The uniaxial nematic phase can be easily aligned by specific interactions between the molecules and the confining boundary surfaces of a given volume. The surface induced alignment is then transferred into the bulk of the liquid crystal by elastic forces, and the resulting director field distribution represents the state of minimum free energy $F$.
Depending on the orientation of molecules towards the substrates, three alignment modes are distinguished: Homeotropic alignment is characterized by the director $n$ perpendicular to the substrates $\left(\theta_0=\pi/2\right)$, while planar alignment is given for $n$ parallel to the surface $\left(\theta_0=0\right)$. The intermediate state between homeotropic and planar alignment is the tilted alignment mode, where the long axis of molecules orients in a defined angle $\theta_0$ towards the substrates $\left(0<\theta_0<\pi/2\right)$.

Schematic drawing of the three alignment modes of nematic liquid crystals on an interface, with additional distinction between free planar alignment and homogeneous planar alignment.

The nematic phase preferres to be in a state of minumum energy which is given by an undisturbed, homogeneous director field. Every deformation of this ideal state causes an increase of the eleastic free energy of the nematic LC and causes restoring forces. There are three fundamental deformations of the director field: Splay, Twist and Bend. Every director field configuration results from a combination of these three fundamental modes.

Splay deformation

Twist - deformation

Bend - deformation

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