Structure-Property Relations in Polymers - American Chemical Society

3

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Spectroscopic Characterization of Polymers Fluorescence Principles Gregory D . Gillispie Department of Chemistry, North Dakota State University, Fargo, N D 58105

The principles of fluorescence that apply to the determination of polymer physical properties are covered in tutorial fashion. Fluores cence is a sensitive technique for probing the microenvironment in large molecules and for following conformational changes and fast (microsecond or less) internal motion. This survey focuses on the spectroscopy of aromatic molecules commonly used as fluorescent tags on synthetic polymers. Individual sections cover the electronic struc ture of aromatic molecules, absorbance and fluorescence spectroscopy, and the dynamical processes that control fluorescence intensity.

T h e conformations o f macromolecules i n dilute solution are typically charac terized b y such terms as flexible coils, rigid rods, a n d globular particles. W h e n a p o l y m e r folds u p o n itself, chemically distinct microdomains a n d microenvironments are created. T h e n u m b e r a n d distribution o f such d o mains are a function o f temperature, pressure, solvent dielectric constant, p H , ionic strength, a n d the concentration o f the macromolecule itself. T h e r e is, therefore, a p r e m i u m o n characterization techniques that (1) can b e directly a p p l i e d to the sample without any manipulation that might disrupt the polymer; (2) are highly specific i n their ability to sense different m i c r o e n vironments a n d the changes i n the microenvironment distribution as b u l k conditions are m o d i f i e d ; a n d (3) are extremely sensitive. Spectroscopic methods, i n c l u d i n g infrared, R a m a n , Ν M R , a n d fluores cence, are often superior to macroscopic techniques, such as viscosity a n d molecular weight determination, i n this regard. Fluorescence is the topic o f 0065-2393/93/0236-0089$ 10.75/0 © 1993 American Chemical Society

Urban and Craver; Structure-Property Relations in Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1993.


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S T R U C T U R E - P R O P E R T Y R E L A T I O N S IN P O L Y M E R S

this chapter; the other optical spectroscopies are covered elsewhere i n this volume. T h e vibrational spectroscopies, i n f r a r e d a n d R a m a n , are applicable to p o l y m e r structure determination (structure i n the sense o f c h e m i c a l b o n d properties) because the stretching a n d b e n d i n g vibrations i n a p o l y m e r closely resemble those i n m o n o m e r s . O f course, i f the vibrational spectra were completely transferable, these spectroscopies w o u l d be worthless as m i c r o e n v i r o n m e n t a l probes. Because the spectral changes w i t h environment are rather subtle, accurate measurement o f small changes i n b a n d position is r e q u i r e d . T h e greatest source o f m o d e l uncertainty is often the v a f i d i t y - r e l i a bility o f the p r o p o s e d relationship between spectral position a n d physical property. Details can be f o u n d i n the c o m p a n i o n overviews of vibrational spectroscopy i n this v o l u m e . W e also note the extensive use o f R a m a n spectroscopy as a p r o b e o f b i o p o l y m e r conformation ( I ) . Fluorescence, i n contrast, is an electronic spectroscopy that, as such, offers little i n f o r m a t i o n about i n d i v i d u a l b o n d properties, but otherwise has some extremely favorable features: • Fluorescence is extremely sensitive. • Fluorescence is inherently a m u l t i d i m e n s i o n a l , selective tech nique. • T h e fluorescence excitation spectrum can readily be deter m i n e d for strongly scattering o r even opaque samples (amorphous solids, t u r b i d a n d f r o z e n solutions, cracked glasses, etc.) for w h i c h the conventional absorbance approach is difficult or even impossible. • Fluorescence provides d y n a m i c a l i n f o r m a t i o n o n a time scale relevant to p o l y m e r internal motions. • W e l l - d e v e l o p e d a n d w e l l - u n d e r s t o o d models are available for data interpretation. Fluorescence is the most sensitive optical spectroscopy. U s e f u l signals routinely can be detected at nanomolar concentrations, a n d at the subpicomolar level i n favorable cases. T h i s sensitivity is c r u c i a l for experiments i n w h i c h a fluorescence probe is c h e m i c a l l y attached to a nonfluorescent p o l y m e r backbone because the p r o b e concentration can be kept l o w enough to avoid influencing the properties o f the p o l y m e r itself. T h e m u l t i d i m e n s i o n a l fea ture, that is, the intensity depends o n two wavelengths (excitation a n d emission) instead o f just one, confers increased detection specificity a n d provides a w i d e r choice o f experimental configurations. T h e d y n a m i c a l i n f o r m a t i o n is directly realized i n p u l s e d excitation experi ments, but rates o f some processes c a n also be i n f e r r e d f r o m steady-state


3.

GILLISPIE

Spectroscopic Characterization of Polymers

91


polarization measurements. A l m o s t every spectroscopic m e t h o d can be ap p l i e d to reaction kinetic studies. H o w e v e r , the i n f o r m a t i o n fluorescence provides o n internal motions a n d rotational dynamics i n the m i c r o s e c o n d to picosecond regime is unsurpassed. F i n a l l y , fluorescence experiments can be interpreted w i t h standard equations d e r i v e d f r o m essentially first principles models, such as those that describe S t e r n - V o l m e r quenching, orientational depolarization, a n d Forster a n d D e x t e r energy transfer processes (2-4). O n the debit side, whereas i n f r a r e d absorption, R a m a n scattering, a n d nuclear magnetic resonance p h e n o m e n a are exhibited b y virtually every molecule, most synthetic polymers are not intrinsically fluorescent a n d must be tagged w i t h covalently attached fluorescence probes. Fluorescence poses an expanded m e n u o f experimental configurations a n d a sometimes daunting array o f n e w concepts a n d terminology. N o t e that fluorescence intensities are inextricably l i n k e d to molecular dynamics considerations (e.g., excited state radiationless processes, quenching, excimer formation, etc.) as opposed to the simple a n d direct intensity versus wavelength picture o f i n f r a r e d or U V - v i s i ble absorbance spectroscopy. T h i s chapter was w r i t t e n as a tutorial o n fluorescence principles, not as a review article o n physical characterization o f polymers b y fluorescence; that aspect is covered b y the research papers i n this v o l u m e . T h e goal here is to provide a compact i n t r o d u c t i o n that serves as a reliable starting p o i n t for consultation o f m o r e advanced treatments o f p o l y m e r photophysics (4). W h e t h e r or not p o l y m e r scientists p e r f o r m fluorescence measurements t h e m selves, they n e e d a basic understanding o f the technique to f o l l o w the literature. M o s t research papers are w r i t t e n at a m o r e specialized level than what is f o u n d i n the standard chapters o n fluorescence a n d phosphorescence i n instrumental analysis textbooks. T h e question " w h y " m o r e than " w h a t " or " h o w " is often the m a i n s t u m b l i n g block to the nonspecialist trying to understand a fluorescence paper. T h u s , the w r i t i n g here has b e e n g u i d e d b y an attempt to anticipate a n d directly address those concepts that experience has shown to be potentially the most confusing. O w i n g to space limitations, selected f r o m the entire range o f lumines cence techniques are those initiated by p h o t o n absorption; other light emis sion methods (chemiluminescence, pulse radiolysis, bioluminescence) f o l l o w similar principles. F o r convenience, fluorescence is used as a generic t e r m for photoluminescence a n d only a f e w comments are made about phosphores cence. O u r major emphasis is o n polymers that have b e e n " t a g g e d " or labeled w i t h polycyclic aromatic or heteroaromatic fluorescence probes such as naphthalene, anthracene, phenanthrene, pyrene, a n d carbazole. T h e probes can be p l a c e d directly into the p o l y m e r backbone, attached as pendant groups, or located as e n d caps o n chain polymers. A f t e r a b r i e f i n t r o d u c t i o n to absorbance spectroscopy a n d electronic structure notation, the sequence o f steps that generate a B o l t z m a n n v i b r o n i c population distribution i n the first excited singlet state, f r o m w h i c h the


92

S T R U C T U R E - P R O P E R T Y R E L A T I O N S IN P O L Y M E R S

fluorescence

process originates, are outlined. These steps i n c l u d e photoab

sorption, vibrational relaxation w i t h i n an electronic state, and internal conver sion between excited singlet electronic states. T h i s is f o l l o w e d b y a discussion of the

fluorescence

spectral distribution, the degree o f structure i n the

spectrum, what this structure does (or does not) mean, the possible m i r r o r image relationship to the absorbance spectrum, a n d wavelength shifts as a function o f solvent. T h e next section covers the decay processes (fluorescence internal conversion to S , intersystem crossing to T 0

l 3

emission,

quenching, excimer

formation, etc.) that depopulate the e m i t t i n g excited state. T h e relative


magnitude o f the radiative a n d nonradiative rate constants fluorescence

controls the

efficiency (quantum yield) whereas their absolute magnitudes

determine the lifetime. T h e quantitative S t r i c k i e r - B e r g equation for radiative decay rates a n d the e m p i r i c a l energy gap l a w f o r radiationless transitions are mentioned. E n v i r o n m e n t a l effects o n radiationless transition rates are a d dressed briefly.

Absorbance Spectroscopy of Aromatic Molecules Jablonski Diagrams and Piatt Notation.

Photoabsorption is the

usual m o d e for creating the excited electronic states f r o m w h i c h

fluorescence

occurs. A b s o r p t i o n a n d fluorescence are complementary photoprocesses that connect u p p e r a n d lower electronic states:

Absorption:

L o w - e n e r g y state 4- p h o t o n —> high-energy state

Fluorescence:

H i g h - e n e r g y state -> low-energy state + p h o t o n

E a c h electronic state has its o w n set o f internal vibrational energy levels. Interstate vibrational transitions (as distinguished f r o m the intrastate vibra tional transitions o f i n f r a r e d spectroscopy) occur simultaneously w i t h the electronic excitation o r deexcitation a n d are responsible for structure (bands, peaks, shoulders) i n the electronic spectra. S u c h vibronic

(vibrational-elec

t r o n i c ) structure is never fully resolved i n solution spectra a n d is sometimes completely lost. T h e creation o f p o p u l a t i o n i n the state that ultimately emits

fluorescence

begins w i t h absorption o f a p h o t o n b y the g r o u n d electronic state, w h i c h is conventionally labeled S

0

( S is the singlet a n d 0 is the n u m e r i c a l index o f

relative energies). A l t h o u g h the

fluorescence

almost always occurs only f r o m

SJL, the first excited singlet state, there are other, higher electronic states into w h i c h the molecule c a n b e excited. A key concept o f monomer


solution

3.

GILLISPIE

fluorescence The

93

Spectroscopic Characterization of Polymers is the following:

fluorescence

spectral distribution (i.e., relative intensity as a

function o f wavelength) does not d e p e n d o n w h i c h

electronic

state is initially excited.


T h e n u m b e r o f excited molecules created, a n d , hence, the n u m b e r o f fluorescence photons subsequently generated, is nearly always a f u n c t i o n o f the excitation wavelength, b u t the fluorescence spectral shape is not. T h e standard molecular orbital m o d e l considers that an excited state is d e r i v e d f r o m the g r o u n d state v i a p r o m o t i o n o f an electron f r o m an o c c u p i e d orbital to a vacant, higher energy orbital. I f all the electrons are spin-paired i n S , w h i c h is usually the case for organic molecules, a one-electron p r o m o t i o n creates t w o singly o c c u p i e d orbitals. I f t h e electrons i n these two orbitals are spin antiparallel, a singlet state results. I n triplet states the two electron spins are parallel. T h e excited singlet states i n order o f increasing energy are labeled S S , S , . . . ; the excited triplet states are similarly labeled 0

1 ?

2

3

Tj, T , T h e lowest triplet state is conventionally designated T , not T , as might b e expected, because the first excited singlet state a n d the lowest triplet state are n o m i n a l l y d e r i v e d f r o m the same electron configuration: 2

x

...(HOMO) (LUMO) 1

0

1

w h e r e H O M O a n d L U M O refer to the highest energy o c c u p i e d molecular orbital a n d lowest energy u n o c c u p i e d molecular orbital, respectively ( i n the g r o u n d electronic state). I n reality, S a n d T often arise f r o m different electron configurations, especially i f S is an η-ττ* state. T h i s is c o m m o n l y l

1

Y

the case for aromatic carbonyls. T h e electronic absorbance spectra o f organic molecules are safely inter p r e t e d solely i n terms o f transitions to excited singlet states o w i n g to the extreme weakness o f the s p i n - f o r b i d d e n s i n g l e t - t r i p l e t transitions. Incorpora tion o f "heavy atoms" into the molecular framework increases s p i n - o r b i t c o u p l i n g a n d thereby partially lifts the spin-forbiddenness, b u t not nearly enough to invalidate the previous sentence. N o t e that although the p h e n o m e n o n is referred to as the heavy atom effect, i t is a nuclear charge dependence, not a mass effect, p e r se. A n external heavy atom effect c a n b e realized w i t h solvents that contain one o r m o r e h i g h atomic n u m b e r atoms (e.g., b r o m o f o r m , ethyl iodide); however, the internal heavy atom effect is usually more effective. Extensive discussions a n d data tabulations o n heavy atom effects a n d s p i n - o r b i t c o u p l i n g are available ( 5 ) . T h e w i d e variation i n absorption strengths for the various electronic transitions connected to S is evident f r o m the spectra o f phenanthrene a n d anthracene shown i n F i g u r e 1. F o r example, the peak molar absorptivity is about 200 times lower i n the phenanthrene S T decay rate (see following discussion o f El-Sayed's rule below), a n d the increase i n fluores cence efficiency c a n b e dramatic. Enhancements b y several orders o f m a g n i tude are possible. Downloaded by MONASH UNIV on April 15, 2016 | http://pubs.acs.org Publication Date: May 5, 1993 | doi: 10.1021/ba-1993-0236.ch003

l

X

Pyrene is often used as a photophysical p r o b e for polymers o w i n g to its proclivity for excimer formation, a topic discussed i n the next section. A different aspect is n o t e d here. Pyrene exhibits a reasonable degree o f structure i n its fluorescence spectrum ( F i g u r e 15). F i v e major bands, labeled I through V , are readily identified. R a n d I, the shortest wavelength major feature, is conventionally called the 0-0 b a n d a n d n o m i n a l l y represents the transition between the S a n d S zero-point levels. A s was discussed earlier, this " b a n d " is actually the overlap o f many v i b r o n i c transitions. Nevertheless, 0

x

ππ ηπ*

• ηπ, •ππ M «β ο

So

bû I C5 Ο

f

APROTIC

HYROGEN-BONDING

SOLVENT

SOLVENT

Figure 14. Illustration of the inversion of the η-ττ* and π-π* states of a heteroaromatic molecule as the solvent is changed from an aprotic to a hydrogen-bonding solvent.


3.

GILLISPIE


I

Γ 360

1

1

1

1

I

1

370

1

113

Y

1

1

1

1

1

380

1

1

1

1

1

1

390

1

I

1

1

1

400

M

1

1

1

1

410

I

420


Wavelength (nm)

Figure 15. Fluorescence spectra of pyrene in water and in heptane. The spectra have been normalized to the same intensity at band III.

it retains considerable true 0-0 character. N o w according to molecular symmetry, the 0-0 b a n d i n an isolated molecule (i.e., gas phase) o f pyrene is f o r b i d d e n . Solvent perturbation can lift this forbiddeness, and i n strongly polar solvents b a n d I is considerably intensified relative to the other bands. T h e p h e n o m e n o n is sometimes referred to as the H a m effect i n h o n o r o f its discoverer (25). T h e standard practice is to use the ratio o f b a n d I to b a n d III intensity; this ratio forms the basis of a solvent polarity scale (26). I n this fashion pyrene can reveal the polarity o f microenvironments, as i n a labeled p o l y m e r system, or w h e n the pyrene is solvated i n a micelle.

Deactivation of the Emitting State The Jablonski Diagram Revisited. T h e discussion n o w turns f r o m the energetic aspects (state diagrams, wavelength distribution) o f fluo rescence to a consideration o f the rate processes that deactivate the e m i t t i n g state. Fluorescence temporal behavior yields the most detailed picture avail able o n the m o t i o n o f p o l y m e r systems o n the fast ( 1 0 " - 1 0 ~ -s) t i m e scale. T h i s section provides an overview o f the important radiationless processes that compete w i t h fluorescence emission a n d h o w the rate constants are d e t e r m i n e d f r o m experiment. 6

12

T h e kinetic processes that deactivate the S state can be separated into radiative (fluorescence), u n i m o l e c u l a r nonradiative (internal conversion to S and intersystem crossing to 7\), a n d b i m o l e c u l a r nonradiative (quenching, e x c i m e r - e x c i p l e x formation, energy transfer) contributions. T h e fluorescence ( f c ) , intersystem crossing ( J t ) , and internal conversion ( k ) processes follow first-order kinetics a n d each is therefore associated w i t h a t i m e - i n d e pendent rate constant, as is illustrated i n F i g u r e 16A. T h e b i m o l e c u l a r steps are vital aids i n revealing the details o f macromolecule internal m o t i o n , but x

0

F

I S C

l c


114

STRUCTURE-PROPERTY RELATIONS IN POLYMERS


(A)

(B)

Figure 16. A: Conventional "vertical" representation of radiationless and radiative intramolecular decay paths from S. B: Schematic energy level diagram indicating that radiationless transitions are horizontal (isoenergetic) processes, but they are followed in solution by much faster vibrational relaxation processes with average rate constant K . VR

w e w i l l first consider the case o f a single c h r o m o p h o r e i n dilute, degassed solution, i n w h i c h the intermolecular processes can b e neglected. T h e directly measurable fluorescence parameters are q u a n t u m y i e l d a n d lifetime. T h e fluorescence q u a n t u m yield, Φ , is the ratio o f n u m b e r o f photons e m i t t e d to t h e n u m b e r o f photons absorbed, o r equivalently, t h e ratio o f the n u m b e r o f e m i t t e d photons to the n u m b e r o f excited molecules initially created b y photoexcitation. Fluorescence quantum y i e l d is related to the first-order radiative a n d nonradiative rate constants b y Ρ

Φ Ε = k /(k F

F

+ k

+ * )

lc

= k /(k

ISC

F

+ k

F

N R

)

(5)

where fc is t h e total nonradiative decay rate constant. E q u a t i o n 5 c a n b e readily d e r i v e d f r o m a photostationary state treatment, b u t i t is applicable to p u l s e d experiments as w e l l . T h e s u m i n the denominator o f e q 5 represents the total rate constant f o r the exponential decay o f the S population. T h e reciprocal o f that s u m is the fluorescence lifetime ( T ) : NR

x

F

T

F

= (k

F

+ fe

IC

+ k

l s c

)~

= (k

l

F

+ k )~

l

NR

(6)

N o t e that t h e t e r m "fluorescence l i f e t i m e " is slightly misleading. M o r e properly, T is the S lifetime. Reference is made to T as the fluorescence lifetime s i m p l y because fluorescence is t h e usual ( a n d b y far t h e most convenient) way to follow t h e S p o p u l a t i o n decay. I f transient absorption f r o m S were followed, the same 8 lifetime should b e f o u n d . E q u a t i o n 5 can b e w r i t t e n m o r e compactly: f

f

x

x

x

Χ

Φ

Ρ

=

kT F

F


(7)

3.

GILLISPIE

115


A t this stage there are two measurable quantities ( Φ , τ ) , but three rate constants ( f c , k , fc ). T h e radiative decay rate, k , can be d e t e r m i n e d f r o m e q 7; then the total nonradiative decay rate, fc , can be d e t e r m i n e d f r o m e q 6. A t h i r d measurement, usually that o f the q u a n t u m y i e l d for triplet formation v i a intersystem crossing, is necessary for a determination of the individual nonradiative rate constants. M a n y times the approximation is made that internal conversion is negligibly slow c o m p a r e d to intersystem crossing i n w h i c h case ρ

F

lc

ISC

ρ

F

NR


*isc

*F) A F

= (1 -

NR

s

FC

(8)

Results for selected polycyclic aromatic hydrocarbons d e r i v e d o n this basis are given i n T a b l e I. H o w e v e r , note that there are cases for w h i c h nonradia tive decay is d o m i n a t e d b y S -> S internal conversion (e.g., stilbenes, polyenes, β-carotene, etc.). I n a strict sense, internal conversion a n d intersystem crossing ought to be represented as isoenergetic processes, as opposed to the " v e r t i c a l " d e p i c t i o n of F i g u r e 16A. F o r example, i n the S -> T intersystem crossing, electronic energy equal to the S -T electronic energy gap is converted into Τ excess vibrational energy ( F i g u r e 16B). H o w e v e r , the radiationless transitions are f o l l o w e d b y m u c h faster vibrational relaxation. T h e internal conversion a n d intersystem crossing might be v i e w e d as rate-limiting steps i n a conventional kinetic picture o f the sequential "reactions": 0

x

x

l

x

l

λ

°o

i

D

S

x

-» Tf

°o -> 2\

where Sf and Tf represent vibrationally excited states w i t h the same total vibronic energy as that o f the S state undergoing the radiationless transition(s). 2

Table I. Photophysical Data for Aromatic M o l e c u l e s " Molecule

Φ

Ρ

Benzene Naphthalene Anthracene Phenanthrene Pyrene Biphenyl Fluorene Perylene Benzo[ ghi Jperylene Carbazole Chrysene a

0.07 0.23 0.36 0.13 0.32 0.18 0.80 0.94

—

0.38 0.14

T

f

(ns)

29 96 4.9 57.5 290 16.0 10 6.4 107 16.1 44.0

1

2.4 2.4 7.3 2.3 1.1 1.1 8 1.5

Χ Χ Χ Χ X X Χ Χ

—

S )

e(S

^(s- )

0

1

10 10 10 10 10 10 10 10

2.3 Χ 10 3.1 Χ 10

6 6 7 6 6 7 7 8

3.2 Χ 8.0 Χ 1.3 Χ 1.5 Χ 2.3 Χ 5.5 Χ 2.X 6 Χ

—

7 6

10 10 10 10 10 10 10 10

3.9 Χ 10 1.9 Χ 10

7 6 8 7

210 300 10,000 220

6 7 7 6

10,000 39,000

—

7 7

Data taken from reference 13.


4,300 700

116


T w o points to note:

1. T h e experimentally d e t e r m i n e d nonradiative rate constants are truly those o f the intersystem crossing a n d internal conversions themselves because the vibrational relaxation is so m u c h faster. 2. T h e radiationless transitions are fundamentally intramolecular processes (i.e.,

solvent-assisted vibrational relaxation is not

necessary) as is demonstrated b y supersonic jet studies o f gas


phase isolated molecules ( 2 7 ) .

Fluorescence Quantum Yield and Lifetime Measurements. T h e fluorescence q u a n t u m y i e l d is a b r a n c h i n g ratio between radiative a n d nonradiative decay, a n d its value must therefore He between 0 a n d 1. A l t h o u g h this chapter is not i n t e n d e d as a methods document, a few words o n q u a n t u m y i e l d measurements are appropriate here. M o s t often fluorescence q u a n t u m yields are d e t e r m i n e d i n a relative sense b y c o m p a r i n g the inte grated fluorescence intensity for the molecule of interest to that o f a standard. O n e approach is to balance (i.e., match) the absorbances o f sample a n d reference c o m p o u n d at a wavelength w h e r e b o t h absorb w e l l , to r e c o r d their separate fluorescence spectra excited at that wavelength (thereby ensur i n g that sample a n d reference each absorb the same n u m b e r of photons), a n d to measure the areas u n d e r the respective fluorescence curves. B e aware, however, that subleties a b o u n d i n the process. Unless the sample a n d reference fluorescences are closely overlapped i n wavelength, the spectra must b e corrected for wavelength response o f the detection system as w e l l as converted to an intensity versus w a v e n u m b e r format (which, i n turn, intro duces a slit correction). O t h e r sources o f error i n c l u d e too great a variation o f the absorbance of either sample or standard over the excitation bandpass or differential sensitivity o f the sample a n d standard to oxygen or self-quench ing. References 28 a n d 29 s h o u l d be consulted for details. M o r e o v e r , the issue still remains o f h o w to determine the absolute fluorescence q u a n t u m y i e l d o f the standard, w h i c h is usually accomplished v i a integrating sphere techniques. T w o examples emphasize the intricacies o f absolute q u a n t u m y i e l d determination. T h e first is the case o f 9,10-diphenylanthracene, used as the standard b y B e r l m a n (13). O v e r the years the r e c o m m e n d e d value has j u m p e d back a n d forth between 0.83 a n d 1.00 a n d there still appears to be less than u n a n i m i t y o n the subject (30). T h e second, a n d i n many ways m o r e striking, example is the recent meticulous w o r k b y Johnston a n d L i p s k y (31) that suggests the long-accepted fluorescence quan t u m y i e l d o f benzene vapor may be too h i g h b y a factor o f almost 4. Nevertheless, w i t h reasonable care it s h o u l d be possible to generally obtain fluid solution relative fluorescence q u a n t u m yields accurate to w i t h i n 2 5 % .


3.

GILLISPIE


117

T h e most straightforward way to determine lifetimes is to populate S m u c h faster than the subsequent excited state depopulation occurs v i a fluorescence and radiationless decay. If all the decay paths are first order, the S population decreases exponentially i n time. A plot of the natural logarithm of fluorescence counting rate versus time is then linear a n d the lifetime is simply extracted as the negative reciprocal o f the slope. x


x

W h e t h e r the excitation step is sufficiently separated i n t i m e f r o m the subsequent decay depends o n the lifetime value and the nature o f the excitation source. T h e r e are many different possible excitation sources a n d the reader is directed to D e m a s (32) for details. W e w i l l m e n t i o n four types here: (1) gas-filled discharge lamps that operate at a few kilohertz w i t h a pulse duration o f a few nanoseconds; (2) low-repetition rate p u l s e d excimer, nitrogen, a n d N d - Y A G lasers w i t h typical pulse durations also i n the few nanosecond range; (3) h i g h repetition rate picosecond duration laser systems (e.g., m o d e - l o c k e d a n d cavity d u m p e d i o n a n d N d - Y A G systems; (4) continu ous excitation sources, c o m m o n l y xenon arc, w i t h their output sinusoidally m o d u l a t e d at tens o f megahertz w i t h acoustooptic or electrooptic devices. Sources of this type f o r m the basis o f phase-resolved fluorescence spec troscopy (33). T h e most attractive feature of phase resolved methods is that w i t h a c o m m e r c i a l spectrofluorimeter one can measure b o t h conventional luminescence a n d excitation spectra as w e l l as lifetimes. I f the fluorescence lifetime is not l o n g c o m p a r e d to the excitation pulse duration, it is necessary to extract the lifetime b y deconvolution, a mathemati cal processing o f the data to give the best agreement between the experimen tal decay curve a n d those calculated for various assumed lifetimes. U n d e r favorable conditions, lifetimes as short as 1/10 the excitation pulse w i d t h have b e e n extracted. T h e precision w i t h w h i c h lifetimes can be measured is m u c h higher than for q u a n t u m yields. Uncertainties of less than 1 % for lifetimes above 10 nanoseconds are routinely achieved. F i g u r e 17 presents illustrative data for anthracene i n solution. I n this experiment the laser p u l s e w i d t h has a duration comparable to the excited state lifetime so deconvolution w o u l d be r e q u i r e d to extract the lifetime. N o t e that the decay is extended i n time w h e n the solution is degassed to eliminate oxygen q u e n c h i n g (see later discussion o f the S t e r n - V o l m e r equa tion).

The Radiative Decay (Fluorescence) Process. T h e rate c o n stant for fluorescence radiative decay f r o m S to S can often be accurately estimated because the spontaneous fluorescence and absorbance processes are related t h r o u g h the E i n s t e i n A a n d Β coefficients (34). Strickler a n d B e r g (35) generalized the E i n s t e i n treatment to molecular systems a n d derived an equation for k that contains the so-called integrated absorbance spectrum (necessarily l i m i t e d to the S \ .

Anthracene (undegassed) \\

Anthracene (degassed)

200H

30

40

50

60


Time (ns) Figure 17. Fluorescence lifetime traces for anthracene in degassed and airsaturated cyclohexane solution, along with the laser excitation time profile. Excitation source was a dye laser and temporal data acquired with a digital oscilloscope. excellent. I f the experimental value is more than a factor o f 2 lower than the calculated value, a weakly absorbing S state b u r i e d i n the long wavelength tail o f a stronger transition to S should be suspected. A n u m b e r o f misassignments have been cleared u p i n this fashion. x

2

A s i m p l i f i e d version o f the S t r i c k l e r - B e r g equation suitable f o r rough estimates is fc^s" ) 1

= 3 X 10-Ve

m a x

Δν

(9)

1 / 2

where ν is the average wavenumber o f the fluorescence, € is the maxi m u m molar absorptivity i n units o f liters p e r mole p e r centimeters, a n d Δ ν is the h a l f - w i d t h o f the electronic transition. T h e average half-width reported b y B e r l m a n ( 1 3 ) is 3600 c m . W e may take e = 100 as the m i n i m u m molar absorptivity to b e expected i n aromatics. F o r a typical emission wavelength o f 350 n m , the radiative decay rate is therefore approximately 1 0 s ; equivalently, the lifetime w o u l d be 1 μ 5 i f fluorescence were the sole S decay path. A n y higher molar absorptivity ( i f S is L , for example) or any contribution o f nonradiative decay w i l l shorten the lifetime. Thus, the long time l i m i t o f processes that c a n b e m o n i t o r e d b y fluorescence is about 1 μ Ξ . Slower processes c a n b e m o n i t o r e d via the longer-lived phosphorescence. I n part, the popularity o f pyrene as a photophysical probe for p o l y m e r physical properties is its long intrinsic fluorescence lifetime [ca. 300 ns for the m o n o m e r i n dilute solution (36)]. m a x

1 / / 2

- 1

m a x

6

- 1

x

x

l

a

T h e reciprocal o f k is sometimes referred to as the radiative lifetime o r pure radiative lifetime. I n other words, it is the excited state lifetime that w o u l d follow i n the hypothetical case where the nonradiative decay is suppressed. F


3.

GILLISPIE

119


Intramolecular Decay: Radiationless Transitions. T h e r e is no reliable radiationless transition rate constant f o r m u l a analogous to the Strickl e r - B e r g equation; a p r i o r i predictions of internal conversion rates a n d intersystem crossing rates are b e y o n d reach n o w a n d the situation is not expected to change soon. Fortunately, there do exist very useful e m p i r i c a l correlations a n d w e w i l l t o u c h u p o n these briefly. T h e theoretical description o f a radiationless transition f r o m an initial state i to a final state f begins w i t h F e r m i ' s G o l d e n R u l e : fc

NR

= 2irAlV | t f

2

P f

(E,)

(10)

i n w h i c h the c o u p l i n g matrix element V is a measure o f the strength of the interaction between the initial a n d final states a n d p is the density o f final vibronic levels at the energy o f the initial state (E ). T h e m o d e r n era o f radiationless transition theory dates to the seminal R o b i n s o n a n d F r o s c h paper ( 3 7 ) . M a n y f o r m a l theory papers a n d review articles (38) were w r i t t e n on the topic i n the 1970s a n d early 1980s. Unfortunately, first p r i n c i p l e calculations have p r o v e n impossible. T h e r e is no reliable theoretical alterna tive to experimental measurements or estimates based o n experimental values i n chemically similar systems.


i f

f

{

In this regard, the correlation o f radiationless transition rate w i t h elec tronic energy gap, first presented b y Siebrand ( 3 9 ) has b e e n extremely useful. A s discussed earlier, internal conversion a n d intersystem crossing are energy-conserving processes, w h e r e i n the electronic energy difference be tween the initial a n d final states must be converted into vibrational energy i n the final (accepting) state. T h e conversion efficiency is enhanced b y the presence o f a large n u m b e r o f final states to accept the energy (the density o f states t e r m i n the G o l d e n R u l e ) and b y a strong c o u p l i n g between the initial and final states (the matrix element term). T h e c o u p l i n g matrix elements can be cast into a f o r m that contains F r a n c k - C o n d o n factor type terms, again between the initial state (with small vibrational q u a n t u m numbers) a n d the final states, w h i c h are characterized b y large vibrational q u a n t u m n u m b e r s . T h e larger the electronic energy differ ence between the two states, the larger the change i n vibrational q u a n t u m n u m b e r r e q u i r e d b y the radiationless transition, and, accordingly, the smaller the F r a n c k - C o n d o n factor. T h e density of states a n d c o u p l i n g matrix ele ments, as a function o f electronic energy gap, follows opposite trends. F o r electronic energy gaps more than a few thousand c m " , the electronic energy difference factor dominates, a n d i n this range the radiationless transition rates decrease nearly exponentially w i t h increasing electronic energy gap. 1

T h e electronic energy gap i n the Siebrand correlation is scaled to account for the relative p r o p o r t i o n o f C - H to C - C oscillators i n the molecule. T h e importance o f C - H stretches is a consequence o f their efficiency i n accepting energy. O w i n g to their h i g h frequency, fewer accepting quanta are r e q u i r e d .


120


S i m p l i f i e d energy gap plots without scaling are shown i n F i g u r e 18. E v e n though the conformance to a straight line is not quite as impressive as for the scaled plots, the energy gap law is still very clearly revealed. D e s p i t e the fact that it is a s p i n - f o r b i d d e n transition, S -> Τ intersystem crossing i n aromatic molecules competes very effectively w i t h the S —» S internal conversion and, i n many cases, dominates. T h e r e are b o t h obvious a n d subtle reasons w h y this is so. T h e obvious reason is that the T state has a m u c h smaller energy gap w i t h S than does S . A more subtle reason is that the intersystem crossing f r o m S c a n p r o c e e d t h r o u g h higher triplet states than T W e h a d n o t e d earlier that the r a p i d internal conversion cascade f r o m higher singlet states slows d o w n at S instead o f p r o c e e d i n g all the w a y to S . The SS electronic energy gap is almost always m u c h greater than the gaps between excited singlet states. N o t e , too, the possibility o f spectroscopically unobserved singlet states contributing to the S -> S internal conversion cascade. x

0

x

x

x

0

x


v

0

x

r

0

x

n

T h e invariably c i t e d a n d most striking exception to Kasha's rule is azulene i n w h i c h the S ~> S fluorescence q u a n t u m y i e l d is itself reasonably strong, 0.03, and, moreover, orders o f magnitude stronger than the S —> S q u a n t u m y i e l d (41). H o w e v e r , azulene is really less anomalous f o r its S fluorescence than i t is for its exceptionally large S - S energy gap. I n fact, the most anomalous feature o f azulene is that the S -> S internal conversion is about 2 orders o f magnitude faster than the energy gap correlation predicts (42). 2

0

x

2

2

x

x

0

T h e energy gap correlation shown i n F i g u r e 18 applies to planar aromatic hydrocarbons. W h e n η-ττ* states are involved, intersystem crossing f r o m S is often greatly enhanced. El-Sayed's rule states that intersystem crossing 1

12

-4

ι

1

5

1

" • • ' 10

15

20

ΔΕ (cm

1

25

30

35

10 )

χ

3

Figure 18. Illustrations of energy gap law for T -> S intersystem crossing and S j -> S internal conversion. Data taken from references 39 and 40. 1

0

0


0

3.

GILLISPIE


121

between an η-ττ* singlet a n d ΤΓ-ΤΓ* triplet state (or vice versa) is m u c h faster than intersystem crossing between two η-ττ* states or two ir-ττ* states (43).


Environmental Effects on Radiationless Transitions. T h e ca pacity of an aromatic solute to absorb radiation a n d become electronically excited is not a strong function o f temperature or solvent. A l t h o u g h i n d i v i d u a l v i b r o n i c bands b e c o m e narrower a n d better resolved at r e d u c e d temperature, the integrated absorption strength is nearly constant. A c c o r d i n g to the S t r i c k l e r - B e r g equation, therefore, any substantial environmental effects o n luminescence intensities must be ascribed to radiationless transitions or b i m o l e c u l a r factors. I n this section w e c o m m e n t briefly o n the role o f environment o n radiationless transitions. A notion that seems to have become rather firmly entrenched is that radiationless transitions are strongly affected b y the rigidity o f the m e d i u m or the structural rigidity of the emitter itself. Several authors have c o m m e n t e d on the "loose b o l t " effect (13), w h i c h expresses the n o t i o n that floppy m o t i o n enhances radiationless transition rates, whereas the i m p o s i t i o n o f rigidity suppresses nonradiative decay. I n o u r o p i n i o n , too m u c h has b e e n made o f this point. F o r every comparison o f two structurally similar molecules i n w h i c h the more rigid one has a higher fluorescence q u a n t u m yield, a counterexample can be offered. Witness the very h i g h q u a n t u m y i e l d o f 9,10-diphenylanthracene ( 0 . 8 - 1 . 0 ) versus the value o f ca. 0.3 for anthracene. T h e p r e c e d i n g paragraph is not a denial o f the experimental fact that luminescence yields are often higher i n rigid media, b u t i n most cases " S o p p i n e s s , " p e r se, is not the reason. F i r s t consider the observation o f phosphorescence, for w h i c h the usual experimental c o n d i t i o n is " i m m o b i l i z a t i o n " of the molecule i n a rigid matrix such as an organic glass at l i q u i d nitrogen temperature; 3-methylpentane, methylcyclohexane, a n d the polar mixture o f solvents that is c o m m o n l y referred to as E P A are p o p u l a r choices for glass-forming solvents. B y way o f contrast, phosphorescence i n fluid solution is a comparatively rare p h e n o m e n o n . I n general, however, freezing the sample to l i q u i d nitrogen temperature does not markedly slow the T —> S intersystem crossing. T h e impact o f the rigidity i m p o s e d b y freezing the sample is to prevent diffusion o f oxygen, w h i c h otherwise quenches the long-lived phosphorescence; triplet-triplet annihilation, similarly a diffusional process, is also suppressed (44). Samples that are very carefully degassed w i l l show phosphorescence i n fluid media. I n fact, any change i n conditions that inhibits oxygen diffusion enhances the phosphorescence: T h e possibilities include i m m o b i l i z a t i o n of the molecule i n a p o l y m e r host ( w h i c h is, o f course, just another f o r m o f organic glass), adsorption o n filter paper or other substrates, or incorporation into cyclodextrins. B y a n d large it is the oxygen q u e n c h i n g that is i n h i b i t e d , as opposed to a significant r e d u c t i o n o f the intramolecular radiationless decay rate constants. X

0


122


T e m p e r a t u r e effects o n fluorescence q u a n t u m yields can be quite large and the usual (but not exclusive) d i r e c t i o n o f change is that increasing temperature tends to reduce the fluorescence. T h e r e is simply not enough space here for a f u l l discussion, but w e w i l l m e n t i o n two classic examples; meso-substituted anthracenes a n d fmas-stilbene (and higher polyenes). I n b o t h cases there is a strong temperature variation o f fluorescence q u a n t u m yield, b u t the cause is the presence o f an excited state that promotes efficient radiationless decay lying just above the e m i t t i n g state. M o s t meso - anthracenes have fluorescence q u a n t u m yields o f unity to w i t h i n experimental error at l i q u i d nitrogen temperature, b u t values o f only 0 . 0 1 - 0 . 1 at r o o m temperature. F o r the parent anthracene the S —> T intersystem crossing, i f forced to occur over the f u l l energy gap o f about 11,000 c m " , w o u l d be quite slow. H o w e v e r , a higher triplet state lies just b e l o w S a n d acts as an intermediate state i n the intersystem crossing. Changes i n solvent do not change the S - T energy gap substantially a n d therefore have little effect o n the intersystem crossing rate. T h e r o o m temperature fluorescence q u a n t u m y i e l d o f anthracene is about the same i n hexane as i n ethanol a n d not m u c h different i n either solvent at m u c h lower temperatures. I n raeso-anthracenes the S state is shifted to lower energy o w i n g to extension o f conjugation along the short in-plane axis (45). T h e shift is just enough to b r i n g the S state b e l o w T . A t r o o m temperature the b r o a d B o l t z m a n n distribution still allows T to be accessed a n d the intersystem crossing can efficiently proceed. A t l o w temperature this channel is closed off and only the direct (and slow) S —» T intersystem crossing remains.


x

l

1

x

1

2

1

x

2

2

x

x

In the case o f frans-stilbene, the B excited state that carries h i g h oscillator strength is just slightly lower i n energy than an A state, w h i c h is radiatively one-photon f o r b i d d e n but t w o - p h o t o n a l l o w e d w i t h the g r o u n d state. A s the molecule is twisted about the central C ~ C b o n d , the B state rises i n energy a n d the A state falls (of course the g a n d u symmetry labels only apply for the planar molecule). T h e r m a l activation f r o m B to A leads to very efficient internal conversion. T h e literature o n the topic is very extensive (46) a n d w e w i l l not discuss it further here. u

g

u

g

u

g

Intermolecular Decay Processes. T h e electronically excited S state can easily " f i v e " l o n g enough to undergo b i m o l e c u l a r interactions, as was discussed i n the context o f phosphorescence i n the last section. O f course, a l l solvent interactions w i t h an excited molecule are essentially o f a b i m o l e c u l a r nature, b u t w e w i l l make some very b r i e f comments o n the interactions w i t h other solutes ( i n c l u d i n g self-interaction o f a b i c h r o mophore). T h e r e are three m a i n cases: q u e n c h i n g o f the excited state (es pecially b y dissolved molecular oxygen), excimer or exciplex formation, and energy transfer. F u l l chapters o n these topics can be f o u n d i n Guillet's monograph (4). x


3.

GILLISPIE

123


Quenching. T h e data i n T a b l e I show that typical fluorescence life times for polycyclic aromatic hydrocarbons are i n the range 1 - 1 0 0 ns, corresponding to total decay rates o f 1 0 ~ 1 0 s . T h e diffusion c o n t r o l l e d second-order rate constant i n fluid m e d i a is o n the o r d e r o f 1 0 M /s. T h u s , i f q u e n c h i n g o c c u r r e d o n every collision, a quencher concentration o f 10" M w o u l d be sufficient to cut the fluorescence intensity i n half. T h e concentration o f dissolved oxygen i n most air-saturated solvents is o f that magnitude a n d oxygen q u e n c h i n g o f fluorescence is not inconsequential. T h e extent of fluorescence q u e n c h i n g strongly correlates w i t h fluorescence life t i m e (13). I n alkane solvent at r o o m temperature, the fluorescence r e d u c t i o n for air-saturated solutions c o m p a r e d to degassed solutions is about 2 0 % for anthracene (lifetime near 5 ns), a m o r e than 10-fold r e d u c t i o n for naphtha lene (lifetime near 100 ns), a n d still m u c h larger yet for the very long-lived pyrene. 7

9

_ 1

10

_ 1


3

Q u e n c h i n g processes are easily incorporated into the kinetic analysis. T h e S (fluorescence) lifetime is shortened b y the q u e n c h i n g for w h i c h a pseudo-first-order rate constant can be w r i t t e n i n terms o f a second-order rate constant, K , and the quencher concentration [Q]. E q u a t i o n 6 is rewritten to incorporate the additional deactivation mechanism: x

Q

a n d the valid.

fluorescence

q u a n t u m y i e l d is similarly r e d u c e d because e q 6 is still

T h e S t e r n - V o l m e r expression F /F 0

=

1 +

fc T [

Structure-Property Relations in Polymers - American Chemical Society

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