilt angle Θ, switching time τ_s and spontaneous polarisation P_s) are found to be independent of the concentration and sizes of the doped NPs. The relaxation frequency f_R of the Goldstone mode is faster in the ferroelectric NPs suspensions of 2.0vol% compared to the paraelectric NPs. In the graphene oxide (GO) - nematic LC (5CB) suspensions, the small GO sizes of mean size 560 nm are more easily dispersible than larger flakes of 2.8 micro metre mean size. As the GO concentration is increased, each of the threshold voltage and splay elastic constant dramatically increases, reaching saturation at ≈1.0wt%. The field driven switching-on time is practically not affected, while the purely elastically driven switching-off time is strongly sped-up. Interestingly, thermotropic and lyotropic LC phases are exhibited in the GO-5CB suspensions when heating the thermotropic liquid crystal into its isotropic phase. The isotropic phase of 5CB acts as a solvent for the GO particles, forming a lyotropic nematic phase with largely reduced birefringence. It is found that the nematic to isotropic phase transition is shifted toward higher temperature for the GO-5CB system compared to the BaTiO3-5CB system. Dispersions of different sizes of GO flakes are prepared in isotropic and nematic fluid media. The dielectric relaxation behaviour of GO-dispersions was examined for a wide temperature range (25-60 ℃) and frequency range (100 Hz-2 MHz). The mixtures containing GO flakes were found to exhibit varying dielectric relaxation processes, depending on the size of the flakes and the elastic properties of the dispersant fluid. The relaxation frequencies in the isotropic media were lower compared to the nematic medium. Relaxation frequencies (~10 kHz) are observed in the GO-isotropic media, which are reduced as the size of the GO flakes are decreased, are anticipated to be inherited from GO flakes. However, the fast relaxations (~100 kHz) that are observed in the nematic suspensions could imply strongly slowed down molecular relaxation modes of the nematogenic molecules. Finally, the phase diagram of lyotropic LC as a function of the lateral dimensions of the GO flakes, their concentration, geometrical confinement configuration and solvent polarity was investigated. Polarising optical microscopy was used to determine isotropic-biphasic-nematic phase evolution. The confinement volume and geometry of the sample relative to the GO size are shown to be vital to the observation of the lyotropic phase. GO LCs have the potential for a range of applications from display technologies to conductive fibres. The confinement related LC phase transition is critical toward their applications. It is also found that the stability of the LC phase is higher for the solvent of higher dielectric constant.

Thermal behavior and molecular packing of alkylated poly(ethylene- alt- maleic anhydride) and poly(styrene-alt-maleic anhydride) were studied by means of differential scanning calorimetry, thermogravimetry, polarizing optical microscopy, and X-ray diffraction. Effects of the length and graft density of alkyl side chains and backbone rigidity on the thermal behavior and on the structure of the mesophases are discussed.

Azobenzene upon photochemical E/Z isomerization changes both its shape and size. The E-azobenzene moiety falls in the class of calamitic liquid crystalline mesogens, producing a wide variety of mesophases. Two series of linear bis(azobenzene) compounds, one with phenyl benzoate linkage and the other with benzyl benzoate linkage were synthesized. The termini of these molecules ranged from a dodecyloxy chain to hydrophobic amphiphilic dendrons up to first generation. We determined the effects of both the linkages and generation number on the mesogenic properties of these compounds. Our results show that the mesogenic behavior of these bis(azobenzene) compounds are highly dependent on the linkages between individual azobenzenes and that for the bis(azobenzene) compounds of the phenyl benzoate series, generation number had an effect on the liquid crystalline mesophase of the compounds

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