Thermal excitation of vibration

At higher frequencies, the laser-Raman effect affords, in principle, the possibility of detecting non-thermal excitation of vibrations. These would be found from a higher than thermal ratio of anti-Stokes to Stokes lines. The Raman effect in biological systems has recently been reviewed by Webb (21). Unfortunately only two relevant measurements have been carried out, so far, but both demonstrate non-thermal excitation. A difficulty affecting reproducibility arises here from the effect of a laser beam on a biological system as discussed in (21), in the case of individual cells. The best way to avoid this appears to be the use of a flow instrumentation so that each cell is subjected to the laser beam for a very short period only (22). 

At room temperature the thermal population of vibrational excited states is low, although not zero. Therefore, the initial state is the ground state, and the scattered photon will have lower energy than the exciting photon. This Stokes shifted scatter is what is usually observed in Raman spectroscopy. Figure la depicts Raman Stokes scattering. 

Isotope fractionations tend to become zero at very high temperatures. However, they do not decrease to zero monotonically with increasing temperatures. At higher temperatures, fractionations may change sign (called crossover) and may increase in magnitude, but they must approach zero at very high temperatures. Such crossover phenomena are due to the complex manner by which thermal excitation of the vibration of atoms contributes to an isotope effect (Stem et al. 1968). 

The vibrational frequency of the CS molecule is 1285.08 cm-1, or (multiplying by the speed of light) v=3.8526 x 1013 s 1. At 300 K, the factor in the exponent of Eq. 8.71 is x = 6.1632. Thus the partition function room temperature the fraction of vibrationally excited CS molecules is very small. However, at T — 5000 K, x = 0.3698, and <7vib=3.235. Thus, at very high temperatures, the thermal population of vibrationally excited molecules becomes significant. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

Cp.iatvib is the contribution from lattice vibrations, CPtintravaj the contribution from intramolecular vibrations, and CPimag is the magnetic or electronic heat capacity arising from thermal excitation of electrons. 

Figure 3.14 Potential energy diagram showing how an electronic transition takes place between vibrational levels of the ground and excited states. The illustration also demonstrates how the width and asymmetry of an absorption band changes at elevated temperature as a result of increased thermal population of vibrational levels of the ground electronic state (— low temperature -------elevated temperature). (Modified from...

At low temperatures, almost all lattice vibrations cease to contribute, leaving the thermal excitations of the electrons dominant [5]. The electronic term contributing to the constant volume heat capacity Cv is proportional to temperature T and the vibrational term is proportional to T3. Consequently, C is expressed as [5],... 

There can be other significant contributions to the optical bandwidths important among these are those that arise when the absorption (or emission) is solvent dependent and there is a distribution of solvation environments in solution or when there is a contribution from the thermal population of vibrational excited states ( hot bands ). Such contributions necessitate an additional term (or terms) in equation (9), so that, in practice, this equation provides an upper limit for Xg. 

In general, all materials have a positive thermal expansion coefficient that is they increase in volume when heated. Thermal expansion results from thermal excitation of the atoms that compose the material [16]. At absolute zero, atoms are at rest at their equilibrium positions (i.e., at r0 in Fig. 1). As they are heated, thermal energy causes the atoms to vibrate around their equilibrium positions. The amplitude of vibration increases as heating is continued. Asymmetry in the shape of the potential well causes the average interatomic distance to increase as temperature increases, leading to an overall increase in volume [15]. 

An alternative model, the hot-band mechanism, found support in studies of the temperature dependence of NVET rates in stilbene sensitization.114,115 In this model, thermal population of vibrational modes of the ground-state acceptor is assumed to provide access to geometries near to the relaxed excited state, as depicted in Figure 2.20. It is supported by the fact that energy differences between triplet donors are reflected almost entirely in the activation entropy rather than in the activation enthalpy, as would be expected from Balzani s treatment. 

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