Recombination, geminal

When the motion of electrons and positive ions in a particular system may be described as ideal diffusion, the process of bulk recombination of these particles is described by the diffusion equation. The mathematical formalism of the bulk recombination theory is very similar to that used in the theory of geminate electron-ion recombination, which was described in Sec. 10.1.2 ( Diffusion-Controlled Geminate Ion Recombination ). Geminate recombination is described by the Smoluchowski equation for the probability density w(r,i) [cf. Eq. (2)], while the bulk recombination is described by the diffusion equation for the space and time-dependent concentration of electrons around a cation (or vice versa), c(r,i). 

There are two kinds of recombination of relevance to photoreceptors, geminate and bimolecular recombination. Geminate recombination is the recombination of a Coulombically bound electron-hole pair. The photogeneration efficiencies of most organic solids are believed controlled by geminate recombination. Bimolecular recombination is the recombination of a free electron and free hole. 

Two types of ion are involved in ion recombination. Geminate ions, which constitute 90 % of the total, recombine within a few nanoseconds since the positive and negative ions which are formed do not escape each others influence. The other 10 % of the ions do escape each others influence and are termed free or non-geminate. They recombine over microsecond time scales. The high percentage of geminate ions in hexane explains why non-polar solvents support high yields of excited states and low yields of radical ions. 

In an all-polymer system, the excitons generate in the donor phase after the absorption of photons in active layer and then transform to the charge-transfer state, which will dissociate into free charge or recombine geminately. Those two processes compete with each other. A promoted efficiency of OSCs requires the inhibition of geminated recombination and the transformation of more excitons into free charges [134,135]. 

In order to answer this question, Mihailetchi et al. [39] measured photogeneration in a blend of poly(2-methoxy-5-(3, 7 -dimethyloctyloxy)-phenylene vinylene (OCICIO-PPV) and PCBM as function of applied voltage and temperature. Presuming that the essential intermediate is an optically generated coulombically bound e-h pair located at an internal donor-acceptor hetero-junction that can either dissociate completely or recombine geminately, they analyzed their data in terms of Braun s model [22]. Based upon a broad distribution of e-h pair distances centered at 1.3 nm and invoking a value of 1 [is for the e-h pair lifetime they were able to rationalize their experimental results that include a measured 60% carrier yield at a built-in field of 7.5 X 10 Vcm at room temperature. However, an open question appears to be their choice of a pair lifetime of 1 [is. Recent experiments on a blend of a polyfiuo-renecopolymer and PCBM reveal a broad distribution of lifetimes albeit centered at a value as short as 1 ns [40]. 

The most optimal conditions for monitoring quantum beats are in non-polar solvents for the following reasons [7] (1) the separation of the radial pair is usually much less than the Onsager radius and the radical ion pairs recombine geminately (2) a strong luminescence signal can be observed due to the small solvation energy ... 

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