Soft matter systems exhibit, in most cases, structural length scales ranging from a nanometer up to a micrometer, and thus are placed within the domain of ‘nanotechnology’. Colloidal systems are well known examples in which this feature is essential to define the range where a very specific type of behavior occurs. Colloids are supramolecular submicron sized substances dispersed in a medium that can be a liquid or a gas. They are much bigger than normal molecules, and hence the medium in a colloidal suspension can often be regarded as ‘background’ with respect to the colloidal size range: this medium may be approximated as a continuum. At the same time, colloids are small enough to present considerable thermal motion in comparison to sedimentation (which is caused by gravitational forces that would become more important for higher-sized particles). Colloids were first discovered by Perrin, who detected Brownian motion as visible manifestation of thermal motion in dispersions of resin colloids in water \cite{perrin1913atomes}.
When colloidal particles have anisotropic shapes, they can be found in liquid crystalline phases. Liquid crystals are substances that have the appearance of a liquid but possess certain levels of molecular arrangement similar to crystals. Liquid crystals were first discovered in 1888 by Friedrich Reinitzer, who noticed that a cholesterol-based substance had two melting points at different temperatures, each of them giving way to a liquid-like phase with different optical properties \cite{reinitzer1888beitrage}. At the early time of Reinitzer only three phases were known (gas, liquid and solid). Over the years, a big number of substances have been discovered to exhibit many states of matter, including liquid crystals that are now widely used in technological advancements such as liquid crystal screens and thermometers \cite{Li_2012}.
The key difference between a liquid crystal and the commonly observed gas, liquid and solid states is that properties in the first one are anisotropic and vary with direction, even though the substance itself remains fluid. These unique properties emerge due to the elongated shape of its building blocks, which promote collective alignment along a certain direction. In other words, liquid crystalline phases are additional states of matter which are intermediate between the dilute gas and the crystalline solid, and whose existence is related to the additional {\em orientational} degrees of freedom anisometric particles have compared to spherical ones.
Among the numerous liquid crystalline phases, different degrees of order can be found, evidenced for instance by diffraction of X-rays and light. Measurements of this kind provide a frame to classify these systems by its similarity to either the gas or the solid phase. Let us consider, as an example, the following liquid crystalline phases:
The {\em isotropic} (I) fluid phase is very similar to the gas and liquid phases for spherical particles and is characterized by a complete absence of positional and orientational order. At the inmediately next stage, we find the {\em nematic} (N) phase, in which particles are homogeneously distributed without positional order as in a liquid phase, but are ordered in their orientation following an average direction: the {\em nematic director} $\bn$. As it will be repeatedly discussed throughout this thesis, in nature one can find particles that, in addition to being anisotropic, present chiral features. This can be due to the arrangement of atoms in a molecular compound, to a (helicoidal) particle shape in some colloidal systems or to a chiral distribution of charges at the surface of the particles, observed for instance in {\em fd} filamentous bacteriophages viral rods \cite{Gibaud_2017}. When chiral particles are in nematic phase, they arrange themselves into a strongly twisted structure. This special case of a nematic phase is often called {\em cholesteric}.
The {\em smectic} (Sm) phase is closer to the solid phase. In smectic liquid crystals, particles are ordered in layers and cannot move freely between them. The smectic phase is, in turn, divided into several sub-phases with slightly different properties. Examples are the smectic A phase (SmA), where particles can move freely inside the layers as in a two-dimensional liquid; or the smectic B phase (SmB), where there is long-ranged positional order: at higher concentrations or lower temperatures, molecules tend to arrange themselves into something more similar to a crystalline lattice.
One sub-classification of liquid crystal materials is based on the mechanism by which they transition from one state to another. {\em Thermotropic} systems, mainly constituted by low molecular weight constituents --and also some polymers--, undergo phase transitions due to changes in temperature. In this thesis, we focus mostly on {\em lyotropic} liquid crystals, which form upon increasing the concentration of solute particles. This is the case of systems formed by high-molecular weight colloidal particles, polymers or surfactants in a solvent.
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Historically, lyotropic liquid crystals were first recognised in the 1920s by Zocher \cite{Zocher}
who investigated nematic textures in solutions of rodlike inorganic vanadiumpentoxide (V$_{2}$O$_{5}$) particles.
Later, similar observations were reported by Langmuir \cite{Langmuir} for clay platelets
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