Dipole orientation distribution

Two additional feature can be incorporated into Eqs. (7.32)—(7.35) the dipole orientation distribution and the concentration distribution in systems consisting of many dipoles. The orientation of the dipole with respect to the surface, described by angles Q = (8, ), affects E and all the other measurables derived from it.(33) Consider a concentration distribution of dipoles in both orientation and distance from the surface specified by C(0, , z). Since the dipoles all oscillate incoherently with respect to one another, the integrated intensity J due to this distribution is simply ... 

One approach to a solution of this problem was put forward by Hansen (14), who derived general equations which express the overall experimental film absorbance in terms of the external reflectance of the substrate. These relations contain within them expressions for the individual anisotropic extinction coefficients in each geometric orientation. Solution of these general equations for the anisotropic extinction coefficients allows for an unambiguous description of the dipole orientation distribution when combined with a defined orientation model. 

X and y components are negligible due to E field nodes at the interface. For the case of external reflectance at the A/W Inter ce, however, finite values of the E field and, hence, finite absorbances are present in all three orientations (2). This complicates the calculation of an overall dipole orientation distribution since all geometric orientations must be considered. 

Figure A2.4.10. Orientational distribution of the water dipole moment in the adsorbate layer for tlu-ee...

FIG. 3 Left density profile, p z), from a 500 ps simulation of a thin film consisting of 200 TIP4P water molecules at room temperature. Right orientational distribution, p cos d), with 3 the angle between the molecular dipole moment p and the surface normal z. The vertical lines in the left plot indicate the boundary z-ranges,... 

The left side of Fig. 7 shows the orientational distribution of the molecular dipole moment relative to the surface normal in various distance... 

The difficulties encountered in the application of the above simple models of dipole-orientational relaxation to the interpretation of the experimental data necessitate the development of more complex models. In a realistic description of the relaxation process, two approaches may be taken one that makes allowance for the distribution of fluorophores in fluorescence lifetimes, and one that makes allowance for their distribution in initial energies of interaction with the environment. The latter approach is more promising, since it allows new experimental data on the excitation wavelength dependence of fluorescence spectra, as well as on the influence of relaxation on this dependence, to be obtained and analyzed. 

In the bare glass case, note that a rather strong peak of intensity is drawn into the glass, maximal at exactly 0 = 0C, but with significant intensity into supercritical angles. The effect is especially pronounced for dipoles oriented perpendicular to the surface, but is present for any position or orientation distribution. 

The collected fluorescence 3F [from Eq. (7.39)] clearly depends on the orientation distribution of the dipoles and the incident polarization through the dependences on 0 and E. We will assume a special but common case here randomly oriented dipoles with a z-dependent concentration near the surface, excited by a p-polarized evanescent wave. 

As discussed in a later section, the expression for X0 was derived using a thermodynamic approach. The key to the derivation is the calculation of the difference in the energy of interaction of the solvent with the reactants when (1) the solvent is at equilibrium with the charge distribution of the reactants, and (2) the solvent assumes the dipole orientations appropriate for electron transfer to occur. 

In addition to describing the conformation of the hydrocarbon chains for amphiphilic molecules at the A/W interface, external reflectance infrared spectroscopy is also capable of describing the orientation of the acyl chains in these monolayers as a function of the monolayer surface pressure. The analysis of the orientation distribution for an infrared dipole moment at the A/W interface proceeds based on classical electromagnetic theory of stratified layers (2). In particular, when parallel polarized radiation interacts with the A/W interface, the resultant standing electric field has contributions from both the z component of the p-polarized radiation normal to the interface, as well as the x component of the p-polarized radiation in the plane of the interface. The E field distribution for these two... 

Even in situations in which the molecules of interest are randomly oriented (e.g. in solution) the orientational distribution of emitting molecules may not be isotropic, due to the fact that the incident (excitation) beam photoselects molecules based upon the relative orientation of the absorption transition dipoles, p abs> with respect to the incident polarization vector, if [7,9,10]. The probability of absorption is proportional to I jfabs if I thus, for example, molecules oriented such that if... 

Microscopic disorder We consider a lattice the sites of which have disordered resonance energies, with a distribution of width Ae, but have the same intersite interactions (same dipole orientation and oscillator strength) as the perfect lattice. This is the so-called substitutional disorder model.122 We assume the disorder width to be smaller than the excitonic bandwidth (4< Be) and examine the bottom of the excitonic band, where the emitting and the absorbing K 0 states lie. In a renormalization-group scheme, we split the lattice into isometric domains of n sites, on which the excitation is assumed to be localized, and write the substitutional-disorder hamiltonian in this basis we thereby obtain a new disorder width An Aen-1/2 and a... 

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