Molecular orientation distribution, second harmonic

Y. Rao, S. Y. Hong, N. J. Turro, and K. B. Eisenthal,/. Rhys. Chem. C, 115, 11678 (2011). Molecular Orientational Distribution at Interfaces Using Second Harmonic Generation. 

Microscopy methods based on nonlinear optical phenomena that provide chemical information are a recent development. Infrared snm-frequency microscopy has been demonstrated for LB films of arachidic acid, allowing for surface-specific imaging of the lateral distribution of a selected vibrational mode, the asymmetric methyl stretch [60]. The method is sensitive to the snrface distribntion of the functional gronp as well as to lateral variations in the gronp environmental and conformation. Second-harmonic generation (SHG) microscopy has also been demonstrated for both spread monolayers and LB films of dye molecules [61,62]. The method images the molecular density and orientation field with optical resolution, and local qnantitative information can be extracted. 

Second harmonic generation is a useful tool in probing the molecular behaviour at the liquid/liquid interface. While its limitations must be taken into account, particularly over the contributions of the observed signals from the bulk phases and the interrelated contributions of molecular density and orientation distribution, the ability to differentiate molecules at the interface from the bulk, is extremely useful. While the related... 

The two terms in the square brackets of Eq. (94) can be identified as a temperature independent internal energy term, and a temperature dependent entropy term resulting from the hard particle pair distribution function. From this equation it can be seen that the calculation of the principal elastic constants of a nematic liquid crystal depends on the first and second derivatives with respect to the angle 9 of the single particle orientational distribution function. Any appropriate angular function may be used for/(f2i, 9(R)), but the usual approach is to use an expansion in terms of spherical harmonics. The necessary mathematical manipulations are complicated, but give relatively compact results. Thus the ingredients of a molecular calculation of torsional elastic constants within the van der Waals... 

In this chapter, firstly a mathematical representation of orientation distribution functions of structural units will be discussed in terms of an expansion of the distribution functions in a series of generalized spherical harmonics and generalized orientation factors. Secondly, the deformation mechanism of polymer spherulites will be shown to be one of the areas where the above theory can be applied. Thirdly, the relationship between the optical anisotropy in oriented polymeric materials and the orientation of the structural units will be described in general by several types of average degrees of molecular orientation. Finally, the mechanical anisotropy in oriented polymeric materials will be discussed in terms of orientation of the structural units. 

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