Rate constant for relaxation

Heidner and coworkers d5v developed pulsed photolysis of NF2 as a convenient source of both NF(a) and NF(JY ). They used time-resolved techniques to examine the kinetics of NF(a) (detected by a-X emission) and NF(X) (detected by LIF of the b-X transition). d5s-i62 photolysis of NF2 yields vibrationally excited NF(X), which facilitated studies of vibrational relaxation. Heidner et determined rate constants for relaxation by CO2 and SFe. They also measured rate constants for the reaction of... 

The reaction of [Fe(CO)2(PMe3)2(Me)(CN)J with CO to form [Fe(C0)2(PMe3)2 C(0)Me (CN)] is second order in some solvents, but the solvent effect upon the kinetics and equilibrium constants is small. The solvent effect is attributed to a small interaction between the intermediate and solvent and the small change in dipole moment during the reaction. The mechanism is shown in Scheme 23. The lower path is favored. Selected values of /c = kj/[CO], where k, is the first-order rate constant for relaxation to equilibrium, are reported in Table... 

Some of the results for the Br + HCl(v ) system were discussed earlier. The rate constants for relaxation of HCl(v == 1) that are given in Table 3 refer to the process... 

Glanzer and Troe have made a quantitative comparison of their experimentally observed rate constants for relaxation of NO (u = 1 and 2) by O and Cl atoms with those predicted assuming that complex formation provides the major path-way. The basis of their calculations was the statistical adiabatic channel model ... 

So far, the discussion is based on the simple model shown in Figure 14.2. However, in most cases the interaction with the interface induces a conformational adaptation (i.e., relaxation) of the adsorbed (bio)polymers. This situation is depicted in Figure 15.4, where the native conformation is denoted n-state and the perturbed, adapted conformation p-state. The rate constant for relaxation is k, and the rate constants for desorption from the n-state and p-state are fej and respectively. It then follows that... 

The yields, lifetimes, and rate constants for relaxation from the thermal vibrational levels in 10-20 torr of benzene vapor near 300°K are given in Table III, Both fluorescence yields and lifetimes are available from several... 

Figure A3.13.3. Dissociation incubation ( iiK.-) and relaxation rate constants for the...

We now discuss the lifetime of an excited electronic state of a molecule. To simplify the discussion we will consider a molecule in a high-pressure gas or in solution where vibrational relaxation occurs rapidly, we will assume that the molecule is in the lowest vibrational level of the upper electronic state, level uO, and we will fiirther assume that we need only consider the zero-order tenn of equation (BE 1.7). A number of radiative transitions are possible, ending on the various vibrational levels a of the lower state, usually the ground state. The total rate constant for radiative decay, which we will call, is the sum of the rate constants,... 

A rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

This expression has been obtained by Skinner and Trommsdorf [1988]. The rate constants for the direct (Jc) and reverse (Jc) transition at / > 1 are proportional to ij( ), and n( ) + 1, respectively, and the relaxation rate equals... 

If two complexes coexist, there will be two relaxation times, and a treatment analogous to the analyses of Schemes III and IV is required. Table 4-2 gives a few rate constants for these reactions.The mechanism of such reactions is believed to consist of at least two steps, shown in simplified form in Scheme IX. 

The decay of M to Mo is called longitudinal relaxation (because it is parallel with the field Ho), it is identical with the spin-lattice relaxation described earlier. The rate constant for this process is therefore l/T,. The decay of M, and My is... 

K = 63 M 1, Kb = 1.4M-1)47 lithium-7 (K = 14 M 1 K" = 0.5 M 1) 49) and for cesium-133 (K, st 50 M-1, K = 4M 1)S0). In the case of sodium-23, transverse relaxation times could also be utilized to determine off-rate constants k ff = 3 x 105/sec k"ff = 2x 107/sec47,51). Therefore for sodium ion four of the five rate constants have been independently determined. What has not been obtained for sodium ion is the rate constant for the central barrier, kcb. By means of dielectric relaxation studies a rate constant considered to be for passage over the central barrier, i.e. for jumping between sites, has been determined for Tl+ to be approximately 4 x 106/sec 52). If we make the assumption that the binding process functions as a normalization of free energies, recognize that the contribution of the lipid to the central barrier is independent of the ion and note that the channel is quite uniform, then it is reasonable to utilize the value of 4x 106/sec for the sodium ion. 

If the equilibrium is suddenly displaced, the results obtained in Chapter 3 show that the re-equilibration process will follow first-order kinetics. It is customary in this field to refer to r, the relaxation time, which is defined as reciprocal of the first-order rate constant for re-equilibration. In this case, we have... 

To conclude, we think that valuable information can ce obtained from such relaxation experiments. They could provide a direct, kinetic proof of the conjecture that the Berry mechanism is the most probable one, as is indicated by some recent experimental and theoretical work. The applicability of this model is however restricted to situations where the energy of the molecule does not depend on the distribution of the ligands on the skeleton and where, as a consequence, there is one rate constant for each process. If this is not true, the present description could be the first-order approximation of a perturbation calculation. Such a work will be undertaken soon. 

Results of relaxation measurements on spin-state equilibria in solution are available for complexes of iron(II), iron(III), and cobalt(II). The results comprise values of relaxation time r, rate constants for the forward and reverse reactions feLH activation parameters AH and AS for the two opposed... 

Table 7. Relaxation times t and corresponding rate constants for the HS - LS conversion in solid iron(II) complexes...

The effect of a pressure of 80 and 150 MPa on the spin-state transition has been also studied [169], a series of spectra obtained at 150 MPa being shown in Fig. 32. The speetra show relaxation effects as line broadening and linewidth asymmetry. Calculated spectra were obtained in the same way as at ambient pressure. Rate constants for a number of temperatures are listed in Table 12, the parameter values resulting from an Arrhenius plot of the rate constants being listed in Table 13. In Fig. 33, the quantity 5g of Eq. (36) has been plotted as a... 

Table 14. Representative values of relaxation rate constants for [Fe(6-Mepy)2(py)tren](C104)j doped into PSS ...

The rate constant for the exponential relaxation of the latter system to the starting system was calculated to be 1.4 x 10 s . From this value, an approximate second order rate constant of 1.0 x 10 L mol" -s"l was calculated for the reaction between IV and CO. Given the above determination of the limiting rate constant for CO dissociation... 

The consequence of Equation (3) is that the relaxation process is related to the sum of the rate constant for the pseudo-first-order association process and the rate constant for the dissociation process. The association process can be influenced by changes in the concentration of H, but the value of k is intrinsic to the system and cannot be manipulated by external parameters, such as concentrations of reactants. The relaxation process can be dominated by the association or dissociation process depending on the relative value of k+[H] compared to k. The lifetime for the relaxation process is the inverse of the observed rate constant (r0bs — l/kefe). 

---