(Xan-Pe2) in which SB-CS competes with excimer formation.50They found that excimer formation occurs irrespective of the solvent polarity indicated by a red shifted, featureless emission and a transient absorption feature in the near infra-red (NIR). In polar solvents, the excimer formation is preceded by SB-CS that, however, ultimately collapses to the excimer illustrating the interference between structural and solvent coordinates.
How this two coordinates interplay and govern the excited-state dynamics and the nature of states that are populated under different interchromphore distances is the question of paper III presented in chapter 5. We will combine the confor-mational control of rigidXan-Pe2and the possibility to sample conformers with larger distances of C3Pe2to get a comprehensive picture of the structure-property relationship for SB-CS.
1.5 Singlet fission
The second multichromophoric process of interest is singlet fission (SF), which is the conversion of a singlet exciton into two lower energy, triplet excitons.51,52 Its technological promise lies in the perspectives to overcome the Shockley Queisser limit and increase the efficiency of single band gap solar cells. In a seminal paper in 1961, Shockley and Queisser described the maximum solar conversion efficiency for a single band-gap photovoltaic cell to be 33.7 %.53 It was assumed that photons with an energy below the band gap (Eg) are not absorbed and photons with a energy> Eg are converted to electricity with a quantum efficiency (QE) of 100 %.
However, the photon energy that exceeds the bandgap,EP hoton−Eg, is lost as heat.
The solar spectrum on the earth (AM 1.5G54) is plotted in Figure 1.5a, illustrating the thermal losses (blue) and non-absorption (red) for the most popular solar cell material, silicon (Eg = 1.1 eV), assuming a QE of 100 %.
Coupling a SF material to a solar cell, can potentially increase the efficiency of those high energy photons by a factor 2. The photon is thereby absorbed by a SF material and split into two low lying triplet excitons, which are separately transferred to the semiconductor, ideally giving two electron-hole pairs. Photons with an energy too low to be absorbed by the SF material are absorbed by the ordinary solar cell material, giving 1 electron-hole pair per photon. In order for SF to be thermodynamically feasible, the energy of the singlet exciton of the monomeric building blocks has to be greater than or equal to twice the triplet exciton energy.a (Figure 1.5b). Furthermore, the key factor for efficient and rapid SF is the conservation of angular momentum during the transition from the photo-populated singlet excited state, to the triplet pair56 (Figure 1.5c). The spins of the two triplets are thereby correlated to a net singlet state (1(TT)), enabling SF on the ps timescale, competitive with radiative and non-radiative decay channels of the chromophores. In contrast to the usually slow ISC to the T1 the conversion of S1S0 to 1(TT) can be interpreted as a special case of internal conversion and
aRecently it has been shown that entropic effects can relax this criterion55
EG
No Absorption Thermal Loss
Si 100% efficiency EG
Ehν -EG
S0 S1
T1 2xT1
S1S0
1(TT)
Energy conservation Spin conservation
a) b) c)
Figure 1.5: a) The theoretical quantum yield in a single band gap solar cell is less than 100 %, due to thermal losses and photons which do not have enough energy to be absorbed. b) Energy conservation for singlet fission (SF) requires the photo-populated singlet state to be at least two times the energy of the monomer. c) In the correlated triplet pair (1(TT)) born from SF, the spins are correlated to a net singlet character rendering SF a spin allowed process.
occurs as fast as∼80 fs in pentacene molecular crystals57and∼700 fs in covalent pentacene dimers58. The overall singlet fission cascade can be described as a three step process:59
S1S0[m(TT)m(T· · ·T)]T1+ T1 (1.3) After population,1(TT) can evolve to 1(T· · ·T) by spatial separation and thus a decrease of electronic coupling and exchange interaction. In a bulk material, spa-tial separation can occur by energy transfer to neighbouring molecules, whereas structural fluctuations are necessary in a covalently linked dimer. Since electronic coupling varies continuously,1(TT) and1(T· · ·T) should be considered as limiting cases and are often merged into a single species, TT. However, different spectral features and dynamics justify the distinction between these two triplet pairs.59,60 In addition to1(TT), the two triplets can also couple to an overall triplet (3(TT)) or quintet state (5(TT)). The four spin states in the two molecules can couple to nine different spin states, 11(TT), 33(TT) and 55(TT).56Inm(TT), the exchange interaction lifts the degeneracy between the different spin states, whereas the ex-change interaction goes to zero in m(T· · ·T). Applying time-resolved electron paramagnetic resonance (EPR) experiments, it has been shown that both 5(TT) and3(TT) can be populated on the ns timescale.61–63
Dephasing or decorrelation is the third step in the mechanistic cascade, describing the loss of spin correlation between the correlated triplet pair by random spin flips and the formation of free triplets (T1+ T1), with the same properties as the T1
state populated by ISC or sensitization studies. This spin conversion has a strong dependence on the coupling between the two sites and therefore on the exchange interaction.63
Depending on the spin character of the correlated triplet pair, two spin-allowed
1.5 Singlet fission 11
Trip-TDI2 Trip-ph-TDI2 Trip-ph2-TDI2
N
Figure 1.6: Chemical structures of bichromophores used to study Singlet Fission.14,65
decay channels further complicate the mechanistic cascade towards T1+ T1:51,64 Singlet channel 1(TT)→S0S0
Triplet channel 3(TT)→T1S0
(1.4) The challenge of developing SF materials is to balance the electronic coupling, which on the one hand increases the rate for internal conversion from S0S1 to the
1(TT), but at the same time also increases the rate of the two parasitic processes shown in equation 1.4. In other words, the sweet spot between triplet pair forma-tion and triplet pair survival to enable the spin conversion to free triplets, has to be found. The SF yield is given by the comparison of the absorbed photons to the populated free triplets, with a theoretical maximum of 200 %.
To study the mechanistic subtleties, covalently linked dimers are often preferred over bulk materials due to the absence of dephasing by energy transfer and the pos-sibility to change the polarity of the environment, which can help to understand the possible influence of the CSS.66 For face-to-face stacked chromophores for which 2ET1≤S1, the diabatic triplet pair state has to be added to the state diagram, in addition to the diabatic LES and CSS (Figure 1.2b and 1.3b). Depending on the type of chromophore, the solvent environment as well as the mutual orientation, the contribution,ci, of the different diabatic states to the lowest energy adiabatic state,|Ψi, differ:
|Ψi=c1(t)|LEAi+c2(t)|LEBi+c3(t)|CSAi+c4(t)|CSBi+c5(t)1(T T) . (1.5) This is elegantly shown by Wasielewski et al. who studied the excited state dy-namics of a series of slip-stacked triptycene-linked terrylenediimide dimers14,65
(Figure 1.6). In Trip-ph-TDI2 and Trip-TDI2, the SB-CS state is populated irrespective of the solvent. However, in Trip-ph2-TDI2, where theπ overlap is the smallest, the triplet features could be observed in apolar toluene indicating a considerable mixing of 1(T T) to the adiabatic state. This features were however absent in polar acetonitrile, illustrating that the SB-CS state can act as trap state hindering SF. Even though this study gives an interesting insight into the popu-lation of the triplet pair as a function of structure, no free triplets are formed due to fast annihilation via the singlet channel.
In paper IV, presented in chapter 6, we will study the structure, solvent polar-ity and viscospolar-ity dependence of a covalently linked bichromophore, in which not only the internal conversion to the triplet pair but also its fate towards the free triplets can be monitored. It therefore gives a comprehensive picture of the whole mechanistic cascade including the parasitic decay channels.