Electrically induced transitions

Concerning the same transition, an induced SmA-SmC transition was observed when an electric field was applied in a chiral compound at a temperature near the transition [136, 137], the SmA-SmC transition temperature increasing under an electric field (Fig. 18). This field-induced transition was attributed to the large spontaneous polarization and to the first order behavior of the transition. Further studies have shown that the first order transition between the polarized smectic A phase and the ferroelectric smectic C phase terminates at a critical point in the temperature-electric field plane [138, 139]. 

In a recent work, isotropic-nematic-smectic A phase transitions in thermotropic liquid crystals were also induced by applying an electric field [140]. The liquid crystal investigated (a mixture of 8CB and lOCB) showed a first order isotropic to smectic A transition. When in the isotropic phase and near the spontaneous transition temperature, a field-induced first order transition was observed from a paranematic to a nonspontaneous nematic phase. For higher values of the applied electric field, another first order transition occurred from the nonspontaneous nematic to a phase exhibiting the same order as a smectic A phase. A phenomenological Landau-de Gennes model has been developed to describe these transitions [141], 

---

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

Fig. 4.1. The La line of the H atom and its structure in the constant electric field (a) and the rotational structure of the vibrational transition (b). Wavy arrows show collision-induced transitions, thick horizontal arrows indicate the optical transitions that mutually interfere.

The response of liquid crystal molecular orientation to an electric field is another major characteristic utilised for many years in industrial applications [44] and more recently in studies of electrically-induced phase transitions [45]. The ability of the director to align along an external field again results from the electronic structure of the individual molecules. 

In much the same way as Stevens operators, the summation in Equation 1.15 is limited to well-defined values for f-electrons, the restriction k <7 holds, while q is limited to those values consistent with the point symmetry of the site. Finally, the even part k = 0, 2,4,6) is responsible for the CF splitting, while the odd part k = 1,3, 5,7) is responsible for the intensity of induced electric dipole transitions in optical spectroscopy [5b, 26]. 

Various types of work in addition to pV work are frequently involved in experimental studies. Research on chemical equilibria for example may involve surfaces or phases at different electric or magnetic potentials [11], We will here look briefly at field-induced transitions, a topic of considerable interest in materials science. Examples are stress-induced formation of piezoelectric phases, electric polarization-induced formation of dielectrica and field-induced order-disorder transitions, such as for environmentally friendly magnetic refrigeration. 

The observation of pores in the anodic oxide with a density in the order of 1011 cnT2 [Agl] supports the so-called fluctuating pore model [Lel3]. This model assumes that randomly distributed pores in the oxides work as charge collecting centers, which lead to oscillations synchronized by the applied external electric field. It should be noted that the observed pore density corresponds well with the roughness at the oxide-electrolyte interface observed after the stress-induced transition of an anodic oxide, as shown in Fig. 5.5. 

According to Equations (5.14) and (5.15), we see that the probability of a particular transition depends on the electric dipole matrix element /x, given by Equation (5.12). These transitions, which are induced by interactions of the electric dipole element with the electric field of the incident radiation, are called electric dipole transitions. Therefore, electric dipole transitions are allowed when p- 0. 

The K quantum number can not change because the dipole moment lies along the molecule s C3 axis and the light s electric field thus can exert no torque that twists the molecule about this axis. As a result, the light can not induce transitions that excite the molecule s spinning motion about this axis. 

X being a 4/ wave function. From this expression, one estimates that the oscillator strengths should be about the same as for an ion situated in a noncentrosymmetric field (P 10 6). A rigorous formal treatment for the vibronically induced electric-dipole transitions has been developed by Satten (32-34),... 

Optical activity arises from the coupling of given electric-allowed transitions with a chiral orientation (coupled oscillator mechanism or two-electron mechanism) or from the electric or magnetic moments of a transition being pertubed by a chiral static field (asymmetrically perturbed field mechanism or one-electron mechanism) in the given one molecule. A similar mechanism of the optical activity can be expected for molecular assemblies which are composed of chiral and achiral ones. This type of optical activity is called induced optical activity and depends on types of inter-molecular interaction modes. 

Quantum mechanics tells us that the probability of an electric dipole induced transition occurring between the states described by tpn and tpm is proportional to... 

Nakata M, Link DR, Takanishi Y, Takahasi Y, Thisayukta J, Niwano H, Coleman DA, Watanabe J, Iida A, Clark NA, Takezoe H (2005) Electric-field-induced transition between the polarization-modulated and ferroelectric smectic-CgPf liquid crystalline states studied using microbeam X-ray diffraction. Phys Rev E 71 011705... 

The probability of a transition being induced by interaction with electromagnetic radiation is proportional to the square of the modulus of a matrix element of the form where the state function that describes the initial state transforms as F, that describing the final state transforms as Tk, and the operator (which depends on the type of transition being considered) transforms as F. The strongest transitions are the El transitions, which occur when Q is the electric dipole moment operator, — er. These transitions are therefore often called electric dipole transitions. The components of the electric dipole operator transform like x, y, and z. Next in importance are the Ml transitions, for which Q is the magnetic dipole operator, which transforms like Rx, Ry, Rz. The weakest transitions are the E2 transitions, which occur when Q is the electric quadrupole operator which, transforms like binary products of x, v, and z. 

The induced CD of an electric dipole transition of a solute intercalated in DNA has been calculated using a matrix method and wavefunctions proposed for the transitions of... 

---