Exponential dissociation rate

Because the reactive group is attached on the chain end, it is pulled by the tension / from the chain. Hence, the potential barrier for the associative group to dissociate is effectively reduced to A — /a. The chain dissociation rate is therefore enhanced to 

The length r of the end-to-end separation above which the reactive group spontaneously dissociates can be roughly estimated by the condition A — /a 0, and hence 

For the physical association, whose binding energy is comparable to the thermal energy, the cutoff lies in the high extension region, i.e., r / = na. 

Insensitivity to the molecular weight indicates that the viscoelasticity is caused by conformational entropy change of the stretched active chains rather than monomeric friction. 

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The values for k+ and k were compared for temperature jump and stopped-flow conditions for DNA concentrations where the decay followed a mono-exponential function and no migration between DNA molecules occurred (see below).94 This report shows the importance of detecting fluorescence signals at the magic angle, which eliminated the fast components in the kinetics due to artifacts. The values for the association and dissociation rate constants obtained by both techniques are similar. 

The filtration conditions (i.e., the rate and time of filtration) should be established in preliminary experiments. The two major considerations are (1) filter washing must be sufficient to minimise the nonspecific retention of radiologand by the filter and (2) the time course of filtration should be sufficiently short that dissociation of the radioligand from its receptor is avoided. In these studies, it is important to have a preliminary estimate of the dissociation rate, i.e., k i in equation23. For a simple exponential reaction, the half-time of dissociation (t./,) is related to the dissociation rate constant by t./, = 0.693/k i... 

Fig. 3.16 The ALIS-MS responses from a dissociation rate experiment for a mixture of Zap-70 ligands using staurosporine as the quench reagent. See text for details. (A) The raw data and its fit curve for NGD-6367, one of the compounds in the mixture. (B) The exponential decay curves fit to normalized...

The NO dissociation rate constants are summarized in Table HI (50) and are smaller than those seen with NO-metmyoglobin complexes. NP2 and NP3 (A ofr 0.1 s ) release NO approximately 10 times more slowly than NPl and NP4 kofs 2-3 s ) at pH 8.0, and the NO release rate for all nitrophorins decreases as the pH is lowered to 5.0. The NO release curves cannot be fit with a single exponential, indicating two off rates at each pH, as previously noted for both recombinant and insect-derived NPl (46), and which has also been recently reported for recombinant NP2 (145). The biphasic kinetics suggest the presence of slowly interconverting conformations. The values obtained are pH and protein dependent, ranging from 2.6 to 0.05 (Table HI) (50), values that are considerably slower than found for sperm whale metmyoglobin... 

Fig. 2.21. (a) Time-resolved LIF decay profiles for two closely spaced rotational levels of vibrationally excited CH3O (X). The solid line is an exponential fit for the decay convoluted with the dump laser pulse shape function, (b) Measured state specific unimolecular dissociation rate constants for CH3O (X) compared to calculated k E, J) curves without and with tunneling corrections. 

The dependence of the dissociation rate on the mole fraction of the organic solvent is depicted in Figure 5. As seen in Figure 5, the rate of dissociation decreases exponentially with the mole fraction of the ethanol. This decrease in rate of dissociation cannot be attributed to the effect of the solvent on the dielectric constant of the solution. At Xethanoi = 0.2, the dielectric constant of the mixture is 66.2 (vs. 77.5 of water), but the rate of dissociation is slowed by an order of magnitude. The proton conductivity of the water—ethanol mixture decreases with the mole fraction of the solvent, but this decrease is not steep enough to account for the measured effect on the rate of dissociation (see Figure 5). This reasoning... 

Determine dissociation rate constant by fitting PE MFI data for all timepoints to first-order exponential decay (Eq. 1) shown below ... 

The dissociation rate can be derived from the ratio of the A and the undissociated AB+ signals. Under the assumption of a single exponential decay rate, the rate can be extracted from the relation... 

Then, for each reaction, we can write that, ( ) = aNf(E - E )/p(E). The total decay rate for the molecule M is then just the sum of all the dissociation rate constants, kj- = 2A ,. The branching ratios, B, toward the various decay channels will be given by the ratio of rate constants, kj/kj. The concentration of A/ as a function of time continues to be given by a single exponential decay with the form, Thus, from the rate... 

Two-Temperature Approximation of CO2 Dissociation Kinetics. Estimate the Treanor factor in the rate coefficient for CO2 dissociation in the two-temperature approximation (5-26)attypicalnon-thermalplasmaconditions(take, for example, Tv = 3000 K, To = 500 K also assume for simplicity that ita = E ). Considering the estimated Treanor factor as a dimensionless part of the pre-exponential factor of dissociation rate coefficient, compare it numerically with the corresponding pre-exponential factor E f T Y appearing in the rate coefficient (5-22) in the one-temperature approximation. 

Values of Ajeo from dissociation rates and values from direct measurement are compared in Table 1.1 and Fig. 1.3. m appears to decrease with temperature for H, O and N. m is between —2 and —3 at T 298 K and m < 2 for T > 2000 K. Recombination of halogens (Table 1.2) seems to behave somewhat differently. As individual values are uncertain within a factor of 2 and as temperature coefficients have been obtained only over small ranges, we cannot be certain of the exact variation of m. Although low and high temperature data can be reconciled quite well with a mean value between —1 and —2, local values may be different. In Table 1.1 and Fig. 1.4 pre-exponential... 

Fio. 1.4, Pre-exponential factors for dissociation rate constants of diatomic molecules data of Tables 1,1 and 1.2 high temperature values measured directly, low temperature values calculated from measured rates of recombination. 

The incorporation of oxadiazole moieties, which are highly electron deficient, into PPV/MEH-PPV as side chains, increases the exciton dissociation rate and promotes the electron transport. The oxadiazole moieties, c.f. Figure 3.13, are attached to the backbone via Cm alkyloxy Unks. The exciton dissociation rate is assumed to follow an exponential decay law. The decay constant (obviously the mean lifetime) x for oxadiazole-containing PPV/MEH-PPV is 0.4 ns, whereas the decay constant for pure MEH-PPV is around 0.65 ns. 

Figure 18.B1 Experimental data showing the exponential decline in the dissociation rate constant, with increasing number of vibrational modes, for a series of alkyl radicals. Reproduced from Hardwidge etal, 3. Chem. Phys., 1973, 58 340, with permission of the American Institute of Physics...

A typical example of measured dissociation rates is shown in Figure 24. B1 for the photodissociation of He CI2. The data are represented in a semi-log plot to emphasize the linear dependence on v[, as well as the exponential dependence on ( tians). which is the same as s(vj)— (vj — 1), i.e. the energy spacing between adjacent vibrational levels (Cline et al, 1986). 

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