Structure of the Isotropic and Nematic Phase

Within these limits, direct integrating is difficult. However, the scattering amplitude may be found using the convolution theorem (Eq. 5.31a). The integral may be presented as a convolution/i(x) /2 W where/i=pi (like in case of parallelepiped) and /2 = cosilnxia). Applying the convolution theorem we obtain the scattering amplitude from the two amplitudes found earlier, see Eqs. 5.29 and 5.36 form = 1  

We have again found the scattering field amplitude in the form of sine integral. The correspondent intensity spectmm is similar to that for the parallelepiped, see Fig. 5.11b, 

However, there is a shift of the entire parallelepiped diffraction spectrum by q on the wavevector scale the curve for a parallelepiped without density modulation is centered at 7 = 0 whereas the curve for the modulated structure is centered at q = qo. Such a shifted angular spectrum of diffraction intensity is very similar to that observed on the freely suspended films of smectic A liquid crystals. It allows the determination of both the smectic layer period and the film thickness. 

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Structure of the Isotropic and Nematic Phase 5.6.1 Isotropic Liquid... 

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