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constants and refractive indices, as well as electrical conductivities of liquid crystals, are physical parameters that characterize the electronic responses of liquid crystals to externally applied fields (electric, magnetic, or optical). Because of the molecular and energy level structures of nematic molecules, these responses are highly dependent on the direction and the frequencies of the field. Accordingly, we shall classify our studies of dielectric permittivity and other electro‐optical parameters into two distinctive frequency regimes: (1) dc and low frequency and (2) optical frequency. Where the transition from the regime (1) to (2) occurs, of course, is governed by the dielectric relaxation processes and the dynamical time constant; typically, the Debye relaxation frequencies in nematics are on the order of 1010 Hz.

      3.3.1. DC and Low‐frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility

      The dielectric constant ε is defined by the Maxwell equation [5]:

      (3.16)upper D Subscript parallel-to Baseline equals epsilon Subscript parallel-to Baseline upper E Subscript parallel-to

      and

      (3.17)upper D Subscript up-tack Baseline equals epsilon Subscript up-tack Baseline upper E Subscript up-tack Baseline period

      Typical values of ε|| and ε are on the order of 5ε0, where ε0 is the permittivity of free space. Similarly, the electric conductivities σ|| and σ of nematics are defined by

      (3.18)upper J Subscript parallel-to Baseline equals sigma Subscript parallel-to Baseline upper E Subscript parallel-to

      and

      (3.19)upper J Subscript up-tack Baseline equals sigma Subscript up-tack Baseline upper E Subscript up-tack Baseline comma

      where J and J are the currents flowing along and perpendicularly to the director axis, respectively. In conjunction with an applied dc electric field, the conductivity anisotropy could give rise to space charge accumulation and create strong director axis reorientation in a nematic film, giving rise to an orientational photorefractive [6] effect (see Chapter 8).

      Most nematics (e.g. E7, pentyl cyanobiphenyl [5CB], etc.) are said to possess positive (dielectric) anisotropy (ε|| > ε). On the other hand, some nematics, such as MBBA, possess negative anisotropy (i.e. ε|| < ε). The controlling factors are the molecular constituents and structures.

Image described by caption.

      For electro‐optical applications, the dielectric relaxation behavior of ε|| and ε for the different classes of nematic liquid crystals, and the relationships between the molecular structures and the dielectric constant, is obviously very important. This topic, however, is beyond the scope of this chapter, and the reader is referred to Blinov [8] and Khoo and Wu [9] and the references quoted therein for more detailed information.

      The magnetic susceptibility of a material is defined in terms of the magnetization Скачать книгу