3. Director and Order Parameter

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Director

The average direction of the molecular long axes in the LC phase defines the director n, which gives the direction of the preferred orientation of LC molecules. In most LCs both directions of the vector n, +n and n are equivalent. However, for molecules with permanent dipole moments this may not be the case, and the sign of n becomes important.

Order parameter

To specify quantitatively the amount of the orientational order in the LC phase, the scalar order parameter S is commonly used (0 < S < 1)

order parameter

where θ is an angle between the individual molecular long axis and the director n and the brackets indicate the average value. In a perfectly oriented system S = 1, and in an isotropic liquid state, with no orientational order, S = 0.

Svstemperature

Figure 4. Scalar order parameter S vs temperature: Tc is clearing temperature

The order parameter of the LC decreases as the temperature increases and typical values are in the range 0.3-0.9.

 

 

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Anisotropy in LCs