Polar alignment orientational distribution function

Polar alignment can be described physically through a knowledge of the orientational distribution function f ) (32). A related quantity that can be expressed as a single number is the order parameter. The order parameter describing the induced polar alignment G is given by... 

Raman spectroscopy has been used to probe interactions occurring in PAni nanotube [23-24] composites, the orientation of nanotube bundles within a matrix [25, 26], and the efficiency of load transfer from the host matrix to SWCNTs [27,28]. Unlike X-ray diffraction (XRD) methods [12], Raman spectroscopy can detect very low concentrations of SWCNTs in a polymer matrix [29,30]. The degree of orientation of aligned nanotubes can be estimated by polarized Raman spectroscopy due to the presence of a strong resonance Raman scattering effect [31,32]. Polarized Raman spectroscopy in combination with a mathematical model [33] has been employed to characterize the orientational order of nanotubes in polymers [34]. Using this model, the polarized Raman intensity of nanotubes is correlated with the orientation order parameters of SWCNTs in a utuaxially oriented system. An orientation distribution function can then be obtained. 

Here we have used the zero-field nematic distribution function PQ( ) for convenience of notation. The degree of net polar alignment can be seen to be enhanced in the liquid crystal over the isotropic case. The limiting cases are isotropic distributions and the Ising model (in which only 6=0 and 6=n are allowed orientations). By retaining only the leading terms in the last equation one sees that in the high temperature limit... 

In the International Countermeasures Handbook (EW Comm., 1975), the author has presented a graph to be used to determine the signal attenuation produced by a chaff cloud. The graph relates normalized two-way attenuation per wave length squared to the number of half-way dipoles per cubic meter, as a function of the dipole orientation K relative to the radar polarization. When the dipoles are uniformly distributed and randomly oriented, K can be as low as 0.115 when the dipoles are aligned with the -field, X = 1.0 and the loss is 10 dB higher when the dipoles are almost crosspolarized to the radar, K = 0.0115, the attenuation will be 10 dB less than the random orientation. For X = 0.115, the attenuation relationship is given by... 

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