Intermediates relaxation time

Since the collective orientational correlation time depends on the structure of a liquid, it is plausible that the rate of structural evolution of the liquid is proportional to this quantity. Thus, at lower temperatures rcon is longer and therefore the structural fluctuations are slower. As a result, motional narrowing is less effective as the temperature is lowered. While less motional narrowing would normally lead to a slower decay in the time domain, in this case the spectral density goes down to zero frequency. Thus, motional narrowing can reduce the spectral density at low frequencies and thereby decrease the intermediate relaxation time. 

Telgmann and Kaatze studied the stmcture and dynamics of micelles using ultrasonic absorption in the 100-KHz to 2-GHz frequency range [100]. They detected several relaxation times in the long (ps), intermediate (10 ns), and fast (0.1-0.3 ns) time scale. The longest relaxation time has been attributed to the exchange of monomer between bulk and the micelles, and the fastest to the rotation of the alkyl chains of the surfactants in the core of the micelle. The intermediate relaxation time has not been assigned to any particular motion. We will discuss later that the intermediate relaxation times in the 10-ns time scale may well be due to solvent relaxation in the Stem layer. 

If a reaction system consists of more than one elementary reversible reaction, there will be more than one relaxation time in general, the number of relaxation times is equal to the number of states of the system minus one. (However, even for multistep reactions, only a single relaxation time will be observed if all intermediates are present at vanishingly low concentrations, that is, if the steady-state approximation is valid.) The relaxation times are coupled, in that each relaxation time includes contributions from all of the system rate constants. A system of more than... 

Relaxation kinetics with a reaction intermediate. Show that the kinetic scheme with a steady-state intermediate I corresponds to the single relaxation time shown ... 

Failure to observe polarization in a particular reaction is significant only to the extent that any negative evidence is significant. If other evidence points to a radical pathway for the reaction, it may well be worth checking that the nuclear relaxation times for nuclei in the product are not unexpectedly short and also that polarization is not observable in a different spectral region from that expected for the final product owing to the formation of a metastable intermediate. 

By measuring the proton relaxation times, and T,p, it is possible to estimate the mobility of polymer chains within the cell wall (11). Proton spin relaxation editing (PSRE) is a method of expressing these results. It separates the components seen in a conventional CP-MAS C spectra into low-mobility and intermediate-mobility components. If PSRE is applied to a experiment (12) the mobility of the... 

Anti-Stokes picosecond TR spectra were also obtained with pump-probe time delays over the 0 to 10 ps range and selected spectra are shown in Figure 3.33. The anti-Stokes Raman spectrum at Ops indicates that hot, unrelaxed, species are produced. The approximately 1521 cm ethylenic stretch Raman band vibrational frequency also suggests that most of the Ops anti-Stokes TR spectrum is mostly due to the J intermediate. The 1521 cm Raman band s intensity and its bandwidth decrease with a decay time of about 2.5 ps, and this can be attributed the vibrational cooling and conformational relaxation of the chromophore as the J intermediate relaxes to produce the K intermediate.This very fast relaxation of the initially hot J intermediate is believed to be due to strong coupling between the chromophore the protein bath that can enable better energy transfer compared to typical solute-solvent interactions. ... 

The first comparison is based on the T values of gaseous, liquid and adsorbed molecules. Unfortunately, no measurements are available for butenes in the gas or liquid phase. Nevertheless a reasonable parallel can be drawn with propylene where the three different phases were investigated (35) at 295 K for the gas (1 atm) Tj of C2 is 0.095 s in the liquid state (2.6. M in CDCI3) 59.9, 58.7 and 65.2 s for Cj, C2 and C3 respectively adsorbed on NaY zeolite 0.81, 1.6 and 0.81 s. The shortest relaxation times characterize the gas phase where the spin-rotation mechanism (NOE factor n = 0) is very effective (30,35). In the liquid, dipole-dipole and spin-rotation mechanisms both play a role and the total relaxation rate is about three orders of magnitude lower than in the gas phase. The adsorbed molecules show therefore an intermediate behaviour between gas and liquid, as it was also suggested by chemical shift data. 

In the category of intermediate exchange the expressions become more complex and the prediction of the relaxation less trivial as e.g., demonstrated by Belton and Hills.16 It should be noted that the rate of exchange depends on the relaxation time scale, i.e., fast and slow exchange correspond to a short and long interchange time, respectively, in comparison to the inherent relaxation times. 

The Fourier transform of this quantity, the dynamic structure factor S(q, ffi), is measured directly by experiment. The structural relaxation time, or a-relaxation time, of a liquid is generally defined as the time required for the intermediate coherent scattering function at the momentum transfer of the amorphous halo to decay to about 30% i.e., S( ah,xa) = 0.3. 

In the discussion on the dynamics in the bead-spring model, we have observed that the position of the amorphous halo marks the relevant local length scale in the melt structure, and it is also central to the MCT treatment of the dynamics. The structural relaxation time in the super-cooled melt is best defined as the time it takes density correlations of this wave number (i.e., the coherent intermediate scattering function) to decay. In simulations one typically uses the time it takes S(q, t) to decay to a value of 0.3 (or 0.1 for larger (/-values). The temperature dependence of this relaxation time scale, which is shown in Figure 20, provides us with a first assessment of the glass transition... 

Figure 20 Temperature dependence of the a-relaxation time scale for PB. The time is defined as the time it takes for the incoherent (circles) or coherent (squares) intermediate scattering function at a momentum transfer given by the position of the amorphous halo (q — 1.4A-1) to decay to a value of 0.3. The full line is a fit using a VF law with the Vogel-Fulcher temperature T0 fixed to a value obtained from the temperature dependence of the dielectric a relaxation in PB. The dashed line is a superposition of two Arrhenius laws (see text).

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