Orienting potential

Islands. All these plants are used in folk medicine. These two systems, the 2,3,4-and the 2,4,5-orientations, potentially give rise, with ammonia, to MMDA-3a and MMDA-2. 

Because of the distinction between the A-oriented potential fields at positions... 

Larmor Precession. When a nucleus with magnetic moment fiN is placed in an external magnetic field B0, and the angle between the two vectors is 8, the orientational potential energy is... 

Given this magnetic field, the orientation of the spin magnetic moment fig in it will produce an orientational potential energy ... 

It has been the merit of Picken (1989, 1990) having modified the Maier-Saupe mean field theory successfully for application to LCPs. He derived the stability of the nematic mesophase from an anisotropic potential, thereby making use of a coupling constant that determines the strength of the orientation potential. He also incorporated influences of concentration and molecular weight in the Maier-Saupe model. Moreover, he used Ciferri s equation to take into account the temperature dependence of the persistence length. In this way he found a relationship between clearing temperature (i.e. the temperature of transition from the nematic to the isotropic phase) and concentration ... 

A. Hiiller, M. Prager, W. Press and T. Seidel, Phase III of solid methane the orientational potential and rotational tunneling.. Chem. Phys., 2008,128, 034503, 1-9. 

In the presence of an orientation potential, one should also consider the effective frequencies corresponding to the harmonic approximation of this potential. The adiabatic elimination procedure (AEP), as developed in Chapter II, should allow us to take into account the inertial corrections to the standard adiabatic elimination, thereby making it possible to determine the influence of inertia on EPR spectra within the context of a contracted description that retains only the variable Q. This allows us to arrive at an equation of the form... 

In this section we shall detail the analytical derivation of the absorption spectrum for a magnetic species in a triplet spin state tumbling in a viscous disordered liquid. This an ytical structure consists of the sum of product of continued fractions. The standard Mori structure of Eq. (2.19) is recovered in the absence of orienting potentials. 

In the absence of an orienting potential we are therefore allowed to write... 

The two algorithms already developed and used to reproduce ESR line-shapes of paramagnetic species in free diffusion are applied in this subsection to the case of spin probes dissolved in liquid crystalline mesophases. The main point of diffoence with the previously examined cases is due to the introduction of an orienting potential v ose nature is directly reflected in the structure of the Fokker-Planck opoator, whidi in the difiusional assumption is given by Eq. (2.6). The explicit form of the potential we use in this... 

We first show that the completely analytic approach developed in Section III.B.2 also holds in the presence of an orienting potential. Later on we apply the general CFP method already applied in Sections III.A and III.C. 

Figure 10. Absorption lineshape for an axial g-splitting interaction for a spin 1/2 system in the presence of an orienting potential. Vertical scales are expressed in the same units. Uq 0. (a) 10 i, (b) Dj 5xl0 ii. The frequency sweep ranges from - -fij to -...

Note that the last contribution to each off-diagonal coefficient of Eqs. (3.63) depends on the orienting potential. This contribution vanishes when the potential is turned off. 

In this subsection we show the effect of the orienting potential on the ESR lineshape of paramagnetic species of particular practical interest, namely, the nitroxide stearic spin probe and Cu ion complex dissolved in a nematic liquid crystal. 

Figure 11. Absorption lineshape for a molecule in a triplet spin state subjected to an orienting potential. Ug = 0. D — 10 t. The frequency sweep ranges from u,- — (i) -f S) to ay...

Via the same procedure we can calculate the continued fraction parameters and then obtain the ESR lineshape. In the following we show the effect on the lineshape in the presence of the orienting potential of varying the r parameter defined in Section III.A. 

Figure 13 shows the absorption spectra for a nitroxide spin probe and compares the case of free diffusion (P2 0) with those obtained for various values of the orienting potential. Such spectra have been calculated for an isotropic diffusion coefficient. Note the drastic change in lineshape at the onset of molecular order. 

Figure 14 illustrates the spectra of a stearic spin probe for two greatly different values of the ratio D /D. For very different diffusion limits in the presence of an orienting potential, this shows how sensitive to changes of the order parameter the dynamics of the spin probe are. The slightly different features of the two series of spectra can be ascribed to the modulation of secular terms of the Hamiltonian of Eq. (3.3). The two series of spectra exhibit virtually the same behavior, except that the senes of curves reproduced in Fig. 14 by the continuous lines seem to be more rigid. 

Finally, as in the case of free isotropic diffusion for a Cu ion complex in a highly viscous solvent, we plan to establish how important the pseudosecular terms are in the pre nce of an orienting potential at diff< ent values of the order parameter. Figure IS shows also that in the high-rigidity case the pseudosecular terms can still affect the relative intensities of the components of the spectrum as in the free diffusion case. 

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