Lesson2GeneralProperties
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The main features of the nematic phase 1. The centres of gravity of the molecules have no long-range order and. 2. The molecules tend to be parallel to some common axis, labelled by a unit vector n, and known as the director. Optically, a nematic is a uniaxial medium with the optical axis along n. (The difference between refractive indices measured with polarizations parallel or normal to n is quite large: typically 0.2 for PAA.) In all known cases, there appears to be complete rotational symmetry around the axis n. 3. The direction of n is arbitrary in space; in practice it is imposed by minor forces. 4. The states of director n and –n are indistinguishable. For instance, if the individual molecules carry a permanent electric dipole, there are just as many dipoles ‘up’ as there are dipoles ‘down’ and the system is not ferroelectric. 5. Nematic phases occur only with materials that do not distinguish between right and left; either each constituent molecule must be identical to its mirror of the right- or lefthanded species.
Dimension and Order of Elastic Constants
fd = [energy] / [cm3] n is dimensionless thus Ki= [energy]/[cm ] (or dynes)
S2
1 2
3co2sq1
,
where q is the angle of a molecule made respect with the director, the brackets means a thermal average.
Frank Elastic Energy
The constraints imposed upon a nematic liquid crystal will give rise to a liquid crystalline material where the orientation varies over the sample.
K1: conformation with div·n = 0, the splay deformation; K2: conformation with n·curl n = 0, twist deformation; K3: conformation with n ×curl n = 0, the bend deformation.
4. E. Kaneko, Liquid Crystal TV Displays: Principles and Applications of Liquid Crystal Displays, KTK Scientific Publishers, Tokyo, 1987.
Orientation Order
Lesson 2 General Properties of (N) LCs
Textbooks for Reference
1. Ernst Lueder, Liquid Crystal Displays: Addressing Schemes and Electro-optical Effects, Hohn Wiley & Sons, 2001.
The free energy density of a locally uniaxial liquid crystal fd(r) = ½ K1[div n(r)]2 + ½ K2[n(r)·curl n(r)]2 + ½ K3[n(r) curl n(r)]2
The three elastic constants are respectively associated with the three basic types of deforma parameter is a measure of the degree of the ordering of a system. For liquid crystals consisting of rod-like molecules and with a cylindrical symmetry, the order parameter can be given as
2. Pochi Yeh, and Claire Gu, Optics of Liquid Crystal Displays, John Wiley & Sons, 1999.
3. Liquid Crystals: Applications and Uses, Ed. Birendra Bahadur, 2nd Ed., World Scientific, 1992.
Dimension and Order of Elastic Constants
fd = [energy] / [cm3] n is dimensionless thus Ki= [energy]/[cm ] (or dynes)
S2
1 2
3co2sq1
,
where q is the angle of a molecule made respect with the director, the brackets means a thermal average.
Frank Elastic Energy
The constraints imposed upon a nematic liquid crystal will give rise to a liquid crystalline material where the orientation varies over the sample.
K1: conformation with div·n = 0, the splay deformation; K2: conformation with n·curl n = 0, twist deformation; K3: conformation with n ×curl n = 0, the bend deformation.
4. E. Kaneko, Liquid Crystal TV Displays: Principles and Applications of Liquid Crystal Displays, KTK Scientific Publishers, Tokyo, 1987.
Orientation Order
Lesson 2 General Properties of (N) LCs
Textbooks for Reference
1. Ernst Lueder, Liquid Crystal Displays: Addressing Schemes and Electro-optical Effects, Hohn Wiley & Sons, 2001.
The free energy density of a locally uniaxial liquid crystal fd(r) = ½ K1[div n(r)]2 + ½ K2[n(r)·curl n(r)]2 + ½ K3[n(r) curl n(r)]2
The three elastic constants are respectively associated with the three basic types of deforma parameter is a measure of the degree of the ordering of a system. For liquid crystals consisting of rod-like molecules and with a cylindrical symmetry, the order parameter can be given as
2. Pochi Yeh, and Claire Gu, Optics of Liquid Crystal Displays, John Wiley & Sons, 1999.
3. Liquid Crystals: Applications and Uses, Ed. Birendra Bahadur, 2nd Ed., World Scientific, 1992.