Bimolecular recombination coefficient

Bimodal polymer, 20 165 Bimodal polymerization, 20 531 Bimodal reactor technology, for high density polyethylene, 20 170 Bimodal weight ratio, 70 17 Bimolecular reaction, 74 625 Bimolecular recombination coefficient, 74 833... 

Pivrikas A., Juska G., Mozer A. J., Scharber M., Arlauskas K., Sariciftci N. S., Stubb H. and Osterbacka R. (2005), Bimolecular recombination coefficient as a sensitive testing parameter for low-mobility solar-cell materials , Phys. Rev. Lett. 94, 176506-1-176506-4. 

The concentration decay in Figure 10.15b at lower temperatures does not follow a simple bimolecular recombination. Instead, Equation 10.12 is used, which, based on the observed time dependence of the mobility, uses a time-dependent bimolecular recombination coefficient j8(t) as... 

Because Qcoii is a direct measure of the charge present in the layer at a delay time fd, the recombination dynamics can be determined via an iterative procedure [171]. For the data shown in Fig. 20, this analysis yields y = 3.5xl0 m s and y= 1.2 X 10 m s for the chloroform as-cast and the annealed P3HT PCBM layer, respectively. The value for the annealed sample agrees very well with the bimolecular recombination coefficient measured by TAS at carrier densities typical for steady-state AMI.5 illumination (see, e.g., [189, 195]). To compare these values to the Langevin limit, the mobilities of the electrons and the holes in the blend must be known. Information on these quantities can be gained from drift-diffusion simulations of the photocurrent transients with different collection biases (see Fig. 20b). This yields mobilities of 1.2 x 10" m and... 

Fig. 21 Effective bimolecular recombination coefficient calculated by Monte Carlo modeling of a phase-separated blend with an average feature size of 4 black) and 35 nm red). Simulations were performed in the absence of energetic disorder squares) or by assuming a Gaussian-type DOS with a width a = 15 meV triangles). Open symbols represent an electric field f = 0 and closed symbols are for F = 10 V/m. The Langevin limit is shown by the dotted line and the dashed line is for Langevin-type recombination limited by the slower carrier. Ref 23 refers to the model in Shuttle et al. [202]. In all cases, the hole mobility was 10 cm /V s. Reprinted with permission from [201]. Copyright 2008 by the American Physical Society...

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

A device model to describe two-carrier structures is basically similar to that used for one carrier structures except that continuity equations for both earner types are solved. The additional process that must be considered is charge carrier recombination. The recombination is bimolecular, R=y(np), where the recombination coefficient is given by 43)... 

Carrier and exciton dynamics in InGaN/GaN MQWs have also been studied at a high optical pumping power [34], At 7 K, a radiative decay lifetime of 250 ps was observed for the dominant transition at a generated carrier density of 1012/cm2. The time-resolved measurement showed that the decay of PL has a bimolecular recombination characteristic. At room temperature, the carrier recombination was found to be dominated by non-radiative processes with a measured lifetime of 130 ps. Well width dependence of carrier and exciton dynamics in InGaN/GaN MQWs has also been measured [35]. The dominant radiative recombination at room temperature was attributed to the band-to-band transition. Combined with an absolute internal quantum efficiency measurement, a lower limit of 4 x 10 9 cm3/s on the bimolecular radiative recombination coefficient B was obtained. At low temperatures, the carrier... 

The probability of bimolecular recombination is proportional to the product of the electron and hole concentrations and may become important for high-intensity exposures. In low-mobility materials, bimolecular recombination is usually described by a theoiy due to Langevin (1903). LangeviiTs expression for the recombination coefficient is... 

Let us examine now the set of equations controlling the creation and annihilation of neutral A and B particles in the Euclidean space which have equal diffusion coefficients D = Dq = D [93]. It has the form of equations (2.2.20) to (2.2.21). Here K is a reaction rate of bimolecular recombination in particular, it can be equal to K = SirDro. Also, and... 

The specific rate constants of interest to the ECD and NIMS are dissociative and nondissociative electron attachment, electron detachment, unimolecular anion dissociation, and electron and ion recombination. The reactions that have been studied most frequently are electron attachment and electron and ion recombination. To measure recombination coefficients, the electron concentration is measured as a function of time. The values are dependent on the nature of the positive and negative ions and most important on the total pressure in the system. Thus far few experiments have been carried out under the conditions of the NIMS and ECD. However, the values obtained under other conditions suggest that there is a limit to the bimolecular rate constant, just as there is a limit to the value of the rate constant for electron attachment. The bimolecular rate constants for recombination are generally large, on the order of 10 7 to 10-6 cc/molecule-s or 1014 to 1015 1/mole-s at about 1 atm pressure. Since the pseudo-first-order rate constants are approximately 100 to 1,000 s 1, the positive-ion concentrations in the ECD and NIMS are about 109 ions/cc. 

Table 2-3. Effective Bimolecular Rate Coefficients (cm3/ molecule s)a for Several Recombination Reactions as a Function of Altitude in the Atmosphere (Zellner, 1978)... 

In this instance, unlike ion-pair recombination, the fraction that escapes to infinity depends on the diffusion coefficient. It s easy to generalize this analysis to describe inhomogeneous bimolecular recombination in d-dimensions ... 

Fig. 20 Determination of the coefficient of bimolecular recombination by performing TDCF experiments with variable delay between the excitation pulse and application of the collection bias, (a) Scheme of the experiment, (b) Experimental TDCF photocurrent transients (open squares) measured on a 200 nm thick layer of slow-dried POFTTiPCBM (1 1) during application of different collection biases Fcoii- The collection bias was applied 150 ns after the laser pulse (t = 0 in this graph). Solid lines show fits to the data using a numerical drift diffusion model with constant electron and hole mobilities. A noteworthy observation is that charges can be fully extracted from these layers within a few hundreds of nanoseconds for a sufficiently high collection bias [171]. (c-f) Q-pre, 2coii> and 2,o, plotted as a function of the delay time for as-prepared and thermally annealed chloroform-cast P3F1T PCBM, and with the pre-bias Fpre set either to 0.55 V (near open circuit) or to 0 V (short-circuit conditions) [172]. Solid lines show fits with an iterative model that considers bimolecular recombination of free charges in competition with their extraction...

The kinetics of the A + B - 0 bimolecular reaction between charged particles (reactants) is treated traditionally in terms of the law of mass action, Section 2.2. In the transient period the reaction rate K(t) depends on the initial particle distribution, but as f -> oo, it reaches the steady-state limit K(oo) = K() = 47rD/ieff, where D — Da + >b is a sum of diffusion coefficients, and /4fr is an effective reaction radius. In terms of the black sphere approximation (when AB pairs approaching to within certain critical distance ro instantly recombine) this radius is [74]... 

Because of the limitations imposed by activity coefficients and specific interactions, a precise quantitative check of experimental data against the collision formula presented here is not possible. However, the frequency factors of bimolecular reactions which are diffusion-controlled (i.e., those which occur on nearly every collision) such as free radical recombinations,... 

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