Lorentzian lifetime distribution

In the present work, we have found that a continuous Lorentzian lifetime distribution (two floating parameters) described by Eqn. 5, best modelled the experimental data ... 

Figure 8. Temperature-dependent Lorentzian lifetime distributions for 10 /xM PRODAN in CF3H.

Generation and trapping of radical cations of a,co-diphenylpolyenes within the channels of pentasil zeolites provides an environment which allows these transient species to be spectroscopically characterized . Similarly, complexation of xanthone in cyclodextrin has made it possible for the triplet state of this molecule to be fully characterized . Association and dissociation processes are related to the dipoles developed in the complex and in solution. A unimodal Lorentzian lifetime distribution for 2-anilinonaphthalene-6-sulphonate B-cyclodextran inclusion complexes have been recovered by multifrequency phase-modulation fluorometry in the presence of the quenchers Cu, acrylamide, and I . Both the fluorescence and phosphorescence spectra of benzo[f]quinoline adsorbed on p-cyclodextrin/NaCl have been determined as a function of temperature . 

Fluorescence lifetime data of 1, 4, 5, and 6 in presence of 10 M -CD were collected with frequency-domain fluorometry. These probes gave only 1 1 complexes with P-CD [58] and, given the association constant values, the complex molar fraction was >0.95 for 4 and 5 and 0.1 for 6. The fluorescence decay of all the probes was best described by unimodal Lorentzian lifetime distribution [51,59] rather than by a mono- or biexponential function corresponding to the emission of the complexed and the free probe. This distribution was attributed to the coexistence of molecules included in the cavity to different extents. It was proposed that, in the case of 4, the apolar benzene ring enters the cavity first and penetrates until the whole naphthalene is included. This is the most stable and, hence, the most populated conformation of the complex. The distribution of the lifetimes suggests that at any time there is an ensemble of molecules in different stages of complexation which have slightly different lifetimes. 

In some circumstances, it can be anticipated that continuous lifetime distributions would best account for the observed phenomena. Examples can be found in biological systems such as proteins, micellar systems and vesicles or membranes. If an a priori choice of the shape of the distribution (i.e. Gaussian, sum of two Gaussians, Lorentzian, sum of two Lorentzians, etc.) is made, a satisfactory fit of the experimental data will only indicate that the assumed distribution is compatible with the experimental data, but it will not demonstrate that this distribution is the only possible one, and that a sum of a few distinct exponentials should be rejected. 

Here A is a constant from the normalization condition j a(r) = 1, rc is the center value of the lifetime distribution, and W is the full-width-at-half maximum for the Lorentzian function. 

The addition of alcohol to the y-CD complex increased the.center lifetime of the Lorentzian distribution and decreased the relative distribution width quite regularly with increasing alcohol size. The environment around 4 became more hydrophobic with increasing alcohol concentration, in agreement with the steady-state measurements. The alcohol locks 4 in a few conformations and the lifetime distribution narrows. 

Fermi level. In a coarse approximation the p-level distribution can be assumed to correspond to that of a Fermi gas of free electrons, or even simpler, to that of a rectangular shaped distribution of equally spaced states (Richtmyer et al. 1934). Assuming equal transition probabilities and a Lorentzian lifetime broadening, the K absorption coefficient follows an arctan curve as a function of energy (cf. fig. 7, Ho) ... 

A new tool for a lifetime distributions analysis of emissions of probes adsorbed onto heterogeneous surfaces was recently developed by our research group [18]. This new methodology allows for asymmetric distributions and uses pseudo-Voigt profiles (Gaussian-Lorentzian product) instead of pure Gaussian or Lorentzian distributions. A very simple and widely available tool for fitting has been used, the Microsoft Excel Solver. This is a convenient way to treat the emission decay... 

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.)...

From Eq. (9) it is seen that at E E, it is the energy-dependence of r(E) fhat affects, in principle, the spectral concentration. The standard assumption is that for narrow resonances F(E) is a constant, whose value at the exact resonance energy is T(E,) s r =, where r is the mean lifetime, Eq. (3b). The distribution is then an exact Lorentzian. The dependence on energy of r in fhe neighborhood E< E, fhus follows the Lorentzian distribution, 1 ( E-Er + r /4 ( = 1)- other hand, the energy-dependence of... 

A nuclear magnetic resonance line is usually found to have one of two ideal lineshapes - Gaussian, or more often, Lorentzian. A Gaussian line is found when there is a random distribution of static fields within the sample. A Lorentzian line by contrast arises because the spin lifetime follows a first-order decay law. Weighting functions can be applied to a free-induction decay to generate... 

The steady-state rate of population of state 2 thus has a Lorentzian dependence on the energy gap 12. As we discussed in Qiap. 2, the Lorentzian function can be equated to the homogeneous distribution of 12 when the mean value of 12 is zero and state 2 has a lifetime of 2/2. Note that, according to Eq. (10.29b), T2II — when pure dephasing is negUgible. If we identily the time ccaistant T2 in Eq. (10.35) with 2T in Eq. (2.71), and identify the energy difference 12 with ( — ), then the factor in the second set of parentheses in Eq. (10.35) must be lulh times the distribution function Re[G( )] in Eq. (2.71). 

This is just an expression for a Lorentzian distribution centered at and of width A, and the broadening is simply due to the finite lifetime of the electron in its adsorbate state. 

Due to collisions or to the finite radiative lifetime the emitted radiation cons-lsts of a distribution of frequencies 0) about the centre frequency which is given by the Lorentzian function... 

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