Orientation factor, optical

Like e, t is the product of two contributions the concentration N/V of the centers responsible for the effect and the contribution per particle to the attenuation. It may help us to become oriented with the latter to think of the scattering centers as opaque spheres of radius R. These project opaque cross sections of area ttR in the light path. The actual cross section is then multiplied by the scattering efficiency factor optical cross... 

The interactions between the molecule and the environment can lead to distortions in the electrical properties due to the susceptibility of the molecules and the properties of the host matrix. The refractive index of the matrix acts as a screening factor, modifying the optical spectra and interaction between charges or dipoles embedded within it. Local field effects change the interaction with an electromagnetic field and should be considered along with orientation factors in the dipolar interaction. 

Kimura, I., Kagiyama, M., Nomura, S., Kawai, H. General description of optical (Dichroic) orientation factors for relating optical anisotropy of bulk polymers to orientation of structural units. Part II. J. Polymer Sci. A-2, 7, 709 (1969). 

Figure 5-36. Optical birefringence A Aiexp as a function of orientation factor/from sound-velocity measurements of different polymers (after H. M. Morgan).

Wenbang [188] reports on the crystalline structure and optical properties of three different types of ramie fibers and different parts of the fibers. The author finds some variation in crystallinity in different parts of the fiber. He also finds tenacity, breaking elongation, and work of rupture of the fibers somewhat correlated to crystallinity and orientation factors of the fibers. 

In Table 13 the values of the optical orientation factor f and that derived from X-ray data (cf. Sections 8 b 3, and 8 c 2, p. 623) are given for xanthate filaments (q = 13) and freshly prepared cellulose filaments (g = 7.0) at various degrees of previous stretching. (The data refer to the objects dried in air after their preparation... 

OPTICAL ORIENTATION FACTOR fo AND THAT DERIVED FROM X-RAY DATA fx FOR CELLULOSE FILAMENTS IN DEPENDENCE ON THE DEGREE OF PREVIOUS STRETCHING... 

OPTICAL AND X-RAY ORIENTATION FACTORS OF SOME NATURAL AND RAYON FIBRES... 

Since attention is now focussed on the amorphous portion of the gel, X-ray analysis can no longer serve to obtain a quite correct measure of orientation and the latter should be derived from measurements of optical anisotropy. We have already seen on p. 638 that in the process of orientation by stretching, the optical orientation factor lags behind that derived from X-ray analysis. On page 593 it has been explained that the optical orientation factor is a measure of the average orientation of both the crystalline and amorphous components. However, since the latter forms the major portion of the gel, it will mainly determine the optical orientation factor. In some favourable cases the contribution of the crystalline component can, moreover, be computed and corrected for. 

None of the molecular network theories thus far discussed, however, is capable of predicting the course of the orientation of the crystallites which form the junction points of the network. It is only known from experiment (see p. 624) that the orientation of the crystallites runs ahead of that of the non crystalline gel component. From a large experimental material covering cellulose gels of various swelling degree and of different preparation, it was found that there seems to be a uniform relation between the optical orientation factor and that derived from X-rays holding for all cases. This relation, which may be of value, for future theoretical considerations, is shown in Fig. 102. 

In interacting systems the optical and orientation factors in a are no longer separable quantities. The induced optical effect is determined both by the single particle scattering [form factor P q)] and by the pair distribution function [structure factor 5( )], the latter being direction-dependent [42]. Since in addition to orientation the electric field causes particle translation, even for spherical particles the radial distribution function g q, /) and the "static" structure factor attain time-dependent induced anisotropy. The deformed surface potential also contributes to this effect. 

Kejcwords amorphous orientation, crystalline orientation, Herman s orientation factor, infrared spectroscopy (IR), IR band assignment, optical birefringence, orientation, structure-property relationships in fibers, X-ray diffraction... 

The orientation factor P2 9) is a convenient measure of the average degree of orientation of polymer chains in the system. Under an ideal orientation state where all polymer chains are aligned perfectly in the direction parallel to the reference axis, the value of PiiS) becomes unity. On the other hand, if polymer chain segments are all perpendicularly aligned, PiiO) becomes -1/2. An optically isotropic system gives the P2 0) value of zero. 

Three basic types of physical phenomenon are responsible for electroopti-cal behavior of a macromolecule in solution dipole moment, diffusion coefficients, and extinction coefficients. Amplitudes and time constants depend on both the properties of the macromolecules and experimental conditions. The sum of relaxation amplitudes is related to the linear dichroism of the solution at saturation, and depends on both the electric and optical properties of the molecule under investigation. The saturating behavior of linear dichroism calculated for a pure permanent moment, a pure induced moment or a mixed orientational mechanism is traditionally used in determining electrical responses and optical anisotropy by fitting the experimental results to a theoretical curve.Pqj. molecules with effective cylindrical symmetry (regarding their orientational behavior), the optical signal observed in the experiment can be represented as a product of orientational factor, < )(j, and a limiting reduced dichroism at infinite field. 

Equations [11] and [12] separate the information on anisotropic molecular optical properties (0(0/) and (4)0(0/) from that on orientation distribution and polarizer orientation ( D and ((4)p5T[JV ) which can be expressed through the parameters chosen to describe the orientation distribution the orientation factors [3], [4], the Saupe matrix elements [8], or the order parameters [9]. 

Extensive studies on the optical anisotropy of hydrated cellulosic gel in relation to deformation have been reported by Kratky " and by Hermanns. "" Kratky studied the deformation mechanism of fibrous materials by means of X-ray diffraction and birefringence, and postulated two kinds of deformation models for the swollen gel, in order to explain the orientation mechanism of the structural units in terms of the orientation distribution (but not in terms of the average degree of orientation of the structural units). Hermanns carried out studies on the same lines as Kratky, and introduced one of the orientation factors as a measure of the average degree of orientation. ... 

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. 

The orientation distribution functions for the structural units cannot be directly determined from any experimental sources, except for the crystalline units from X-ray diffraction measurements. Usually the orientations of structural units are obtained as several kinds of averages, i.e. the second and/or fourth orders of the orientation factors from optical measurements such as birefringence and absorption/emission dichroism. 

As can be seen from equations (78) and (79), the dichroic orientation factors are represented by the product of the orientation of the chromophoric group and its intrinsic optical constants. The constants, however, cannot be obtained from the absorption dichroism alone and must be determined from other sources. When the orientation factors F% and F22 obtained from equations... 

Experimental methods for determination of the orientation factor of fibres are well established. It is most often evaluated from the optical birefringence" or from the sonic modulus. " ... 

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