A method to rapidly predict the injection rate in Dye Sensitized Solar Cells

1
A method to rapidly predict the injection rate in
Dye Sensitized Solar Cells

• Daniel R. Jones and Alessandro Troisi
• PG Symposium 2009

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Outline

• Introduction
• What is a dye sensitized solar cell?
• How can theory help?
• Theory
• How do we compute the rate of electron transfer?
• Results
• The rate of injection by this method.
• Continuations
• Where do we go from here?

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Dye Sensitized Solar Cell
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Dye Sensitized Solar Cell

• Attractive third-generation solar technology
  offering up to 11 IPCE
• Cheap material and processing costs mean that it
  may compete with fossil fuels in terms of W/
• Ideally needs to be more efficient to increase
  uptake.
• Liquid electrolyte is not ideal

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How can theory help?

• Designing the optimum chromophore is still an
  active area of research
• Screen candidate molecules for their potential
• Minimize efficiency losses
• Better understanding of the electron transfer
  reaction mechanisms
• Aspire to a multiscale model of the functioning
  cell

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Goal

• To provide a method to screen candidate molecules
  for their potential in dye sensitized solar cells
  (DSSC) which is
• computationally inexpensive
• not reliant on experimental parameterization
• Compute the rate of electron transfer from the
  photoexcited chromophore into the conduction band
  of the TiO2

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For example

• Li et al investigated Anthraquinone dyes1
• Found they produced cells with efficiency worse
  than that of naked TiO2
• Chemical intuition does not always work
• Can we do better by computational screening?

1 Li et al. Solar Energy Materials and Solar
Cells 2007, 91, 1863-1871.
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Outline

• Introduction
• What is a dye sensitized solar cell?
• How can theory help?
• Theory
• How do we compute the rate of electron transfer?
• Results
• The rate of injection by this method.
• Continuations
• Where do we go from here?

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The Method
1)
2)
3)
Chromophore dye system modelled by separating
into 3 subsystems
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The Method

• It can be shown that the effective Hamiltonian
  for the state can be written
• The self energy, S, is complex, and can be
  separated into real and imaginary components
• The imaginary part of self energy, Gs, can be
  calculated using

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The Method

• To compute the coupling terms, Vsl, the states on
  the semiconductor and the states on the
  chromophore are recast in an atomic basis set
• The energy dependent density matrix ?kk.
• The self energy on the molecule in an atomic
  basis set
• The self energy on the first excited state

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The Method
1)
Csm, E
2)
Gmn
Vmk
3)
?kk
Chromophore dye system modelled by separating
into 3 subsystems
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Coupling - Vsm
Rutile (110) surface Ti-O(mol) 2.07 Å
Ti-Ti-O(mol) 80
Anatase (101) surface Ti-O(mol) 2.16
Å Ti-Ti-O(mol) 70
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Computing ?kk

• Electronic structure computed using B3LYP/6-31G.
• Clusters embedded in a volume of point charges to
  model bulk electrostatics.

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Chromophore

• Chromophores electronic structure and geometry
  computed using B3LYP/6-31G
• csm comes from the DFT output
• The energy of injection, E, can be approximated
  in one of 2 ways.
• Using the energy of the LUMO
• Take the difference between the energy of the 1st
  excited state from TD-DFT and the energy of the
  cation.

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Outline

• Introduction
• What is a dye sensitized solar cell?
• How can theory help?
• Theory
• How do we compute the rate of electron transfer?
• Results
• The rate of injection by this method.
• Continuations
• Where do we go from here?

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Variation of rate with injection energy
E in this range
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Real Chromophores realistic rates?
b)
a)
Dye rutile (110)/ fs anatase(101) / fs
a 2.83 1.43
b 56.7 53.9
c 2.25 0.18
d 1.81 5.96
e 3.58 6.20
f 9.99 4.09
d)
c)
f)
e)
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Molecular Engineering?

• Perylene derivatives
• Substitution at the 2 position means the LUMO is
  less localised on the carboxylic acid group.
• Rutile (110) lifetimes

27.3 fs
12.3 fs
7.99 fs
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Importance of injection energy

• Rapid variation of injection rate with changing
  energy.
• Energy of injection computed using the LUMO
  energy of the neutral chromophore compared to
  that computed using ETDDFT-ECation differ by 1.5
  eV

2.83 fs

• Computed rate using ELUMO and ETDDFT-ECation
• Qualitatively different, the more sophisticated
  computation matches much better with experimental
  evidence

2260 fs
56.5 fs
195 fs
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Conclusions and closing remarks

• We have developed a method to rapidly compute the
  rate of electron transfer from chromophore to
  semi-conductor in DSSC
• We note the importance of choosing the correct
  injection energy
• Our method may be improved by aligning the energy
  levels with experiment
• This method is modular, so may be improved
  relatively easily if more accurate computations
  for any of the subsystems are available

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Outlook

• All chromophores considered so far have been
  connected by a carboxylic bridge, consider other
  anchoring groups
• Compute the rate of recombination, where an
  electron in the conduction band neutralises the
  chromophore, more difficult to guess
  qualitatively
• Try to find better ways to treat the
  semiconductor surface
• Write a thesis

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Acknowledgements

• Alessandro Troisi
• His group, past and present
• Dave Cheung, Natalia Martsinovich,
• Arijit Bhattacharyay, Sara Fortuna,
• Dave McMahon, Jack Sleigh, Konrad Diwold
• EPSRC and University of Warwick for funding.
• and you for your attention