Vibrational anharmonicity excitation

Due to vibrational anharmonicity, this transfer is resonant only for the K = 1 exchange, which has been considered in a previous section, but it remains, in the liquid, faster by several orders of magnitude than V-T relaxation for diatomics. Relaxation of highly excited I2 and Br2 close to the vibrational dissociation limit has been observed in the dense gas (at liquid densities). These indirect measurements of T, were correlated with the gas diffusion coefficient and should hence be more reasonably accounted for in the framework of an isolated binary interaction model. This interesting exjjerimental system raises the question of the influence of the change in molecular dimensions in higher excited states, due to anharmonicity, on the efficiency of collisional deexcitation. This question could jjerhaps be answered by more precise direct relaxation measurements. 

Typically, molecules vibrate anharmonically. A vibration is anharmonic when the frequency of oscillation depends on the level of excitation. The classical Morse oscillator, with energy... 

To look into this further, we show in Fig 4, in part (a), the behavior of the heat capacity of polypropylene, in units of J/K.(mol of -CH2-CH2(CH3)- repeat units) (35,36) in comparison with that of the molecular liquid 3-methyl pentane (37) (divided by 2 to have the same mass basis as the polymer repeat unit) (38). It is seen that the liquid heat capacity of the hexane isomer (x 0.S) falls not much above the natural extrapolation to lower temperatures of the heat capacity per repeat unit of the polymer. This implies that the main effect of polymerization, as far as the change in heat capacity at Tg is concerned, is to postpone the glass transition until a much higher vibrational heat capacity has been excited. This not only reduces the value of ACp but has a disproportionate effect on the ratio Cp,i/Cp,g at Tg. This happens despite a lower glassy heat capacity in the polymer than in the molecular liquid at the same temperature. The latter effect is a direct consequence of the lower Debye temperature (and lower vibrational anharmonicity) at a given temperature for in-chain interactions in the polymer than for intermolecular interactions in the same mass of molecules. 

The vibrational anharmonicity gives a first additional term in the vibrational energy of — xdtfv + he, [The second term is the coefficient of (v + i) and is shown by observed spectra to be negligibly small.] Here, Xe is the (first) anharmonicity constant and is the equilibrium wave-number, for small displacements. The energy of the vth vibrationally excited state is then given by... 

Finally, a few comments shall be made on the concept of local modes as compared to normal modes [3,33-35], The main idea of the local mode model is to treat a molecule as if it were made up of a set of equivalent diatomic oscillators, and the reason for the local mode behavior at high energy (>8000 cm ) may be understood qualitatively as follows. As the stretching vibrations are excited to high energy levels, the anharmonicity term / vq (Equation (2.9)) tends, in certain cases, to overrule the effect of interbond coupling and the vibrations become uncoupled vibrations and occur as local modes. ... 

Figure 13. Photodissociation spectrum of V (OCO), with assignments. Insets and their assignments show the photodissociation spectrum of molecules excited with one quanmm of OCO antisymmetric stretch, v" at 2390.9 cm . These intensities have been multiplied by a factor of 2. The shifts show that Vj (excited state) lies 24 cm below v ( (ground state), and that there is a small amount of vibrational cross-anharmonicity. The box shows a hot band at 15,591 cm that is shifted by 210 cm from the origin peak and is assigned to the V" -OCO stretch in the ground state.

Fig. 7. Predicted diffusion coefficients for hydrogen (H) and deuterium (D) in niobium, as calculated by Schober and Stoneham (1988) from a model taking account of tunneling between various states of vibrational excitation and comparison with experimental measurements (solid lines). Theoretical curves are shown both for a model using harmonic vibrational wave functions (dashed lines) and for a model with anharmonic corrections (dashed-dotted lines).

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