Chromophores number density

A — 1.064 /xm using the instrumentation and data analysis procedures described above. Typical d33 values at zero time were found to be in the range 0.1 -1.0 x 10 esu. These magnitudes agree well with those expected for the chromophore number densities employed (N = 0.4-1.9 x 10 /cm ), assuming literature Mz zzz values for the chromophore and the applicability of an isolated chromophore, molecular gas description of the field-induced chromophore orientation process (7,8). 

In Fig. 3, the values for the electron-number-related static hyperpolarizability fiJN312 obtained for these ionic chromophores (open symbols) have been compared with the same values for the best dipolar, neutral chromophores reported so far (diamonds).31 32 These chromophores, with a reduced number of electrons N equal to 20, have dynamic first hyperpolarizabilities approaching 3000 x 10 30 esu at a fundamental wavelength of 1.064 pm, in combination with a charge transfer (CT) absorption band around 650 nm. It is clear that at this point, the neutral NLOphores surpass the available ionic stilbazolium chromophores for second-order NLO applications, however, only at the molecular level. The chromophore number density that can be achieved in ionic crystals is larger than the optimal chromophore density in guest-host systems. 

Frequently, values of P for wavelengths where experimental data do not exist are estimated by extrapolation using a two-level model description of the resonance enhancement of P (see Appendix). Levine and co-workers [170] have also shown how to estimate the wavelength (frequency) dispersion of two-photon contributions to p. Because of the potential of significant errors associated with each measurement method, it is important to compare results from different measurement techniques. Perhaps the ultimate test of the characterization of the product of pP is the slope of electro-optic coefficient versus chromophore number density at low chromophore loading. It is, after all, optimization of the electro-optic coefficient of the macroscopic material that is our ultimate objective. 

Fig. 7. EO coefficient data, as a function of chromophore number density, for FTC (circles), CLD (squares), GLD (diamonds), and CWC (cross) chromophores (see text and synthetic schemes) in PMMA. Also shown are theoretical curves computed treating FTC as an ellipse (solid line) and as a sphere (dashed line). The slope of the various graphs at low number density is determined by pPF. Consistent with EFISH and HRS measurements, GLD and CWC appear to have larger pP values than FTC and CLD...

Fig-8. EO coefficient data, as a function of chromophore number density, for FTC (circles) and FTC-2H (diamonds) chromophores in PMMA. Also shown is the theoretical curve computed for FTC. Note that for FTC-2H, the two butyl groups (attached to the thiophene ring) are replaced by protons. The more ellipsoidal FTC-2H exhibits a smaller maximum electrooptic activity and the position of the maximum is shifted to lower number density. Consistent with EFISH, HRS, and other measurements, the dipole moments and molecular first hyperpolarizabilities of these two chromophores are comparable (The values for FTC-2H may be slightly larger)... 

Fig-9. EO coefficient data, as a function of chromophore number density, for CLD-type chromophores with (solid circles) and without (open triangles) isophorone protection of the polyene bridge. The maximum achievable electro-optic activity is smaller for the naked polyene bridge structure and the maximum of the curve is shifted to lower number density. The dipole moment and molecular first hyperpolarizability values are comparable (The unprotected polyene bridge variation may exhibit slightly higher values of p(3)... 

In the following sections, we shah demonstrate that the observed behavior of electro-optic activity with chromophore number density can be quantitatively explained in terms of intermolecular electrostatic interactions treated within a self-consistent framework. We shall consider such interactions at various levels to provide detailed insight into the role of both electronic and nuclear (molecular shape) interactions. Treatments at several levels of mathematical sophistication will be discussed and both analytical and numerical results will be presented. The theoretical approaches presented here also provide a bridge to the fast-developing area of ferro- and antiferroelectric liquid crystals [219-222]. Let us start with the simplest description of our system possible, namely, that of the Ising model [223,224]. This model is a simple two-state representation of the to-... 

Fig.12. Computation by Monte Carlo methods of the first four order parameters of an ensemble of 1000 chromophores (of dipole moment 13 Debye) existing in a medium of uniform dielectric constant. At the beginning of the calculation, the chromophores are randomly ordered thus, ==O. During the first 400 Monte Carlo steps, an electric poling field (600 V/micron) is on but the chromophore number density (=10 7 molecules/cc) is so small that intermolecular electrostatic interactions are unimportant. The order parameters quickly evolve to well-known equilibrium values obtained analytically from statistical mechanics (black dots in figure also see text). During steps 400-800 the chromophore number density is increased to 5xl020 and intermolecular electrostatic interactions act to decrease order parameters consistent with the results of equilibrium statistical mechanical calculations discussed in the text. Although Monte Carlo and equilibrium statistical mechanical approaches described in the text are based on different approximations and mathematical methods, they lead to the same result (i.e., are in quantitative agreement)...

Individual molecules will contribute to macroscopic electro-optic activity in an additive manner hence, the linear dependence on chromophore number density, N, in the master equation for electrooptic activity, rss = 2N j8 /(principle element of the electro-optic tensor,... 

Workers at IBM and Lockheed-Martin [68], at Akzo [69], and elsewhere have redefined the chromophore number density, N, in terms of the weight fraction of chromophore in the polymer, w, to obtain the following relationship between r33 and /3 ... 

FIGURE 7 Graphs of normalized electro-optic coefficient versus chromophore number density N. The symbols have the same meaning as in Fig. 6. 

FIGURE 8 Experimental (diamonds) and theoretical (solid line) values of normalized electro-optic coefficient versus chromophore number density for the DR chromophore of Table 2. The theoretical graph corresponds to D = 3.83 x 10 and the assumption of spherically symmetric symmetry. 

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