Longitudinal cooling relaxation

It is sometimes convenient to compare longitudinal (T ) relaxation to the process of heat flow (also a first-order process). When we apply a pulse to the spins, we heat them up, and as they return to equilibrium they cool down again to the temperature of their surroundings. We can even define a spin temperature (Ts) as the temperature corresponding to a given population difference between the a and p states ... 

As the fluid is cooled, the relaxation times of the system become comparable with (Awi)"1, and the viscoelastic nature of polymer liquids must be taken into account. The longitudinal velocity becomes (13) ... 

Figure 17.8 Variation of the storage relaxation modulus, E, with temperature measured during a cooling experiment. Ep represents the actual value of the storage relaxation modulus in absence of contraction forces which increase the longitudinal tension.

Fig. 40. (a) Temperature dependence of the longitudinal acoustic-phonon frequencies of Smo Y jsS in the [111] direction for four different values of the wavevector q (see Mook et al. 1981). (b) Temperature dependence of the bulk modulus Cg of Sm Y 25S measured by Bril-iouin scattering. Cg continues to soften upon cooling below 200 K, uniike the behavior of the phonon mode frequencies for qaO.l (flg. 40a). (c) Temperature dependence of the charge relaxation rate derived from the experimental data in figs. 40a and 40b (open circles) and calculated from theory (Schmidt and Miiller-Hartmann 1985) (solid line). The theoretical curve has been matched at 300 K to the experimental value. 

Consider first an anisometric molecule with the longitudinal p, and transversal p, permanent dipole moments in an isotropic phase. There are two relaxation modes mode 1, rotations of p, around the long axis, and mode 2, reorientation of p,. Figure 10-1. The mode 1 has a smaller relaxation time, Tj < Tj, because of the smaller moments of inertia involved. When this isotropic fluid is cooled down into the NEC phase, the dynamics is affected by the appearance of the nematic potential associated with the orientational order along the director n. The mode 1 remains almost the same as in the isotropic phase, and contributes to both the parallel and perpendicular components of dielectric polarization (determined with respect to n). Mode 2 is associated with small changes of the angle between p, and n it contributes to the parallel component of dielectric polarization. Mode 3 is associated with conical rotations of p, around the director (as the axis of the cone) it is effective when the applied electric field is perpendicular to n and contributes... 

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