Ultrafast photoinduced processes in multichromophoric systems

Thesis

Reference

Ultrafast photoinduced processes in multichromophoric systems

DUVANEL, Guillaume

Abstract

Durant cette thèse, des techniques spectroscopiques de pointe ont été utilisées pour étudier des phénomènes ultrarapides de l'ordre de la picoseconde. Parmi ces techniques, la fluorescence résolue dans le temps a été la plus utilisée en sus de l'absorption transitoire. Les dynamiques de des états excités de divers systèmes moléculaires comportant des chromophores tels que le BODIPY ont pu être mesurées et comprises grâce à ces techniques. De plus, durant ce travail, de nombreuses améliorations ont été apportées au montage expérimental de la fluorescence dite « up-conversion », la principale étant le changement de source laser qui permet de varier la longueur d'onde d'excitation de 340 nm à 520 nm, ce qui ouvre de nouvelles perspectives quant au nombre de potentielles molécules étudiables.

DUVANEL, Guillaume. Ultrafast photoinduced processes in multichromophoric systems . Thèse de doctorat : Univ. Genève, 2010, no. Sc. 4177

URN : urn:nbn:ch:unige-56700

DOI : 10.13097/archive-ouverte/unige:5670

Available at:

http://archive-ouverte.unige.ch/unige:5670

Disclaimer: layout of this document may differ from the published version.

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U

G

F

S

Département de Chimie Physique Professeur Eric Vauthey

Ultrafast Photoinduced Processes in Multichromophoric Systems

Thèse

présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention chimie

Par

Guillaume Duvanel

De

Brot-Dessous (NE, Suisse)

Thèse N^o 4177

GENÈVE

Atelier Repromail

Janvier 2010

Ce travail de thèse a été réalisé au département de Chimie Physique de la Section de Chimie de l’Université de Genève sous la direction du Professeur Eric Vauthey. Je le remercie sincèrement de m’avoir accueilli au sein de son groupe et de m’avoir permis de travailler dans les meilleures conditions possibles pour cette thèse. En effet, outre sa disponibilité de tous les instants, j’ai toujours pu compter sur son enthousiasme à promulguer de nombreux conseils enrichissants.

Je tiens également à remercier le Dr Robert Pansu, du Laboratoire de Photophysique et Photochimie Supramoléculaires et Macromoléculaires de Cachan (France), et Dr Andrew Beeby, du Département de Chimie de l’Université de Durham (Royaume-Uni) pour avoir accepté de s’engager comme experts lors de la soutenance et à ce titre de lire ce mémoire.

Ce travail de thèse n’aurait pas été possible sans les grandes compétences de tous les scientifiques qui ont mis leurs connaissances au profit d’enrichissantes collaborations : le Professeur Stefan Matile ainsi que son groupe, le Professeur Michel Geoffroy, et le Dr Manuel Lejeune de l’Université de Genève, Anne Schuwey et le Professeur Albert Gossauer de l’Université de Fribourg, le Professeur Patrice Jacques et le Dr Viencent Diemer de l’Université de Mulhouse et le Professeure Mireille Blanchard-Desce de l’Université de Rennes et son groupe.

Je remercie également mes collègues et amis du groupe et de l’Université qui ont permis de passer ces 4 années dans d’excellentes conditions, soit (sans aucun ordre de préférence), les anciens comme Alexandre, Angela, Anatolio, Natalie et François ou les actuels Didier, Sophie, Jakob, Oksana, Irina, Bernhard, Vesna, Piotr, Marina, et Diego.

Grâce au soutien et à l’amitié de mes proches et de ma famille, ces dernières années ont pu se dérouler dans les meilleures conditions possibles. Je remercie tout particulièrement Thi- Thanh, ma femme, qui, depuis de nombreuses années, me soutient et me couvre de tout son amour, tous deux m’ont permis d’avoir un cadre professionnel et personnel optimal.

P REFACE

Over millennia, Man tried to explore all the aspects he can in space and also in time. The discovery and developments of several powerful tools such as microscope and telescope have permitted to investigate very small or remote objects which are far beyond human perception. Furthermore, the temporal aspects were not neglected as shown for example by the numerous experiments implemented to determine the speed of the light.^[1-3] A parallel could be drawn between this high velocity and the temporal resolution needed to observe motion in a molecule. Indeed, the velocity of an atom is of the order of 1 km/s.

Consequently, the time-resolution needed to observe a 1 Å-motion of an atom is approximately 100 femtoseconds (1 femtosecond is equivalent to 10^-15 s). Consequently, the development of femtosecond pulsed laser and based-on techniques since about 25 years open a large variety of possibilities for exploring new photophysical domains.

Since its beginning, femtochemistry has been considerably developed and is nowadays a matured science that is still progressing. In its early stages, only small gas phase molecules could be really investigated. Now, new techniques such as multidimensional spectroscopies or ultrafast X-ray or electron diffraction open totally new horizons. This field was also acknowledged by the award of the Nobel Prize in 1999 to A. Zewail. All these techniques permit to study ultrafast processes occurring in Nature. Indeed, Nature is a source of perpetual interrogations, photosynthesis being one of them. Reproducing its efficiency in artificial devices could be a source for large daily applications such as photovoltaic devices.

This application is even more topical nowadays because of the global warming and also because of the predicted shortage of oil in a few decades. Nevertheless, to access to such mechanisms, an understanding of all the steps involved during these processes is necessary.

During this thesis, several collaborations with synthetic chemists have provided a large number of interesting molecules. Some of them have been built to better understand the role of the different molecular parts in a system where excitation energy transfer occurs (Chapter 3). Other systems have been synthesized for two photons excited fluorescence applications like biological markers (Chapter 4). Chapter 5 deals with molecules synthesized for possible applications in molecular switches as they react very fast to external stimuli. Chapter 6 explores the influence of the molecular structure on electron transfer processes. The last chapter will show different projects in which I contributed by doing fluorescence spectroscopic investigations. All these results were possible using spectroscopic tools such as fluorescence up-conversion and transient absorption. These techniques and the basic concepts of photophysics are mentioned in the two first chapters.

I Basic Concepts of Photophysics ... 1

I.A Basic Concepts of Photophysics ... 1

I.A.1 The Light ... 1

I.A.2 The Absorption of Light ... 2

I.A.3 The Jablonski Diagram ... 4

I.A.4 The Fluorescence ... 6

I.A.5 The Fluorescence Anisotropy ... 9

I.A.6 Non-Equilibrium Excited-State Dynamics ... 11

I.A.7 Excited-State Dynamics with Bimolecular Interactions ... 15

II Experimental Techniques ... 29

II.A Time-Correlated Single Photon Counting ... 30

II.B Fluorescence Up-Conversion ... 32

II.B.1 Fluorescence up-conversion data treatment ... 35

II.C Transient Absorption... 35

II.D Samples ... 38

II.E Appendices ... 39

III Phenyleneethynylene Oligomers ... 41

III.A Introduction ... 41

III.A.1 OPEs Photophysics ... 44

III.A.2 Porphyrins Photophysics ... 48

III.B Excited-State Dynamics of OPEs in Solution ... 51

III.B.1 Introduction ... 51

III.B.2 Experimental Details ... 51

III.B.3 Steady-State Measurements ... 52

III.B.4 Time-Resolved Fluorescence... 53

III.B.5 Transient Absorption Measurements ... 56

III.B.6 Discussion – The Excitonic Model ... 59

III.B.7 Conclusions ... 63

III.C OPE as a Bridge in a Donor-Bridge-Acceptor System ... 64

III.C.1 Donor-Bridge System ... 64

III.C.2 Donor-Bridge-Acceptor System ... 70

IV Boron Dipyrromethene Arrays ... 87

IV.A Introduction ... 87

IV.A.1 Two-Photon Absorption And Excitation Fluorescence ... 87

IV.A.2 BODIPY Photophysics ... 89

IV.B Phenylethynyl Cores Photophysics ... 91

IV.B.1 Time-resolved Fluorescence ... 92

IV.B.2 Transient Absorption Measurements ... 95

IV.C Boron Dipyrromethene Arrays Photophysics ... 98

IV.C.1 BODIPYs Array1 ... 99

IV.C.2 BODIPYs Array2 ... 109

IV.C.3 BODIPYs Array3 ... 117

IV.C.4 BODIPYs Array4 ... 121

IV.D Discussion ... 125

IV.E Conclusions ...132

V Phosphaalkene Derivatives ... 135

V.A Introduction ... 135

V.B Disphosphaalkene OPE Derivatives ... 137

V.B.1 Introduction ... 137

V.B.2 Steady-State Measurements ... 139

V.B.3 Time-Resolved Fluorescence ... 141

V.B.4 Transient Absorption Measurements ... 144

V.B.5 Discussion ... 148

V.B.6 Conclusions ... 151

V.C Disphosphaalkene Anthracene ... 152

V.C.1 Introduction ... 152

V.C.2 Steady-State Measurements ... 152

V.C.3 Time-Resolved Fluorescence ... 153

V.C.4 Transient Absorption Measurements ... 155

V.C.5 Discussion ... 158

V.D Conclusion ... 159

VI Pyridinium Phenolates Derivatives ... 161

VI.A Introduction ... 161

VI.A.1 Steady-State measurements and Ab Initio Calculations ... 163

VI.B Time-Resolved Measurements ... 166

VI.B.1 Fluorescence Up-Conversion ... 166

VI.B.2 Transient Absorption Measurements ... 168

VI.C Discussion ... 170

VI.D Concluding Remarks ... 176

VI.E Appendices ... 176

VI.E.1 Successive reactions scheme ... 176

VI.E.2 Igor implementations ... 178

VII Collaboration Projects ... 181

VII.A 2007 Publications ... 182

VII.B 2009 Publications ... 191

VIII Concluding remarks & Perspectives ... 215

IX Bibliography... 219

BASIC CONCEPTS OF PHOTOPHYSICS 1

C HAPTER 1

I B

C

P

During this thesis, spectroscopic tools, presented in Chapter 2, have been used to investigate the photophysical behavior of several molecules upon light excitation. To understand such inter- and intramolecular processes, this chapter gives the basis of the photophysics going from the description of the light to all the different investigated processes such as dynamic Stokes shift or energy transfer.

I.A B

C

P

I.A.1 T

L

The phenomena presented in the following chapters are due to the interaction between light and matter. Light is classically described as an electromagnetic wave. It consists of an electric field, , , and a magnetic field,  , , oscillating perpendicularly to each other.

The angular frequency is termed ω, the wave propagates along the wave vector, :

,   · · ·

,   · · ·

where is the electric field vector, · · its phase at time t and the position vector. The amplitude of the wave vector can be calculated from the wavelength, λ:

  2

2 BASIC CONCEPTS OF PHOTOPHYSICS

The angular frequency is related to the wavelength and to the frequency, υ. The speed of light, c, is also included in this relation:

 2 2

I.A.2 T

A

L

A beam of light passing through a solution of absorbing molecules transfers its energy to the molecules, and thus its intensity or irradiance, I, decreases. The process is due to the energy transfer from the electromagnetic field to the molecules. The decrease of I can be related to the path length, dx, to the concentration of the absorbing molecules, C, and to a factor depending on the wavelength and on the molecule, ε’:

  · ·

After integrating this equation, the relation between the initial irradiance and the intensity of light after his passage through a sample of thickness, l, can be expressed as:

· · 10 · 10

where A is the absorbance or the optical density (OD) and is equal to the product of ε, C and l. ε being termed the molar extinction coefficient or molar absorption coefficient (ε'=ln10^.ε). As the absorbance is dimensionless, if the thickness of the sample is expressed in cm and the concentration, in mol^.l^-1, ε has to be in l^.mol^-1.cm^-1. The previous equation is known as the Beer-Lambert law. A plot of the absorbance of a sample as a function of either wavelength, wavenumber or frequency is called an absorption spectrum. The light can be absorbed by the molecule only if its frequency corresponds to a resonance of the oscillating dipole induced in the molecule. In a quantum mechanical picture, a molecule can only go to a state b of energy Eb from a state a of energy Ea by absorbing light at frequency υ if the following relation holds:

BASIC CONCEPTS OF PHOTOPHYSICS 3

Absorption requires light to interact with a transition dipole moment of the molecule. The transition dipole moment is a quantity which couples two stationary states a, and b. Both states are described by the wave functions, ψa and ψb, respectively. The transition moment dipole is termed and is defined as:

Ψ | ̂|Ψ

where ̂ is an operator corresponding to either the electronic dipole moment, the magnetic dipole moment or to the electronic quadrupole. Nevertheless, for an allowed transition in an organic molecule, the relative magnitude of these different dipoles is 10⁷:10²:1, respectively.^[4] Consequently, due to the smaller relative magnitude of the other dipole moments, it is more common in the case of optical spectroscopy to deal with electronic dipole moment.

The transition dipole moment is related to the absorption spectrum of a molecule expressed in extinction coefficient as a function of wavenumber by the following relationship:

4.3 · 10

8

3 | |

where f is termed the oscillator strength, and m^e is the mass of the electron, υ0 the frequency of the transition, e the charge of the electron and is wavenumber in cm^-1. Usually, the oscillator strength value is comprised between 0 and 1 depending on whether the transition is allowed or forbidden. Nevertheless, a value above 1 can be found in conjugated electronic systems (see Chapter 3).

4 BASIC CONCEPTS OF PHOTOPHYSICS

I.A.3 T

J

D

The Jablonski diagram is a useful tool to illustrate all the different intramolecular or intermolecular processes that occur in the excited states. Its form can thus be very different depending on the investigated system.

In a closed-shell organic molecule, the first transition occurs usually from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).

After the promotion of one of the electron to the LUMO, the excited state can exist in two distinct forms: (1) a singlet state, S, or (2) a triplet state, T, depending on the total spin of the unpaired electrons. Additionally to this criterion, the energetic states are called, according to their energy sequence, from 1 to n. As a consequence, the electronic ground state is termed So, the first excited state, S1, and the first triplet state, T1.

As the energy gap between the electronic states and the ground state is significantly larger than kT, only the electronic ground state is populated at ambient temperature. Although it is theoretically possible to populate several excited states by warming up the sample, it is practically impossible because of the decomposition of the molecule upon such heating. To populate an excited state, the molecule needs thus an external stimulus, for example that of light. By definition, an excited state is not the less energetic state of the molecule;

consequently, it has a finite lifetime. As mentioned before, several processes can be involved into the dissipation of the energy. Some are termed radiative if light is emitted involved during the processes, the others are termed non-radiative. Both types of processes are shown in the following Jablonski diagram.

BASIC CONCEPTS OF PHOTOPHYSICS 5

Figure I.1: Typical Jablonski diagram representing the possible pathways for population and relaxation of excited states. Full arrows represent radiative transitions and dashed arrows, non-radiative transitions.

Fluorescence (see section I.A.4) and phosphorescence are radiative processes involving respectively two states of the same spin multiplicity, and two states of different spin multiplicity. Phosphorescence is forbidden and thus the emission rate constant is low (10³- 10⁰ s^-1). The phosphorescence lifetime is typically from the milliseconds or seconds, but it can be even larger for example with the “glow-in-the-dark” toys. In this case, the phosphorescence can last for several minutes after light irradiation.^[5]

Internal conversion refers to a non-radiative process which brings the molecule from an electronic excited state to a vibrationally excited state of a lower electronic state. In most organic molecules, internal conversion from higher excited states to the lowest or “first”

excited singlet state occurs much more rapidly than the decay from the lowest excited state to the ground state, i.e. the internal conversion rate constant, kIC, is usually about ~10¹² s^-1. The measured fluorescence thus occurs mainly from the lowest singlet excited state even if the molecule is initially excited to a higher state. This generalization is called Kasha’s rule because of Michael Kasha, who first formalized it.^[6] Nevertheless, exceptions to this rule exist: azulene or zinc tetraphenylporphine (ZnTPP) are two well-known exceptions to this rule as they display S2 fluorescence.^[7,8]

Internal conversion is quickly followed by vibrational energy relaxation, VER. VER is a process bringing the molecule from an vibrationally excited state of an electronic state to

6 BASIC CONCEPTS OF PHOTOPHYSICS

the lowest vibrational state of the same electronic state (see section I.A.6). Depending on the energy gap between the two involved states, both internal conversion and VER can occur on the same time scale. Nevertheless, the internal conversion rate goes as the exponential of the energy gap between the 0-0 vibronic levels of the two electronically excited states, and thus its rate can be either large or small depending on the energy levels of the involved states.

A non-radiative process involving the change of the spin state of the molecule and thus converting a singlet state to a triplet state or vice-versa is termed intersystem crossing.

Such a transition is by definition forbidden. As a consequence, the change of the spin has to be coupled to a change of the angular momentum associated with the orbital motion of the electrons. This is possible via spin-orbit coupling. This is at the origin of the El-Sayed rules.^[9] El-Sayed rules state that the rate constant of intersystem crossing is large if the radiationless transition involves a change of orbital type. The rate constant of intersystem crossing, kISC, is typically in the order of 10⁷-10¹¹ s^-1 depending on both the spin-orbit coupling and the energy gap between the states involved. This rate can be increased by paramagnetic molecules such as oxygen or heavy atoms such as halogens or metals. These heavy atoms can be in the molecule (internal heavy-atom effect) or in its surrounding (external heavy-atom effect).

I.A.4 T

F

Like phosphorescence, fluorescence can be experienced in everyday life. For example, the green or the red-orange glow observable in several antifreezes is due to fluorescein or rhodamine, respectively; fluorescence of hexachloro-fluorescein is also used for DNA sensing. Moreover, applications of fluorescence are quite old. Indeed, one of the main advantages of the fluorescence is its high sensitivity. In 1877, this was used to demonstrate that Danube and Rhine were connected.^[5] Fluorescein was thrown in the Danube and after several hours, the typical green color of fluorescein could be detected in a river confluent of the Rhine.

As observed with the Jablonski diagram, the energy of the emission is always lower than that of the absorption. This phenomenon is termed Stokes shift, because of it first

BASIC CONCEPTS OF PHOTOPHYSICS 7

observation in the middle of the 19^th century by Sir G. G. Stokes at the University of Cambridge.^[10] Energy losses are observed universally with fluorescent molecules in solution. Two main aspects are responsible for this: first, the rapid decay to the lowest vibrational state of S1 after excitation, secondly the fact that fluorescence does not only decay to the lowest vibrational state in S0. Furthermore, the Stokes shift can also be due to the effects of the environment.

As mentioned before, Kasha’s rules state that the same fluorescence is observed independently of the excitation wavelength. A similar observation has been done several years before by Vavilov which documented the fact that the fluorescence quantum yield does not change with the excitation wavelength.^[11] Moreover, the emission spectrum is usually the mirror-image of the absorption spectrum. This is due to the fact that in most cases, the vibrational progressions in the first excited state and in the ground state are similar. Consequently, excitation from S0 to a vibrational excited state of S1 is similar to emission from the lowest vibrational state of S1 to vibrational excited state of S0. The only observed difference between the two spectra is due to the Stokes shift. To make a rigorous test of the mirror image rule, the absorption and emission spectra have to be corrected and depicted in the appropriate units. The best symmetry can be observed as a function of wavenumber with the absorption spectrum expressed by the extinction coefficient divided by the wavenumber and the emission spectrum divided by the wavenumber at the third power.^[5] Nevertheless, exceptions to this mirror image rule exist, as shown in Chapter 3.

To characterize a fluorophore, the two most important parameters are the lifetime and the fluorescence quantum yield. To understand these two quantities, a few concepts have to be introduced. The radiative rate constant is the probability per unit time that a molecule goes from state b to state a upon emission of a photon. From the radiative rate constant, the radiative lifetime can be calculated as follows:

As a general rule, a lifetime, τi, can be calculated as the reciprocal of the rate constant of related process, ki.

8 BASIC CONCEPTS OF PHOTOPHYSICS

The temporal evolution of the spontaneous fluorescence intensity, Ifl(t), decays exponentially. If only a single population of fluorophores contributes to the emission, and if emission is the only channel, the emission decay is given by:

0 · exp  ·

If the mirror-image law is obeyed, the radiative rate constant, krad, can be calculated from the absorption spectrum and more precisely from the oscillator strength and consequently from the transition dipole moment responsible for this process.

 2

 · 2

3 ·

If the excited state has only the fluorescence as deactivation pathway, its population decreases exponentially with a time constant equal to τrad. Nevertheless, most often, several non-radiative deactivation processes occur from the excited state, for example ISC and IC.

The sum of all the radiative and non-radiative rate constants gives the S1 decay rate constant, :

…

where knr is the non-radiative rate constant corresponding to the sum of all the non- radiative rate constants.

The fluorescence quantum yield, Φfluo, is defined as the ratio of the number of emitted photons and the number of absorbed photons. Consequently, the closer to 1 the fluorescence quantum yield, the brightest the emission of the fluorophore will be. It is thus given by the following equation:

 ∑

In practice, the radiative and the non-radiative rate constants are not always known. The fluorescence quantum yield is thus determined using a reference. As the fluorescence intensity is proportional to the number of emitted photons, the integral of the whole fluorescence spectrum yields a quantity which is proportional to the number of emitted

BASIC CONCEPTS OF PHOTOPHYSICS 9

photons. Therefore, to determine the fluorescence quantum yield of an unknown sample, a comparison between the integral of the whole fluorescence spectra of the sample and of the reference is done. Nevertheless, as the fluorescence quantum yield also depends on the number of absorbed photons, the absorption of both samples has to be compared as well.

Moreover, the solvents in which the different fluorophores are dissolved can also influence the measurements, and must also be taken into account in the relationship between the reference and the sample. These aspects lead to the following equation:^[5,12]

,   · · 1 10

1 10 · _,

where nx is the refractive index of the solvent, Ax is the absorption at the excitation wavelength and is the integral of the whole emission spectrum of both reference and sample.

I.A.5 T

F

A

The fluorescence anisotropy measurements are based on the principle of photoselective excitation of the fluorophores by polarized light. The probability for a molecule to absorb light is larger if the electric vector of the light is aligned along the transition dipole moment of the fluorophore. Indeed, the absorption intensity is proportional to the square cosine of the angle between the electric vector and the transition dipole moment. Consequently, upon excitation with polarized light, only the fluorophores having a large component of their transition dipole moment parallel of the electric vector absorb (Figure I.2). This results to a partially oriented population of excited fluorophores and thus to partially polarized emission.

10 BASIC CONCEPTS OF PHOTOPHYSICS

Figure I.2: Effects of polarized excitation and rotational diffusion on the emission anisotropy.

Because light intensity is directly proportional to the number of emitters, it is possible to access to the orientational anisotropy by measuring the fluorescence polarization anisotropy. This is performed by measuring the emission intensity parallel to that of the excitation, , and then perpendicular to it, :

2 ·

The anisotropy value also depends on the angle, Θ, between the transition dipole moment responsible for the absorption and that for the emission:

3 · cos θ 1 5

The anisotropy generally varies between 0.4 which is the value for two parallel transition dipole moments and -0.2 corresponding to the case where they are perpendicular to each other. Moreover, its value is zero when the angle is equal to 54.7°. This particular angle is termed the magic angle. Anisotropy can reach values larger than 0.4 with either multiphoton excitation^[5] or degenerate transitions.^[13] As in solution the molecules diffuse, the anisotropy changes as a function of time. The fluorescence anisotropy generally goes to zero after some time and this corresponds to the randomization of the orientation of the molecules. The time-dependent anisotropy can thus be calculated from the polarized fluorescence intensity decays. Most often, the fluorescence anisotropy decays exponentially with time. Nevertheless, in some cases, a multiexponential function is needed to reproduce correctly the decay of fluorescence anisotropy (see chapter 3).

BASIC CONCEPTS OF PHOTOPHYSICS 11

2 · · exp  /

where r0 is the initial anisotropy value from which the angle between the absorption and the emission transition dipole moments can be derived, and τrot is the rotational correlation time which describes how fast the molecules rotate by diffusion in the solvent. The rotational time depends: (1) on molecule properties like its volume, V, its shape which is related to the factor f in the equation below, (2) on solvent properties such as its viscosity, η (expressed in cP), and (3) on the interactions between the solvent and the molecules like for example H-bonding. This factor is related to C in the equation. If the C value is superior to 1, the interaction between the solvent and the molecule is termed stick, in the other case, slip. This is directly linked to the number of solvent molecules carried away by the rotation of the molecule. This equation comes from the Stokes-Debye-Einstein equation. The volume of the molecule can be estimated using atomic increments based on the van der Waals radii.^[14]

· · ·

I.A.6 N

-E

E

-S

D

I.A.6.1 INTRAMOLECULAR VIBRATIONAL ENERGY REDISTRIBUTION

In the case of optical excitation, it is rare that the populated excited-state is the lowest vibrational state of the electronic excited-state. In most cases, this is called excess excitation energy. Excess energy is transformed as heat through vibrational or solvent relaxation. As the rate constant of these processes is typically 10¹² s^-1 which is significantly larger to that of radiative transitions, this phenomenon is directly responsible for the independence of the emission spectrum on the excitation wavelength, as stated by the Kasha’s and Vavilov’s rules. Nevertheless, these rules do not have been taken as totally true when considering ultrafast time-resolved spectroscopy where several deactivation processes occur on the same time scale. To have a better understanding of these processes, VER has been intensively studied over the past years.^[15,16]

12 BASIC CONCEPTS OF PHOTOPHYSICS

VER has usually been discussed in terms of two consecutive processes, namely intramolecular vibrational energy redistribution (IVR) and vibrational cooling (VC).

Directly after excitation, only “Franck-Condon active” vibrational modes are excited. IVR is a process where the excitation energy is redistributed in the other vibrational modes while keeping the total energy constant. IVR results in the establishment of a vibrational temperature which can be in principle very high.^[17] The “hot” molecule is then quickly cooled down by VC. This cooling is due to the interactions of the molecule with its surroundings. Recent observations indicate that both IVR and VC processes occur on not so different time scales and are strongly entangled.^[15,16]

VER can be observed with femtosecond resolution experiments. To determine if such a process occurs, its spectroscopic signature has to be known. After excitation, the “Franck- Condon active” vibrational modes distribute the excess of energy on all the isoenergetic vibrational states. In other words, the emission can occur from every state having the same vibrational energy. The emission spectrum after excitation is broad (Figure I.3), then it narrows upon VC. The early fluorescence dynamics measured at wavelengths located on the blue or on the red edge of the fluorescence spectrum show a fast decay, whereas at wavelengths near the center of the fluorescence spectrum, a fast rise is observed.

BASIC CONCEPTS OF PHOTOPHYSICS 13

Figure I.3: Schematic effect of VER on the fluorescence spectrum. Just after excitation the spectrum is broad (dark spectrum, t = 0), it then progressively narrows as VER takes place (light grey, Æt)

I.A.6.2 ENVIRONMENTAL RELAXATION

If upon excitation, the dipole moment of the molecule changes, surrounding polar solvent molecules will adapt their orientation. This effect is called solvent relaxation or solvation.

The change of the electronic transition energy of a molecule caused by the solvent is termed solvatochromism. This process has been intensively investigated using both steady-state^[18]

and time-resolved spectroscopies.^[19] Solvation can be described as both an energetic and a dynamic phenomenon. Although all aspects of solvation dynamics are not fully understood yet, a consensus model explains this phenomenon with a simple solute-solvent model. Let’s consider a dipolar molecule embedded in a dipolar solvent (Figure I.4(a)): right after excitation, the nuclei have not the time to change their position (Figure I.4(b)). Most often, the permanent dipole moment of the molecule is not the same in the ground state than in the electronic excited state; consequently, the position and direction of the solvent molecules close to the excited fluorophore has to change to reach the energy minimum of the excited-state (Figure I.4(c)). From this minimum, the fluorophore relaxes to the ground state (Figure I.4 (d)). Again, due to the difference between both permanent dipole

14 BASIC CONCEPTS OF PHOTOPHYSICS

moments, the solvent molecules must rearrange to reach the initial energy minimum.

During the solvent relaxation process, molecules can relax in a radiative way and thus, in the early fluorescence dynamics, a time-dependent Stokes shift is observed as a red-shift of the fluorescence band. At wavelengths on the blue edge of the fluorescence spectra, a fast decay is observed, whereas at wavelengths on the red edge, a fast rise is observed.

Figure I.4: Schematic effect of the time-dependent Stokes shift.

Several different interactions are at the origin of the solvation such as dispersion and induced-dipole interactions, dipole-dipole interactions, and specific interactions such as H-bonding.^[19] The solvation dynamics depends on the nature of the solvent, but not of the solute according to the linear response theory assuming that the dynamics Stokes shift is only due to dipole-dipole interaction. The solvation dynamics is most often split in two distinct parts due to (1) inertial and (2) diffusive motions. The inertial part, which is ultrafast and which is not always fully resolved experimentally, is due to librational motions, namely hindered rotations, and intermolecular vibrations in the solvent network.

The second part, which is slower, involves rotational and translational diffusive motion of solvent molecules, mainly in the first shell of solvation. The first observation of this inertial response was reported in water^[20-22]; nevertheless further investigations indicate that both inertial and diffusive motions are also responsible for the solvation of solutes in various organic solvents^[23] and even in ionic liquids.^[24]

BASIC CONCEPTS OF PHOTOPHYSICS 15

I.A.7 EXCITED-STATE DYNAMICS WITH BIMOLECULAR INTERACTIONS I.A.7.1 FLUORESCENCE QUENCHING

The initial intensity of fluorescence can be decreased by several external factors. These processes are referred as fluorescence quenching, if they lead to a restoration of the ground state population. Among the quenching mechanisms, one can mention energy transfer (section I.A.7.2), electron transfer (section I.A.7.3), paramagnetic quenching or concentration quenching. The quenching processes can be intermolecular or intramolecular. In the case of intermolecular quenching, the reaction partner, termed quencher, has to diffuse in the solution to meet the fluorophore, to interact with it and then to deactivate it. This type is termed dynamic quenching. Nevertheless, in the case of a formation of complex between the quencher and the fluorophore, the quenching is termed static.

As dynamic quenching results from collisions between quenchers and fluorophores, the fluorescence intensity upon addition of quenchers is directly dependent of the quencher concentration. The Stern-Volmer equation gives a relation between the ratio of the fluorescence intensity in presence and in absence of quencher molecules and the quencher concentration, [Q]:

Φ

Φ 1 · Q 1 · · Q

where Fx is the fluorescence intensity, in the presence (q) or in absence of quenchers (0), KSV is the Stern-Volmer constant and is equal to the bimolecular quenching rate constant, kq, multiplied by the fluorescence lifetimes in the absence of quencher, τ0. As the molecules need to diffuse in the solution to interact with the fluorophore and if the quenching occurs at the first encounter, the limiting factor of such process is the diffusion, with a rate constant given by:

8 · 10 3

where η is expressed in cP. The bimolecular quenching rate constant can be related to the diffusion rate constant by the quenching efficiency factor, fq:

16 BASIC CONCEPTS OF PHOTOPHYSICS

·

The static quenching is due to the formation of a complex in the ground state between the quencher and the fluorophore. Consequently, the static quenching rate constant is directly proportional to the association constant for complex formation, KA. Considering that the fraction of fluorophores associated with the quencher does not emit, this gives:

1 · Q

Thus, both dynamic and static quenching leads to a linear dependence of the ratio of the fluorescence intensity with or without quencher as a function of the concentration of quencher. To discriminate static and dynamic quenching, several measurements can be performed. For the static quenching, the quencher only deactivates the fluorophore which is attached to it. Consequently, only the fluorescence intensity is affected. A lifetime measurement gives the same lifetime even if the quencher concentration is high, the ratio between the lifetime in presence or in absence of the quencher is thus equal to 1 in case of static quenching. Nevertheless, this is only true if the lifetime of the fluorophore-quencher complex is significantly shorter than the time resolution of the experimental setup. Indeed, if the temporal resolution is high enough, a biexponential behavior is observed due to the emission of the complex and the free molecules. Moreover, upon addition of the quencher, the amplitudes of the fast decay component, due to the complex, will increase whereas that of the slow decay, due to the unquenched fluorophores, will decrease proportionally.

Another way to discriminate both kinds of quenching is to inspect steady-state absorption spectrum. Indeed, in the case of the formation of a complex, the complex usually absorbs and this new absorption band is usually located at red wavelengths relative to the fluorophore absorption band.

BASIC CONCEPTS OF PHOTOPHYSICS 17

I.A.7.2 ENERGY TRANSFER

Another way for an excited molecule (D, the Donor) to return to the ground state is to transfer the excitation energy to another molecule (A, the Acceptor). The result is that A is in an excited state:

Excitation energy transfer (EET) processes can be sorted in two main categories. The first one called trivial mechanism is a radiative process in which the excited donor emits one photon absorbed by the acceptor. Nevertheless, this process cannot be defined as a quenching process, because no reduction of the lifetime or of the fluorescence quantum yield occurs. The second one groups all non-radiative mechanisms described below. The Fermi golden rule describes the probability than a transition between two states due to a weak perturbation occurs. It can be used to define the EET rate constant, kEET:

2 | |

where V^DA is the coupling energy between the donor and the acceptor, and is assumed to be small. ρDA is the density of states. The coupling is the sum of two contributions:

| | | | | |

where Vc and Ve represents the Coulombic and exchange interaction, respectively. The Coulombic interaction is quantitavely described by the Förster theory, and the exchange interaction by Dexter theory. Consequently, the EET rate constant is the sum of the energy transfer rate constants due to the Coulombic, kc, and exchange, ke, interactions:

18 BASIC CONCEPTS OF PHOTOPHYSICS

a) The Dipole-Dipole Approximation: The Förster Mechanism

In the middle of the forties, Theodor Förster developed a model to calculate the EET rate constant associated with the electrostatic interactions.^[25] The main assumptions are: (1) the system has to be in thermal equilibrium; (2) the coupling between A and D is small (3) the electronic coupling is due to electrostatic interaction. The last assumption is true if both molecules are enough far away to each other so that no orbital overlap exists. The main contribution to the coupling VDA is due to dipole-dipole interaction and can be expressed as the interaction energy between two punctual dipoles:

( ) ( )

⎪⎩

⎪⎨

⎧

⎪⎭

⎪⎬

⋅ ⎫

⋅

⋅

− ⋅

= ⋅

= ^∗ ₃ ^{∗ ∗} ₅ ^∗

0

3 4

1

DA AA DA D DA

D DA

AA D D dip

DA r

r r

r V

V r

r r r r r

r

r μ μ μ

μ πε

μ κ μ

πε ⋅

⎪⎩

⎪⎨

⎧

⎪⎭

⎪⎬

⋅ ⎫

= ^∗ ₃ ^∗

4 0

1

DA AA D D

DA r

V r

r r

where μD*D is the emission transition dipole moment of D*, μAA* is the absorption transition dipole moment of A, rDA is the distance between A and D, and κ is a factor accounting for the spatial orientation of the two transition dipole moments (Figure I.5), defined as:

(

)

(

) (

)

cos r r r r r r

∗

∗

∗

∗ − ⋅

= μ μ μ μ

κ 3

Figure I.5: Effect of the relative orientation of the two transition dipole moments on the factor κ.

Moreover, VDA has to be corrected if the solute is embedded into a dielectric medium. The most used correction factor is the Lorentz factor, fL, defined as:^[26]

2 3

BASIC CONCEPTS OF PHOTOPHYSICS 19

Where n is the refractive index of the medium. The corrected coupling for two transition dipole moments in a dielectric medium is thus given by:

μ κ μ

πε ⋅

⎪⎩

⎪⎨

⎧

⎪⎭

⎪⎬

⋅ ⎫

= ₂ ^∗ ₃ ^∗

0 2

4 DA

AA D L D

DA n r

V f r

r r

where VDA is expressed in cm^-1, the transition dipoles in Debye and the distance in nm.

Furthermore, taking into account that the electronic transitions are not associated with sharp lines but broad bands, kEET can be expressed as:

,

9000 · 10

128 ·  

| | ·Θ

In this equation, NA is the Avogadro constant, the distance between the two transition dipole moments is expressed in angstroms, and Θ is the overlap integral between the absorption spectrum of the acceptor, ε_A , and the normalized emission spectrum of the donor, F_D , weighted by a factor υ^--4:

Θ ^{FD · εA · ·} FD · d

Nevertheless, a more convenient way to calculate kEET,dip has been developed more recently:^[27]

, 1.18 · · Θ

where kEET,dip is expressed in ps^-1, VDA in cm^-1 and Θ is the overlap integral between the absorption spectrum of the acceptor and the emission spectrum of the donor, both spectra are area-normalized and displayed versus wavenumber.

b) The Exchange Interaction: The Dexter Mechanism

The previous subsection dealt with the Förster mechanism. This mechanism can be efficient at long distance with two well-separated acceptor and donor molecules or parts of a molecule. Moreover, it supposes the transition dipole moments as punctual. Dexter proposed in 1953 to consider the electron exchange in addition to the Coulombic interaction.^[28] The mechanism can be viewed as two simultaneous electron transfers. One

20 BASIC CONCEPTS OF PHOTOPHYSICS

electron will be transferred from the LUMO of the donor to the LUMO of the acceptor and as the same time one electron will be transferred from the HOMO of the acceptor to the HOMO of the donor (Figure I.6). The exchange energy transfer can be derived from the Fermi’s golden rule and by calculating the coupling due to the exchange interaction:

,

2 | | 2

| | Θ

Energy transfer by exchange needs a spatial overlap of the orbitals of the donor and the acceptor. Therefore, the exchange coupling is strongly dependent of the distance:

| | · exp  ·

where rDA is the center-to-center distance between the donor and the acceptor, |V0| is the magnitude of the coupling at contact and β is a constant describing the distance dependence of the coupling.

Figure I.6: Schematic representation of the excitation energy transfer through the exchange mechanism.

This distance dependence implies that the dipole-dipole mechanism is the dominant mechanism at long distance between the acceptor and the donor. Nevertheless, in some cases, the exchange mechanism can play an important role even if the distance becomes large:^[29]

1) When the donor and the acceptor are linked by a spacer, or a bridge, which has empty orbitals close in energy to the HOMO of the donor and to that of the acceptor. This leads to very small β value and to a long distance energy transfer (see ref ^[30] or chapter 3)

2) When the transitions are not dipole allowed.

BASIC CONCEPTS OF PHOTOPHYSICS 21

I.A.7.3 ELECTRON TRANSFER

Electron transfer (ET) is involved in many processes in chemistry and biology, such as oxidation, photosynthesis, photography, and corrosion. Various technical applications are based on this process like solar energy conversion, light-emitting diodes, or molecular electronics devices. In the middle of the fifties, this process was modeled by Marcus who received the Nobel Prize in 1992. Nevertheless, the understanding and the control of ET reactions is always an active research area mostly due to the development of ultrafast techniques.^[31-33] Photoinduced ET (PET) can be schematized as:

(1)   ^{·  ·} 

(2)   ^{·  ·} 

This type of reaction is called charge separation (CS) and A and D are respectively the electron acceptor and the electron donor. In many cases, the radical ions recombine to form neutral species in the ground or excited state:

(1) ^{·  ·}   

(2) ^{·  ·}  (3) ^{·  ·} 

This process is termed charge recombination (CR). As for excitation energy transfer, a ET reaction can be either intramolecular or intermolecular. Figure I.7 gives a general scheme for a bimolecular PET in solution.

Figure I.7: General scheme of a photoinduced electron transfer reaction in a polar solvent.

On the energetic points of view, the PET reaction occurs only if it is thermodynamically favorable. The Gibbs free energy, ΔGET, can be estimated from the oxidation potential of the donor, Eox(D), the reduction potential of the acceptor, Ered(A), the energy of the excited

22 BASIC CONCEPTS OF PHOTOPHYSICS

state, E00, and a Coulombic term, C, which represents the energy gain when the two ions are brought from infinite to the reaction distance:

∆

In this expression proposed by Rehm and Weller, the E00 is expressed in Joule, the redox potentials are in Volt and the elementary charge, e, is in Coulomb. The energetic diagram below shows all the energy levels involved in the reaction.

Figure I.8: Energetic levels scheme of a PET reaction.

The factor, C, is difficult to estimate, but in the charge point model, it can be estimated by the product of the charge of the two ions, q1 andq2, divided by both the distance, d, and the dielectric constant of the solvent, ε (equation below). Typically, in polar solvent, C is about -0.1-0.2 eV or less and is thus often neglected.^[34]

a) The Classical Marcus-Hush Theory

Marcus and Hush developed 50 years ago a model linking the thermodynamics and the kinetics of an ET reaction.^[35-41] This model stays nowadays the most popular model for ET reactions in many areas of chemistry. However, it is based on transition state theory which limits its applications in several cases. The main assumption are (1) the system is at quasi- equilibrium with its environment along the whole pathway from the reactants to the

BASIC CONCEPTS OF PHOTOPHYSICS 23

products, which implies that the electron transfer has to be slower than the solvent relaxation (2) the nuclear tunneling is not taken into account.

This following discussion will only treat the case of non-adiabatic ET. A non-adiabatic ET is characterized by a weak coupling, V, between the donor and the acceptor leading to two distinct energy potentials for the reactants and the products. Both potentials can be represented as a function of the solvent coordinate (Figure I.9). Whereas the crossing point between the two potential curves determines the activation free energy, ΔG*, the driving force for electron transfer, ΔGET, corresponds to the energy difference between both potentials minima and the reorganization energy, λ, to the energy needed for the reactants to reach the equilibrium configuration of the products or vice-versa. The total reorganization energy is equal to the sum of the solvent reorganization energy, λs, and the intramolecular reorganization energy, λi.

Figure I.9: Free energy curves of the reactants and products along the reaction coordinate in the Marcus-Hush theory.

The Marcus-Hush classical theory assumes that both free energy curves along the reaction coordinate are parabola with equal curvature. The ET rate constant can be related to an Arrhenius type equation:

A · exp  ∆ ⁄

where the pre-exponential factor, A, of the Arrhenius equation is proportional to the probability of the crossing from the reactant to the product. The pre-exponential factor, A,

24 BASIC CONCEPTS OF PHOTOPHYSICS

depends on the adiabaticity of the reaction. Several expressions have been proposed. The most commonly used definition of A in the non-adiabatic limit is:

2 4

Because of the parabolic geometry of the potentials, the activation energy can be calculated as a function of the ET driving force and of the total reorganization energy.

∆ ∆

4

The combination of the two previous equations gives the classical Marcus-Hush equation:

A · exp  ∆ 4

This equation leads to a non-linear dependence of the ET rate constant on the ET driving force. Indeed, at constant reorganization energy, the ET rate constant follows a Gaussian dependence on the driving force. Three different regimes are distinguished: (1) the normal region (2) the barrierless region (3) the inverted region depending on the difference between the driving force and the reorganizational energy (Figure I.10). In the first case (normal region), when |ΔG*ET|>λ, kET increases with the exergonicity of the reaction. When

|ΔG*ET|≈λ, a maximum value of kET is reached. This region is called the barrierless region. If the exergonicity keeps on increasing by keeping λ constant, kET starts decreasing.

Consequently, in this inverted region, the ET rate constant decreases with increasing driving force. This regime was only univocally observed in the middle of the eighties.^[42]

BASIC CONCEPTS OF PHOTOPHYSICS 25

Figure I.10: Illustration of the normal, barrierless and inverted Marcus regions. The Gaussian dependence of the ET rate constant as a function of the exergonicity is shown in the lower part of the figure.

b) The Semi-Classical Marcus Theory

As previously mentioned, the inverted region has been observed for many types of electron transfer, except for photoinduced bimolecular charge separation in solution.^[31]

Nevertheless, the electron rate constant observed was always found to be lower than that predicted by the classical Marcus-Hush theory. The semi-classical model includes the high frequency intramolecular vibrational quantum modes of the products and the vibrational states of the reactants (Figure I.11). This allows the ET to occur from thermally populated vibrational levels of the reactants to high-frequency vibrational levels of the products. In other words, nuclear tunneling is considered in this model. This has the effect to lower the classical barrier in the inverted region, but has no effect on the normal and barrierless regions. Furthermore, the ET rate constant has thus to be considered as the sum of all the ET rate constants occurring from the reactants level to the high-frequency vibrational levels of the products in which the individual ET rate constants are derived using time-dependent perturbation theory:

26 BASIC CONCEPTS OF PHOTOPHYSICS

· exp  ∆ 4

where λs is the solvent reorganizational energy and takes into account the coupling between the reactants and the products which is no more an electronic coupling only but also a vibrational one. In some cases, a fully quantum mechanical model is required.

Nevertheless, such a model will not be described here (see ref ^[41] for more details).

Figure I.11: Inclusion of high-frequency intramolecular modes into the non-adiabatic electron transfer theory.

C HAPTER 2

II E

T

This chapter deals with the techniques used to obtain the results presented in the next chapters. It will focus mainly on time-resolved techniques namely transient absorption and fluorescence up-conversion and also on the data analysis for both methods. At the end of the chapter, an appendix with the routines used for the fitting procedures with IGORpro are presented as well.

For time-resolved techniques, two principal approaches are possible. They are differentiated mainly by their detection methods, and thus by their time-resolution: (1) electronic methods and (2) optical methods. The electronic methods use only electronic devices on contrary of optical methods for which the pathway difference between a “pump”

pulse and a “probe” pump is used for the temporal resolution. The first technique has typically a time resolution in the best case of several tens of picoseconds due to the limitation of the electronics (see next section on the time-correlated single photon counting, TCSPC, for further information). In the case of optical methods, the time- resolution is significantly reduced and is mainly due to the pulse lengths and the optics used in the setup (see the fluorescence up-conversion and transient absorption, TA, section). With the setups used during this thesis, the time-resolution of both TA and fluorescence up-conversion is typically in the order of one or two hundreds of femtoseconds.

30 EXPERIMENTAL TECHNIQUES

II.A T

-C

S

P

C

The concept of the TCSPC technique is that the probability distribution for emission of a single photon after an excitation event yields the actual fluorescence intensity versus time distribution of all the photons emitted as a result of excitation. The principle is exposed in Figure II.1. A conventional TCSPC setup is depicted in Figure II.2. A trigger generates an electric pulse at a time correlated with the optical excitation pulse generated by laser diodes in the setup used. The excited sample fluoresces and as a photon arrives on the detector, the capacitor, whose charge was initiated by the trigger, discharges. This signal amplitude is proportional to the time elapsed between the trigger initial capacitor charge (START pulse) and its discharge due to the arrival of the photon (STOP pulse). At each period, a electronic signal corresponding to the temporal difference between the START and STOP pulses is send to the computer. The total signal is thus the sum of the randomly distributed pulses corresponding to the detection of the individual photons.^[43] In several periods, no photon is detected; most periods contain one photon pulse. Periods with more than one photon are very rare. After many photons and consequently detection periods, the distribution of the detection times is fully built up in the memory and represents the shape of the fluorescence.

Figure II.1: General principle of time-correlated single photon counting.

EXPERIMENTAL TECHNIQUES 31

For practical reasons, the TCSPC technique is often operated in a reverse-mode. Both codons START and STOP are inverted, meaning that the arrival of a photon gives the start signal of the capacitor to charge and the trigger gives the STOP signal and consequently its discharge. This mode permits to work at higher repetition rate.

Figure II.2: Schematic representation of a conventional time-correlated single photon counting.

In the present work, excitation was performed at a repetition rate of 10–40 MHz with < 90 ps pulses generated by laser diodes either at 395 nm (Picoquant model LDH-P-C-400B) or at 470 nm (Picoquant model LDH-P-C-470). The average power was about 0.5 mW.

Fluorescence was collected at 90^o at magic angle with respect to the polarisation of the pump pulses. A 420 nm or 560 nm cut-off filter placed in front of the photomultiplier tube (Hamamatsu, H5783-P-01) ensured that no scattered excitation light could reach the detector, the output of which was connected to the input of a TCSPC computer board module (Becker and Hickl, SPC-300-12). Additionally, a tunable continuous bandpass filter was placed after the sample when required. The full width at half maximum (FWHM) of the IRF was around 200 ps. The IRF was recorded by placing a scattering solution (toluene- water mixture) at the sample position. As for steady-state measurements, all TCSPC measurements were performed in a 1 cm quartz cell and the absorbance of the samples was kept below 0.1 at the absorption maximum. The accuracy on the lifetimes is of about 0.1 ns.

32 EXPERIMENTAL TECHNIQUES

II.B F

U

-C

As the time-resolution of TCSPC is of the order of several tens of picoseconds, it is not short enough to observe many processes. To have a better time-resolution, an optical-based technique is needed, in order to bypass the limit of the electronic detection. The fluorescence up-conversion is a technique whose time-resolution is only limited by the laser pulse duration and the optics used. In the best case, it can reach less than one hundreds femtoseconds. This technique is based on the sum frequency generation between a gate pulse and the fluorescence (Figure II.3). The electric polarization of a material, , can be expressed as a power series of the electric field:

· · · . . .

In this expression, is the linear optical susceptibility and corresponds to the susceptibility at low field intensity, is the second-order nonlinear optical susceptibility, and the third-order non-linear optical susceptibility. The ratio between , and is typically 1:10¹²: 10²³.^[44] This ratio implies that a non-linear relationship between the polarization and the electric field is possible only with very high electric fields, as those found in short optical pulses generated by lasers.

Let’s consider a radiation field oscillating at two frequencies, it can be expressed as:

, · cos · cos 

Considering a material with non-zero second-order susceptibility, the nonlinear polarisation depends on the square of the electric field which is equal to:

, 1

21

2 cos 2 1

2 cos 2

· cos cos 

Consequently, the new polarization contains: (1) a time-independent component (2) two components at the double of the initial frequencies (2ω1 and 2ω2) (3) a component at the sum of the initial frequencies (ω1+ω2) and (4) a term at the difference of the frequencies

EXPERIMENTAL TECHNIQUES 33

(ω1-ω2). The material polarization can thus generate electromagnetic fields at these different frequencies. The generation of light at the double of the initial frequency is termed second harmonic generation (SHG) and that at the sum of the initial frequencies is termed sum-frequency generation (SFG). One of the main conditions which have to be fulfilled to generate new frequency is the so-called phase-matching condition. The phase matching is related to the conservation of the momentum: . To fulfill this phase-matching condition in the case of SHG, the refractive index of the material has to be the same for the incident beam and the created one.^[44] The only possible way to be in the right conditions is thus to use birefringent materials such as uniaxial crystals, for example barium or bismuth beta borate (BBO and BiBO, respectively).

Figure II.3: schematic representation of a fluorescence up-conversion setup.

For time-resolved fluorescence measurements shown in the following chapters, a single fluorescence up-conversion setup was used. Nevertheless, during this PhD, the laser source was changed from a Tsunami Ti:sapphire laser (Spectra Physics) delivering ~100 fs pulses centered at 800 nm at ~82 MHz to a Mai Tai Ti:sapphire laser (Spectra Physics) whose emission wavelength is tunable between 680-1040 nm. The pulse duration and the repetition rate of the Mai Tai are approximately similar to those of the initial laser. As the excitation beam is generated by SHG from the initial beam, the excitation wavelength can

34 EXPERIMENTAL TECHNIQUES

also be tuned from 340 nm to 520 nm. Even if the output energy of the Mai Tai is larger than of the previous laser, the input energy is adjusted to have about 600 mW using a combination of halfwave plate and Glan-Taylor polarizers directly put before the entrance of the experimental setup depicted in Figure II.3. This input beam is split into two parts:

40% goes into the optical delay line and the remaining energy is directed to the SHG crystal to generate the excitation beam. The polarization of the generated excitation beam is adjusted with a half waveplate just before the sample. The sample is put into a 0.4-1 mm thick rotating cell and its absorbance at 400 nm was about 0.1. The fluorescence is then collected and focused into the second crystal. The 40% of the initial beam, after going into the optical delay line, are focalized into this crystal as well. If both pulses arrive at the same time into the BBO crystal, the SFG signal is generated. This UV signal goes then into a monochromator and to a photomultiplier. The wavelength of the fluorescence is selected by: (1) the angle of the SFG BBO crystal to fulfill the phase-matching condition and (2) the monochromator adjusted for the right UV signal wavelength. The dynamics at the chosen fluorescence wavelength is recreated by scanning the length of the gate beam pathway (Figure II.4).

Figure II.4: Principle of temporal sampling of the fluorescence up-conversion technique.