Amplitude or Torsional Motion

It is now well known that certain molecules form a twisted intramolecular charge-transfer (TICT) state upon excitation, provided the molecule is equipped with suitable electron donating and accepting functionalities. Many 

A comprehensive study of the solvent dependence of the photophysical properties of 9,9 -bianthryl shows that the fluorescence lifetime is essentially constant in low polarity solvents. In more polar solvents, light-induced electron transfer occurs to form a perpendicular ICT state having D2d symmetry and which is weakly fluorescent. Reports have appeared that describe the photoisomerization of 4-nitrobenzaldehyde, 5-hydroxytropolone, 4-hydroxybenzonitrile, methyl-benzonitrile, and cinnamaldehyde.  

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The idea is formally very appealing since, from the spectroscopic viewpoint, it implies a collective mobility of the polymethylene chain which accounts for the observed longitudinal mobility, surface melting, or disordering and transport of matter without requiring large-amplitude libro-torsional motions which are not detected by vibrational spectroscopy, as previously discussed. 

Like the rXH absorption bands, the yXH bands become markedly broader as their frequency drops. This behaviour also appears to be explicable in terms of an increasing amplitude and anharmonicity of the yXH vibrations leading to interaction with y or <5 (RXH YR ) modes or (in the limiting case of no H-bond) with torsional motions of the RXH molecule as a whole. 

Evidently, there are two distinct frequencies, where either the numerator or the denominator of the complex impedance becomes zero. However, the case of zero impedance is determined exclusively by the serial capacity, whereas the parallel determines the frequency of infinite impedance. These two frequencies thus correspond to the resonance frequencies of the two part circuits mentioned above and are also correctly reproduced in the frequency spectrum of the QCM. Observable side resonances (as shown especially in the insert with lower span) can be traced back to mechanical oscillations that differ from the main one one is the result of antisymmetric thickness shear oscillation, the other of a twist oscillation. The ratio of intensity between the desired thickness shear wave and the side resonances is mainly defined by the ratio between electrode diameter and quartz substrate thickness. This is illustrated in Fig. 4, where the damping spectra for both a 10 MHz and a 5 MHz device are given. In both cases the electrode diameter here is 8 mm (the spectra in Fig. 3 were recorded with 4 mm electrode diameter). Evidently, the 5 MHz QCM shows the desired response pattern, where the shear resonance by far dominates the electrical behaviour. The 10 MHz QCM, however, shows very pronounced side resonances. The rather large electrode diameter (compared to the thickness) very strongly favours the occurrence of torsional motions within the substrate, thus reasonable amplitudes are generated for this mode. 

In the dynamic resonance experimental technique, a body is forced to vibrate and the constants are determined from the resonant frequencies. The types of vibration utilized are usually the longitudinal, flexural or torsional modes. The first two allow E to be determined and the last gives the shear modulus. It is usually easier to excite flexural waves than longitudinal ones, thus the use of flexural and torsional waves will be emphasized in this discussion. To use the dynamic resonance approach, the solution to the differential equations of motion must be known and this has been accomplished for several specimen shapes. In particular, it is common to use specimens of rectangular or circular cross-section, as solutions are readily available. Vibrations in the fundamental mode usually give the largest amplitude and are, therefore, the easiest to detect. 

The frequency and amplitude of torsional segmental motions increase as the temperature is raised and the glass transition is approached. Close to Tg, the frequency of torsional motions increases dramatically and gives rise to true rotational motions typical of rubbery materials. However, in glasses well below Tg, the intramolecular backbone motions occurring over time scales of seconds or microseconds are much less extensive than in rubbers and are believed to be primarily torsional oscillations (68). 

As already stated at the end of Section 3.18, we have measured the temperature-dependent band widths and the frequency of the CH2 d mode for several crystalline n-alkanes and polyethylene and found no sizable broadening or upward frequency shifts until they approach the melting point. All the theoretical models that imply large amplitude librotorsional motions are not supported by the spectroscopic criteria discussed in Section 3.18. We found evidence of large-amplitude libro-torsional oscillations only when the n-alkane chains are included as clathrates in various systems. 

Before considering particular test methods, it is useful to survey the principles and terms used in dynamic testing. There are basically two classes of dynamic motion, free vibration in which the test piece is set into oscillation and the amplitude allowed to decay due to damping in the system, and forced vibration in which the oscillation is maintained by external means. These are illustrated in Figure 9.1 together with a subdivision of forced vibration in which the test piece is subjected to a series of half-cycles. The two classes could be sub-divided in a number of ways, for example forced vibration machines may operate at resonance or away from resonance. Wave propagation (e.g. ultrasonics) is a form of forced vibration method and rebound resilience is a simple unforced method consisting of one half-cycle. The most common type of free vibration apparatus is the torsion pendulum. 

When the number of torsional degrees of freedom is increased, the intramolecular motion in gaseous molecules is increased as well. At the same time the theoretical treatment of the motion becomes more complex, and the problems that the electron-diffraction method has to face are more difficult to handle. The molecules of this category that have been subject to quantitative conformational analysis by electron diffraction so far, are limited to cases with two or a few degrees of freedom, though qualitative observations about large amplitude motion have been made also for considerably larger molecules. 

Aside from solitons, there is a continuous spectrum of torsional modes, or rotons. These excitations are the eigenstates of the linearized Hamiltonian. To obtain their spectrum, one replaces the last term in (7.68) with a harmonic potential. This approximation implies that the vibrational amplitude of a rotor must be small enough compared with the large amplitude motion of a rotor participating in a soliton. The frequencies of rotons obey the dispersion equation ... 

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