The recombination reaction between injected electrons and molecular acceptors represents an unwanted electron transfer reaction that lowers the light harvesting efficiency of DSSCs. Understanding and impeding these unwanted reactions has been the focus of numerous studies56,38,44,111,113–120, but despite this, interfacial electron transfer reactions remain poorly
understood. An experimental difficulty is relating the observed rate constants, abstracted from time resolved kinetic data, to the actual interfacial electron transfer step. Recombination kinetics are dispersive, stretching from the nanosecond to the microsecond timescales and beyond. A number of explanations have been given to explain the slow recombination kinetics, including the reaction occurring in the Marcus inverted region121–123 and/or that the kinetics
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dominated by electron/hole transport discussed above.124–126 Though often difficult to
understand, the charge rectification imparted by the large discrepancy in the electron injection rate versus that for charge recombination ultimately allows for efficient charge separation and DSSC performance.
Common approaches to modeling charge recombination kinetics are to use a sum of exponential functions127 or a stretch exponential function, also known as the Kohlraush-
Williams-Watts function (KWW) 56,128,129, Equation 1.4. The time required for half the
injected electrons to recombine, t1/2, are often reported in lieu of kinetic modelling.58
∆ = ∆ ( ) (1.4)
Even with extensive kinetic modeling the abstracted rate constants often give little insight into the recombination mechanism.38 The initial reaction conditions can greatly influence the
abstracted rate constants requiring systematic studies, where only a single parameter is intentionally varied, in order to gain meaningful insights into the recombination mechanism.
It is worth noting that a study published by Kelly et al. saw that recombination kinetics between TiO2 and an oxidized Ru sensitizer followed an second-order equal-concentration
kinetic model.108 A single rate constant was abstracted from concentration dependent kinetic
data. Although there are reports of this second-order kinetic model being utilized by other123,
it has not been broadly adopted by the field. In one recent study, Brigham and Meyer monitored charge recombination when an electrochemical bias was applied to sensitized TiO2
electrodes.56 The electrochemical bias was used to establish either an excess of oxidized
sensitizer or electrons in the substrate. This was used to create pseudo-first order conditions for either participant, so that the reaction order could be determined. The kinetics were modeled
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with a KWW function. The concentration of electrons when the oxidized sensitizers were in excess was varied through the laser intensity and its influence on recombination was quantified. The reaction was found to be first order in electrons. The recombination reaction was also found to be first order in oxidized sensitizer when the oxidized sensitizer was in excess.
The application of a light or electrochemical bias can have a significant influence on the recombination rate,58,117,119,130–132 with important ramifications for functional DSSCs.
There are expected to be ~20 electrons in each nanocrystallite at the power point condition.117,133 Under these conditions, Hu et al. showed that the increased charge
recombination rates under these conditions leads to incomplete sensitizer regeneration in functional DSSCs that decreases the devices .117 The connections between electron
concentration and the rate of recombination has led to the development of different recombination models that attempt to rationalize interfacial electron transfer behavior.
Figure 1.10: Contributions from both the charge carrier diffusion thought/across the TiO2 and the
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The increased rate and less dispersive recombination kinetics reported by Durrant et. al has been used to develop several models for charge recombination. These models involve both electron diffusion through the TiO2, invoking a trap/detrap model, and kinetic parameters
governing the electron transfer event.60,101 Electron transfer reactions that are limited by
diffusion are known to follow Equation 1.5, where is the observed electron transfer rate constant, is the diffusion coefficient, is the intrinsic electron transfer rate constant and is an equilibrium, = / .56 As diffusion becomes slow relative to , the reaction is
dominated by diffusion, Figure 1.10. Understanding the diffusional components for charge recombination would likely lead to better insights into interfacial electron transfer.
= + (1.5)
A study Farnum et al. reported charge recombination on sensitized indium doped tin oxide (ITO) nanocrystalline thin films.134 Unlike TiO
2, ITO is metallic in nature without a
forbidden energy gap, i.e. bandgap, between the valence and conduction bands. This allows rapid electron transport. The recombination processes for these films were monitored over a series of applied potentials, with the difference between the applied potential and the Ru3+/2+
reduction potential was taken to be the driving force for the reaction. The rate constants found followed Marcus-Gerisher theory. It is likely that similar kinetics would be observed for TiO2
films if the diffusional contribution to recombination was eliminated or minimized.
Ultimately, charge recombination represents an unwanted process in DSSCs. Several tactics have been employed to slow charge recombination. Surface passivation with insulating layers applied by atomic layer deposition represents one of the most prevalent methods.135–137
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Molecular approaches have also be employed to slow recombination to molecular sensitizers22,53,90,116,138,139 Extending the distance between the TiO
2 and the sensitizer can also
slow charge recombination,89,138 but may also lower the quantum yield for electron injection,
as the increased distance lowers electronic coupling between the excited-sensitizer and the TiO2.37,140 To avoid this, dyad systems are often employed, where a sensitizer is covalently
linked to an electron donating moiety. After injection, the sensitizer rapidly transfers the hole to the acceptor, increasing the distance between the acceptor and the interface.90,118 In some
cases, this approach can greatly slow charge recombination relative to simple sensitizer systems. Molecular bridges between the donor and acceptor were recently shown to influence recombination, suggesting a through bond recombination mechanism.118