Constants and Refractive Indices

Dielectric 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 stractures of nematic molecules, these responses are highly dependent on the direction and the frequencies of the field. Accordingly, we shall classify om 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 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 is on the order of 10 ° Hz. 

Typical values of and Sj are on the order of 5% where o is the permittivity of free space. Similariy, the electric conductivities an and aj of nematics are defined by 

Most nematics (e.g., E7, 5CB, etc.) are said to possess positive (dielectric) anisotropy 8 ). On the other hand, some nematics, such as MBBA, possess negative anisotropy (i.e., ey 8 ). The controlling factors are the molecular constituents and structures. 

For some nematic liquid crystals this changeover in the sign of Ac = Cy — occurs at a much lower frequency (cf. Fig. 3.5 for phenylbenzoates ). This changeover frequency is lower because of the long three-ringed molecular structure, which is highly resistant to the rotation of molecules around the short axes. 

For electro-optical applications, the dielectric relaxation behavior of 8y and 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 and Khoo and Wu and the references quoted therein for more detailed information. 

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Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

The role of the medium, in which contacting and pull-off are performed, has been mentioned but not considered so far. However, the surroundings obviously influence surface forces, e.g., via effective polarizability effects (essentially multibody interactions e.g., by the presence of a third atom and its influence via instantaneous polarizability effects). These effects can become noticeable in condensed media (liquids) when the pairwise additivity of forces can essentially break down. One solution to this problem is given by the quantum field theory of Lifshitz, which has been simplified by Israelachvili [6]. The interaction is expressed by the (frequency-dependent) dielectric constants and refractive indices of the contacting macroscopic bodies (labeled by 1 and 2) and the medium (labeled by 3). The value of the Hamaker constant Atota 1 is considered as the sum of a term at zero frequency (v =0, dipole-dipole and dipole-induced dipole forces) and London dispersion forces (at positive frequencies, v >0). 

Since metals have high dielectric constants and refractive indices, they have much higher Hamaker constants than those of non-conducting materials. 

Dielectric constants and refractive indices of solvents used in dipole moment measurements... 

The characteristic adhesion distance In Eqs.( 1) and ( 4) lies in a molecular scale a = 3 =0 0.3 - 0.4 rum. It depends mainly on the properties of liquid-equivalent packed adsorbed layers and is to be estimated for a molecular interaction potential minimum. Provided that these molecular contacts are stiff enough compared with the soft particle contact behaviour influenced by mobile adsorption layers due to molecular rearrangement, this separation ap-o is assumed to be constant during loading and unloading in the interesting macroscopic pressure range of o = 0.1 - 100 kPa. The Hamaker constant solid-liquid-solid Ch,jIs acc. to Lifschitz theory is related to continuous media dependent on their permittivities (dielectric constants) and refractive indices, see Israelachvili [23]. 

Since relative dielectric constants and refractive indices are related according to the MaxweU theory, = er, polarizability and refractive index can be expressed one as a function of the other by... 

OPTICAL DIELECTRIC CONSTANTS AND REFRACTIVE INDICES 3.4.1. Linear Susceptibility and Local Field Effect... 

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