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 Fluorescence 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 photons 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 photon (hv F) or phosphorescence 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.