Water vibrational relaxation time

The frequencies of rotational transitions are much smaller than vibrational frequencies, which means that the rotational motion is slower than the vibrational one. For a free molecule, the period of rotational motion is within 10 12-10 9 s. In condensed media the rotational motion is even slower, its period being respectively greater. At this stage it is more correct to speak of the relaxation time of the molecules. The latter essentially depends on the phase state of the medium. For example, in liquid water the relaxation time of molecular dipoles in an external electric field is about 10 11 s, whereas in ice (at 0°C) it is — 1 () 5 s. 

Two subsequent simulation studies for low-frequency vibration systems clearly show that the strong and striking dominance of Coulomb force effects found for CH3C1 in water is by no means so clear-cut (or even true) in low-frequency diatomic systems. In the first of these, related to experiments by the Barbara group (24,25), Benjamin and Whitnell (26) found that for the diatomic I2 of frequency 115 cm, with a vibrational relaxation time of about 1 ps, the presence of Coulomb forces accelerated the VET in water by about a factor of 4, a noticeable but somewhat muted effect considering that one is comparing an ion to a neutral (with the same frequency). The authors noted the importance of the fact that the short-range non-Coulomb forces themselves are quite efficient at the low I2 frequency. 

The total cross section (Ttot( o) will be sensitive to the intermolecular potential, which operates at the different collisional orientations. From the order of magnitude of experimentally determined dissociation rate constants, one can conclude that fftot( o) is of the order of the gas kinetic cross section. However, pronounced differences in collision efficiencies, e.g. of water or some atoms as collision partners, may be ascribed to long range forces which increase intermolecular forces obtained from vibrational relaxation studies can probably also be used for dissociation. However, the influence of these forces on vibrational relaxation times and on dissociation rates is completely different, owing to the difference between complex collisions on the one hand and simple transitions between levels separated by large energy intervals on the other. 

Alternatively, it is possible to heat the reaction medium using a high-intensity near-infrared laser pulse (typically, >200 mJ), which will be preferentially absorbed by the solvent— usually in one of its vibrational overtone bands. The time resolution of this technique is limited by the resistance of the cell where the reaction is studied to the high-intensity laser pulse, by the laser pulse and by the relaxation time of the vibrational and rotational states of the solvent in the near-infrared region. For example, for water this relaxation time is < 10" sec. However, we also have to consider thermal equilibration in the region under study, and, consequently, the time resolution of this technique is of the order of tens of picoseconds. 

First, as the molecule on which the chromophore sits rotates, this projection will change. Second, the magnitude of the transition dipole may depend on bath coordinates, which in analogy with gas-phase spectroscopy is called a non-Condon effect For water, as we will see, this latter dependence is very important [13, 14]. In principle there are off-diagonal terms in the Hamiltonian in this truncated two-state Hilbert space, which depend on the bath coordinates and which lead to vibrational energy relaxation [4]. In practice it is usually too difficult to treat both the spectral diffusion and vibrational relaxation problems at the same time, and so one usually adds the effects of this relaxation phenomenologically, and the lifetime 7j can either be calculated separately or determined from experiment. Within this approach the line shape can be written as [92 94]... 

In Section V the reorientation mechanism (A) was investigated in terms of the only (hat curved) potential well. Correspondingly, the only stochastic process characterized by the Debye relaxation time rD was discussed there. This restriction has led to a poor description of the submillimeter (10-100 cm-1) spectrum of water, since it is the second stochastic process which determines the frequency dependence (v) in this frequency range. The specific vibration mechanism (B) is applied for investigation of the submillimetre and the far-infrared spectrum in water. Here we shall demonstrate that if the harmonic oscillator model is applied, the small isotope shift of the R-band could be interpreted as a result of a small difference of the masses of the water isotopes. 

Capillary forces in mixed fluid phase conditions are inversely proportional to the curvature of the interface. Therefore, menisci introduce elasticity to the mixed fluid, and mixtures of two Newtonian fluids exhibit global Maxwellian response. For more details see Alvarellos [1], his behavior is experimentally demonstrated with a capillary tube partially filled with a water droplet. The tube is tilted at an angle (3 smaller than the critical angle that causes unstable displacement. Then, a harmonic excitation is applied to the tube in the axial direction. For each frequency, the amplitude of the vibration is increased until the water droplet becomes unstable and flows in the capillary. Data in Figure 3 show a minimum required tube velocity between 40 and 50 Hz. This behavior indicates resonance of the visco-elastic system. The ratio of the relaxation time and characteristic time for pure viscous effect is larger than 11.64. 

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. 

A rather less opaque indication that Coulomb force effects could be significant is the short population relaxation time (Ti) found in pioneering experimental measurements of the CN ion in water (17) an extrapolation to infinite dilution indicated a T value of about 25 ps for a vibration of about 2100 cm, a time much shorter than for comparable frequency diatomics in, for example, rare gas solvents (8). That this was not a singularity was subsequently shown for several triatomic ions (8,18). 

At all events, the role of Coulombic forces for VET in solution was first examined in a molecular dynamics simulation for the 680 cm-1 C-Cl vibration of the CH3CI molecule (modeled as a diatomic) in water solvent by Whitnell et al. (19). The (classical) relaxation time Ti was determined both by nonequilibrium simulations and by use of the classical Landau-Teller (LT) formula (1,3,19,20). 

Methane is known to be a very efficient partner for the deactivation of oxygen [271,272] the bending mode v2 of CH4 (see Figure 3.17), with frequency 1526 cm-1 (18.92 x l0-2eV), closely matches the vibrational frequency of Os [1556 cm-1 (19.29 x 10-2eV)]. Since water vapor [v2 = 1595 cm-1 (19.77 x 10-2 eV)] can deactivate 02 vibrations very efficiently, it is thus not surprising that vibrational relaxation in CH4 is also greatly affected by HsO. Monkewicz [273] observed that at 310°K a 2% H20 mixture shifted the relaxation time by a factor of about 2. 

Fig. 1. Spectral evolution of the hot s-like state of hydrated electron generated in two 6.2 eV photon ionization of light water. The arrows indicate the trends observed in the direction of longer delay times of the probe pulses. Panel (a) demonstrates the evolution between 500 fs and 1.2 ps, showing considerable blue shift and fast decay of the IR features. Panel (b) shows the slow relaxation regime that is observed after 1.2 ps (note the logarithmic scale). In this regime, the band maximum is locked within 20 meV and the spectral evolution is due to relatively slow, isotope sensitive narrowing of the spectral envelope on the red side of the spectrum. This narrowing is likely to be caused by vibrational relaxation of the hot s-like state. See Ref 28 for more detail.

In addition to measurements of lifetime of these vibrational excited states, time-resolved nonlinear IR could also give precise information on the mechanisms of deexcitation of these states. It could thus be shown that relaxation of the first excited state of modes of water molecules in liquid water was mainly due to resonance interactions of these modes with excited bending modes (65). As a result of the analysis of ID IR spectra shown above, Fermi resonance with bending modes allows the energy of the first excited state of to be transferred to the overtone of the bending band. It offers a fast relaxation path toward vibrational levels of a lower energy. Time-resolved nonlinear IR spectroscopy shows that this process is the main relaxation mechanism of and is at the origin of an unexpected increase of the relaxation time when temperature increases (66, 67). 

Time-resolved nonlinear IR spectroscopy is a modem version of ordinary IR spectroscopy examined above. It has been referred to all along the preceding chapters. In Ch. 4 it has been shown to convey information on the dynamics of the surrounding of the studied vibration, in addition to information on this vibration itself, which is the main type of information conveyed by ordinary IR spectroscopy, also named ID IR. This supplementary information appears through the measurements of the lifetime or relaxation time of the studied vibration. Most results obtained up to now with such methods concern liquid water. They have been described in Ch. 4, because they may be applied to any H-bonded system. They have given values of relaxation times of bands of water molecules in liquid water and have thus shown a marked isotopic dependence. Thus the relaxation time of... 

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]. 

We should remark that no one of the mechanisms previously elaborated for water enables analytical description of the above fall of e"(v) for the case of ice. This phenomenon probably characterizes the transition from collective motions in a fluid typical for Debye relaxation, characterized by the relaxation time td, to vibration of individual molecules, characterized by much shorter lifetimes Tor, rq, Tjj. The latter times have the same order of magnitude in water and ice, but td drastically differs in these fluids. That is why the theory of far-IR spectra is rather similar in ice and water. On the contrary, it appears that the molecular theory pertaining to the low-frequency ice spectra (which still is not elaborated)... 

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