Second-order susceptibility polymers

In this section, the experimental techniques described in the previous section are applied to the study of thin Langmuir-Blodgett films of chiral molecules and polymers. We will show in detail how the second-order susceptibility of chiral thin films can be analyzed and discuss the influence of chirality on the nonlinear optical response of these films. 

Absolute Values of Second-Order Susceptibility Components of Helical Polymer Shown in Figure 9.21, Classification of Components as Chiral or Achiral... 

The susceptibility tensors measure the macroscopic compliance of the electrons. Since the second order polarization is a second rank tensor, SHG is zero in a centrosymmetric or randomly oriented system. To make the material capable of SHG, the NLO dopants must be oriented noncentrosymmetricaly in the polymer matrix (2-3). When modeling the poled, doped films using a free gas approximation, the poled second order susceptibilities are given by (2.19)... 

In the limit of the oriented gas model with a one-dimensional dipolar molecule and a two state model for the polarizability (30). the second order susceptibility X33(2) of a polymer film poled with field E is given by Equation 4 where N/V is the number density of dye molecules, the fs are the appropriate local field factors, i is the dipole moment, p is the molecular second order hyperpolarizability, and L3 is the third-order Langevin function describing the electric field induced polar order at poling temperature Tp - Tg. 

The electro-optic coefficient in a poled polymer film can be related to the second-order susceptibility as shown in Equation 5. 

EO response can be introduced into polymers containing the donor-conjugation-acceptor moieties by applying a very strong electric field while the polymer is heated to its Tg. The field-induced order is subsequently frozen in by cooling the polymer films well below Tg. The achievable second-order susceptibility... 

Detailed information about the components of the second-order susceptibility y2)(-2w to, w) can be obtained from second harmonic measurements on well-defined samples such as single crystals or oriented thin films, the latter obtained by procedures such as the asymmetric Langmuir-Blodgett deposition technique or electric-field poling of NLO chromophore-doped polymers.31 In the case of single-crystal samples, the second harmonic is... 

For these classes of conjugated molecular and polymer structures, the principal property is that their nonreson-ant, nonlinear optical responses are dominated by ultrafast, virtual excitations of the ir-electron states. This was directly demonstrated by MNA (2-methyl-4-nitroaniline) single crystal measurements of macroscopic second order susceptibilities at do (j 3) and optical frequencies (13-1 ) and combined second harmonic measurements and theo-... 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

The requirement of non-centrosymmetry is not restricted to the molecular level, but also applies to the macroscopic nonlinear susceptibility, which means that the NLO molecules have to be organized in a non-centrosymmetric alignment. The first measurements of the macroscopic second-order susceptibility, have been performed on crystals without centrosymmetry [5]. However, many organic molecules crystallize in a centrosymmetric way. Other condensed oriented phases such as Langmuir-Blodgett (LB) films and poled polymers therefore seem to be the most promising bulk systems for NLO applications. 

Several techniques have been developed for determining the second-order susceptibility [24]. Of practical importance are methods that may be employed for aligned polymeric systems containing polar moieties [4, 8]. Methods making use of the Pockels or linear electro-optic (EO) effect are based on the measurement of the variation in the refractive index of thin polymer films induced by an external electric field. In this way, values of the electro-optic coefficients rss and in are obtained, which are related to the corresponding values through Eq. (3.16). 

Useful optical polymers with high second order susceptibilities should be both completely transparent. Hence semicrystalline and polycrystailine samples as well as incompatible blends have to be avoided, while anisotropy by a large number of oriented p -molecules or fragments is demanded. The latter can be achieved by applying an external electric field to the polymer. The sequence as used by many investigators and introduced some 10 years ago at our laboratories is outlined In figure 15 for a dipole dissolved in PMMA, the pre-eminent optical polymer 2)... 

Amidation is particularly well adapted to use as a polymer-forming condensation reaction. The reaction is rapid above 180° to 200°C, it is remarkably free from side reactions, no catalysts are required (indeed, none are known), and the process is of the second order so that the molecular weight increases directly as the time of reaction. Molecular weights of 20,000 to 30,000 are attainable with no great difficulty under favorable conditions. This is not true of particular polyamide reactants susceptible to side reactions, as, for example, in the reaction of a diamine with glutaric acid wherein the inherent instability of the glutaric amide unit leads to decomposition. 

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