Photon absorption rate

That is, the semi-classical approximation to the photon absorption rate is equivalent to a Landau-Zener treatment of the probability of hopping from Vj -i-hco to Vf induced by the electronic coupling perturbation p, f (s,0,Q). 

Let us now consider how similar the expression for rates of radiationless transitions induced by non Bom-Oppenheimer couplings can be made to the expressions given above for photon absorption rates. We begin with the corresponding (6,4g) Wentzel-Fermi golden rule expression given in Eq. (10) for the transition rate between electronic states Ti,f and corresponding vibration-rotation states Xi,f appropriate to the non BO case ... 

For anions that are electronically bound, the anion s electronic energy Vj (Q) lies below the neutral molecule s electronic energy Vf (Q) as depicted in Figs. 2-5. Hence, because E is a positive quantity, there are no geometries for which the argument of the delta function in the above expression vanishes and, as a result, the non BO rate can not be cast in terms of shifted intersecting energy surfaces as can the photon absorption rate. 

Two-Photon Absorption Rates Under Continuous-Wave Excitation. 189... 

Fig. 17 TPA and single-photon absorption rates versus incident photon flux density calculated using parameters from Table 1 for the case of excitation by pulsed SPDC soimce. Diameter of the irradiated area is 0.8 xm. The dashed lines emphasize the photon flux density and the entangled photon TPA rate provided by the model source...

Fig. 18 Dependencies of TPA and single-photon absorption rates on the irradiation area at the constant photon pair arrival rate of 10 MHz. Vertical dashed lines emphasize the rates obtained for areas having the indicated diameters...

Regardless of the photo catalyst employed, repetitive laser pulse illumination increased 0hcho in the oxygenated suspensions by a factor of ca. 1.5 in comparison with CW illumination, although in both modes of photolysis the time-averaged photon absorption rate was approximately the same [82], Previous studies on intermittent illumination in Ti02 photocatalysis offer no satisfying explanation for this observation [86-91]. 

Cornu et al. investigated the quantum yield, 4>f, of photocatalytic formate oxidation in oxygenated acidic Ti02 suspension under continuous and periodic pulse illumination [91]. For very short illumination times in periodic pulse photolysis, Cornu et al. demonstrated that 4>f was identical to the value obtained under continuous illumination at the same time-averaged photon absorption rate. This is in sharp contrast to the results of Wang et al. for photocatalytic methanol oxidation [82],... 

Table 11 Dependence of the reaction rate on the photon absorption rate...

Cm = 0.05 X 10 g cm, the reaction rate is proportional to the square root of the LVRPA throughout the reaction space. Consequently, in a photoca-talytic slurry reactor, where low, intermediate, and high photon absorption rates can coexist, the complete reaction rate equation must be used. 

In these equations, n is the exciton concentration, t is time, a is the absorption coeflScient for the incident light, Z is the intensity of the incident light, K is the two-photon absorption rate constant at 532 nm, (3 is the reciprocal of the exciton lifetime, and y is the exciton-exciton annihilation rate constant. 

We then assumed that the light intensity was uniform within each of these 900 equal-area segments. The total number of excitons present at equilibrium was then calculated for a given total number of excitons in a pulse by summing the theoretically calculated equilibrium density in each of the segments. The variation in light intensity over the area of the beam was taken into account in a similar fashion when we calculated the two-photon-absorption rate constant k. 

Laser pulses of 3 jis duration and a typical fluence of 1.0 J/cm and Infrared absorption cross sections of 10 -10 cm yield photon absorption rates of 10 -10 photons/s, which are much slower than the rate of Intramolecular vibrational energy redistribution In systems such as benzyl anion. Hence, the anions are excited In a sequential process In which the vibrational energy Is redistributed before the next photon Is absorbed. This means that such experiments cannot determine In which vibrational mode(s) the energy resides. 

It has also been demonstrated ( ), by studying the competition between electron loss and a unlmolecular decomposition of known activation energy, that sequential Infrared absorption continues to occur even after the anion has achieved enough total Internal energy to reach Its electron detachment threshold. This Implies that, near threshold, electron ejection must not be occurlng faster than the 10 -10 s photon absorption rate. These experiments do not, however, allow one to conclude with much certainty how far above... 

D. Two-Frequency Distributive Two-Photon Absorption Rate Equations for Fluid Media... 

The various actinometer systems applicable to all types of photoprocesses have been summarized by Kuhn et al. (1989) for the International Union of Pure and Applied Chemistry Commission on Photochemistry. The fundamental problem is that actinometry is a technically demanding task, and it is then a complicated matter to relate the photon absorption rate to a reaction rate applicable to a particular experimental setting. In the following sections, the procedure will be briefly described for chemical actinometry and quantum yield determination then it will be explained that the rate of a photochemical reaction can be predicted from knowledge of the quantum yield and the incident photon intensity. Finally, treatment of experimental rate data for a photostability study will be covered in detail. 

The photon absorption rate in the inner glass tube wall can be estimated from the difference between the total radiative flux transmitted through the inner tube and the total incoming radiative flux. 

Photon absorption rate by a material particle of the suspension. At this point we would like to know the LVRPA by the solid and to be able to isolate this value even if the liquid would also absorb radiation. To do this we need to model absorption by a material particle of the suspension. In the continuum mechanics sense, a material point in space is a volume for which every property can be well defined by a single value. For a catalytic suspension, it will be made of the liquid and the solid phases. Let us consider a small volume V of the suspension space representing this material particle. This volume is located at a point in space x (Figure 6.11). Any point inside V can be defined in terms of a local reference frame f. 

The LVRPA or the photon absorption rate as a function of position results in ... 

From quantum mechanical considerations the two-photon absorption rate (s )... 

Initially, we will focus on the mesoscopic description associated with the radiative transfer equation. Then, we will introduce the single-scattering approximation and two macroscopic approximations the PI approximation and two-flux approximation. AH of these discussions are based on the configuration shown in Fig. 6. Collimated emission and Lambertian emission wiU also be considered in the discussion later they correspond to the direct component and the diffuse component of solar radiation, respectively. Throughout our study, the biomass concentration Cx is homogeneous in the reaction volume V (assumption of perfect mixing), and the emission phenomena in V are negligible. The concentration Cx is selected close to the optimum for the operation of the photobioreactor the local photon absorption rate. 4 at the rear of the photobioreactor is close to the compensation point A.C (see Section 5 and chapter Industrial Photobioreactors and Scale-up Concepts by Pruvost et al.). 

In this section, we present a Monte Carlo algorithm for estimation of the specific photon absorption rate (xq) at any location Xq within any photobioreactor s reaction volume confined by two diffuse-reflective surfaces (7Z and JF) with uniform reflectivity and p, respectively, where T is Lambertian emitting with uniform surface flux density n,i/ is non-... 

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