Kerr effect relaxation times

This outline of the response theory has for simplicity been limited to molecules with axial symmetry of y and Aa and to the field on, field off cases, but can be extended in both respects without basic difficulties. Detailed comparisons with experiment have not yet been made, but it already is clear that Kerr effect relaxation data can now provide more valuable and better defined information about orientational dynamics of biopolymers and other molecules than was previously possible. With the increasing accuracy and time resolution of digital methods, it should be possible to study not only slow overall rotations of large molecules (microseconds or longer) but small conformational effects and small molecule reorientations on nano and picosecond time scales. Moreover, one can anticipate the possibilities, for simple problems at least, of extending response theory to other quadratic and higher order effects of strong electric fields on observable responses. 

Note that the steady-state a.c. Kerr-effect is not simply related in the general case to the transient Kerr-effect in the time-domain (86-88), but exact relations can be given if the model for reorientation is specified. For example Benoit gave the necessary relations for the small-step diffusion model for axially-symmetric molecules (85). In this case Kjjj(t) = exp[-m(nH-l)Dj t] where Dr is the rotational diffusion coefficient (see also refs. 86,89). Thus for the case where the permanent dipole moment contribution to K greatly exceeds the "induced dipole moment contribution, the effective relaxation time for step-on response,... 

Whilst the equilibrium theory outlined above is well-known, the time-correlation function representation is not so well-known. Time-correlation functions have been used frequently in the recent literature for a variety of relaxation, spectroscopic and scattering phenomena for liquids and solids. The analysis of Kerr-effect relaxation (Beevers and co-workers, 1976), fluorescence depolarization (Valeur and... 

Figure 6.19 Kerr effect on PTFEparticles. The Kerr relaxation time is plotted against the viscosity of a waterjglycerol mixture relative to the viscosity of water (L = 388 nm and b = 167nm)...

A measurement of the Kerr relaxation times in succinoni-trile(SN)as a function of temperature is shown in Fig. 2. The Kerr relaxation times measured show the effect of temperature on the rotational motion of the SN molecules as they undergo a change from the liquid to the plastic crystal phase. The data obtained from the Kerr gate measurement is shown along with a best fit curve from depolarized Rayleigh scattering (dotted line), and a best fit curve from dielectric relaxation measure-... 

The display of intramolecular motion in rigid-chain polymers can also be observed if the kinetics of the Kerr effect is studied for a series of fractions of relatively high molecular we t. In fact, as already mentioned (p. 171), the kinetics of the behavior of a polar chain molecule in the electric fidd is determined by relative values of relaxation times of its orientation tq and deformation tj. Since tq increases with M proportionally to M(rjl, and tj is independent of M, it might be expected that at relatively high M the inequality tq > rj will hold and, hence, the polarization and the anisotropy of the solutmn in the electric field will follow the deformational mechanism. 

The subpicosecond time-resolved optical Kerr effect was used to determine the nonresonant optical nonlinearity. A power law dependence of the second-order hyperpolarizability y, of the polybenzonitrile molecule on the average degree of polymerization was discussed. Based on the transient response, which was primarily pulse limited, the relaxation time of the samples was shorter than the laser pulse width. 

FIGURE 4.38. Relaxation times associated with nematic order fluctuations n and with molecular relaxation (t2) as functions of temperature (Kerr effect in 5CB) [225]. 

Transient Kerr effect measurements have been used primarily to study large molecules (polymers and biopolymers) or smaller molecules at sufficiently low temperatures as discussed by G. Williams. The limitations are because the relaxation time scale must not be shorter than the time resolutions for available transient field generators and optical detectors. Wntil recently this has set short time limits of 10 ° to 10 seconds at best. These are too large for useful studies of small molecules in liquids at ordinary temperatures but developments in pump and probe laser tectmiques have already made some measurements possible with picosecond resolution (as discussed by Kenney-Wallace In this volume) and it should be possible to do much more with availability of fast solid state switching and optical coupling devices. 

One can hope that these will not greatly affect comparisons of macroscopic relaxation functions rather than microscopic functions and that better treatments as from Fulton s methods for example will clarify these questions. Even so, It seems fair to claim that a better basis now exists for extracting useful information from Kerr effect measurements and to explore questions of whether rotational reorientations in time are diffusion or Brownian motion like at one extreme infrequently by large jumps at the other or something in between. With developments in instrumentation of the sort suggested above there appear to be real possibilities for studies of dynamics of simpler molecules to complement those by other methods. 

Thus this simple model requires all angular time-conelation functions to be equal to X (0- This model accomodates the dielectric and Kerr-effect data for certain viscous molecular liquids, e.g. fluorenone in o-terphenyl (Beevers and co-woricers, 1977b) and tritolyl phosphate (Beevers and co-wotkers, 1977 a). In view of the ami-larities between the o-relaxations of such small-molecule systems and of amorphous polymers it seems possible... 

Only recently a dynamic Kerr effect study on QPVP and NaPSS [169] investigated the effect of intermolecular interaction on the field-free decay of the birefringence at very low polyion concentration without added salt, with the remarkable result that a maximum of the decay time is observed in each of the two relaxation processes at approximately the same concentrations where the viscosity displays a maximum and the scattering techniques show a structure peak (Fig. 10). Whereas the longer relaxation process is identified as the overall rotation of the polyion, the fast relaxation has become a matter of extensive speculation. 

Later, Piazza and Degiorgio [270, 271] performed dynamic Kerr effect measurements on lower molar mass PSS where the fast relaxation is not observed, because it most probably has moved out of the time window of the instrument. The resulting relaxation times were interpreted in terms of the rotational diffusion of worm-like chains according to Monte Carlo simulations of Hagerman and Zimm [291] and to Yamakawa [292]. The resulting persistence lengths are at the upper limit of experimental values derived from other techniques discussed above. 

Pretransitional dynamics in the isotropic phase of nematics was also studied by other optical methods. Wong and Shen [74, 75], Flytzanis and Shen [76] and Prost and Lalanne [77] have used the optical Kerr effect to induce nematic ordering in the isotropic phase. Using a Q-switched laser they could measure the relaxation time of the induced birefringence. They found a good agreement with the Landau-de Gennes theory (see Fig. 5) and with the results of Stinson and Litster. 

Figure 5. Relaxation time of the order parameter as determined from the optical Kerr effect in MBBA [24]. The solid line is a best fit of the form. ...

The transient grating Kerr effect experiments were performed in the isotropic phase of 5CB [80, 149] and MBBA [82] over a very large temperature interval. For very short (picosecond) time scales, an additional noncritical relaxation was observed that was attributed to the individual molecular motion. Far above T, a deviation of the relaxation rates from the de Gennes theory was observed [80]. 

Experimentally, the Kerr effect was intensively studied in the 1970s. The relaxation times associated with the order parameter fluctuations increase when approaching (critical slowing down) but still in the submicrosecond range. 

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