Solvent orientational distribution

In order to understand the dynamics of the solvent fluctuation, many experimental as well as theoretical efforts have been made intensively in the last decade. One of the most convenient methods to observe solvent reorganization relaxation processes within the excited state molecule is time resolved fluorescence spectroscopy. By using time resolved techniques a time dependent fluorescence peak shift, so ( ed dynamic Stokes shift, has been detected in nanosecond picosecond >, and femtosecond time regions. Another method to observe solvent relaxation processes is time resolved absorption spectroscopy. This method is suitable for the observation of the ground state recovery of the solvent orientational distribution surrounding a solute molecule. 

In words, s describes the interaction of the solute charge distribution component p, with the arbitrary solvent orientational polarization mediated by the cavity surface. The arbitrary weights p,, previously defined by (2.11), enter accordingly the definition of the solvent coordinates, and reduce, in the equilibrium solvation regime, to the weights tv,, such that the solvent coordinates are no longer arbitrary, but instead depend on the solute nuclear geometry and assume the form se<> = lor. weq. In equilibrium, the solvent coordinates are correlated to the actual electronic structure of the solute, while out of equilibrium they are not. 

When Stokes shifts are plotted as a function of the orientation polarizability A f (Lippert s plot, see Section 7.2.2), solvents are distributed in a rather complex manner. A linear relationship is found only in the case of aprotic solvents of relatively low polarity. The very large Stokes shifts observed in protic solvents (methanol, ethanol, water) are related to their ability to form hydrogen bonds. 

Nonequilibrium effects. In applying the various formalisms, a Boltzmann distribution over the vibrational energy levels of the initial state is assumed. The rate constant calculated on the basis of the equilibrium distribution, keq, is the maximum possible value of k. If the electron transfer is very rapid then the assumption of an equilibrium distribution over the energy levels is not valid, and it is more appropriate to treat the nuclear fluctuations in terms of a steady-state rather than an equilibrium formalism. Although a rigorous treatment of this problem has not yet appeared, intuitively it seems that since the slowest nuclear fluctuation will generally be a solvent orientational motion, ke will equal keq when vout keq and k will tend to vout when vout keq (a simple treatment gives l/kg - 1/ vout + 1/keq). These considerations are... 

A new formulation of the theory of paramagnetic shifts particularly suited to shifts in liquid crystalline solvents has been presented. (29) The Hamiltonian expression used allows for the inclusion of effects of preferential orientational distribution of the solute molecules. 

Unie resolved ground state hole spectra of cresyl violet in acetonitrile, methanol, and ethanol at room temperature have been measured in subpicosecond to picosecond time region. The time correlation function of the solvent relaxation expressed by the hole width was obtained. The main part of the correlation function decayed much slower compared with that of the reported correlation function observed in time dependent fluorescence Stokes shift. Some possible mechanisms are proposed for understanding of the time depencences of the spectral broadening under the condition with the distribution of the relaxation times in fluid solution based on the entropy term in the solvent orientation as well as the site dependent response of the solvent. 

Figure 10. (a) The orientation distribution function (TV f -N i )/TVr for an oriented two-state array of dipoles in the Mott and Watts-Tobin/BDM model (Refs. 59 and 60) for various values of the interaction parameter Vc/ kT in Reference 60 [see Eq. 28]. (b) The configurational entropy and the librational entropy 5 for the two-state model of solvent orientation of electrodes as a function of (corresponding to data in Fig. 10a). (From B. E. Conway and L. G. M. Gordon, J. Phys. Chem. 73 (1969) 3609.)...

For different solvents, different spectral shapes of the 2H polymer signal resulted, which allowed conclusions on the orientational distribution of the polymer segments. The spectra in Fig. 21 were simulated as a superposition of quadrupolar splittings A with a distribution function P(A). In air (a) the spectral shape was explained by a distribution function P(A) with a maximum at A =200 Hz. The spectral shape in CCI4 (Fig. 21b) resulted from a distribution with a maximum at zero splitting. 

The orientational contribution to the entropy, of a solute (or a solvent) molecule, 2 (or s), is determined by the orientational distribution function... 

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