Polar alignment order parameter

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... 

Fig. 8. Simple model of order-disorder or displacive ferroelectric phase transition. Left, ferroelectricity by relative displacement of the anion and cation sublattices (a) displacive model, where r — 0 in the HTP and the atoms are translated by r/0 in the LTP. The order parameter is r. (b) Order-disorder model in the high-temperature phase, the ions are symmetrically disordered with equal probabilities p+ — p — 1/2 over two positions r — +rQ. In the low-temperature phase, the occupancies of the sites become unequal with probabilities p p +. The order parameter is the difference Ap — p+—p. The spontaneous polarization Psocr and PsccAp for the displacive model and order-disorder model, respectively. Right, ferroelectricity by alignment of molecular dipoles (c) displacive model in the HTP, all the molecules are aligned with a = 0 in the LTP, the molecules are rotated around the center of inversion with angles +a/0, the order parameter is a. (d) Order-disorder model. The spontaneous polarization Ppx ct and PsccAp for the displacive model and order-disorder model, respectively.

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. 

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