Thesis
Reference
Excited-state dynamics in electron-donor-acceptor systems of increasing complexity
YUSHCHENKO, Oleksandr
Abstract
Excitation energy transfer and charge separation are crucial steps in natural photosynthesis that allows the conversion of solar light into chemical energy. Understanding the nature of these processes is determinant for designing efficient synthetic analogues of these natural systems. This thesis describes ultrafast spectroscopic studies of the excited-state dynamics several systems, from simple molecules to multichromophoric systems, which are based on various chromophores arranged according to different motifs. To better understand the properties of these complex multichromophoric systems, systematic investigations of the individual units and model systems of different complexity have been performed. It allowed key factors enhancing the efficiency of excitation energy transfer and charge separation to be determined. The investigation of these processes in real time has been realized using various time-resolved techniques, which permit monitoring process occurring on timescale ranging from a few tens of femtosecond to several hundreds of microseconds.
YUSHCHENKO, Oleksandr. Excited-state dynamics in electron-donor-acceptor systems of increasing complexity . Thèse de doctorat : Univ. Genève, 2017, no. Sc. 5060
URN : urn:nbn:ch:unige-938222
DOI : 10.13097/archive-ouverte/unige:93822
Available at:
http://archive-ouverte.unige.ch/unige:93822
Disclaimer: layout of this document may differ from the published version.
UNIVERSITÉ DE GENÈVE FACULTÉ DE SCIENCES Section de chimie et biochimie
Département de chimie physique Professeur Eric Vauthey
Excited-State Dynamics in Electron-Donor-Acceptor Systems of
Increasing Complexity
THÈSE
présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention chimie
par
Oleksandr YUSHCHENKO
de
Vinnytsia (Ukraine)
Thèse No 5060
GENÈVE Atelier ReproMail
2017
An expert is a person who has made all the mistakes that can be made in a very narrow field.
Niels Bohr
Remerciements
La recherche couverte dans cette thèse a été réalisée au département de Chimie Physique de l’Université de Genève (Suisse) sous la supervision du Professeur Eric Vauthey. Je voudrais le remercier de m'avoir donné l'occasion de réaliser ma thèse dans son groupe, ainsi que pour sa supervision, son assistance, ses discussions perspicaces sur la recherche que nous avons eu, et finalement pour sa patience à toutes les difficultés que j'ai eues pendant mon doctorat. Ses conseils m'ont aidé tout au long de la recherche et de l'écriture de cette thèse.
En plus de mon directeur de thèse, j'aimerais remercier le reste de mon comité de thèse: la Prof. Natalie Banerji (Université de Fribourg, Suisse) et le Prof. Andreas Hauser (Université de Genève, Suisse) pour leurs excellents commentaires et le temps qu'ils ont passé à lire ce mémoire, mais aussi pour la discussion et les idées qui ont été extrêmement précieuses.
Ce travail n'aurai pas été possible sans toutes les personnes avec lesquelles j'ai eu la chance de collaborer aussi bien à l'Université de Genève, qu'à d'autres endroits du monde. Merci au groupe du Prof. Stefan Matile (Université de Genève), au groupe du Prof. S. V. Bhosale (Université RMIT, Melbourne), au groupe du Prof. Oliver S. Wenger (Université de Bâle), et au groupe du Prof. Andreas Hauser (Université de Genève).
Je tiens également à remercier tous les membres actuels et anciens du groupe avec lesquels j’ai travaillé: pour leur collaboration, des discussions stimulantes, de longues heures dans le laboratoire, et pour tout le plaisir que nous avons eu durant ces années.
Je voudrais remercier particulièrement notre technicien Didier Frauchiger pour l'aide remarquable avec le travail mécanique, et Sophie Jacquemet pour sa grande aide concernant les questions administratives.
Enfin, je remercie mon épouse, Diana, qui m'a toujours soutenu pendant tout ce temps. Son encouragement, sa patience et son amour m'ont aidé à traverser cette période de la manière la plus positive. Sa tolérance totale à mes heures irrégulières à la maison, quand je restais tard à l'Université, m'a permis de passer la plupart du temps sur cette thèse.
Table of Contents
Chapter 1 Introduction ... 1
Chapter 2 Fundamentals of Photophysics and Photochemistry ... 3
2.1 Introduction ... 3
2.2 Photophysical Processes ... 5
2.2.1 Non-radiative Processes ... 7
2.2.2 Radiative Processes ... 8
2.3 Photoinduced Energy and Electron Transfer Processes ... 9
2.3.1 Energy Transfer ... 10
2.3.1.1 Coulombic Mechanism ... 11
2.3.1.2 Exchange Mechanism ... 14
2.3.2 Electron Transfer ... 15
Chapter 3 Experimental Part ... 21
3.1 Nonlinear Optics ... 21
3.1.1 Second-order Nonlinear Optics ... 22
3.1.2 Third-order Nonlinear Optics ... 24
3.1.3 Optical Pulses ... 25
3.2 Steady-State Spectroscopy ... 26
3.3 Time-Resolved Fluorescence ... 26
3.3.1 Time-Correlated Single Photon Counting ... 27
3.3.2 Fluorescence Up-conversion ... 28
3.4 Transient Absorption ... 29
3.4.1 Principles ... 29
3.4.2 Setups ... 31
3.4.2.1 Femtosecond Transient Absorption ... 31
3.4.2.2 Sub-nanosecond Transient Absorption ... 33
3.4.3 Data Analysis ... 35
3.5 Samples ... 37
3.5.1 Solvents ... 37
(Chapter 5) ... 37
3.5.4 Porphyrin-Naphthalenediimide Dyads (Chapter 6) ... 37
3.5.5 Porphyrin-Naphthalenediimide Arrays (Chapter 7) ... 38
3.5.6 Benzodifuran Based Triads (Chapter 8) ... 38
3.5.7 Triarylamine and Ru(bpy)3 2+ dyads (Chapter 9) ... 38
3.5.8 An Anthraquinone-[Ru(bpy)3]2+-Oligotriarylamine- [Ru(bpy)3]2+-Anthraquinone Pentad (Chapter 10) ... 38
Chapter 4 Naphthalenediimides ... 39
4.1 Introduction ... 39
4.2 Steady-State Spectroscopy ... 41
4.3 Transient Absorption ... 42
4.3.1 rNDI ... 42
4.3.1.1 S1 ← S0 Excitation ... 43
4.3.1.2 S2 ← S0 Excitation ... 46
4.3.2 pNDI ... 48
4.4 Quantum Chemical Calculations ... 51
4.5 Discussion ... 54
4.6 Conclusion ... 56
Chapter 5 Naphthalenediimide Triad in Solution and of Solid Films ... 58
5.1 Introduction ... 58
5.2 Steady-State Spectroscopy ... 60
5.3 Time-Resolved Fluorescence ... 63
5.4 Transient Absorption ... 66
5.4.1 Triad ... 66
5.4.2 SOSIP ... 73
5.5 Discussion ... 77
5.6 Conclusion ... 81
Chapter 6 Porphyrin-Naphthalenediimide Dyads ... 83
6.1 Introduction ... 83
6.2 Steady-State Spectroscopy ... 84
6.3 Time-Resolved Fluorescence ... 89
6.4 Transient Absorption ... 95
6.4.1 ZnP-HNDI in Toluene ... 95
6.4.2 ZnP-HNDI in THF ... 99
6.4.3 FbP-HNDI ... 102
6.5 Discussion ... 109
6.6 Conclusion ... 116
Chapter 7 Photophysics of Porphyrin-Naphthalenediimide Arrays ... 118
7.1 Introduction ... 118
7.2 Steady-State Spectroscopy ... 119
7.3 Time-Resolved Fluorescence ... 120
7.4 Transient Absorption ... 122
7.4.1 Transient Absorption Measurements in THF ... 122
7.4.2 Transient Absorption Measurements in Toluene ... 127
7.5 Conclusion ... 131
Chapter 8 Benzodifuran Based Triads ... 133
8.1 Introduction ... 133
8.2 Steady-State Spectroscopy ... 135
8.3 TPA-BDF-TPA ... 136
8.3.1 Steady-State and Time-Resolved Fluorescence Measurements ... 136
8.3.2 Transient Absorption Measurements ... 138
8.4 AQ-BDF-AQ ... 139
8.4.1 Steady-State Measurements ... 139
8.4.2 Transient Absorption Measurements ... 140
8.5 AQ-BDF-TPA ... 142
8.5.1 Steady-State Measurements ... 142
8.5.2 Transient Absorption Measurements in cyclohexane ... 143
8.5.3 Transient Absorption Measurements in THF ... 144
8.6 TCAQ-BDF-TCAQ ... 146
8.6.1 Steady-State Measurements ... 146
8.6.2 Transient Absorption Measurements ... 147
8.7 TCAQ-BDF-TPA ... 148
8.7.1 Steady-State Measurements ... 148
8.7.2 Transient Absorption Measurements ... 148
Chapter 9 The Role of the Bridge in a Donor-Bridge-
Acceptor System ... 151
9.1 Introduction ... 151
9.2 Steady-State Spectroscopy ... 152
9.3 Transient Absorption ... 153
9.3.1 Femtosecond TA Measurements ... 153
9.3.2 Sub-nanosecond TA Measurements ... 156
9.4 Discussion ... 159
9.5 Conclusion ... 161
Chapter 10 Photoinduced Accumulation of Multiple Electrons ... 162
10.1 Introduction ... 162
10.2 Steady-State Spectroscopy ... 163
10.3 Transient Absorption ... 164
10.3.1 Femtosecond TA Measurements ... 164
10.3.2 Sub-nanosecond TA Measurements ... 170
10.4 Conclusion ... 175
Chapter 11 General Conclusions ... 176
References ... 179
Appendices
Appendix A: Résumé de la Thèse ... 198Appendix B: List of Publications ... 202
Chapter 1
Introduction
At the time of the world’s increasing demand for energy, it is not surprising that scientists are looking for new effective methods of energy conversion. For this reason they turned to one of the best-known consultant, nature. In nature, plants efficiently convert the sunlight into chemical energy by using photosynthesis. For this purpose, plants use highly organized photosystems. These systems are based on light-harvesting antennas that are built from a large number of identical, self-organized chlorophylls, which absorb light energy and transfer it to the photosynthetic reaction center, where electron-hole separation occurs. In such a way, natural photosynthesis depends crucially on light absorption, excitation energy transfer and charge separation processes for efficient solar energy conversion. For this reason over the past years, a lot of efforts have been invested into the development of molecular systems aimed to mimic the function of the photosynthetic systems. The design of such artificial systems involves two important steps:
the collection of light over a wide spectral range and the population of a long-lived charge-separated state. Understanding of these concepts has motivated scientists and engineers to design assemblies with similar properties that eventually can provide the knowledge and technology necessary to construct artificial devices for solar energy conversion. Thus, it became the fundamental basis for photovoltaic technologies.
Despite the rapid development of photovoltaic industry, there is still a limited understanding of the fundamental photophysics and photochemistry of artificial systems, since most of the work has been mainly focused on
material development and device optimization. For this reason, our goal was to investigate the processes following photoexcitation, a better understanding of which is necessary for an optimal design of efficient architectures for photovoltaic devices. In order to obtain insights into the nature of these processes, a variety of multichromophoric systems were synthesized by our colleagues, and investigated by us using spectroscopic methods.
In the next chapter, we will briefly review the fundamentals of photophysical and photochemical processes that are dominant in the explored systems after absorption of light. As energy and electron migration are among the fastest events in chemistry, and are taking place on time scale ranges from tens of femtoseconds to few nanoseconds. This is why time- resolved spectroscopy has been applied as a main tool to monitor the dynamic of these processes in a real time. The principles and the experimental details of the techniques used during the thesis will be described in Chapter 3. In the following chapters, the main projects carried out during my thesis will be presented. We will start our discussion with the excited-state dynamics of small molecules (Chapter 4), which are later on used as active units in more complex systems that can find potential applications in solar energy conversion (Chapter 5). Besides that, we will examine intramolecular photoinduced charge transfer in other systems, dyads (Chapter 6), triads (Chapter 8), and a pentad (Chapter 10). In Chapter 9, we will take a deeper look at the effect of the bridge on the electron transfer processes in donor-bridge-acceptor systems, while in Chapter 7 we will explore how the rate of charge separation is affected by increasing the number of acceptor attached to an electron-donor.
Chapter 2
Fundamentals of Photophysics and Photochemistry
2.1 Introduction
This chapter provides an introduction to the photophysical and photochemical fundamentals required for a better understanding of the results that are discussed in this thesis. In general, both photophysics and photochemistry deal with interaction of light with matter, however photophysics is focused on physical changes caused by such type of interaction, while photochemistry on the further provoked chemical reactions. The first law of photochemistry (Grotthuss-Draper law) states that only absorbed light is effective in photophysical and/or photochemical transformation.1 According to quantum theory, light exhibits properties of both waves and of particles. In this case, light can be defined as a composition of particles known as photons, the energy (𝐸) of each is given by the Planck-Einstein relation:
𝐸=ℎ𝜈=ℎ𝑐
𝜆 (2.1) where ℎ is the Planck’s constant, 𝜈 the frequency of the light, 𝜆 its wavelength, and 𝑐 is the speed of light.
According to Bohr’s postulate, for light to be absorbed, the photon
energy has to match the energy difference between two possible energy levels of the atom:2
∆𝐸=𝐸!!"!!"−𝐸!"#$%=ℎ𝜈 (2.2) It is usually the energy spacing between the lowest energy level (𝐸!"#$%), called ground state, and any of its higher energy state (𝐸!!"!!").
The value that measures how much of the entered light has been absorbed called optical transmittance (𝑇):
𝑇(𝜆)= 𝐼(𝜆)
𝐼!(𝜆) (2.3) where 𝐼(𝜆) and 𝐼!(𝜆) are the incident and transmitted intensity of the radiant light at the given wavelength, respectively. However, most spectrophotometers give their results in optical absorbance (𝐴), or optical density (OD), which is defined as:
𝐴 𝜆 =𝑙𝑜𝑔1/𝑇 𝜆 =𝑙𝑜𝑔𝐼!(𝜆)
𝐼(𝜆) (2.4) The proportion of the light that is absorbed depends also on how many molecules are interacting with it, and is expressed in the linear relation known as the Beer-Lambert law:
𝐴 𝜆 =𝜀 𝜆 𝑐𝑙 (2.5) where 𝜀 𝜆 is a wavelength-dependent proportionality constant called molar absorptivity or molar absorption coefficient, 𝑐 and 𝑙 are the concentration and the optical pathlength in the solution.
Another factor that determines the probability of absorption between two states is the interaction between the light and the transition dipole moment of the molecule. The optical electric field interact with the charges distributed over the molecule inducing oscillations in the electron density that act as a transition dipole moment, and cause the system to exchange energy with the light. The transition dipole moment can be expressed as:
2.2 Photophysical Processes
𝜇!" = 𝜓!𝜇𝜓!𝑑𝜏 (2.6)
where 𝜓! and 𝜓! are the wavefunctions of the initial and final states, respectively, and 𝜇 the molecular dipole operator. A transition between two states occurs if it is associated with a non-zero transition dipole moment 𝜇!".
The square of the transition moment is proportional to the oscillator strength (𝑓):1
𝑓=8𝜋!𝑚!𝜈!"
3ℎ𝑒! 𝜇!"! ≈4.7×10!!𝜈!"𝜇!" ! (2.7)
where 𝑚! and 𝑒 are the mass and the charge of the electron, respectively, 𝜈!"
is the frequency of the transition. The oscillator strength is an important quantity in spectroscopy that allows to measures the intensity or probability of an optical transition. Also, it is related to the integrated absorption band of a transition, and thus can be determined experimentally through the molar extinction coefficient (𝜀):
𝑓=4.3×10!! 𝜀(𝜈)𝑑𝜈 (2.8)
2.2 Photophysical Processes
Thus, according to equation 2.2 the energy acquired by a molecule due to absorption of a photon causes a molecule to be promoted to a higher electronic energy level called excited state. The general scheme that illustrates processes, which are taking place after molecule has been excited, is called Jablonski diagram. This diagram represents the electronic states of a system and the transitions between them, like one depicted in Figure 2.1.
Here, the electronic states are represented by thick horizontal lines, while
vibrational states by thin lines.* Singlet (S) and triplet (T) states refer to the spin multiplicity of the electronic state and are collected in separate columns.** All states are arranged in vertical order and indicate the relative energies each, and are labeled consecutively by increasing energy, where S0
is the singlet ground state, and v = 0 is the lowest vibrational state.
Figure 2.1 Jablonski energy diagram describing molecular energy levels and possible transitions between different singlet and triplet states: absorption, internal conversion, vibrational relaxation (VR), intersystem crossing (ISC), fluorescence and phosphorescence processes.
The first process is the absorption of a photon of a particular energy by the molecule. The following photophysical processes can be radiative or radiationless transitions between different states, and commonly indicated as straight and wavy arrows on Jablonski diagram, respectively.
* Usually only a fraction of these vibrational states are presented due to a vast number of possible vibrations levels in a molecule. Additionally, in the gas phase each of these states can be subdivided even further into rotational energy levels, however, usually such levels are omitted in Jablonski diagrams.
** Note that horizontal displacement does not indicate a change in structure, and is only used to group states by their spin multiplicity.
2.2 Photophysical Processes
2.2.1 Non-radiative Processes
Let us follow now the processes that are taking place after a system has been excited to a higher electronic and vibrational state. Such state usually called “hot”. Once the system is there, it will slowly relax to the lowest vibrational level by giving the excess energy away to other vibrational modes within the same molecule, or transferred to the surrounded molecules. In a condensed medium, there are many collisions between the molecule and its environment, so the excess vibrational energy is converted into heat, which can be easily absorbed by neighboring “cold” solvent molecules. This process is very fast and typically occurs on the order of 10-12 s, thus it has a high probability to occur first after a photon has been absorbed.3
Further relaxation requires the intramolecular transformation of electronic energy into vibrational energy, and takes place when the lowest vibrational level of a higher state overlaps with the highest vibrational levels of the lower state. This process called internal conversion (IC) when the molecular spin remains the same, and intersystem crossing (ISC) when it changes. In most cases the separation between energy states, which are greater than the lowest excited sate, is small, and gives a high degree of coupling between vibrational and electronic levels. That is why a spin- allowed IC occurs with a high probability and in the same time frame as vibrational relaxation (VR). The rate constants of such transitions have been established both theoretically and experimentally and known as the energy gap law, which states that non-radiative decay rate increases exponentially as the energy gap decreases.4
At the same time, ISC is usually forbidden by the rule of conservation of angular momentum, as it involves a change of spin multiplicity. As a result, this process generally occurs on very long time scales. However, El-Sayed’s rule states that the rate of ISC is relatively large if the radiationless transition involves a change of molecular orbital type, e.g.
the nπ* → ππ* transition (Figure 2.2).5 In such case the change of spin is compensated by change of the orbital angular momentum keeping the total angular momentum constant. The required spin flip is achieved by the action of a magnetic field invoked by spin-orbit coupling.6 Spin-orbit coupling is enhanced in the presence of heavy atoms that is known as the heavy atom
effect.
Figure 2.2 Schematic representation of the El-Sayed’s rules for ISC.
2.2.2 Radiative Processes
As discussed above, the separation between the lowest electronic state and the ground state is usually greater than between higher states, additionally there is a poor overlap between vibrational and electronic states, thus IC and ISC to the ground state becomes relatively slow. Such slow down recovery permits other processes compete with IC (or ISC) from the lowest excited state, one of which is the return to the ground state by emission of light. This process is called fluorescence when it occurs between two states of same multiplicity, and phosphorescence when the multiplicity is different. The ultrashort lifetime of upper electronic excited states and the long lived lowest excited state underlie the Kasha-Vavilov’s rule that states that emission takes place from the lowest electronic excited state, namely the S1 and T1 states, and that the emission quantum yields do not depend on the excitation wavelength.7 There are many exceptions, however, like azulene that emits mostly from the S2 state.
The efficiency of emission is characterized by the quantum yield (QY) of luminescence.8 It is defined as the ratio of photons absorbed to photons emitted. The QY of fluorescence can come close to 1, while the phosphorescence is usually weak because it is spin-forbidden process thus its rate is much smaller than the rate of radiationless deactivation.
Also, luminescence QY can be defined by the rate of excited state decay:
Ф= 𝑘! 𝑘!
! (2.9)
2.3 Photoinduced Energy and Electron Transfer Processes
where 𝑘! is the luminescence (or radiative) rate constant, and !𝑘! is the sum of all radiative and non-radiative decay rates of the excited state. Rate constants are inverse of time constants, for example the radiative (𝜏!) and the excited-state (also called fluorescence, 𝜏!) lifetimes are expressed as:
𝜏! = 1
𝑘!, 𝜏!= 1 𝑘!
! (2.10)
2.3 Photoinduced Energy and Electron Transfer Processes
As we have just seen, the decay of an excited molecule is characterized by the sum of its own rate constants given by equation 2.10.
Such electronically excited state is highly reactive, and when the above discussed intramolecular deactivation processes are sufficiently slow, an excited molecule (A*) may interact with another molecule or species (B). In such a case, new deactivation pathways of an electronically excited state that lead to the dissipation of energy can be operative.
All the systems explored in this thesis are multichromophoric (or supramolecular). That is why we will concentrate more on the processes occurring in such systems, namely on those containing of two or more units, the excitation of which leads to an excited state that is substantially localized on one of them. It may causes to the energy migration with or without the transfer of an electron from one unit to another (equations 2.11-2.14, for simplicity, two unit A-B supramolecular system is considered, where A is the light-absorbing molecular unit, and B is another involved in the light induced processes). Such systems can be imagined as an assembly of weakly interacting molecular components, the properties of which are similar to the isolated components, and oxidation-reduction properties of a supramolecular species can substantially be described as the oxidation and reduction of the individual species. However it is important to note that the relative positions between the two redox centers can be affected by the interunits interactions and so influence the dynamics of the process.9
𝐴−𝐵+ℎ𝜈→𝐴∗−𝐵 photoexcitation (2.11)
𝐴∗−𝐵→𝐴!−𝐵! oxidative electron transfer (2.12)
𝐴∗−𝐵→𝐴!−𝐵! reductive electron transfer (2.13)
𝐴∗−𝐵→𝐴− ∗𝐵 electronic energy transfer (2.14)
2.3.1 Energy Transfer
Energy transfer is very important process in nature and technology, as it allows to obtain an excited state not only due a direct absorption of light, but also through transferring electronic energy from other excited species that has absorbed the light in the first place. It permits excitation of molecules that do not absorb the incident light. The common examples can be found in the photosynthesis, where the energy is absorbed by the light harvesting antennas and transferred to the photosynthetic reaction center.10 For this, the energy level of the excited state of A* has to be higher than that of B*, additionally the time scale of the energy transfer process has to be faster than the lifetime of A* to compete with the deactivation processes.
Energy transfer processes can be viewed as a radiationless transition between two ‘‘localized’’, electronically excited states (equation 2.14), and the rate constant (𝑘!!") can be described through an expression depending on the coupling between the two states, known as Fermi's golden rule:
𝑘!!" =4𝜋!
ℎ 𝑉!" !𝜌!" (2.15) where 𝑉!" is the electronic coupling between the two units, and 𝜌!" is the density of states at the energy of the transition. The total interaction energy can be expressed as a sum of two terms: a Coulombic term (𝑉!) and an exchange term (𝑉!"). The two terms have different dependence on the parameters of the system and thus one of them can become predominant.
That is why we will now discuss the two mechanisms for energy transfer separately.
2.3 Photoinduced Energy and Electron Transfer Processes
2.3.1.1 Coulombic Mechanism
If the interunit distances are much larger than the sizes of the individual unites, the Coulombic term, representing the dipole-dipole interaction between the transition moments of A* and B, predominate. It does not require physical contact between A and B, and can be imagined as two coupled transitions (Figure 2.3). In this case an energy matching between two states is required. This energy matching is similar to the one required for light to be absorbed, and is referred to as a resonance condition (section 2.1).
Figure 2.3 Schematic representation of EET by the Coulombic (Förster) mechanism.
Förster quantified the efficiency of the dipole-dipole induced electronic energy transfer process. Therefore this mechanism is associated with his name as Förster resonance energy transfer (FRET). Förster derived his famous expression for the rate constant (𝑘!) from classical consideration, i.e. the interaction between two dipoles, and the Fermi's golden rule, when showing 𝑘! is proportional to 𝑉!"! (equation 2.15). In the Förster theory, the excited donor is treated as an oscillating dipole that undergoes an energy exchange with the dipole of the acceptor with a similar resonance frequency.
The interaction energy between two dipoles in a dielectric medium is given by (A is designated the donor and B the acceptor):
𝑉!" =𝑉!= 𝑓!!
4𝜋𝜀!𝜀!"
𝜇!𝜇!
𝑟!"! 𝜅 (2.16) where 𝜀! is the permittivity of vacuum, 𝜀!"≃𝑛!is the dielectric constant at optical frequencies, 𝑛 being the refractive index of the solvent, 𝑓!=(𝜀!"+ 2)/3 is the Lorentz local field correction factor, 𝜇! and 𝜇! are the transition
dipole moments of the donor and the acceptor, respectively, 𝑟!" is the distance between the two dipoles, and 𝜅 the orientation factor.
The orientation factor (𝜅) describes the influence of the orientation of the donor’s dipole relative to the acceptor’s dipole, and is defined by equation 2.17:
𝜅=𝑐𝑜𝑠𝜃!"−3𝑐𝑜𝑠𝜃!𝑐𝑜𝑠𝜃! (2.17) where 𝜃!! is the angle between the two transition moments, 𝜃! and 𝜃! are the respective angles between these dipoles and the intermolecular vector 𝑅 (Figure 2.4). Depending on the relative orientation of the transition dipole moments 𝜇! and 𝜇!, 𝜅! can range from 0 (when the dipoles are perpendicular) to 4 (for collinear transition dipoles). In general, 𝜅! is assumed to be 2/3, which is the value for randomly oriented dipoles.
Figure 2.4 Angles defining the orientation factor κ.
The final expression for the rate constant (𝑘!) was obtained by combining the equations 2.15 and 2.16. Here, Förster expressed the density of states (𝜌!") as the overlap integral (Θ) between acceptor absorption spectrum and the area-nomalised donor emission spectrum, 𝜇! through the radiative rate constant (𝑘!"#), 𝜇! in terms of the oscillator strength of the transition and the molar extinction coefficient (equation 2.7):
𝑘!=9ln (10)𝜅!Ф!!𝑘!!
128𝜋!𝑁!𝑛!𝑟!"! Θ (2.18) where Ф!! is the fluorescence quantum yield of the donor in the absence of transfer, 𝑘!! is the decay rate constant of the donor in the absence of acceptor unit and the inverse of the time constant 𝑘!! =1/𝜏!!, 𝑁! is Avogadro’s constant. The spectral integral Θ is defined as:
2.3 Photoinduced Energy and Electron Transfer Processes
Θ= 𝐹!(𝜈)𝜀!(𝜈)𝜈!!𝑑𝜈
𝐹!(𝜈)𝑑𝜈 (2.19) where 𝐹!(𝜈) is the emission spectrum of the donor and 𝜀! is the molar absorption coefficient of the acceptor, and ν represents units of frequency in cm-1.
Since the rate of energy transfer depends on the rate of excited donor state population relaxation, therefore it is commonly written as:
𝑘!=𝑘!! 𝑅! 𝑟!"
!
(2.20)
here 𝑅! is the critical distance or Förster radius, expressed as:
𝑅!! =9 𝑙𝑛10 𝜅!Ф!!
128𝜋!𝑁!𝑛! Θ (2.21) When the distance 𝑅=𝑅!, then 𝑘! =𝑘!! , thus energy transfer and spontaneous decay of the excited donor are equally probable.
However, in this thesis we have chosen to represent the energy transfer rate constant via an overlap integral of normalized absorption and fluorescence spectra and the interaction between electronic states:11
𝑘!=1.18𝑉!Θ′ (2.22) here 𝑘! is expressed in ps-1, 𝑉 in cm-1, and Θ′ is the overlap integral between the donor fluorescence and acceptor absorption spectra normalized to 1 on the cm-1 scale, and it is defined as:
Θ′= 𝐹!(𝜈)𝜀!(𝜈)𝑑𝜈
𝐹!(𝜈)𝑑𝜈 𝜀!(𝜈)𝑑𝜈 (2.23) Thus, from the above equations the conditions for the Coulombic mechanism can be determined:
• a large spectral overlap (Θ) between the emission spectra of the donor species and the absorption spectrum of the
acceptor species that leads to many resonant transitions;
• the Donor-Acceptor separation is smaller than the critical distance required for efficient energy transfer;
• a large radiative rate constant (𝑘!"#) for the donor and molar absorption coefficient (𝜀!) for the acceptor to possess large oscillator strengths, and so be strong oscillators to induce the oscillation of accepting dipoles;
• donor and acceptor have to be aligned so energy transfer is favorable and fast;
• the fluorescence lifetime of the donor (𝜏!!) should be long enough to not compete with other deactivation processes
• as the transition dipole moments are involved in the FRET mechanism, the spin conservation principle is met only for spin-allowed energy transfer.
2.3.1.2 Exchange Mechanism
The second possibility of energy transfer is known as exchange type or Dexter energy transfer. This mechanism is based on quantum mechanical exchange interactions, therefore it requires strong spatial overlap of the wavefunctions of A and B. It implies that the excited donor and ground state acceptor should be close enough so the exchange may happen. A schematic representation of the Dexter energy transfer is shown in Figure 2.5. It can be viewed as a double electron transfer process, where one electron moving from the LUMO of the excited donor to the LUMO of the acceptor, while the other from the acceptor HOMO to the donor HOMO. The electron exchange interaction is the second contribution to the coupling 𝑉!", and the rate constant for the exchange mechanism (𝑘!") can be expressed as:
𝑘!"=2𝜋
ℎ 𝐾Θ′exp −2𝑟!"
𝐿 (2.24) where 𝑟!" is distance between the two unites, Θ! is the spectral integral defined in equation 2.23, 𝐾 is an orientation factor, taking the geometric orbital interactions into account, 𝐿 is the average Bohr radius of the orbitals between which the electron is transferred (the exact value cannot be
2.3 Photoinduced Energy and Electron Transfer Processes
calculated but it is typically in the order of 0.1-0.2 nm).
Figure 2.5 Schematic representation of EET according to the exchange (Dexter) mechanism.
Since the overlap of the electronic wavefunctions decays exponentially with distance, it is can be expected that the rate constant for the exchange mechanism decreases even more rapidly with the distance between the units than that expected for FRET. Another difference between two mechanisms that the rate of the exchange-induced transfer is independent of the transition dipole moments, thus the Dexter mechanism can be effective for both spin-allowed and spin-forbidden energy transfer.
2.3.2 Electron Transfer
Besides the above discussed photophysical processes the excited state can lose the energy of excitation through photochemical reactions.
Photoinduced electron transfer represents simplest photochemical reactions, however at the same time it is viewed as one of the most attractive methods to convert light energy or to store it for further applications.12
Photoinduced electron transfer (ET) involves the transfer of an electron within an electron donor-acceptor pair, and was described by equations 2.12 and 2.13. Here the processes taking place between two units after excitation, where the excited unit can donate or accept an electron, resulting in the population of a charge separated state (CSS). Afterwards, it usually followed by spontaneous back-electron transfer reactions (electron- hole recombination), and regenerate the starting ground state:
𝐴!−𝐵!→𝐴−𝐵 back oxidative electron transfer (2.25)
𝐴!−𝐵! →𝐴−𝐵 back reductive electron transfer (2.26)
The difference between a photoreaction and a regular thermal reaction that in the last one the system never leaves the potential surface of the ground state, while in a photoreaction, there is a crossover from a excited state potential energy surface to that of the ground state where every reaction eventually ends. The new redistribution of electrons associated with electronic excitation of a molecule effects its physical properties, in particular makes the excited species both stronger oxidants and reductants.
The photoinduced charge separation (CS) occurs when it is thermodynamically favorable, i.e. exergonic. The CSS energy (𝐸!"") as well as the free energy of photoinduced CS (∆𝐺!") can be estimated from the oxidation potential of the donor 𝐸!" 𝐴 and the reduction potential of the acceptor 𝐸!"# 𝐵 using the Weller equation:13
∆𝐺!"=𝐸!""−𝐸∗=𝑒 𝐸!" 𝐴 −𝐸!"# 𝐵 +𝐶+𝑆−𝐸∗ (2.27)
where 𝐸∗ is the energy of the excited state from where CS takes place, 𝐶=−𝑒!/(4𝜋𝜀!𝜀!𝑑!") is a correction term that represents the Coulombic
interaction between the charged units at a distance 𝑑!" and screened by a solvent of dielectric constant 𝜀!. Finally, S is factor accounting for a dielectric constant of the solvent different from that used for the determination of the redox potentials, 𝜀!!:
𝑆=− 𝑒! 8𝜋𝜀!
1 𝑟!+ 1
𝑟! 1 𝜀!+ 1
𝜀!! (2.28) where 𝑟! and 𝑟!are the radii of the reacting units.
From a kinetic viewpoint, the photoinduced electron transfer was described by Marcus.14-15 In this theory, the CS is treated by transition state theory where the reactant state is the excited A*-B and the product state is the CSS (Figure 2.6). Here the states of the system are represented by identical parabolic functions that are displaced vertically and horizontally along the reaction coordinate. The vertical displacement corresponds to the driving force of the reaction (−∆𝐺!"), and can be calculated using
2.3 Photoinduced Energy and Electron Transfer Processes
equation 2.27. The horizontal displacement represents the difference between equilibrium geometries of the two states, and described by the nuclear reorganizational energy (𝜆). This energy separated into two independent contributions corresponding to the reorganization of the inner (𝜆!) shell, which characterizes the changes in bond length and angles, and the outer reorganization energy (𝜆!), which refers to the reorientation of the surrounding solvent molecules:
𝜆=𝜆!+𝜆! (2.29)
Figure 2.6 Schematic representation of free-energy curves for the ground state (AB), the excited state (A*-B, reactant state), and the charge-separated state (A+-B-, product state) according to the classical Marcus theory.
The outer reorganizational energy is solvent dependent, and can be estimated using the Born-Hush approach:
𝜆!= 𝑒! 4𝜋𝜀!
1 𝑛!−1
𝜀! 1 2𝑟!+ 1
2𝑟!− 1
𝑟!" (2.30) where e is the electronic charge, 𝑛 is the refractive index of the solvent, 𝜀! is the permittivity of the solvent, 𝑟! and 𝑟! are the radii of the reactants, and 𝑟!"
is the centre to centre distance between them. An important consequence deriving from equation 2.30 is that 𝜆! is large when the reaction occurs in a polar solvent between reactants separated by a long distance.
The inner reorganization energy can be estimated within the harmonic-oscillator approximation, and is given in terms of its force constants 𝑓! and the change in equilibrium positions Δ𝑥! between the reactants and the products:
𝜆!= 𝑓!(𝑅)∙𝑓!(𝑃)
𝑓! 𝑅 +𝑓!(𝑃) (Δ𝑥!)! (2.31)
where 𝑓! 𝑅 is the force constant for the reactants and 𝑓!(𝑃) is that for the products.
Within this theory, knowing the above discussed parameters for
∆𝐺!" and 𝜆, the activation barrier (∆𝐺!"! ) for the thermal electron transfer
can be estimated via quadratic relationship:
∆𝐺!"! =(∆𝐺!"+𝜆)!
4𝜆 (2.32) When ET is a thermally activated process with known barrier and weak electronic coupling between reactants, the rate of charge separation
(𝑘!") can be expressed through the Arrhenius equation:16
𝑘!"=𝐴𝑒𝑥𝑝 −∆𝐺!"!
𝑘!𝑇 =𝐴𝑒𝑥𝑝 − ∆𝐺!"+𝜆 !
4𝜆𝑘!𝑇 (2.33)
where 𝑘! is the Boltzmann constant and 𝑇 is the temperature.
Equation 2.33 predicts that the dependence of 𝑘!" on ∆𝐺!" is Gaussian for constant 𝜆, and involves three regimes (Figure 2.7):
• an activationless (or optimal) regime (−𝜆≈∆𝐺!"), when the electron transfer rate reaches its maximum value;
• a normal regime (−𝜆<∆𝐺!"), when the electron transfer rate increases with larger driving forces;
• an ‘‘inverted’’ regime (−𝜆>∆𝐺!"), when the electron transfer rate decreases with increasing driving force
2.3 Photoinduced Energy and Electron Transfer Processes
Figure 2.7 (top) The three regimes of electron transfer according to the Marcus theory; (bottom) the corresponding reaction rate dependence as a function of the.
The classical Marcus model works well in the normal region but the electron transfer rates in the inverted region were found to be higher than predicted. The situation in the inverted region is better described by semi- classical Marcus theories based on a quantum-mechanical description of electron transfer, a detailed description of which can be found, for example, in ref 16. In a few words, from a quantum mechanical viewpoint, the electron transfer processes can be viewed as radiationless transitions between two electronic states, and thus its rate constant can be expressed through Fermi's golden rule (equation 2.15) considering the density of states at the intersection point of the reactant and the product energy surface (Figure 2.8, left). Taking higher-energetic molecular vibrations into account opens additional electron transfer channels that can occur in parallel, thus resulting in a greater rate of charge separation in the inverted region. Consequently, the quantum mechanical model predicts a more linear decrease of the rate constant with increasing driving force in the inverted region then the parabolic one found with the classical Marcus theory (Figure 2.8, right).
Figure 2.8 (left) Free energy surfaces including the high-frequency intramolecular vibrational modes of the product state (A+-B-); (right) schematic representation of the Marcus according to the classical and semi- classical Marcus theories.
Chapter 3
Experimental Part
3.1 Nonlinear Optics
The aim of this chapter is to introduce the most used spectroscopic techniques during this thesis for investigating excited-state dynamic processes. Firstly, lets briefly discuss some basic concepts of nonlinear optics in order to better understand the working principles of the setups.
During a long time all optical media could be explained as linear, up to 1960 when the first invented laser17 allowed to examine the light behavior in optical materials at high intensities. After the first laser, optical media were shown not to follow linear behavior at high intensities and to exhibit changes of refractive index and frequency of light by going through nonlinear optical material, breakdown of the superposition principle, and ability to interact and impact of one beam on another.18
The interaction between matter and light induces a macroscopic polarization, P.19 Thus, as long as the applied electric field is weak, the dependence between the polarization and the electric field, E, is linear:
𝑃=𝜀!𝜒𝐸 (3.1) where 𝜒 is the proportionality constant, called the electrical susceptibility of the medium, 𝜀! is the permittivity of free space. However, when the electric field is very intense, this dependence is not liner anymore and the polarization is expressed as a sum of linear, PL, and nonlinear, PNL, part of it:
𝑃=𝑃!+𝑃!"=𝜀! 𝜒 ! ∙𝐸+𝜒! ∙𝐸!+𝜒 !𝐸!+. . . (3.2)
where 𝜒 ! , 𝜒! ,… are the second-, third- and higher-order nonlinear electric susceptibilities, respectively, that account for nonlinear effects.
3.1.1 Second-order Nonlinear Optics
Let us now consider only the second-order term in the equation 3.2 as the response to two electric fields oscillating at angular frequency ω1 and ω2:
𝑃! 𝑡 =𝜀!𝜒! 𝐸! 𝑡 (3.3)
The electric field can be described as:
𝐸 𝑡 =𝐸!𝑒!!!!!+𝐸!𝑒!!!!!+𝑐.𝑐 (3.4)
Then the nonlinear polarization is given by:20
𝑃! 𝑡 =𝜀!𝜒! 𝐸!!𝑒!!!!!!+𝐸!!𝑒!!!!!!+2𝐸!𝐸!𝑒!!(!!!!!)!+
2𝐸!𝐸!∗𝑒!!(!!!!!)!+𝑐.𝑐 +𝜀!𝜒 ! 𝐸!𝐸!∗+𝐸!𝐸!∗ (3.5)
The resulting polarization can oscillate at the frequency, ω3, equal to the double frequencies, 2ω1 or 2ω2, as well as oscillating at the sum frequency, ω1+ω2, or the difference frequency |ω1-ω2| (Figure 3.1).19 In practice, all these cases are not present at the same time. In order to create one or another of these new frequencies, the linear momentum conservation conditions called phase matching conditions have to be fulfilled. Due to it, the new field intensity is the greatest when:21
∆𝑘=𝑘!"#− 𝑘!" =0 (3.6) where ∆k is the wavevector (or phase) mismatch, where kin and kout are the
3.1 Nonlinear Optics
wavevectors of the incoming and of the new outgoing field, respectively. In fact, phase matching conditions is the representation of momentum conservation (p=ħk).19, 21
Figure 3.1 Energy level representation of second-harmonic generation (SHG), sum-frequency generation (SFG) and difference-frequency generation (DFG).
The effect when ω3 = 2ω1 (or 2ω2) is called second-harmonic generation (SHG). It is valid when the kω3= 2kω1 phase matching condition is fulfilled. SHG is commonly used to generate light at the double frequency of the applied one, and is widely used in the experiments presented below to convert the output laser light, which is usually at 800 nm, to 400 nm.
The phenomenon with ω3 = ω1 + ω2 is called sum frequency generation (SFG), and is used during the thesis to convert a weak spontaneous fluorescence signal by mixing it with the laser beam in the up- conversion technique (section 3.3.2). While the one at ω3 = ω1 - ω2 is called difference frequency generation (DFG), and underlies two other important effects, as optical parametric generation (OPG) and amplification (OPA). In OPG an incident laser pulse, called pump pulse at ω1, is divided into two lower-frequency pulses that are called idler, ω2, and signal, ω3. OPA is used to amplify the signal. In this process, a high-intensity beam transfers its energy to a low-intensity signal beam and generates a third idler beam. The non-collinear geometry of OPA (NOPA) is used in this work to generate pulses between 380 and 700 nm. The required phase match condition for SFG is defined as kω3= kω1+ kω2, and for DFG as kω3= kω1−kω2.
It is important to mention here that second-order (or even order) optical properties occur only in non-centrosymmetric materials, as the
second order nonlinear susceptibility of centrosymmetric materials is zero.19 Centrosymmetric materials in turn exhibit the third-order nonlinear optical susceptibility as the lowest nonlinear order response.
3.1.2 Third-order Nonlinear Optics
Third-order nonlinear processes can occur in all materials. In general, these effects are much weaker than second-order analogues and thus require high intensity electric fields. Such increase of the intensity effect the refractive index by making it intensity-dependent:22
𝑛=𝑛!+𝑛!𝐼 𝑡 (3.7)
where 𝐼 𝑡 is the intensity of laser radiation, n0 is the linear refractive index, and 𝑛! is the nonlinear refractive index related to the third-order nonlinear susceptibility, 𝜒! :22
𝑛!= 2𝜋
𝑛!
!
𝜒! (3.8)
Such a change of the refractive index in response to an applied electric field is known as optical Kerr effect (OKE). It is the underlying principle of such important effects such as self-phase and cross-phase modulation.
Self-phase modulation causes a time-dependent phase shift in the pulse that leads to spectral broadening. It comes from the time dependence of the intensity of electric field and of the refractive index (equation 3.8). As a consequence, it causes a nonlinear or time-dependent phase, 𝜙 𝑡 , in the material:22
𝜙 𝑡 =𝜔
𝑐 𝑛!𝐼 𝑡 𝐿 (3.9) where 𝐿 is the pathlength, and so it gives rise to a time dependent frequency of the pulse:22
3.1 Nonlinear Optics
∆𝜔 𝑡 =𝜕𝜙 𝑡
𝜕𝑡 =𝜔 𝑐 𝑛!𝐿𝐼!
𝜏 (3.10) where ∆𝜔 the resulting spectral broadening of the pulse, 𝐼! is the peak intensity of the optical pulse, and τ is the duration of the pulse. We used self- phase modulation in this work to generate a white light continuum in the transient absorption experiments by focusing the output of a standard Ti:sapphire amplified laser system into a CaF2 window, or a sapphire plate in NOPA.
Another similar effect is cross-phase modulation. The difference is that in this case the phase shift caused by interaction of two laser pulses, where the phase of a weak pulses is affected by another intense pulse due to the change in the refractive index of the medium. As a result, it gives rise to a phase shift of the weak pulse.
3.1.3 Optical Pulses
In order to monitor ultrafast events, an experiment needs time resolution, i.e. the optical pulses should be short enough to follow the processes under investigation. Thus time resolution in ultrafast spectroscopy comes from such short optical laser pulses. They are usually characterized by the duration, 𝜏, and its spectral width, ∆𝜈, and for a Gaussian pulse is expressed as:23
∆𝜈𝜏≥2ln2/𝜋 (3.11)
where ∆𝜈 and 𝜏 are the full width at half maximum of the laser-pulse spectrum and time, respectively. Consequently, equation 3.11 shows inverse proportionality between time and frequency. This is an important characteristic that allows to establish the right spectral width required to get a desired pulse duration. For example a short pulse that has a pulse duration of 100 fs has a frequency bandwidth of at least 4 × 4112 Hz (133 cm-1).
3.2 Steady-State Spectroscopy
Absorption spectra were measured on a Cary 50 (Varian) spectrometer, whereas fluorescence emission and excitation spectra were recorded on a Cary Eclipse (Varian) or a FluoroMax-4 (Horiba Scientific) fluorometer. The latter setup has the advantages of a higher sensitivity, a larger dynamic range and an extended detection into the near-infrared region.
All emission spectra were corrected for the wavelength-dependent sensitivity of the detector. The steady-state measurements were performed in 1 cm thick quartz cells.
The fluorescence quantum yields, Ф!", were calculated as:8
Ф!"= 𝐹(𝜆) 𝐹!"#(𝜆)
𝑛! 𝑛!"#!
1−10!!"#
1−10! Ф!",!"# (3.12)
where Ф!",!"#is the fluorescence quantum yield of a reference compound;
𝐹(𝜆) and 𝐹!"#(𝜆) are the integrated intensities of sample and reference spectra, respectively; 𝑛 and 𝑛!"# the refractive index of the sample and reference solution, respectively; 𝐴 the absorbance at the excitation wavelength.
3.3 Time-Resolved Fluorescence
One of the ways for an excited molecule to dissipate its energy is fluorescence. Many processes, like radiative and non-radiative relaxation, intersystem crossing, excitation energy and charge transfer, etc. can influence the excited-state dynamic of the molecule, hence its fluorescence intensity and dynamics. In time-resolved fluorescence measurements, the molecules are promoted to the excited state by using a laser pulse and the resulting fluorescence spectrum is monitored as a function of time. In this work, fluorescence dynamics were measured on sub-nanosecond and femtosecond timescales using the time correlated single photon counting (TCSPC) and fluorescence up-conversion techniques, respectively.
3.3 Time-Resolved Fluorescence
3.3.1 Time-Correlated Single Photon Counting
The TCSPC technique is one of the most widely used methods to measure fluorescence dynamics on the nanosecond timescale.24-25 In this technique, the time between the excitation pulse and the detected photon is measured electronically. Sometimes it is compared to a fast stopwatch, where the clock is started by the Start signal pulse and stopped by the Stop signal pulse. In a typical TCSPC set-up, the Start pulse is generated from a small part of the excitation light and forwarded to a photodiode to produce the trigger pulse, which starts to charge a capacitor. An emitted photon from the sample is directed to the detector (photomultiplier or micro channel plate), and stops the charging of the capacitor. The time measured for a Start-Stop cycle represents the arrival time of the photon. The measurement is repeated many times and stored in a histogram, where x-axis represents the time difference and y-axis the number of the detected photons over the measured time difference. TCSPC is a statistical method and is based on the detection of single photons to represent the fluorescence decay of the sample.
Setup. The TCSPC setup has been described in detail previously.26-27 The sample was excited at 395 nm (PicoQuant model LDH- P-C-400B) or 470 nm (PicoQuant model LDH-P-C-470) with ~60 ps excitation pulses. The average power was about 0.5 mW at the repetition rate in the range of 10-40 MHz. Fluorescence was collected at 90o, and passed through an analyzer set at the magic angle with respect to the excitation polarization, and a narrow bandpass filter located in front of a photomultiplier tube (Hamamatsu, H5783- P-01). The detector output was connected to the input of a TCSPC computer board module (Becker and Hickl, SPC-300- 12). The full width at half maximum (FWHM) of the instrument response function (IRF) was ~200 ps. The IRF was determined from the signal scattered from a solution of LUDOX at the sample position.
All measurements were performed in 1 cm quartz cells. The accuracy on the lifetimes is of ca. 0.1 ns. The obtained fluorescence time profiles were analyzed with the convolution of the measured IRF and mono- or multiexponential functions with MATLAB (The Mathworks Inc.) using a script written by Dr. Arnulf Rosspeintner.
