Kerr-effect relaxation

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. 

The physical quantity of interest from an experimental point of view and which is appropriate to Kerr effect relaxation is the electric birefringence function K(t) defined by [69]... 

Here the term (cos 29) which is the average pertaining to the Kerr-effect relaxation is at least of the order pF /kTy [35] so that for the linear response we are fully justified in setting... 

This system of equations can be solved by the method suggested by us [20, 48, 49] in the theory of dielectric and Kerr effect relaxation. 

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)...

The 8- and 4.5-nm particles are at most weakly emissive and the polarizations of spectral features assigned to these particles are determined by polarized bleach measurements. The bleach anisotropy was determined using femtosecond pulses, with the probe delayed a few picoseconds from the pump. This delay ensures electronic and vibrational relaxation as well as relaxation of optical Kerr effects induced in tire solvent. As a control, transient absorption experiments were performed with excitation at 475 nm and detection at 550 nm. This detection wavelengtli is to the red of the wavelengths at which a bleach would be observed and provides a measure of the transient absorption intensity in this general spectral... 

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 approach developed may also be extended to treat all the other averages (P (cos i)))(t) characterizing orientational relaxation in fluids [43]. In particular, the evaluation of the average of the second-order Legendre polynomial (/Tfcos 0))(t) (e.g., this quantity describes the dynamic Kerr effect [8]) is given in Appendix III. 

In the transient (step-off) Kerr-effect response, it is also possible to obtain from Eqs. (273)—(275) for l = 2 the system of recurrence equations for the Laplace transforms of the corresponding relaxation functions < " (t) (m = 0,1,2) pertaining to that response, namely,... 

Comparable behavior has been observed by Payer et al. in a series of subpicosecond transient grating optical Kerr effect measurements on the reorientation of byphenyl molecules in neat biphenyl and n-heptane solutions [66,67]. They have shown that on the ultrafast timescale (r < 2 ps) the dynamics of the probe is controlled by librational motions having an inertial character, although diffusive reorientational relaxation of the whole molecule and internal torsional motions can also have a role. 

Mode-locked Nd-glass oscillator amplifier system for studies of electron relaxation processes and optical Kerr effects in liquids. See text for details. 

The rotational diffusion constant has been measured by relaxation of the Kerr effect,and by dynamic light scattering. The experimental results are in accordance with the theoretical predictions... 

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. 

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