Bimodal lifetime distribution

The phenomenon of such bimodal lifetime distribution proposed for reaction 1 on the basis of direct quasiclassical trajectory calculations were tested experimentally with the reaction of diaza-[2.2.1]bicycloheptane to [2.1. Ojbicyclopentane [Equation (2)].6 8 Experimental study on reaction 2 showed that the exo isomer 5x is formed favorably over the endo isomer 5n by about 3 1 in the gas phase. One explanation for the preferential formation of 5x invokes a competitive concerted and stepwise mechanism the concerted pathway directly from 4 to 5 gives 5x with the inversion of configuration at the carbon from which N2 is departing, whereas the stepwise pathway goes through the radical intermediate and leads to both 5x and 5n in equal amount. Alternatively, the product stereochemistry can be rationalized by dynamic matching between the entrance channel to the cyclopentane-1,3-diyl radical intermediate and the exit channel to bicyclo[2.1. Ojpentane as was assumed for reaction 2. 

Pressure effect on the product distribution in supercritical media would resolve the problem. If the reaction proceeds via the competitive concerted/ stepwise mechanism, the reaction under a higher pressure is expected to give more exo isomer because the activation volume is considered to be smaller for concerted process than the stepwise one and hence more concerted reaction is expected under a higher pressure. If, on the other hand, bimodal lifetime distribution of trajectories is the origin of the stereoselection, the product ratio is expected to approach to unity under high-pressure conditions, since energy randomization is more effective under a high pressure. 

The latter point to a conformational transition of the protein at Tin. The time-resolved fluorescence studies indicated that the intrinsic Trp fluorescence emission of the protein was represented by a bimodal distribution with Lorential shape and was strongly affected by the protein conformational dynamics (Bismuto et al., 1999 D Auria et al.,1999). Parameters of the temperature dependence of the bimodal lifetime distribution, such as fraction relative intensity, the position of centres, and the distribution line widths,... 

Figure 4.5. Left side. Temperature dependence of the bimodal lifetime distribution parameters of Sulfolobus solfataricus (3-glycosidase. Long-lifetime component (squares) short lifetime component (circles). Right upper side W3/4H dependence on temperature thermal denaturation of Sulfolobus solfataricus p-glycosidase at pD 7.4 (continuous line) and pD 10.0 (dashed line). The lines were obtained by monitoring the amide l width calculated at 3A of the amide height (W3/4H) as a function of the temperature. Right bottom side dependence on temperature for Sulfolobus solfataricus p-glycosidase. (Likhtenshtein et al., 2000). Reproduced with permission.

Another common symptom of reactions that display nonstatistical behavior is a bimodal distribution of trajectory lifetimes. The nonstatistical trajectories have much shorter lifetimes than predicted by TST or RRKM. Trajectories will then cluster in two (or more) groups, the very short lifetime group and those with a much longer lifetime, consistent with statistical dynamics. Both direct trajectories that seemingly avoid local minima and bimodal lifetime distributions will be seen in many of the examples to follow. 

FIGURE 1. Continuous bimodal lifetime distribution function (fractional contribution to the total intensity versus lifetime) for open (left) and closed (ri t) reaction center of Photosystem II at 4 C under anaerobic conditions. Inserts ow the respective phase (a) and modulation (X) data as a function of frequency (MHz) with the best bimodal distribution fit (-). Sanples were excited at 580 nm with a collimated 1 mW laser beam. Emission was observed through a monochromator at 680 nm (FWHM bandpass 16 nm) and a Hoya R-64 cut-off filter to eliminate scattered excitation light. 

Figure 5.1. Representations of double-exponential and bimodal Lorentzian distribution analyses of DPH fluorescent decay lifetimes in liver microsomal membranes. Results (see Table 5.2) are normalized to the major component. The double-exponential analysis, represented by the vertical lines, recovers lifetimes near the centers of the Lorentzian distributions. The width of the distributions represents contributions from a variety of lifetimes. (From Ref. 17.)...

Simulations have revealed a systematic tendency of the lifetime analysis technique to split broad distributions into two or possibly more narrow ones. The separation of the pore size distributions shown in Figure 7.19 is not as clear as for the smaller lifetime components. As an example the bimodal result shown in Figure 7.19 was used to create a noisy dataset. A second set was simulated from a lifetime distribution where the two pore size distributions were smeared into one broad component. Care was taken not to shift the mean lifetime and the intensity share of the distribution compared to the total was kept constant. The simulation input is shown in Figure 7.26. 

Figure 7.26 Simulated lifetime distributions based on a 23% porogen load sample. The bimodal distribution was smeared out into a monomodal one. The magnitude of the shorter lifetimes exceeds the displayed range.

Even though the lifetime distributions appear to be quite different, the recreated data are almost identical except for a small deviation near 200 ns and less obvious ones at shorter times. If the relative differences are plotted, systematic differences beyond the statistical noise are noticeable up to 200 ns, particularly when several channels are binned together. Given sufficient statistics, in principle, one can tell the difference between a bimodal and a monomodal distribution. The shown simulated spectra are based on 108 counts, five to 10 times the amount collected for the data discussed here. 

Although very broad molecular weight distributions will result from slow exchange between one dormant and one reactive propagating species, the distribution will always be monomodal. However, the molecular weight distributions of many carbocationic polymerizations are bimodal. Bimodal molecular distributions are produced in systems with two propagating species with either different reactivities, or with identical reactivity but different lifetimes in their active form [268]. Unfortunately, there is not enough experimental detail on the evolution of M and polydispersity as a function of conversion to interpret and explain all of the literature data reported. 

In the use of lifetime distributions, each d y time component is associated with three variables. Of, T, and the half-width (a or T). Consequendy, one can fit a coni dex decay with fewer exponential components. For instance, data which can be fit to three dfscrete decay times can picaUy be fit to a bimodal distribution motfel. In generri, it is not possible to /n Hngiii h between the discrete rrail-tiexponential model (Bq. [4.26]) and the lifetime distribution model (Eq. [4 J3]), so the model selection must be based on one s knowledge of the system. ... 

In the ensemble-averaged measurements described in Sec. IV, the biexponential fluorescence decays of MG molecules were tentatively ascribed to bimodal structure of the host matrices [11,12], By virtue of single-molecule fluorescence lifetime measurements we for the first time found evidence for bimodal distribution of sites for individual CV molecules on a thin film of PMMA [15], Recently, a theoretical study appeared foreseeing bimodality of a supercooled liquid [91],... 

Bimodal or not bimodal—critical comments Is the bimodal distribution as observed by beam based positron lifetime analysis (BPALS) real or a systematic effect of the data analysis To date the answer cannot be given with certainty. Arguments could be made why such a distribution is not observed by SAXS and is observed by BPALS in data shown here [62], and in work by Gidley et al.[46] Positrons are implanted at specific depths and only after measuring at different mean depth can one... 

For now, the bimodal distribution may be an artifact. The two lifetimes can be considered as lower and upper bounds of the pore size distribution. This technique is the only one available that can provide non-destructive depth profiles without sample preparations other than mounting them in the vacuum system. Depth profiled lifetime data are currently being collected. This is practical due to the high data acquisition rate of 3TO3 to 104 lifetime events per second, depending on the implantation depth. 

Carpenter, B. K. Bimodal distribution of lifetimes for an intermediate from a quasi-classical dynamics simulation, J. Am. Chem. Soc. 1996,118, 10329-10330. 

Indeed, in many of the polymerization reactions studied in these investigations when bimodal distributions were obtained, the lower molecular weight peak could be reduced in amount or completely eliminated by the replacement of either the TBC or BC cocatalyst with TPMC. These results also suggest that for reactions carried out in methylene chloride, free ion endgroups are present which have shorter kinetic lifetimes and form lower molecular weight polymers than the ion pair endgroups. 

Merkel et al. [2002, 2003] carried out studies of gas and vapor permeability and PALS free volume in a poly(4-methyl-2-pentyne) (PMP)/fumed silica (FS) nanocomposite. It was observed that gas and vapor uptake remained essentially unaltered in nanocomposites containing up to 40 wt% FS, whereas penetrant diffusivity increased systematically with the spherical nanofiller content. The increased diffusivity dictates a corresponding increase in permeability, and it was further established that the permeability of large penetrants was enhanced more than that of small penetrants. PALS analysis indicated two o-Ps annihilation components, interpreted as indicative of a bimodal distribution of free-volume nanoholes. The shorter o-Ps lifetime remained unchanged at a value T3 2.3 to 2.6 ns, with an increase in filler content. In contrast, the longer lifetime, T4, attributed to large, possibly interconnected nanoholes, increased substantially from 7.6 ns to 9.5 ns as FS content increased up to 40 wt%. 

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