Director

The nematic phase is the least ordered liquid crystalline phase and features a long-range orientational order only. This order is relatively weak, the nematic phase is quite similar to the isotropic liquid phase except for a small additional amount of order. The elongated molecules in the nematic phase can freely rotate about all their axes. However, the relaxation times for the rotation about the short axes of the molecules is several magnitudes faster than for the rotation about the long axes. As a result, all molecules in the nematic phase point on average in the same direction. This orientational order in the nematic phase can be characterized by the director n, which depicts the local preferable direction of molecules within a certain volumne.

Order_parameter

The scalar Order parameter S as a function of reduced temperature.

The director orientations n and -n are indistinguishable by means of physical properties, therefore the director is not a vector in mathematical strict sence, but a pseudo-vector that considers this symmetry. The degree of orientational order in the nematic phase can be expressed by a scalar order parameter S, which can be expressed given by

S=\frac{1}{2}\left\langle 3\cos^2\left(\theta\right)-1\right\rangle.

The angle \theta is thereby given by the angle between the director n denoted for a given volume V and the long axis of the molecules within this volume. The nematic order parameter is a function of temperature, with increasing temperature the degree of orientational order decreases.

Anisotropic properties

Being a uniaxial liquid crystal, the nematic phase exhibits anisotropic physical properties , i.e. the physical properties are not scalar but tensor measures. The most prominent anisotropic properties are the dielectric anisotropy \Delta\epsilon=\epsilon_{\parallel}-\epsilon_{\perp} and the birefringence \Delta n= n_{e}-n_{o}.

Birefringence

Measured refractive indices of a nematic phase as a function of reduced temperature.

Permittivity

Measured permittivities of a nematic phase as a function of reduced temperature.

 

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