Macroscopic Electric Dipole Moment

The macroscopic electrical dipole moment, p, expressed in C.m, is the summation of all the contributions of individual microscopic electric dipole moments  

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As first realized by Meyer in 1974, when the molecules making up the C phase are non-racemic, the resulting chiral C phase can possess no reflection symmetry. Thus, the maximum possible symmetry of a C phase is C2, and the phase must possess polar order (21). One of the macroscopic manifestations of polar order can be a macroscopic electric dipole moment (the polarization P) associated with orientation of molecular dipoles along the polar axis. While the existence of polar order is not sufficient to assure an observable polarization (just as chirality does not assure optical activity), in fact many FLC materials do possess an observable P. 

We feel that these data in fact show that the o-nitroalkoxy functional array is indeed oriented along the polar axis in the FLC thin film as evidenced by the observed sign and magnitude of the macroscopic electric dipole moment of the film. This, of course, means that the molecular associated with this functional array must also be oriented along the polar axis of the film, which should therefore possess a substantial X(2). 

Furthermore, in FLCEs the macroscopic electric dipole moment provides a handle to apply a strong torque onto the director (see Fig. 14a). The resulting switching occurs on the cone of the so-called c-director, the projection of the director on the smectic layer plane (see Fig. 14a). Soon after the discovery of the potential of chiral smectic-C phases, the search for LC polymers with these phases started [130-132]. However, as ferroelectric switching is the final proof for the assignment of the phase, the more closely studied ferroelectric LC polymers were limited to several LC polysiloxanes, which have a low Tg and a relatively high switching speed [25, 66, 133-136] (see Scheme 1). These polymers form the basis for most of the FLCEs discussed here. 

A recently developed thermal detector for infrared radiation is based on the pyroelectric effect [4.59]. Pyroelectric materials are good electrical insultors which possess an internal macroscopic electric dipole moment, de-... 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Two polarization mechanisms are possible. If the molecules possess a permanent electric dipole moment pbp rm, each molecule can align its moment with the field direction by reorientation, producing a macroscopic dipole moment. Even if perm = 0 in the field-free limit, each molecule can achieve a field-dependent dipole moment pind by induction. The induced dipole moment is proportional to field strength, pind = a , where a is the electric polarizability of the molecule. In both cases, work must be performed on the system to achieve the macroscopic polarization. Molecules with large permanent dipole moments correspond to high k. 

P is the macroscopic polarization. It consists of a lattice polarization b21 w originating from the electric dipole moment arising from the mutual displacement of the two sublattices, and of a second term b22 P originating from the pure electron polarization. According to definition, P and E are connected by... 

Second, after an appropriate time interval to allow the gas pulse to reach an optimum position between the cavity mirrors, a 1 qs pulse of monochromatic microwave radiation is introduced into the cavity, which is itself tuned to the correct matching resonant frequency. The pulse carries with it a band of frequencies Av 1 MHz, centred at the resonant frequency v of the cavity. The cavity has a bandwidth of approximately 1 MHz, so that the microwave radiation density is high. If the molecular species under investigation has one or more resonant frequencies within this bandwidth, an appreciable macroscopic polarisation is induced, corresponding classically to a phase-coherent oscillation of the molecular electric dipole moments. The microwave pulse must arrive at the correct time interval after the gas pulse. 

Among all the methods which have hitherto been brought forward for the determination of the electric dipole moment of molecules, the molecular-beam method occupies a special position, for it enables us to investigate the behaviour of individual free molecules in the electric field directly. It also has the great advantage that the effect of the field on the dipole moment of a single molecule occurs in it as a directly measurable quantity, so that it avoids the uncertainties of all other methods, which are chiefly due to the fact that in their case it is the macroscopic actions between the field and the dielectric (gas or liquid) which are measured and the mutual effects of the molecules can neither be eliminated entirely nor be allowed for accurately. 

Macroscopic organizations possessing a permanent electric dipole moment like electrets have a finite Maxwell field E which may be externally measured, for instance, as a plate capacitor field. 

The dipole moment p may be the resultant dipole moment of a molecule, many molecules, or a whole region. Polarization P [Cm/m = C/m ] is the electrical dipole moment per unit volume (dipole moment volume density). It is therefore a more macroscopic concept than the dipole moment of molecules or atoms. P is a space vector having the same direction as the E-vector in isotropic and linear materials ... 

In principle, each of these can be used to formulate an exact theory of water. The choice of the particular level depends on the questions we want to ask about the system. If we are interested only in explaining some macroscopic thermodynamic properties of pure water, we might be satisfied with the choice of a relatively simple mixture model. If we want to compute the pair correlation function, then a rigid model for water molecules may be used. If we are also interested in the dielectric properties of pure water or the solvation of ions in water, we need to assign an electric dipole moment, or perhaps a quadrupole moment, to our rigid water molecule. If we want to allow for dissociation into ions, then clearly a rigid model for water molecules will not be appropriate, and we need to consider a lower level of treatment such as a collection of and 0 . Finally, if we are interested in the chemical reactivity of water molecules, we must start from the more elementary description of the system in terms of electrons and various nuclei and solve the Schrodinger equation for all the molecules involved in the chemical reaction. 

In the meantime Debye, who the year before had been appointed professor of theoretical physics at the University of Zurich, in 1912 introduced the idea of polar molecules , i.e., molecules with a permanent electric dipole moment (at that time a hypothesis) and worked out a theory for the macroscopic polarization in analogy with Langevin s theory of paramagnetic substances. He found, however, that the interactions in condensed matter could lead to a permanent dielectric polarization, corresponding to a susceptibility tending to infinity for a certain temperature, which he... 

It is the molecular property underlying the refractive index rv(wi) of a macroscopic sample with number density A/". For a non-polar molecule, i.e. without permanent electric dipole moment, the relation between them can be shown to be ... 

Ferroelectric domains are those macroscopic (greater than 20 A) regions in a solid having natural crystal polarity which is constant, but whose direction of polarity can be altered irreversibly by a practically imposable electric field. Implied in this definition is the existence within the material of a spontaneous electrical dipole moment hence the existence of piezoelectricity, and the reversing effects of applied fields hence the existence of hysteresis, and of the probability that at some temperature before complete crystal disruption the spontaneous polarization will be destroyed or directionally randomized on an atomic scale. At this temperature the dipolar instability between the decision of order or disorder will usually produce a high peak value of incremental permittivity. 

In order to obtain information about molecular dynamics from a dielectric relaxation spectrum, the complex dielectric permittivity is related to the correlation function of the electric dipole moment m, of the ith species and the dipole moment Mj of a small (in comparison with the whole sample) macroscopic volume V surrounding m,. Mj is the sum of permanent dipole moments in this volume Mi N being the number of dipole moments in the volume. The... 

The summation runs over repeated indices, /r, is the i-th component of the induced electric dipole moment and , are components of the applied electro-magnetic field. The coefficients aij, Pijic and Yijki are components of the linear polarizability, the first hyperpolarizability, and the second hyperpolarizability tensor, respectively. The first term on the right hand side of eq. (12) describes the linear response of the incident electric field, whereas the other terms describe the nonhnear response. The ft tensor is responsible for second order nonlinear optical effects such as second harmonic generation (SHG, frequency AotAAin, frequency mixing, optical rectification and the electro-optic effect. The ft tensor vanishes in a centrosymmetric envirorunent, so that most second-order nonlinear optical materials that have been studied so far consists of non-centrosyrmnetric, one-dimensional charge-transfer molecules. At the macroscopic level, observation of the nonlinear optical susceptibility requires that the molecular non-symmetry is preserved over the physical dimensions of the bulk stmcture. 

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