Chromophores randomly distributed

The excitation transport problem among chromophores attached to macromolecules is considerably more difficult than the corresponding EET problem in systems of randomly distributed chromophores. The lack of translational invariance and correlated polymer statistics increase the complexity of the theoretical analysis. Advances in the treatment of many-body EET in polymers have only recently been possible because of the emergence of powerful theoretical tools in the solution of the transport problem for randomly distributed chromophores. 

For the case of EET among randomly distributed chromophores in an infinite volume th no correlations among chromophore positions a... 

In Figure 8 we have plotted Equation (62) as well as the two body self-consistent approximation and the three-body rational self consistent approximation for this problem. The three-body rational approximation is believed to describe excitation transport on an ideal chain quite accurately [12]. Although the agreement between curves 3R and 2C is not as good as was observed for the case of randomly distributed chromophores in an infinite volume [13], the two body cumulant is bounded by the two-body and three- ody curves. Thus, it should give a quantitative approximation to G (t). It should be obvious that combination of Equation (57) for C with Equation (62) should lead to a straightforward determination of from measurement of the transient fluorescence anisotropy. 

Since the dipoles of chromophore molecules are randomly distributed in an inert organic matrix in amorphous PR materials, the material is centrosymmet-ric and no second-order optical nonlinearity can be observed. However, in the presence of a dc external field, the dipole molecules tend to be aligned along the direction of the field and the bulk properties become asymmetric. Under the assumption that the interaction between the molecular dipoles is negligible compared to the interaction between the dipoles and the external poling field (oriented gas model), the linear anisotropy induced by the external field along Z axis at weak poling field limit (pE/ksT <[Pg.276]

Clearly, situations intermediate between perfect order and random distributions occur in arrays of absorbing chromophores, and a treatment is required that allows expression of the orientational distribution of structural units such as crystallites or segments which may be fluorescent in a bulk sample having uniaxial or biaxial symmetry. A complete mathematical approach using a herical harmonic expansion technique has been developed which expresses the distribution as spherical harmonics of various orders in terms of the Euler angles which specify the orientation of the coordinate system in a fixed structural unit with respect to the coordinate system in the bulk sample This is of use in solid systems, where time dependence is not observed. 

Fig. 24. Static field poling mechanism of dipolar molecules. Before applying electric field the dipole moments are randomly distributed. At higher temperatures the dipole moments of NLO chromophores are mobile and orient in the direction of the applied external field. The orientation is frozen by cooling to low temperature and/or photo- or thermal crosslinking...

Chromophores attached to a polymer present an Inhomogeneous medium for excitation transport. Rather than being randomly distributed, as in a solution, the positions of the chromophores are correlated through the covalent bonds of the polymer. Also, the finite size of the polymer limits the number of sites the excitation can sample. This inhomogeneity in the chromophore distribution resulting from the requirements of polymer chain structure can... 

In this section, we describe a theory for calculating observables resulting from incoherent excited state transport among chromophores randomly distributed in low concentration on isolated, flexible polymer chains. The pair correlation function used to describe the distribution of the chromophores is based on a Gaussian chain model. The method for calculating the excitation transfer dynamics is an extension to finite, inhomogeneous systems of a truncated cumulant expansion method developed by Huber for infinite, homogeneous systems (25.26). 

If the transition dipoles of the chromophores in a solid polymer matrix are randomly oriented, the main source of depolarization in these experiments will be due to excitation transport. The initially excited ensemble is polarized along the direction of the excitation E field and gives rise to polarized fluorescence. Transport occurs into an ensemble of chromophores with randomly distributed dipole directions and the fluorescence becomes unpolarlzed. The random distribution is assured by the low concentration of the chromophores. To a slight extent, on the time scale of interest, depolarization also occurs as a result of chromophore motion. In this case the fluorescence anisotropy is approximately... 

The polymers investigated had a small amount of chromophoric hard segments incorporated and randomly distributed within the poly (ester urethane) chain the basic structure of these systems is illustrated in Fig. 11. 

---