JOURNAL OF RESEARCH of th e Na tiona l Bureau of Sta nda rds- A. Physics and Chemistry Vol. BOA , No. 3, M ay-June 1976 Quantum Yield Measurements*

J. B. Birks

University of Manchester, Manchester, U.K.

(April 9, 1976)

Four molecnla r jlnorescence pa rameters describe the behaviour of a flu orescent molecul e in very dilute ( - 10 -6M ) solution:

(i) the flu orescence spectrum FII (Il); (ii ) the flu orescence pola ri zati on PM: (iii) the radiative transition probability kr M; a nd (iv ) the radiation less transition probability kIM.

These parameters and their tempe rature and solvent de pe ndence are those of primary inte rest to the photoph ys icist and photoche mi st. FII (v ) and PM can be determined directl y, bu t krM a nd kloll can only be found indirectly fro m measurements of the seconda ry para meters,

(v) the flu orescence li fe time 7 .11 , and (vi ) the flu orescence quantum e ffi cie nc y qr M,

wh ere k"M= qrMi7M a nd kIM = (1 - qr M ) 7M.

The real jlnorescence para meters F (iJ) , 7 a nd cpr of more concent rated (c> 10- 5 M ) solutions usuall y diffe r from the molecul a r para meters FM (iJ) , 7 .11 and q"M due to concentrati on (self) quenching, so that 7 > 7 .\, and cp" < q" M. The concentration quenc hing is due to excimer formati on a nd dissocia­ ti on (rates kOMc and k.1I0, respecti vely) a nd it is often accompani ed by th e appearance of an e xcim er flu orescence spectrum Fo{li) in addition to F.II (v) , so that F (v) has two components. The excimer jlnorescence parameters Fo( iJ ), Po, k,.,) a nd kID, together with k"", a nd k.1I0, and the ir solve nt and tem­ perature de pende nce, a re also of primary scie ntific interest. The observed (technical) jlnorescence pa ra meters F T (v)_ 77' a nd cpUn more concentrated so1!!0 Q.1ls usually diffe r from the real paramete rs F ( v ), 7 and cp,.... due to the effects of self-absorption a nd sec­ ondary flu orescence. The technical para me ters a lso de pend on th e optical geometry a nd the excitati on wavelength . The probl e ms of determining the real paramete rs from the observ ed, and the molecul ar parameters from th e real, wi ll be di scussed. Method s are avail abl e fo r the accurate dete rmination of F T (v) and 7 T The usual method of deter­ mining cpT involves compari son with a reference solution R , a lthough a fe w calorimetric and othe r a bsolute determinati ons have been made. For two solutions excited under identi cal conditions and observed at norma l incid ence

cp r n' JfTCv) dv

cpr" n ~ JF J,CJj)dV

where n is the solv ent refractive index. Two refere nce so lution standards have been proposed, quinine sulphate in N H 2 S0 4 which has no self- absorption, and 9,10-diphenyla nthracene in c yclohexane which has no self-que nc hing_ The relative me ri ts of these solutions will be discussed, and possible candidates for an " ideal" flu orescence standard with no self- absorption and no self-quenc hing will be considered.

Key words: Fluorescence lifetime; fluorescence qua ntum effi ciency; flu orescence quantum yields; flu orescence spectrum; flu orescence standards: molecular flu orescence paramete rs; observed (tech­ nical) flu orescence parameters; polarizati on; radiative and non-radiative transition proba bilities; real flu orescence pa ra me ters_

*Paper prese nt ed at the Workshop Seminar ·Standa rd izat ion in Spectrop hotometry and Luminesce nce \\tlea suremenl s' hel d at th e National Bureau of S tandards. Ga ithersburg. Md., No v. 19-20. 1975. 389 1. Introduction (vi) Many biological molecules are luminescent. These include Most atoms, molecules, polymers and crystals emit ultraviolet, visible or infrared following exci­ (a) aromatic amino-acids (tryptophan, tyrosine, tation of their electronic energy levels. This emission phenylalanine) in proteins; or luminescence is classified according to the mode of (b) nucleotides (adenine, guanine, uracil, cyto­ excitation: sine, thymine) in DNA and RNA; (c) retinyl polyenes in the visual pigments; photoluminescence due to optical (non-ionizing) (d) chlorophylls and carotenoids in the photo­ radiation; synthetic chloroplast; and cathodoluminescence due to cathode rays (elec­ (e) several vitamins and hormones. tron beams); radioluminescence (scintillations) due to ionizing The study of biomolecular luminescence is an important radiation; area of biophysical research [5]. electro luminescence due to electric fields; (vii) Aliphatic molecules, such as the paraffins and thermoluminescence produced thermally after cyclohexane, once considered to be nonluminescent, prior irradiation by other means; are now known to emit in the far ultraviolet (- 200 nm) triboluminescence due to frictional and electro­ with low quantum yield [6]. This list, which is not ex­ static forces; haustive, illustrates the wide range of luminescent sonoluminescence due to ultrasonic radiation; materials and their applications. chemiluminescence due to a chemical process, commonly oxidation; . 2. Luminescence of Aromatic Molecules electro chemiluminescence due to a chemical process, initiated by an electric field; and 2.1. Radiative transitions bioluminescence due to a biological process, usually enzymatic in origin. The initial discussion is limited to aromatic molecules (i), but it will be later extended to other luminescent Luminescent materials can be divided into several materials (ii)-(vii). Most aromatic molecules have an broad groups. even number of 7T-electrons, giving a ground singlet electronic state 50 in which the electron s pins are (i) Aromatic molecules constitute the largest group. paired. The excited 7T electronic states of the molecule They emit luminescence in the vapour, liquid, polymer are either and crystal phases and in fluid and rigid solutions singlet states: 5 [,52 • • • 5 p; or [1)1. They are used extensively in organic liquid, triplet states: T1, T2 . . . Tq. plastic and crystal scintillators [2], luminescent dyes A spin-allowed radiative transition (luminescence) be­ and paints, detergent and paper whiteners, lumines­ tween two states of the same multiplicity (e.g. 5 I ~ So, cent screens, dye lasers, etc. Sp ~ 50' Tq ~ Td is called fluorescence (F). A spin­ (ii) Many inorganic crystals, including diamond, forbidden radiative transition between two states of ruby, alkali halides, zinc sulphide and calcium tung­ different multiplicity (e.g. TI ~ 50) is called phosphor­ state, luminesce efficiently. The emission is usually escence (P). The energy difference between the initial from impurity centres (activators) or, in the absence and final electronic state is emitted as a fluorescence of such impurities, from crystal defects [2]. Lumines­ (hv F) or photon (hvp). cent inorganic crystals are used as scintillators [2], The fluorescence occurring immediately after the luminescent screens, solid-state lasers, jewels, etc. initial excitation of S 1 (or 5 p) is known as prompt (iii) Noble gases (He, Ne, Ar, Kr, Xe) luminesce in fluorescence. In some molecules or molecular systems the vapour, liquid, and solid phases and in liquid and there are mechanisms by which 51 (or 5p ) may become solid solutions [2, 3]. They are used in discharge excited subsequent to the initial excitation, resulting lamps, gas lasers and scintillators. in delayed fluorescence. The two principal mechanisms (iv) Many simple inorganic molecules luminesce in are as follows [1]. the vapour phase [4] . Some, like H 2 , D2 , N 2 , and Hg are used in discharge lamps; others, like N 2 , Iz, and (i) Thermal activation of molecules in the lowest CO2 are used in gas lasers. triplet state Tlo which is long-lived because the TI ~ So (v) Some inorganic ions , notably those of the rare transition is spin-forbidden, repopulates the fluorescent earth elements, are luminescent. They are used as singlet state St, resulting in E-type (eosin-type) activators in inorganic crystals (see (ii) above), glasses delayed fluorescence, so called because it occurs in and chelates. Applications include inorganic crystal eosin and other dye molecules. and glass scintillators and Nd glass lasers. (ii) Diffusional interaction between pairs of T1-ex­ cited molecules in solution or Tl excitons in a crystal creates singlet-excited molecules by the process

I Fi gures in brac kets indicate the literature references at the end of this paper. (1) 390 resulting in P-type (pyrene-type) delayed fluorescence, IC 52 IC 5- so called because it occurs in pyrene and other aro­ o , 5", I ,1 matic hydrocarbons. , :VR I I IC 51 \!II5e 2 .2. Radiationless Transitions :S; ,TI" I 1 1 1 1 , I 1 Radiative transitions are between electronic states , , F2 'VR 1 , I of different energy. In a complex molecul e or crystal VR' :VR 15C V TI there are also radiationless transitions between different So", FI I electronic states of the same energy. T hese isoener­ I 1 getic radiationless transitions are induced by molecular ,VR P or crystal vibrations. , I 1 I A spin-allowed radiationless transition between two 1 I states of the same multiplicity is called internal conver­ ,1 I sion (IC). A spin-forbidden radi ationless transition ,,\)t 50 V V between two states of different multiplicity is called F IGURE 1. Schematic diagram of radiative (solid vertical Lines), intersystem crossing U5C) . radiationless (wavy horizontal lines), and vibrational relaxation (b roken vertical Lines) transitions between electronic states (so lid horizontal lines) $" 5" T, and 50 of an aromatic molecule in a 2.3 . Vibrational Relaxation co ndensed medium.

F = fluorescence. P = phosphorescence. Ie = internal conv(' rsion. ISC = intersyst em After the initial excitation or after an isoenergetic crossing. VR = vibrational relaxation. radiationless transition, the molecule is usually in a vibronic state 5 ~ (or Tn corresponding to a vibra­ is forbidden since 52 and 5 I have the same parity tionally-excited level of a particular electronic state (ungerade) [1]. Sp (o r Tq ). In a cond ensed medium (solution, liquid, 51, from (a), decays by polymer , crystal) or a hi gh-pressure vapour the excess (d) 51 ~So flu orescence F ,; vibrati onal e nergy s~-sg (o r T ~- T~) is rapidly (e) ISC to n, followed by VR to T,; or di ssipated collisionally to the environme nt leading to (f) IC to sr, followed by VR to 5 o· vibrational relaxation (VR). T" from (e), decays by The dissipative VR process, which is di stinct from (g) T, ~So phosphorescence P; or the nondissipati ve IC and I5C processes, plays a n (h) ISC to 56', followed by VR to So essential role in the thermal equilibration of the excited molecules. At normal temperatures VR is F , P, IC, and ISC are the rate-determining processes, rapid ( ~ 1O - '2 -10- 13 s, depending on the excess since VR is much faster. kA/3 is defined as the rate vibrational energy to be di ssipated) and much faster parameter of the B ~ A process, where B is the initial than IC , ISC, F or P. state and A is the product radiation (F or P) or final Isolated excited molecules in a low- pressure vapour, state (for IC or I5C) [1]. Subscripts G=5o, T= Tt, where VR is inhibited by the low collision rate, behave M = 51, and H = 52 indicate the different states. in a different manner than those in the condensed phase [6]. In an isolated molecule the fluorescence occurs from the vibronic state 5 J~ initially excited or 52 (H) from isoenergetic vibronic states 5 t, 5: . . . . of ,1 lower electronic states populated by Ie. This phenom­ ena is called resonance fluorescence. In the condensed : kMH 51 (M) phase VR brings the excited molecules rapidly into , V , thermal equilibrium and all the processes (F, p, IC , , and IS C) occur from an equilibrated system of 1 1 k : molecules. TM kGH k GM : kFM kFH T, (T) 1 1 V 1 1 2 .4. Photophysical Processes and Parameters 1 I , Figure 1 s hows schemati cally the photophysical kGT,: k pT processes that can occur in an aromatic molecular , 1 , system in very dilute solution ( ~ 10 - 6 M) following V ~ 50 (G) excitation into 5 2. V 52 decays by FIGURE 2. Rate parameters of radiative transitions (so lid vertical (a) IC to st, followed by VR to 51; lines) and radiationless plus vibrational relaxation transitions (b) IC to 5 0*** , followed by VR to So; or (broken vertical Lines) between electronic states (solid horizontal (c) 52 ~ So flu orescence F2 • lines) 5" 5 I , T I, and 50 of an aromatic molecule in a co ndensed medium. 52 ~ 51 fluorescence, which could potentially occur, The notation of the states. radiatio ns and rate parameters is indicated. 391 Figure 2 shows the rate parameters corresponding to (3a) the processes of figure 1. In the rate parameter description the VR subsequent to each IC or 15C is (4a) omitted, but the distinction between the isoenergetic radiationless transitions and the vibrational relaxation respectively, where 711 , 7.(1 and Tr are the 52, 51 and should not be overlooked. TI lifetimes in a solution of molar concentration c. An The 52, 5 I and TI decay parameters are given by exact treatment also considers the rate parameters of the excimers produced by the concentration quench­ kll = kVII + k.\f/I + k(;H = I/TH (2) ing and their dissociation [1] , but the Stern-Volmer approximation of (2a)-(4a) is adequate for the present (3) discussion. The quantum yield 1> of any photophysical process (4) in a solution of concentration c is defined in the same manner as the quantum efficiency, except that the where T f/ , TM and Tr are the 52, 51 and Tl lifetimes, limitation to very dilute solutions is removed. The respectively. 52 -'; 50 and 5 1-'; 50 fluorescence quantum yields are, The quantum efficiency q.·I/J of any photophysical res pecti vely process, rate kAII , from an excited state B is defined as the fraction of the excited molecules in that B (12) decay by that process, so that (5)

The 52 -'; 50 and 5 1-'; 50 fluorescence quantum efficien­ cies are, respectively. and the TI -'; 50 phosphorescence quantum yield is (6) qp'!' (14) (7) 1 + Kc'!'c

the TI -'; 50 phosphorescence quantum efficiency is The parameters K eH (= kCfdk/f), K c.I/ (= kC.\llkJld and Kcr(kc'!'/ kr ) are the 5tern-Volmer coefficients of (8) concentration quenching of 52, 51 and T 1 , res pectively. The 52 -'; 5 t internal conversion ~quantum yield is the 52 -'; 5 t internal conversion quantum efficiency is

kWf/ q.\1/1 (9) 1> .\1 f/ = _-,c:..:.:...._ (15) kl/ + kCHc 1 + K cllc

and the 5 I -'; T t and T I -'; 5 0* intersystem crossmg and the 5 1-'; Tt and TI -'; 5oT- intersystem crossing quantum efficiencies are, res pectively, quantum yields are, respectively, (10) (16) (11)

The rate parameters (fig. 2), the decay parameters (17) and lifetimes (2)-(4), and the quantum efficiencies I+KC'J'c (5)-(11) are molecular parameters. They refer to very dilute ( ~ 10 - 6M) solutions, containing no dissolved The above expressions for quantum efficiencies and oxygen or other impurity quenchers. yields all refer to direct excitation of the state from An increase in the solution molar concentration c which the process occurs, and they require revision does not change the unimolecular rate parameters, when the state is not excited directly. Thus for excita­ but it introduces bimolecular processes due to inter­ tion into 52 , the 5 I -'; So fluorescence quantum yield actions between excited molecules in 52, 51 or TI and IS unexcited molecules in 50, producing concentration quenching. To a first approximation the 52, 51 and TI (18) concentration quenching rates may be expressed as kCf/c, kc.\Ic and kcrc, and the 52, 51 and TI decay For excitation into 5 I, the TI -'; 50 phosphorescence parameters become quantum yield is

(2a) (19) 392 2.5. Vavilov's Law and Kasha's Rules tion in the 5 ~ -750 fluorescence spectrum. In the va pour (voo) F coincides with (VOO) A, the corresponding It is commonly assumed that cPMH = 1.0 for 52 -7 5~ 5 g-7 5 \1 0-0 absorption transition. In solution, due to IC and that cP= 1 for IC between higher e xcited states so lv e nt polarization effects within the singlet (5 p ) manifold, so that cPFM is inde pe n· dent of the excitation wavele ngth Aex up to the ioniza· tion potential. This assumption, known as VaviLov's (VOO) II - (voo),..= ~ voo (20) Law, has been confirmed for many co mpounds in solu· tion. Major deviations from Vavilov's law have, how· where ~voo vari es from 0 to a few hundred c m- I de­ e ver, been observed for solutions of be nzene, toluene, pe nding on the solvent [1). In be nzene the 0-0 fluores­ p·xylene, mesityle ne, fluorobe nzene, naphthalene, cence and absorption transitions are symmetry-forbid­ 2·methylnaphthalene, 1,6·dimethylnaphthalene [1], den and they are absent from the vapour spectra. They tryptophan, tyrosine and phenylalanine [7]. In each appear as weak solve nt-induced bands (the Ham bands) in solution spectra, the intensity de pe nding on the case it is observed that cP;'!MlcPF.ll = cPMH < 1. In be nzene solvent and its derivatives and possibly in the other com· [1]. pounds, the effect is due to effi cie nt 5 2-7 5;** IC At low temperatures the 51-750 (=5?-750) (k CH ) co m peting with 52 -7 5 ~ IC (k MH ) [8]. In fluores· fluorescence spectrum F.II (jj) consists of a com pl ex cence quantum yield measurements it is essential seri es of a few hundred narrow lines of differe nt eithe r to verify th at Vavilov's law applies, or to limit intensiti es, which may be analysed into progression s and co mbinations of th e diffe re nt vibrational modes the excitation to the region of th e 50 -75 I absorption spectrum. of the un excited molecul e. Whe n th e te mperature is Kasha's ruLes [9] , a nother well· known generalization, increased, th ermal broade ning a nd solv ent-solute state that in a co mplex molecule luminescence occurs interactions obscure most of th e vibrational struc ture. only from the lowest excited state of a giv en multi· At room temperature F.\1 (jj) commonl y consists of a plicity, i.e., 5 1-750 fluorescence a nd TI -750 phos· few promine nt broad bands with little other struc ture. phorescence. For ma ny years azule ne and its de riva· Thus F.\/ (jj) for a nthracene in cyclohexane solution tives, whi c h emit 52 -7 50 flu orescence and negli gible cons ists of a progression of 5 broad bands, s paced 5 1-7 50 fluorescence, were the main exceptions to about 1400 c m- I apart, corres ponding to CC vibra­ Kasha's rul es. Recently the pi cture has c ha nged ti onal modes. Simila r vibrational progressions occur d ramati call y. in F\I (/J) [or oth er conde nsed hydrocarbons [1). For large molecul es, e.g., dyes, with many degrees of In addition to th e normal 5 I -750 flu orescence, weak 52 -7 50 fluorescence has been observed in benze ne, vibrational a nd/or rotational freedom, FII (jj) at roo m tolu ene, p-xylene, mesityle ne, naphthale ne, pyrene, te mpe rature ofte n consists of a s in gle broad ba nd with 1 : 2-benzanthracene, 3:4-benzopyrene, 1: 12- benzo­ no vibrati onal structure. Berlman [1 2) has recorded peryle ne a nd ovalene, weak 53 -7 50 flu orescence has the flu orescence s pectra of many aromatic molecul es. been observed in p -xyle ne, mesitylene, naphthale ne, The solve nt has a strong influe nce on F\I (jj) at pyre ne and l:2-benzanthracene, and weak 54 -7 50 room te mpe rature. In a polar solv ent like ethanol the fluorescence has been observed in pyrene and fluoran­ vibrational bands are broad and poorly resolved, a nd the ne [6, 10]. the separati on ~ jjoo between the absorption and Such fluorescence from hi gher excited s tates was fluorescence 0-0 bands is relatively large. In a non­ predi cted by the author in 1954 [I1J. Its detection is polar aliphatic hydrocarbon solve nt, like cyclohexa ne or n-hexane, the spectral resolution is improved and difficult, since it occurs in the region of the 50 -7 5 p absorption spectrum, a nd its quantu m yield is only ~jjoo is reduced. In a fluorocarbon solve nt, like per­ fluoro-n-h exane (PFH), each of the vibrational bands - 10- 5 cPFA'/ [6]. Subsequent attention will be focused has a well-resolved fin e structure, similar to that in on the main 5 I -750 fluorescence. the vapour phase, and ~jjoo = O [13]. PFH is an ideal 2.6 . The Fluorescence Spectrum s pectrosc.opic solvent, apart from cost and the low solubility of aromatic molecules in PFH. The 51 -750 flu orescence spectrum occurs from a At temperatures above about -100 °C the " hot" system of 5 I excited molecules in thermal equilibrium vibrationally·excited 51 molecules with a Boltzmann in solution. The frac tion of these molecules with vibra­ di stribution of energies 51" (=5?+ ]f:v) also contribute tional e nergy E v is proportional to exp (-E vi kT) , to FM(f/). Each component 5r -7 50 spectrum is similar wh ere k is Boltzmann's co nstant and T is the absolute to the 5?-750 spectrum, except that it is shifted by te mperature . A large majority are in the zero point a n a mount ED towards hi gher e nergies, and its in­ le vel 5?, a nd to a first a pproxima ti on the fluorescence of tensity is proportional to exp (- E,./ /rT) . Most of th e the " hot" molecules can be di s regarded. 5t-750 spectral distribution li es below the 5?-750 The 5~ -7 50 flu orescence occurs into 5g, the zero­ s pectrum and is obscured the re by. However, each point level of 50, and into the many vibrational levels compone nt 5t-750 s pectrum exte nds beyond /Joo to of 50. The 5~ -7 5g transition, or 0-0 fluorescence transi­ jjoo+ E v, giving ri se to hot fluorescence bands, th e tion, of wavenumber (VOO)F is the highest ene rgy transi- inte nsity and extent of whic h in crease with te mpera- 393 ture. These hot fluorescence bands, which are an reciprocal of the average value of ii - 3 over the fluores­ integral p'art of the 5, ~ 50 fluorescence spectrum cence spectrum, E (ii) is the decadic molar extinction FM (ii) at room temperature, occur in all aromatic coefficient, and the integral is taken over the 50 ~ 5\ molecules, although they are not often recorded. The absorption spectrum. Relation (23) has been tested for emission bands are in the same region as the 50 ~ 5, a number of molecules, and excellent agreement be­ absorption, and special care is needed to observe tween kFM and k}'M has been obtained for several them [6]. molecules in different laboratories [1, 12, 16, 17, 18]. Such molecules may be useful as fluorescence 2.7. The rate parameters standards. If the solvent optical dispersion is small nF nA = Observations of qFJ! and TM for a very dilute solution = enable n, and (23) can be simplified to (21) (24)

where (k~M)O is a molecular constant, independent of to be determined. Birks and Munro [14] have reviewed the solvent and the temperature. Relation (24) has been methods of measuring TM. Observations of qTM verified for several solutes in different solvents over (= knrl k\l ), by one of the several methods described a wide temperature range [19]. by Wilkinson [15], enable k T.I! and k r;\1 to be evaluated. In some molecules there are large discrepancies The measurement of q!'T and TT permits kp-r and kG?' between kFM and k~M' A detailed study of these anoma­ to be determined [1]. Thus measurements of five lies has revealed the presence of electronic states not quantities qF.\I, T.\I, qn-J, qPT and T1' are required to observed spectroscopically [20, 21]. The nature and determine the five 5, and T, unimolecular rate param­ origin of such radiative lifetime anomalies are dis­ eters kpM , krM ' k(;M, kP'/' and kG7 ,. cussed elsewhere [22]. The factors determining the Observations of T~-J and T~ (or CPFM and CPPT) as a other 5 \ and T\ rate parameters kTM' kCM' kPT and kCT function of the molar concentration c enable the have been considered previously [1, 6, 8]. bimolecular rate parameters kCM and kCT to be de­ termined. The observations and analysis may be ex­ 2.9. Molecular Fluorescence Parameters tended further to obtain the fluorescence (k FD ), I5C The 51 ~ 50 fluorescence of an aromatic compound (kTD ), IC (kCD) and dissociation (kMD ) rate parameters of the singlet excimer [1]. This involves observations in very dilute solution is characterized by the follow­ of the molecular (cpFM) and excimer (CPFD) fluores­ ing molecular parameters. cence quantum yields of concentrated solutions. It is the rate parameters and .their dependence on (a) The fluorescence spectrum FM (ii) depends temperature, solvent, substitution etc. that are the on the solvent and temperature (see 2.6). quantities of interest to the photophysicist and photo­ (b) The fluorescence polarization PM depends chemist, and not the properties from which they are on the direction of the transition dipole derived. The latter may be of technical interest for moment relative to the molecular axes. For particular applications. Of the three quantities qFM, a 1T* I ~ 1T electronic transition this lies in the TM and q1'M required to determine the 5, rate pa­ molecular plane along one of two orthogonal rameters kFA-J, k1'M and kCM' the published values of axes depending on the symmetry of 5 \. For qFM (or CPn-J, which is often implicitly equated to naphthalene the fluorescence is long-axis qEM) show the largest scatter. When the solution polarized; for anthracene it is short-axis concentration C is increased, self-absorption effects polarized [1]. introduce difficulties in the determination of CPFM. It (c) The fluorescence rate parameter kFM is pro­ is hoped that this paper will help to improve the portional to the square of the transition dipole situation. moment [1]. In the absence of any anomalies 'kFM /n 2 is independent of the solvent and temperature (24). 2.8. The Fluorescence Rate Parameter (d) The 5 \ radiationless rate parameter kiM (= knl + k CM) describes the processes competing A theoretical expression for knl has been derived with the fluorescence. kIM usually depends from the Einstein radiation relation using the zero-order markedly on the solvent and on the tempera­ Born-Oppenheimer approximation [16, 17] ture [1].

n~ - JE(v)dv FM (ii) and PM can be observed directly. The 9 3 ktFM =2 . 88x 10 - - (vF- ) Av- \ --- (23) nA v evaluation of kFM and kIM involves measurements of two secondary parameters: where np and nA are the mean refractive indices of the solvent over the 5, ~ 50 fluorescence and 50 ~ 5, (e) The fluorescence lifetime TM; and absorption spectra, respectively, (v -f) -iv is the (f) the fluorescence quantum efficiency q FM.

394 Several accurate me thods are available for measuring The inorganic luminescence terminology predates 7M[14]. Reliable methods are available for measuring the di scovery of electron spin, and it has not been qPM, but they are often used incorrectly [23]. adjusted to take account of this. Because of spin, The molecular fluorescence para meters FM (Ii) , processes l ea) and l (b) differ in lifetime by a factor of PM, k pM and kIM are !ndependent of the molar con­ up to lOS , and it would seem appropriate to di stinguish centration c. The secondary flu orescence parameters the m. In 1933 Jablonski [24] , the ori gi nator of figure 7M and

TABLE 1. Terminology 0/ photophysical processes A quantum counter is a system which has a consta nt flu orescence quantum yield over a broad spectral P rocess Organi c Inorgani c range. To achieve this it should have a high and 1. Luminescence, relatively constant absorption over the spectral range (a) spin-allowed Fluorescence (F ) Fluorescence of interest, it should have negligible self-absorption (no (b) spin-forbidden Phosphorescence (P) Fluorescence ov erlap of fluorescence and absor ption spectrum), (c) thermall y- activated E·type delayed Phos phores· it should obey Vavilov's law, and it should be stable delayed flu orescence cence 2. Radiationless transiti on photochemically. Systems commonly used as quantum (a) spin·all owed Internal conversion counters include: (lC) (i) 3 gl- I Rhodamine B in ethyle ne glycol (b) spin·forbidden I ntersystem crossing (lSC) (2 10-530 nm), 3. Vibrational relaxati on Vibrati onal relaxa­ (ii) 4 gl - I quinine s ulphate in N H 2S04 (2 20-340 ti on (VR ) nm), and 4. Radiationl ess tra nsi· IC (o r ISC) an d VR Multi phonon (iii) ,1O - 2M I -dimethylaminonaphthalene 5-(o r 7-) ti on plu s vibrational process relaxati on sodium s ulphonate in 0.1 N Na 2C0 3 (2 10 - 400 nm). 395 An extension of this list would be advantageous. determinations of 4>1'.11 are difficult and uncommon, Three common optical geometries are used in fluor· and it is normal practice to measure 4>rll by comparison escence measurements; with a standard of known fluorescence quantum yield (a) front·surface or reflection geometry, in which 4>TII' If Ffl (v) and FH v) are the corrected fluores­ the fluorescence from the irradiated sur­ cence spectra of the specimen and standard, respect­ face of the specimen is observed; ively, excited under identical conditions (same exci­ (b) 90° geometry, in which the fluorescence is tation wavelength, optical density and geometry) and observed in a direction normal to the incident observed at normaL incidence in reflection, then beam; and (c) transmission geometry, in which the fluores­ n" { ' cence is observed from the opposite side of 4>{M FX~(v)dv the speciment to the excitation. (25) For very dilute solutions (- 10 -6M) the three geome­ 4>1'FR n~ 10'" FJ; (v)dv tries give the same fluorescence spectrum, quantum efficiency and lifetime. The 90° geometry, used by Birks and Dyson [17] and others. has the advantage of where nand nR are the refractive indices of the speci­ minimizing background incident light and of allowing men solution and the standard solution, respectively. the fraction of incident light absorbed in the specimen The integrations are often made using a quantum to be monitored directly. co UTi ter [28]. An increase in the solution concentration c reduces The refractive index term is a correction for the solution optical geometry. The angular dependence of qf.'M and T.l1 to 4>1' ,11 and T.1/ , respectively, due to con­ centration quenching. It also attenuates the hi gh­ the fluorescence flux F (4)) from a small isotropically energy region of F.II Cv) due to self-absorption arising emitting source behind an infinite plane surface in a from the overlap of the absorption and fluorescence medium of refractive index n is spectra. As c is increased the intensity of the 0-0 fluorescence band decreases towards zero due to its F(4)) = Fo( cos 4»n- 1 (n2 - sin"4» - 1/2 (26) overlap with the 0-0 absorption band. At room tem­ perature and hi gh c the self-ab sorption may extend to where Fo is a constant (cr:4>FII) and F(4)) is the flux the 0-1 and 0-2 fluorescence bands, which overlap (i n quanta cm" s - I) falling on a small aperture at an the 1-0 and 2-0 hot absorption bands, due to thermally angle 4> from the normal to the face. For 4> = 0° (26) activated molecul es in the fir st and second vibrational reduces to levels of So. These self·absorption effects are a max­ imum in the transmi ssion geometry (c), somewhat F (O)=Fo/n" (27) reduced in the 90° geometry (b), and they are least in the re fl ection geometry (a), which is normally used leading to (25). Relation (26) has been verified by for fluorescence studies of more concentrated solutions. Melhuish [29] who recommended the use of cuvettes The effect of self-absorption on F.l1 (v) observed in with blackened back and sides for fluorescence yield reflection can be minimized by Berlman's technique measurements to minimize internal reflection errors. [12] of excitation at an intense absorption maximum, Shinitzky [30] has pointed out a further potential source of error in flu orescence quantum yield and thereby minimizing the penetration depth d ex of the exciting li ght. This technique does not, however, lifetime measurements. When a fluorescent system is compensate for the secondary fluorescence produced excited by un polarized light and its emission is de­ by the self-absorption and which modifies 4>1'.11 and tected without a polarizer, the emission intensity has T,\! , as discussed below. a typical anisotropic distribution which is directly related to its degree of polarization. This effect can 4.2. Fluorescence Quantum Yields introduce an error of up to 20 percent in all fluores­ cence quantum yield and lifetime measurements, but Absolute determinations of fluorescence quantum it is eliminated when the flu orescence is detected at yields have been made using integrating spheres to an angle of 55 ° or 125 ° to tl-.e direction of excitation, collect the flu orescence emission over a full 47T solid provided that the emission detection system is un­ angle, by calorimetry to distinguish radiative processes biased with respect to polarization. Procedures for from radiationless processes and vibrational relaxa­ the elimination of polarization errors for partially ti on, by actinometry to integrate light intensities polarized excitation and biased detection systems photochemically, and by polarization and scattering were developed by Cehelnik, Mielenz. and Velapoldi measurements. These methods have been reviewed [31] and Mielenz. Cehelnik. and McKenzie r3n by Lipsett [27] and Demas and Crosby [28]. If n and nil differ, it is recommended that the speci­ The superscript T is introduced to refer to the men and reference solutions be excited at 55° inci­ observed (technical) fluorescence parameters FII (v), dence angle and observed at normal incidence, to 4>{,11 and Ti~ , which may differ from the true fluores­ eliminate the polarization effect and simplify the refrac­ cence parameters F.II (v), 4>1'.11 and T.\I, due to self­ ti ve index correction. The latter correction disappears absorption and secondary fluorescence. Absolute if n = nil, and the excitation and front-face observation 396 directions need only diffe r by 5S 0. The angles of inci­ de nce and " refl ection" s hould diffe r to minimize scattered li ght. The self-absorption attenuates th e hi gh-e nergy e nd T of FI/ (v), but it does not affect the low-ene rgy end.

A .\I - Arl a = . (28)

A .\1 = J: F\/( ii) dii (29) c (M )

F IGU I1 E: 3. 9,1O· diphenylanthracene in benzene. = di/ (30) Front-sudace uhservati on al A"x = 365 11m . Tec hni cal fiuor csccllCt' q uantum yield cb~" A~~ f'F ;{~ (v) (+) and true flu orescence quantum yie ld CPf·.\f (0) agains t molar concentratio n c. Data o from Mclhu ish 1361. re presents the sel/abso rption probability. This normal­ izati on procedure, introduced for anthrace ne cr ystal th e wh ole range of c, thus de monstrating that DPA is fluorescence [33], has been applied by Birks and Christ­ immune to co ncentrati on que nchin g [36]. ophorou [34] to co ncentrated solutions of aromatic The seconda ry flu orescence contribution to ¢rll hydrocarbons. S ubstitution of A .\1 in pl ace of A ;C in in creases with decrease in the excitation penetration (25) giv es ¢FM in place of (Pr- It For ma te rials of low depth dex . Berlma n's [12] c hoice of an inte nse absorp­ ¢F.\1 « 0. 3), the linear S te rn -Vo lm er plots of qF.It/¢ F\I ti on band for excitation P." cx=265 nm for DPA) mini­ again st c of gradie nt K CM (13) confirm the validity of mizes d ex ' This minimizes the effect of self- absorption the procedure, whi ch correspond s to assuming on FII (ii), but it also maximizes the effect of secondary flu orescence on ¢r.\I ' To reduce the laller, a weak (3 1) a bsorption region should be c hosen for excitati on, and c should be kept as low as possible. This relation neglects the secondary fluorescence To summari ze, th ere are no particular proble ms in resulting from the self-absorption. Allowing for this, determining ¢n.'1 for (a) very dilute solu tions (b) more the author [11,35] has show n that co ncentrated olutions observed in the trans mi ssion or 90° geometries, and (c) more concentrated solutions = (1- a)¢FM "'1' (32) of ¢FAI < - 0.3 observed in the refl ection geometry. '1-'1'.1/ 1 - a¢/.'JI The effects of self-absorption and secondary fluores­ cence are, however, diffi c ult to co mpensate in concen­ which approximates to (31) wh en a¢F\I «i 1, and that trated solutions of hi gh ¢VM observed in the re fl ection geometry. One simple solution is to abandon the re­ (33) fl ection geome try and to observe such systems in the more tractable transmission geometry. The alternative is to utilize one of the numerous mathematical rela­ Relation (33) is consid ered to be gene rally valid. tions, some simple [11, 35], some complex [27, 36], Relation (32) is considered to be valid for the trans­ which have been developed to describe self-absorption mission and 90° geo metries. It is also valid for the and secondary fluorescence. reflection geometry, except for specimens of hi gh ¢F.41. Unde r the latter conditions the secondary flu orescence contributes ma rkedl y to the observed flu orescence 4.3. Fluorescence Standards intensity, so that ¢Tu> ¢F.\1 in re fl ection, although Melhuish [36] proposed the use of a S X 10 - 3M solu ­ ¢Tu< ¢v.\1 in trans mi ssion as predi cted by (32). Figure tion of quinine bisulphate (QS) in I N s ulphuric acid 3 plots Melhuish's observations [36] of ¢f.MaS a func­ as a fluorescence standard. From careful measure­ tion of c for 9,l0-diphe nylanthracene (DPA) in be nzene ments he obtained ¢FM = 0.5 10 for c= S X 10 - :J M in­ solution, excited at 366 nm with front-face observa­ creasing to qFM= 0.546 at infinite dilution at 2S 0c. tion. Due to secondary flu orescence ¢f.M increases The value of ¢f'M at any other concentration can be from qFM = 0.83 in very dilute solution to ¢LF 1.0 at e valuated using the Stern-Volmer relation (13). The c"'" 1.S X 10- 3M. Correction for self-absorption and QS solution is sta ble under prolonged irradiation , its secondary flu orescence, using a much more co mplex flu orescence is not quenched by di ssolved air (unlike relation than (32), showed that ¢f' A/ = 0.83 ± 0.02 over most aromati c molecules), and it has a vel)' small over· 397 lap of the absorption and fluorescence spectra. It yield of ¢T.\1 = 1.0, due to self-absorption and secondary suffers from three minor disadvantages: fluorescence, although the true fluorescence quantum yield is ¢VM= q" ',lr= 0_83 (± 0.02) (fig. 3). Relation (25) (a) concentration quenching; requires that the specimen and standard be compared (b) the temperature coefficient of ¢FM is about under identical conditions of excitation and optical -0.25 percent per degree over the range 10° density, so that the 1O- 3M DP A solution standard is to 40° C; and only suitable for observations of ¢JM on concentrated (c) sulphuric acid is not a conventional solvent solutions in reflection geometry. The QS standard is for aromatic molecules and this necessitates more versatile since it does not limit the specimen using the refractive index correction in (25). concentration or optical geometry. Berlman [12] observed TIl with heterochromatic Nevertheless the QS standard, and various secondary excitation and nl (jj) with monochromatic excitation standards derived therefrom, have been adopted in (these parameters need to be observed under identical this and many other laboratories [28, 37]. Quinine is conditions for (32) and (33) to be applicable [35]). He the fluorescent entity, and the use of quinine sulphate evaluated ¢TM by comparison with FJ; (jj) for the DPA in place of the bisulphate does not appear to qffect the values of qPM and ¢PM [28]. Unfortunately many standard observed under similar conditions, although authors have chosen to use 0.1 N sulphuric acid as the the optical densities and excitation wavelengths of solvent, rather than 1 N as recommended by Melhuish the specimen and standard appear to have differed. [36], while assuming his fluorescence quantum yield Apart from the usual hot band elimination and some values to be unchanged. There is evidence that ¢FM 0-0 band attenuation, FI,( jj) approximates to the increases by 6-8 percent on increasing the solvent molecular spectrum FM (v) . ¢LIf and TI, do not cor­ normality from 0.1 N to 1 N [f8]. respond to qVM and Till , as implicitly assumed by Table 2 lists comparative data on TM and qFM for Berlman [12], who used them to "evaluate" k" ·M. very dilute solutions of several aromatic compounds They require correction for self-absorption and obtained using the QS standard [16-18]. The con­ secondary fluorescence to obtain ¢VM and Til, and sistency of the data from three different laboratories is these parameters need correction for concentration gratifying. The close agreement between the experi­ quenching to obtain qV\I and T\I. Birks [1] tried to ment values of k FAr (= qFAr /TM) and the theoretical correct Berlman's ¢TM data [12] by renormalizing them values of k~'M from (23) for several compounds shows to ql'R = 0.83 for DPA, but this procedure has sin ce the error in q FMfor the QS standard to be s mall. Gelernt been shown to be invalid [23]. et al. [36] have recently calorimetrically determined It is of interest to note the effect of substituting dif­ qPM for QS in 1 N sulphuric acid at 25 ° C. The calori­ ferent fluorescence parameters in the relations used metric value of qFM=0.561 (±O.039) agrees satis­ to evaluate kFM and kIM. From (3a), (13), (21), (22), factorily with the fluorimetric value of q FM = 0.546 [34]. (32) and (33) Other fluorescence standards have been discussed by Demas and Crosby [28]. qFAr = ¢r;M = kFM (34) TABLE 2. Fluorescence lifetimes (7",,) and quantum efficiencies TM TM ( q",,) of very dilute solutions

Compound Solvent T ,II (ns) q,',11 k,.,.dk)' 11 Ref. (35) Quinine Bisulphate IN H,SO, 20.1 0.54 0.73 [17] IN H,SO, 19.4 .54 .75 [18] (36) Perylene benze ne 4.9 .89 .93 [17] TM benze ne 4.79 .89 .90 [16] benze ne 5.02 .89 .90 [18] (37) , k IM + kCMc. Acridone ethanol 11.8 .83 1.02 [16] TM ethanol 12.5 .825 1.05 [18]

9-Aminoacridine ethanol 13.87 .99 1.15 [16] An ideal fluorescence standard for aromatic solu­ ethanol 15.15 .99 1.02 [18] tions should

9,10-Diphenyl benzene 7.3 .85 0.99 [17] anthracene benzene 7.37 .84 .98 [18] (i) have no self.absorption, (ii) have no concentration quenching, (iii) be in a common solvent suitable for other Berlman [12] used a 1O-3M solution of 9,1O-diphenyl­ aromatic molecules (to eliminate the refrac­ anthracene (DPA) in cyclohexane, excited at 265 nm tive index correction), (an absorption maximum) and observed in reflection, (iv) be readily available as a high-purity material as a fluorescence standard_ Under these conditions (or be insensitive to impurities), and the DPA solution has a technical fluorescence quantum (v) be photochemically stable. 398 QS satis fi e s (iv) and (v) and it approximates closely 18) Birks, .I. B., Organic Molecular Photophys ics, Vol. I, Ed. Birks, to (i) , but it does not sati sfy (ii) and (iii). DPA meets .1 . B. (Wil ey·lnterscie nce, London, a nd New York, p. 1, 1973). [9) Kasha , M., Di sc. Faraday Soc. 9, 14 (1950). criteri a (ii)-(v) , but it exhibits strong self-absorption. (10) Nic ke l, B., Chem. Phys. Lett ers 27,84 (1974). To minimize self-absorption in an aromati c hydrocar­ (11) Birks, .I . B., Phys. Rev. 94,1567 (1954). bon solution it is necessary that 51 is a 1Lb state, so 1l2) Be rim an, I. B., Handbook of Fluorescence S pectra of Aro matic that the S o ~ 51 absorption is weak, and not a 1L a Mo lecul es (Acade mi c Press, New York. 1st edition, 1965: 2nd edition, 1971). state, giving strong 50 ~ 51 absorption, as in DPA [1]. [1 3) Lawson, C. W. , Hiraya ma, r., and Lipsky, S., .I . C he m. Ph ys . There are two hydrocarbons which exhibit no concen· 51,1590 (]969). tration que nching (ii), have 5 = 1 Lb so that self-absorp­ [14] Birks. J. B.. and Munro. L. H., Progress in Reacti on Kin eti cs. 4 , tion (i) is reduced, and sati sfy (iii) and (v). These 239 (1967). [1 5] Wilkinson, F., Orga nic Molecular P hotophys ics, Vo l. If, Ed. compounds, phenanthrene and chrysene, merit con· Birks, .I. B. (W il ey·lnterscience, London, and New York, sideration as flu orescence standards. They can be p. 95, 1975). obtained, but are not yet readily available, as high· [16) S tric kler, S. J., and Be rg. R. A. , J . Che m. Phys. 37, 8]4(1962). purity mate rials (iv). [l7] Birks, .I. B., and Dyson, D. .I. , Proc. Roy. Soc. A275, 135 (1963). [18] Wa re, W. R., a nd Baldwin , B. A., .I . C he m. P hys. 4 0, 1703 Aromatic excimers satisfy all the criteri a for a fluores­ (1964). cence sta ndard, since th ey have no self-a bsorption [1 9] C undall R. B., a nd Pere ira, L. c., .J. Che m. Soc. Fa raday T rans. (i) or concentration quenching (ii) [1]. In concentrated II, 68, 11 52 (1972). solutions the excim er spectrum F D (v) can be readily [20] Birks, J. B., and Birch, D. J. S., Che m. Ph ys. Letters, 31, 608(1975). . . distinguished from the attenuated monomer spectrum [21] Birc h, D. .I . S. , and Bi rks, .I. B. , C he m. Phys. Le tt e rs, in press. F ;(~(v) [34], although the presence of the latter may 122] Bir ks, J. B. , Z. P hys. C he m. (N .F.) s ubmitted fo r publicat ion. be undesirable. It can be eliminated by the use of a [23] Birks, .I. B., .I . Luminescence 9 , 311 (1974). pure liquid or crystal. A pyrene crystal has

399