ISSN:
0449-2978
Schlagwort(e):
Physics
;
Polymer and Materials Science
Quelle:
Wiley InterScience Backfile Collection 1832-2000
Thema:
Chemie und Pharmazie
,
Physik
Notizen:
The orientation distribution function for noncrystalline structural units in polymer systems cannot be determined completely from any experimental source; only the second and/or fourth moments of the distribution function, i.e., the second and/or fourth orders of the generalized orientation factors Flmj, can be evaluated. It is there-fore necessary to estimate the distribution function from F2mj and F4mj. In this paper, a graphical representation of the state of orientation is first discussed in terms of plots of F40j against F20j for several types of distribution functions for uniaxial orientation. These are three types of extreme concentration of the distribution at particular polar angles θ0 given by θ0 = 0, 0〈θ0〈π/2, and θ0 = π/2; five types of rather realistic distributions having single maxima at θj = 0, θ0, π/2 and double maxima at θj = 0, π/2, and a single minimum at θj = θ0; and four types of more realistic distributions including Kratky's floating rod model in an affine matrix. Second, estimation of the distribution function for uniaxial orientation from F40j and F20j is discussed quantitatively in terms of the mean-square error by three approximation methods: (a) expansion of the distribution function in finite series of spherical harmonics through the fourth order, (b) approximation of the distribution function as a composite of two components, random orientation and a particular orientation distribution given by Na (cos2θj)a, Na being a constant, and (c) approximation of the distribution function by Na (cos2θj)a alone. It is concluded that when the orientation distribution is sharp, estimation by the second method of approximation gives a smaller error than the first.
Zusätzliches Material:
10 Ill.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1002/pol.1971.160090302
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