Orientation time

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Whether or not a polymer is rubbery or glass-like depends on the relative values of t and v. If t is much less than v, the orientation time, then in the time available little deformation occurs and the rubber behaves like a solid. This is the case in tests normally carried out with a material such as polystyrene at room temperature where the orientation time has a large value, much greater than the usual time scale of an experiment. On the other hand if t is much greater than there will be time for deformation and the material will be rubbery, as is normally the case with tests carried out on natural rubber at room temperature. It is, however, vital to note the dependence on the time scale of the experiment. Thus a material which shows rubbery behaviour in normal tensile tests could appear to be quite stiff if it were subjected to very high frequency vibrational stresses. 

It should be pointed out that the view of the glass transition temperature described above is not universally accepted. In essence the concept that at the glass transition temperature the polymers have a certain molecular orientation time is an iso-elastic approach while other theories are based on iso-viscous. 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

In the first case, that is with dipoles integral with the main chain, in the absence of an electric field the dipoles will be randomly disposed but will be fixed by the disposition of the main chain atoms. On application of an electric field complete dipole orientation is not possible because of spatial requirements imposed by the chain structure. Furthermore in the polymeric system the different molecules are coiled in different ways and the time for orientation will be dependent on the particular disposition. Thus whereas simple polar molecules have a sharply defined power loss maxima the power loss-frequency curve of polar polymers is broad, due to the dispersion of orientation times. 

In the case of polymer molecules where the dipoles are not directly attached to the main chain, segmental movement of the chain is not essential for dipole polarisation and dipole movement is possible at temperatures below the glass transition temperature. Such materials are less effective as electrical insulators at temperatures in the glassy range. With many of these polymers, e.g., poly(methyl methacrylate), there are two or more maxima in the power factor-temperature curve for a given frequency. The presence of two such maxima is due to the different orientation times of the dipoles with and without associated segmental motion of the main chain. 

As outlined in Section 9.2.1, orientational heterogeneity may affect the determination of a distance distribution, especially in the case of static orientation. Time-resolved fluorescence experiments provide an apparent average distance and an apparent distance distribution containing contributions from both distance and orientation (Wu and Brand, 1992). 

Figure 4. Water dipole (a) and the water H-H vector (b) orientational time correlation functions. In both panels, the dotted line is for the first layer, the solid thick line is for bulk water, the dashed line is for the second layer, and the thin solid line is for the third layer from the Pt( 100) surface (T = 300 K).

The mode coupling theory of molecular liquids could be a rich area of research because there are a large number of experimental results that are still unexplained. For example, there is still no fully self-consistent theory of orientational relaxation in dense dipolar liquids. Preliminary work in this area indicated that the long-time dynamics of the orientational time correlation functions can show highly non-exponential dynamics as a result of strong in-termolecular correlations [189, 190]. The formulation of this problem, however, poses formidable difficulties. First, we need to derive an expression for the wavevector-dependent orientational correlation functions C >m(k, t), which are defined as... 

The Second ingredient is the expression of the rotational friction in terms of the orientational time correlation functions. We have earlier derived an expression for this which was based on Kirkwood s formula [190]. The full expression should be derived by following an approach similar to that of Sjogren and Sjolander [9]. In addition, the coupling to rotational currents (the vortices) have not been touched upon. 

Persuading management, in a commercial, project-oriented, time-managed setting, to allow the thinking and R D time needed for evaluation and development. 

Figure 1. Intensity profile of optical Kerr effect of NB at 25°C vs. time. The zero time is arbitrary and the peak transmission of the Kerr effect is about 10%. The rise time is 5.3 ps and the decay time is 15.2 ps. This decay time corresponds to a molecular orientation time of 30.4 ps (6).

Since either type of distribution can be present without association, dielectric loss measurements do not provide a diagnosis of H bonding. Nevertheless, dispersion behavior often can be explained in terms of rearrangements dependent on H bonding. Type I curves may result from the various molecular sizes and shapes of the H bonded polymers. Type II curves may occur when a H bond equilibrium has a relaxation time considerably different from the orientation time giving the main peak. This happens, for example, in supercooled liquid n-propanol (416). Consequently, this tool deserves more detailed attention. 

As already mentioned (pp. Ill and 112) the deformational mechanism is characteristic of kinetically flexible molecules for which the orientation time to is greater than the deformation time Tj, i.e. the time during which the molecule in solution retains a random conformation (relaxation time of the conformation). 

Gottke et al. [5] offered a theoretical treatment of collective motions of mesogens in the isotropic phase at short to intermediate time scales within the framework of the Mode coupling theory (MCT). The wavenumber-dependent collective orientational time correlation function C/m(, t) is defined as... 

Despite extensive investigation of phase behavior of liquid crystals in computer simulation studies [97-99], the literature on computational studies of their dynamics is somewhat limited. The focal point of the latter studies has often been the single-particle and collective orientational correlation functions. The Zth rank single-particle orientational time correlation function (OTCF) is defined by... 

Figure 9. Orientational relaxation in the model liquid crystalline system GB(3, 5, 2, 1) (N = 576) at several densities across the I-N transition along the isotherm at T = 1. (a) Time dependence of the single-particle second-rank orientational time correlation function in a log-log plot. From left to right, the density increases from p = 0.285 to p = 0.315 in steps of 0.005. The continuous line is a fit to the power law regime, (b) Time dependence of the OKE signal, measured by the negative of the time derivative of the collective second-rank orientational time correlation function C t) in a log-log plot at two densities. The dashed line corresponds to p = 0.31 and the continuous line to p = 0.315. (Reproduced from Ref. 112.)...

Figure 12. Orientational dynamics of the discotic system GBDII (N = 500) at several temperatures across the isotropic-nematic transition along the isobar at pressure P — 25. (a) Time evolution of the single-particle second-rank orientational time correlation function in a log-log plot. Temperature decreases from left to right, (b) Time dependence the OKE signal at short-to-intermediate times in a log-log plot. Temperature decreases from top to bottom on the left side of the plot T = 2.991,2.693,2.646, and 2.594. The dashed lines are the simulation data and the continuous lines are the linear fits to the data, showing the power law decay regimes at temperatures. (Reproduced from Ref. 115.)...

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