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3. PHOTO-ORIENTATION BY PHOTOISOMERIZATION                                JO,


               and Equation 3.24 resumes to Fisher's stationary state relation for thermally
                irreversible systems:

                                                                              ,,, ,, c-
                                                                              (J.2.J I
                                                     a
                So, when photo-orientation analysis is not performed at the irradiation
               wavelength, the order parameter at infinite irradiation intensity of spectrally
                overlapping isomers reads:

                              2 PI (cos M B) + aP 2 (cos a> A) . ,  e A
                        ^  = — __ - _ - wicn a = r.                    / « /  s j.z,oj
                                                               S
                              13          1 + a                 B  e Acf) AB
                ? 2 (cos a) A) and P 2 ( cos W B)  are tne  second-order Legendre polynomials of <t) A
                and W B, which are the angles between the irradiation and analysis transitions
                of isomers A and B, respectively. a) A and <M B can be experimentally determined
                by a two-step photo-orientation experiment: irradiate at a wavelength Aj and
                analyze at A 2; irradiate at A 2 and analyze at Aj. Although S changes for each
                step, F 2 (cos a> B] and P 2 (cos a) A) remain unchanged, and their determination is
                straightforward, a can be determined beforehand by determining the cis
                spectrum by Fisher's method and the quantum yields by photo-orientation
                analysis at the irradiation wavelength.



      3.4 PHOTO-ORIENTATION OF AZOBENZENES: INDIVIDUALIZABLE ISOMERS

                In spectrally overlapping isomers, such as cis- and trans-DRl, both forms
                may be simultaneously isomerized and the molecule may rotate in each
                isomerization reaction, i.e., the trans—»cis photoisomerization, and the photo-
                induced and thermally activated back cis->trans reactions. All three reactions
               may happen simultaneously given that both the trans and cis isomers exhibit
                their absorption maximum in the same visible region (see Figure 3.2 for
                trans- and cis-DRl), and the lifetime of the cis isomer is relatively short (4 to
                                                  16
                5 seconds in polymethyl-methacrylates).  In contrast, azobenzene-containing
                polymeric films are more appropriate for closely probing this reorientation
               process in each of the three isomerization reactions. The trans and cis isomers
                of azobenzene present different absorption bands in the UV (around 360 nm)
                and the visible (around 450 nm) regions (see Figure 3.6). The lifetime of the
                azobenzene cis isomer is generally on the order of hours, depending on the
                polarity of the host material, which may be a polymer or a solvent; therefore,
                the azobenzene cis isomer can be considered stable on a time scale of minutes,
                i.e., the time scale of the experiment. It will be shown that azobenzene
                molecules are oriented within both the direct trans—>cis photoisomerization
                and the thermal cis—Mrans back isomerization.


      3.4.1 Reorientation within the transacts Photoisomerization
               Figure 3.7 shows the dichroism observed in spin-cast films of an azo-
               polyglutamate (see the formula in the caption for Figure 3.6). These UV-vis
               spectra were obtained after irradiation with linearly polarized UV light
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