Of molecular orientation

We now consider this issue in a more rigorous fashion. The inference of molecular orientation can be explamed most readily from the following relation between the surface nonlinear susceptibility tensor and the molecular nonlinear polarizability... 

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

FigureBl.5.10 Euler angles and reference frames for the discussion of molecular orientation laboratory frame (v, y, z) and molecular frame (x y, z).

Thus, a well-defined measure of molecular orientation is uiferred from the measurement of the macroscopic... 

Heinz T F, Tom H W K and Shen Y R 1983 Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation Phys. Rev. A 28 1883-5... 

It is occasionally desirable to retain a small proportion of molecular orientation, in order to quantitate the dipolar interactions present, whilst minimizing their contribution to the linewidth. Partial orientation may be achieved by using a nematic solvent. In large, magnetically anisotropic molecules it may occur naturally at the highest magnetic fields. 

This approach works quite well for species at metal surfaces. It has been used extensively in recent years to ascertain information about organic thin films on metal surfaces. Of particular interest in many of these studies, and indeed the real forte of this technique, has been the deterrnination of molecular orientation on surfaces from such studies. Few other techniques are quite so useful for unambiguously ascertaining molecular orientation. 

The reason for the activity of the above named classes of liquids is not fully understood but it has been noted that the most active liquids are those which reduce the molecular cohesion to the greatest extent. It is also noticed that the effect is far more serious where biaxial stresses are involved (a condition which invariably causes a greater tendency to brittleness). Such stresses may be frozen in as a result of molecular orientation during processing or may be due to distortion during use. 

Polarization effects are another feature of Raman spectroscopy that improves the assignment of bands and enables the determination of molecular orientation. Analysis of the polarized and non-polarized bands of isotropic phases enables determination of the symmetry of the respective vibrations. For aligned molecules in crystals or at surfaces it is possible to measure the dependence of up to six independent Raman spectra on the polarization and direction of propagation of incident and scattered light relative to the molecular or crystal axes. 

In the studies carried out by one of the authors [52], the values of Ea and E were determined for PET fibers of the microfibrillar and of the lamellar substructure. The results have been presented in Tables 8 and 9. The results obtained show that for both types of substructure the resistance to deformation, that is, the value of E, depends on the degree of molecular orientation of the amorphous material of the fiber fa) and the density of this amorphous phase of the fiber da)- However, this dependence assumes a different form for the microfibrillar and for the lamellar substructure. In the first case, it has the form ... 

Ward, I. M. Determination of Molecular Orientation by Spectroscopic Techniques. Vol. 66,... 

Table 8-12 Effect of molecular orientation on the impact properties of polypropylene films...

Wilkes, G. L. The Measurement of Molecular Orientation in Polymeric Solids. Vol. 8, pp. 

Thermodynamics of Crystallization of Flexible-Chain Polymers Under Conditions of Molecular Orientation. 217... 

A characteristic feature of the structure of samples obtained under the conditions of molecular orientation is the presence of folded-chain crystals in addition to ECC. Kawai22 has emphasized that the process of crystallization from the melt under the conditions of molecular orientation can be regarded as a bicomponent crystallization in which, just as in the case of fibrous structures in the crystallization from solutions, the formation of crystals of the packet type (ECC) occurs in the initial stage followed by the crystallization with folding . 

In principle, it is possible to obtain ECC in the absence of molecular orientation if the crystallization is carried out very slowly at high temperatures close to the melting temperature. Thus, Mandelkern obtained polyethylene crystals similar to ECC in their thermodynamic characteristics by a 40 days crystallization of an isotropic melt28. These experiments also characterize one of the possible paths of the generation of order in polymers order through fluctuations 29 (see below). 

Effect of Molecular Orientation on Crystallization of Flexible-Chain... 

We carried out thermodynamic studies on the crystallization from melts of flexible-chain polymers uniaxially stretched at various degrees of molecular orientation in the melt and studied the effect of the stretching stress on thermodynamic parameters such as degree of... 

Fig. 4) for relatively long chains37. However, under conditions of molecular orientation, the distribution function is usually displaced towards higher fi and the analysis of the crystallization process should be carried out over a wide range of fi values. 

To avoid misunderstanding, it should be emphasized that if the transition from one type of crystallization to the other one is considered, this does not imply a transformation of crystals of one type into the other one during stretching. In contrast, if the molecule enters a folded-chain crystal, it is virtually impossible to extend it. In this case, we raise the question, which of the two crystallization mechanisms controls the process at each given value of molecular orientation in the melt (this value being kept constant in the crystallization process during subsequent cooling of the system). At /J < /3cr, only folded-chain crystals are formed whereas at / > only fibrillar crystals result at /8 /3cr, crystals of both types can be formed. 

Figure 11 shows that the molecular weight distribution in the melt (presence of short chains) can account for the coexistence of two types of crystals in the absence of molecular orientation or at a slight stretching of the melt. However, there is a purely thermodynamic reason for the appearance of this main structural feature of samples crystallized under conditions of molecular orientation, even at high degrees of orientation, when virtually the whole distribution function is displaced into the region of /S > /3cr. 

Mechanism of the Formation of ECC Under the Conditions of Molecular Orientation... 

---