Order parameter polymer orientation

An approach simpler than the "general" method has been used by Bower and coworkers [52,53] and has proved to be useful to determine the order parameters of uniaxially oriented polymers. This approach, called "cylindrical" method, requires a smaller number of spectra that are easily measurable, but it assumes that the Raman tensor associated with the vibrational mode under study is cylindrical. In such case, at — a2 — a so that the depolarization ratio R so of an... 

Because the determination of the order parameters by Raman spectroscopy is not straightforward, some works have focused on using intensity ratios to evaluate the molecular orientation (see above). Frisk et al. [56], in particular, have shown that the simple parameter R = 1 — Ixx/Izz — 1 — (axx)/(azz) can efficiently, although qualitatively, characterize orientation in polymers. 

B. Schartel, Y. Wachtendorf, M. Grell, D.D.C. Bradley, and M. Hennecke, Polarized fluorescence and orientational order parameters of a liquid-crystalline conjugated polymer, Phys. Rev. B, 60 277-283, 1999. 

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This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

Fig. 12a-c. Polymer concentration dependence of the orientational order parameters S for three liquid-crystalline polymer systems a PBLG-DMF [92,93] b PHIC-toluene [94] c PYPt-TCE [33], Marks experimental data solid curves, theoretical values calculated from the scaled particle theory. The left end of each curve gives the phase boundary concentration cA... 

We assume the system under consideration to be a single domain. Then the orientational state of the system can be specified by the order parameter tensor S defined by Eq. (63), The time evolution of S is governed by the kinetic equation, Eq. (64), along with Eqs. (62) and (65). This kinetic equation tells us that the orientational state in the rodlike polymer system in an external flow field is determined by the term F related to the mean-field potential Vscf and by the term G arising from the external flow field. These two terms control the orientation state in a complex manner as explained below. 

The use of an electric field is not the only effective way to influence the LC polymer structure, magnetic fields displays a closely similar effect167 168). It is interesting as a method allowing to orient LC polymers, as well as from the viewpoint of determining some parameters, such as the order parameter, values of magnetic susceptibility, rotational viscosity and others. Some relationships established for LC polymer 1 (Table 15), its blends with low-molecular liquid crystals and partially deuterated polyacrylate (polymer 4, Table 15) specially synthesized for NMR studies can be summarized as follows ... 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

Strzelecki has studied the orientation of a nematic polymer in its LC state in a 0.3 T magnetic field by X-ray diffraction and found that the sample had an order parameter of 0.64 The orientation of LC polymers in a magnetic field has also been observed by others using X-ray techniques I Extruded fibers have been studied by Roviello and Sirigu to measure the degree of orientation achievable in mesomorphic polymers by shear field, but only solid samples were studied and even though they were oriented, the results gave little quantitative indication of the order of the mesophase... 

From the knowledge of the order parameter from the measurement of the variation of the optical absorption spectrum due to poling, one can estimate the x parameter (Eq. (43)) intervening in the above developments. For poled polymers one can use also another alternative description of linear and nonlinear optical susceptibilities by expanding the orientation distribution function in the series of Legendre polynomials, where the expansion coefficients are order parameters ... 

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