Hermans molecular orientation function

R.P. Wool (University of Illinois, Urbana) A few years ago, we determined changes in the Hermans molecular orientation function vs molecular weight, electric field strength, by computer simulation on reptation chains. Have you looked at experimental DMA systems and how do they compare with your result ... 

Nematic phases are characterised by a uniaxial symmetry of the molecular orientation distribution function f(6), describing the probability density of finding a rod with its orientation between 6 and 6 + d0 around a preferred direction, called the director n (see Fig. 15.49). An important characteristic of the nematic phase is the order parameter (P2), also called the Hermans orientation function (see also the discussion of oriented fibres in Sect. 13.6) ... 

Most properties are strongly influenced by chain orientation. Birefringence, thermal expansivity, thermal conductivity and the elastic modulus depend on the Hermans orientation function according to relatively simple formulae. However, the elastic modulus of ultra-oriented polymers depends more directly on the macroscopic and molecular draw ratio. The latter reflects the extension of the end-to-end vector and the axial chain continuity. 

For unidirectional molecular orientations, such as for uniaxially drawn polymers, these dichroic parameters can be related to the Herman orientation function, F. This quantity is equivalent to the second moment of the orientation distribution function for the molecular axis and is given by [19]... 

Fortunately, the Herman orientation function, F, can be determined by a number of independent techniques, including X-ray diffraction, birefringence, sonic modulus, and refractive index measurements. These methods, coupled with IR dichroic measurements of absorption, can be used to calculate quantitative values for the transition-moment angles by using Eq. (2.15). A plot of F measured by X-ray diffraction versus (i — )/(/ -f 2) will be linear with a zero intercept. A least-squares evaluation of the data from this line will yield the slope, (/ o + 2)/(Ro — ) When is 0° (parallel to the molecular chain axis) the slope equals 1.0 and when equals 90°, the slope equals —2.0. A quantitative value of the transition-moment angle can then be calculated. Transition-moment angle measurements have been published for isotactic polypropylene and some of the results are as follows [22] ... 

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