Hydrogen vibrational relaxation time

Data on vibrational relaxation times from interferometric studies, reported by White and Moore (Ref 8), show the rapid decrease of relaxation time with rise of relaxation zone temperature. Addition of up to 1% H2 to C>2 is shown to reduce the relaxation time and accelerate the reaction, but not to affect the maximum density. At a pressure of 0.001 atm, about 0.8 tort, the relaxation times would be in milliseconds instead of microseconds. The induction times for exothermic reaction are inversely proportional to the square root of the product of the number of moles of oxygen ([O2]) and the number of moles of hydrogen (IH2I) Per Hter, over the entire C J/LC ] range, to a good approximation. 

The product of the induction time and that square root decreases with rise in temperature. The vibrational relaxation times even for the mixtures rich in hydrogen, which have... 

Shock-tube investigations of vibrational relaxation times in hydrogen, deuterium, and their mixtures with argon and krypton have been reported by Kiefer and Lutz [129] and by Moreno [196]. By fitting their measurements to a Landau-Teller temperature dependence, Kiefer and Lutz give, for D2-D2 collisions (1100-3000°K),... 

The laser-beam deflection technique was first employed to determine the vibrational relaxation times of hydrogen [9] and deuterium [10]. The... 

The localized-electron model or the ligand-field approach is essentially the same as the Heitler-London theory for the hydrogen molecule. The model assumes that a crystal is composed of an assembly of independent ions fixed at their lattice sites and that overlap of atomic orbitals is small. When interatomic interactions are weak, intraatomic exchange (Hund s rule splitting) and electron-phonon interactions favour the localized behaviour of electrons. This increases the relaxation time of a charge carrier from about 10 s in an ordinary metal to 10 s, which is the order of time required for a lattice vibration in a polar crystal. 

A simple empirical relation which correlates most of the available experimental relaxation times available at temperatures in the neighbourhood of 300 °K is the Lambert-Salter plot30, which is shown in Fig. 10. Molecules fall into two classes, differentiated by the presence or absence of hydrogen atoms, each class showing a linear relation between log Zu 0 and vmIn. It is difficult to see any clear theoretical explanation of this striking correlation between vibrational frequency and transition probability which neglects entirely the influence of both mass and inter-... 

Our findings for rs and th may be compared with results of computer simulations for water. Values between 1 and 2 ps are stated for the average lifetime of a hydrogen bond by different authors (121-123), in satisfactory agreement with our experimental values. It is also interesting to compare with the frequency shift correlation function of the vibrational modes of water obtained from MD computations (124). Recently a slower component of this function with an exponential time constant of 0.8 ps was predicted for HDO in D20 at 300 K and a density of 1.1 g/cm3 (pressure %2 kbar). The existence of the slow component is a necessary prerequisite for the observation of spectral holes and the spectral relaxation time rs reported here. The faster component of the frequency shift correlation function with rc = 50 fs (124) represents rapid fluctuations that contribute to the spectral bandwidths of the spectral species and of the spectral holes. 

Relatively few measurements have been reported of vibrational energy transfer at low temperatures. Aside from the NO studies of Billingsley and Callear, already discussed, Miller and Millikan [190] have reported relaxation times for mixtures of CO with helium and hydrogen down to 100°K. A very clear deviation from the Landau-Teller linear extrapolation [191] was observed below 300°K for both mixtures. Shin [192] has examined the CO + He case in more detail, using the WKB approach and a Morse interaction potential. At low temperatures, he concludes, there are three important considerations ... 

V-V exchange between two hydrogen halides has been observed by Chen, Stephenson, and Moore [218] utilizing laser-excited vibrational fluorescence. The vibration-vibration transfer rate for HC1-HI collisions was determined by measurement of the exponential decay of HC1 Av = 1 fluorescence following excitation by an HC1 laser pulse. The relaxation time for the process... 

Two companion papers by Millikan and by Millikan and Switkes [97] describe the latest experimental results on the vibrational relaxation of CO by hydrogen. It is found that for temperatures above 600°K there is no observable difference between the deactivation efficiencies of n-Ha and p-Ha. Below 600°K,/ -Ha is clearly more efficient, and at 300°K the ratio is approximately 2. For temperatures between 600°K and 2700°K, the relaxation time for CO-Ha collisions is given by... 

All theoretical studies on benzoic acid dimer underlined the need for a multidimensional potential surface. These studies have investigated the temperature dependence of the transfer process They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al. [26] have calculated the temperature dependence of the spin-lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be... 

We shall prove below that the isotopic dependence of the vibrational contribution As(v) on the permittivity e(v) is small, unlike the ID of the reorientation contribution 0r(v). It appears that the relaxation time td differs in HW from that in OW, since td strongly depends not only on the structure of liquid water but also on the strength of an individual hydrogen bond (a detailed analysis of dependence of td on water structure is given by Agmon [18]. 

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