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Quantum yield and brightness
Journal of Luminescence 224 (2020) 117256
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Review
Quantum yield and brightness Ka-Leung Wong a, Jean-Claude G. Bünzli a, b, Peter A. Tanner a, * a b
Department of Chemistry, Hong Kong Baptist University, Waterloo Road, Kowloon Tong, Hong Kong, S.A.R., PR China Institute of Chemical Sciences and Engineering, Swiss Federal Institute of Technology, Lausanne, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Brightness Quantum yield Radiance Luminance luminescent materials
Brightness has different meaning in different contexts and some of these are reviewed. The scientific definition of brightness does not represent our perception. The current definition is that from the IUPAC Gold Book and is mainly restricted to solutions. We propose a definition for solids that requires the use of an integrating sphere. Terms related to quantum yield and efficiency are clarified as well as those characterizing light properties.
1. Introduction A search for “luminescence” and associated terms in any biblio graphic database or web search engine typically returns hundreds of thousands of articles, pointing to the importance of this phenomenon. Indeed, applications as diverse as lighting, lasers, displays, telecom munications, road and security marking, bioanalysis or bioimaging rely on luminescent materials and probes. The search for efficient and highly luminescent materials is an on-going process that has been greatly stimulated by the advent of nanomaterials. While a colored material is optically characterized by its refractive index and molar absorption coefficient (abbreviated to absorption coefficient in the following), luminescent substances are more difficult to describe precisely. There are several reasons for this. Firstly, luminescent materials convert excitation energy into photons and this conversion is usually not 100% efficient due to various losses occurring through alternative deactivation paths. Therefore, two addi tional parameters have to be defined, the quantum yield and the quan tum (energy) efficiency [1]. Exact definitions are provided below (Section 3). Typically, if we refer to photoluminescence, the luminescent substance is acting as a wavelength-converting material by transforming the excitation photons into (commonly) lower energy photons. There fore, even if the quantum yield is 100% (1 photon produced per photon absorbed), the quantum efficiency will be lower since the emitted photons have lower energy (longer wavelength). In addition, if the excitation is not direct, e.g., if the luminescent material consists of a matrix doped with a luminescent activator, or a metal complex, the activator is excited through an energy transfer process in which the
matrix (and not the activator) is absorbing light, then the definition of the quantum yield has to be refined. The phenomenon outlined above (i. e., λem > λexc) is called “downshifting” but the concept of quantum yield is also valid for other types of wavelength-converting materials exhib iting downconversion in which a higher energy photon is converted into several lower energy ones, or upconversion in which several lower en ergy photons are combined to yield a higher energy photon, see Scheme 1. Several different definitions are used in the literature to describe these processes and we attempt to clarify them in this paper. Secondly, scientists developing luminescent materials very often mainly focus on getting a high quantum yield. However, when one looks at a luminescent substance, what is important is the number of photons it emits per area and per second: i.e., both absorption of light and quantum yield are important since a high quantum yield coupled with low absorption of light will yield a poorly luminescent material. The concept of brightness - sometimes also referred to as luminosity - is meant to reflect this interplay and is particularly useful when comparing different luminescent materials or probes. Brightness is easy to define from a (photo)physical point of view, namely the product of absorption coefficient and quantum yield, but the reality of practical applications is often much more complex in that the physiological perception of light depends on wavelength. In addition, a score of different concepts and specific units is in use when it comes to quantify light and light sources, such as luminous flux, luminance and radiance. The purpose of this commentary is to give fresh and systematic insight into these parameters and to provide researchers active in the synthesis and characterization of luminescent materials a clear view of the concepts and definitions used across the literature, with
* Corresponding author. E-mail address: [email protected] (P.A. Tanner). https://doi.org/10.1016/j.jlumin.2020.117256 Received 19 February 2020; Received in revised form 26 March 2020; Accepted 26 March 2020 Available online 2 April 2020 0022-2313/© 2020 Elsevier B.V. All rights reserved.
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Journal of Luminescence 224 (2020) 117256
Scheme 1. Simplified schematic representation of resonant emission, downshifting (see text), downconversion, and upconversion; Φ is the quantum yield and η the quantum efficiency (see Section 2); ic means internal conversion.
recommendations as to which ones are the most adequate.
3. Quantum yield
2. Parameters characterizing light
3.1. Definitions and concept
Light is an electromagnetic wave (or radiation) consisting of photons and can be characterized in a medium by wavelength (λ, unit: m) and speed s (unit: m s-1), where the latter is equal to:
Rubin and Braslavsky [1] have described the history of the term quantum yield and the nomenclature employed prior to its first use in 1925. The IUPAC definition of (integral) quantum yield, Φ(λ) is [6]:
s ¼ c=n; with n ¼ λ0 =λ;
(1)
ΦðλÞ ¼
where n is the refractive index of the medium; wavelengths λ and λ0 are those in the medium and in vacuum, respectively (n ¼ 1 for vacuum), and c is the speed of light in vacuum (2.998 � 108 m s-1). The photon energy (in Joules, J) is given by: E ¼ hν ¼ hc=nλ
number of events number of photons absorbed
(3)
where Φ(λ) can be used for photophysical processes (such as intersystem crossing, luminescence, ejection of electrons in the case of photo multipliers, or photochemical reactions). More usually, it is written for emission of light:
(2)
where ν (unit: s-1 or Hz) is the frequency and h is Planck’s constant (6.626 � 10-34 J s). Since a light wave comprises photons, one has to define other quantities to characterize its actual energy and the way it is perceived, see Table 1. When the light source is polychromatic, the problem be comes more complicated as the number of emitted photons and their energy depend on the wavelength. Therefore, new parameters are defined per unit of wavelength interval (λ) or per unit of frequency in terval (ν) and prefixed by “spectral”. Finally, since the physiological response of the human eye is a function of the wavelength, two new SI units have been defined for quantifying the emission of a light source: the candela (cd) and the lumen (lm). The candela (cd) is the luminous intensity, in a given di rection, of a source that emits monochromatic radiation of frequency 5.40 � 1014 Hz (a wavelength of 555 nm in standard air, corresponding to the maximum sensitivity of the human eye) and that has a radiant intensity in that direction of (1/683) W sr-1 [2]. The luminous flux is given in lumen, 1 lm ¼ 1 cd sr [3]. The physiological parameter called luminous intensity differs from the radiant intensity in that it is the radiant intensity weighted by the standard luminosity function of the human eye V(λ) (Fig. 1a). Recent progress in neuroscience and vision however has shown V(λ) being biased in the short wavelength range and a new “universal luminous efficiency function” U(λ), comprising all wavelengths to which the retina is sensitive, has been proposed [4]; it is also shown on Fig. 1a. Luminance is the luminous intensity per unit area (cd m-2) and illuminance is the luminous flux incident upon a surface per unit area (lm m-2). The latter composite unit is called lux. The perception of the luminance of an object by the human eye also depends upon the background in which this object is represented, adding to the complexity of the problem (Fig. 1b).
Table 1 Quantities characterizing light [2,3]. Ω is the solid angle and A the area of the light source. Note that radiant flux (power) and quantum yield (see Section 3) are both represented by the same symbol Φ. The subscript v stands for visual: do not confuse with ν. Quantity
Symbol Definition
Units
Radiant energy Radiant flux (power)
Q Φ
J (kg m2 s-2) W ¼ J s-1 (kg m2 s-3)
Radiant intensity
I
Irradiance (flux density)
E
Radiance
L
Spectral flux (power)
Φλ Φν
Spectral intensity
Iλ Iν
Spectral radiance
Eλ Eν
Luminous intensity Luminous flux Luminance
Iv Φv Lv
Illuminance Ev Luminous efficacy of a light source η
2
dQ Φ ¼ dt dΦ I ¼ dΩ dΦ E ¼ dA
d2 Φ dΩ dAsource dΦ Φλ ¼ dλ dΦ Φν ¼ dν d2 Φ Iλ ¼ dΩ dλ d2 Φ Iν ¼ dΩ dν d3 Φ Eλ ¼ dΩ dA dλ d3 Φ Eν ¼ dΩ dA dν See text Φv ¼ Iv dΩ
L ¼
dIv dA See text Lv ¼
dt η ¼ dΦv dQ
W sr-1 W m-2 W sr-1 m-2 W m-1 W s-1 W sr-1 m-1 W sr-1 s-1 W sr-1 m-3 W sr-1 m-2 s-1 cd lm (¼ cd sr) cd m-2
lm m-2 (lux) lm W-1
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Journal of Luminescence 224 (2020) 117256
The term quantum efficiency η refers to energy and not to the number of photons [6]:
η¼
number of photons emitted number of photons absorbed
3.1.1. Doped phosphors and metal complexes In an emissive material consisting of an activator doped into a ma trix, e.g., the red phosphor YVO4:Eu3þ (3–5%), or of a coordination compound, e.g. Cs3[Eu(dpa)3] where dpa ¼ pyridine-2,6-dicarboxylate, the matrix or the organic ligand acts as an antenna, absorbing light and then transferring energy onto the activator (or metal ion). The process within the antenna involves at least one donor state that can be any type of state but is often a triplet or a charge transfer state (Fig. 2). In reality, several states can be involved, as well as several mechanisms [7]. First, considering direct excitation into a luminescent level of the activator or metal ion (E), the intrinsic quantum yield is defined as:
(4)
The wavelength λ refers to that of the photons absorbed and other variables such as temperature, the form under which the sample is measured, the irradiance (particularly relevant for upconverting nano particles), or the emission wavelength range considered should be cited when reporting quantum yield data. As written, the equation is not time dependent. The quantum yield therefore reflects the relative importance of radiative and nonradiative processes in the chromophore: kr P ΦðλÞ ¼ kr þ knr
(6)
It is only equal to quantum yield for a primary photochemical process, e. g., resonant luminescence from a two-level system (Scheme 1). When the emitting entity is not excited directly into one of its energy levels, there is need for defining two different quantum yields, the intrinsic quantum yield and the overall quantum yield. However, different meanings are sometimes assigned to these parameters in the literature, depending on the field of study. These are clarified in the following sections.
Fig. 1. (a) Normalized luminous efficiency of the human eye, V(λ) (black: data downloaded from http://www.cvrl.org/lumindex.htm) and universal luminous efficiency function, U(λ) (red: data from Ref. [4]); (b) To the eye, the central, constant luminance, rectangle appears to be brighter on the left hand side when it is inside the non-uniform background. However, it appears to be equally bright when it is outside. (Figure adapted from Ref. [5]).
ΦðλÞ ¼
energy output energy input
Φint ¼
Nem ðmetalÞ kr τobs ¼ ¼ Nabs ðmetalÞ kr þ knr τr
(7)
where N is a number of photons per unit time, τobs is the measured decay lifetime and τr is the radiative lifetime of the relevant state. Hence Φint represents the probability that a photon is emitted after the system has been excited to its emitting state E. The rate constants kr and knr are those of radiative and nonradiative decay pathways of E. The latter is usually a sum of rate constants since several quenching mechanisms can be operating. In addition, if the metal ion is not directly excited into the luminescent level E, but into a higher accepting level A, one would have to take nonradiative internal conversions into consideration (kic nr). In ternal conversions between levels close in energy are fast and often nearly quantitative. However, the situation may be more complex, for instance if the excited levels are much higher in energy, also emissive, and/or subject themselves to nonradiative deactivations (e.g., via interaction with charge transfer states). Hence, if the direct sensitization pathway to state E (dashed arrow in Fig. 2) is not operative, then the
(5)
where kr and knr are the first-order rate constants for emission (radia tive) decay and nonradiative processes (intersystem crossing, energy transfer, multiphonon relaxation, etc.). The quantum yield for down shifting processes is often smaller than 100% and this value can only be attained in a resonance situation (Scheme 1) or if the excited level transfers its energy quantitatively to the emitting level. Note that luminescence is a generic term. When the implied transition occurs without spin change (ΔS ¼ 0) it is named “fluorescence” whereas when ΔS > 0, the phenomenon is termed “phosphorescence”. Fluorescence is allowed by the spin rule whereas phosphorescence is not, explaining why the former is a much faster process.
Fig. 2. Simplified schematic representation of (left) the antenna effect in a transition metal chelate and (right) the energy transfer scheme, with corresponding definitions. Key: N ¼ number of absorbed (A) or emitted (E) photons per unit time; D ¼ donor, A ¼ acceptor, and E ¼ emissive state; k’s are first-order rate constants and η’s are the components of the sensitization efficiency, while Φ’s are quantum yields (see text). A real metal chelate comprises many more ligand singlet and triplet states. 3
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sensitization efficiency would contain an additional term referring to the efficiency of the conversion between the excited and the luminescent level, η3. We also note that several authors use the term “internal quantum yield” for Φint but since this adjective is used in other fields with slightly different definitions, we prefer to keep to the term “intrinsic”. The overall quantum yield (i.e., number of photons emitted/number of photons absorbed by the matrix/ligand), Φovl, is given by: Nem ðmetalÞ Φovl ¼ ¼ ηsens � Φint ¼ η1 � η2 � η3 � Φint Nabs ðmatrix=ligandÞ
Φext ðor EQYÞ ¼
¼ Φint � ηinjection � ηextraction Φint ðor IQYÞ ¼
(8)
(11b)
3.2. Measurement of quantum yield It has become the norm to list measurements of quantum yield when discussing luminescent materials. Between 1960 and the end of 2019, this term was used in 78,839 scientific documents, Fig. 3, with most of these concerning chemistry. 3.2.1. Measurement of quantum yield for solutions using a relative method Early measurements of quantum yield for an optically dilute solution (Φx), with particular attention to experimental errors and sample purity, involved the comparison of the integrated emission spectrum of the sample (x) with that of a standard (s) with quantum yield Φs, such as quinine sulphate, or with a scatterer [12]:
3.1.2. Quantum yield of downconversion processes The quantum yield of downconversion (quantum cutting) processes can be larger than 100% since more photons are emitted than absorbed. Its maximum value is n � 100% where n is the number of lower energy photons produced per absorbed photon. The quantum yield of photon cutting processes has been estimated from measurements of branching ratios [8], with neglect of nonradiative processes, or by assuming unit quantum yield for the high-energy feeder level.
Φx ¼ Φs �
EðexÞs AðexÞs Fx n2x � � � EðexÞx AðexÞx Fs n2s
(12)
where E(ex) is the excitation irradiance, A(ex) the absorbance at the excitation wavelength, and Fx, Fs are the integrated emission spectra (corrected for the instrumental function) of sample and standard, respectively, in units of photons; ni (i ¼ x,s) are the refractive indices [13]. Linearity between the concentration and emission intensity is only maintained if A(ex) < 0.05, so that care must be taken to keep the so lutions dilute enough. If not possible, the terms A(ex) in Eq. (12) should then be replaced with (1-10-A(ex)). If λ(ex)s ¼ λ(ex)x then the terms E(ex) can be neglected and absorbance can be as large as 0.5 without intro ducing distortions. If the same solvent is used for sample and standard, then the refractive indices can be neglected since the solutions are dilute. A good protocol for precise determination of solution quantum yields
3.1.3. Quantum yield of upconversion processes The quantum yield of upconversion processes can be determined by careful measurements of photons emitted and absorbed, which is not easy a task since the quantum yields tend to be small and high laser power is used for excitation. Its maximum value is 100%/n where n is the number of summed up photons. If n ¼ 2, then Φmax ¼ 50%. We draw the attention of the readers to the fact that when triplet-triplet annihi lation (TTA) is considered for upconverting light, it is common practice to scale up the observed quantum yield by the factor two; this has to be avoided since it does introduce an unwanted distortion of data! A dis cussion of the efficiency of photon upconversion is provided in Ref. [9]. 3.1.4. The special cases of solar cells and light emitting diodes In the literature regarding solar cells, the term quantum efficiency is often used both for energy efficiency and for quantum yield. To be consistent with our definitions, the quantum yield of a solar cell is: number of electrons produced number of photons at reactive surface
number of emitted photons number of electron-hole recombinations
(11a)
where ηinjection represents the proportion of electrons passing through the device that are injected into the active region (i.e., electron current/ total current) and ηextraction is the proportion of photons produced that escape the device [10], since there are, for example, Fresnel and critical angle losses. IQY represents radiative recombination yield. The external quantum efficiency of a LED is defined as the total power of output photons (J s-1 ¼ W)/{input electric power, (V � A ¼ W)}, which matches the definition of Eq. (6).
here ηsens is the overall energy transfer efficiency from the ligand to the activator/metal ion luminescent state E; if the donor state is a triplet state, η1 includes the intersystem crossing S → T. The efficiency of the internal nonradiative process (η3 ) is usually overlooked, or assumed to be unity, but care should be exercised (see above). It is also important to stress that Φovl � Φint. The overall quantum yield is sometimes referred to as “external quantum yield” but, again, this may be confusing in view of other def initions of this parameter. Therefore, we suggest keeping to Φovl. Since all this terminology may be unclear when applied to phosphors, it is essential that the reported parameters should always be defined by an equation. Sometimes “internal” and “external” have been applied with reference to absorbed and incident photons, respectively.
ΦðλÞ ¼
number of emitted photons number of electrons passing into the device
(9)
The quantum yield falls to zero above λ ¼ hc/Ebg where Ebg is the bandgap energy of the semiconductor. For practical devices, and for the sake of comparison, the efficiency of solar cells is defined as the fraction of incident power converted into electrical power (under AM 1.5 illu mination and at 25 � C); it is expressed as:
ηext ðor EQEÞ ¼
Pm PS � A
(10)
with Pm (W) being the maximum cell power output (i.e., for maximum output voltage), PS the surface input power (W m-2), and A the cell area (m2). For light emitting diodes, the quantum yields are defined as:
Fig. 3. Number of publications per year concerning quantum yield. The red fit uses a first order exponential growth function, R2adj ¼ 0.9915. Data from Ref. [11].
4
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Box 1 Measurement of quantum yield of a powder using the integrating sphere. (Figures adapted from Ref. [16] for Cs3[Tb(dpa)3]).
is to prepare several solutions with different absorbances (<0.05) and to plot integrated emission versus absorbance. The gradients G of the ob tained linear dependences can be used to calculate the quantum yield: Φx ¼
Gx n2x Φs Gs n2s
3.2.4. Quantum efficiency in energy transfer The process of energy transfer between donor and acceptor species has been extensively studied both experimentally and theoretically, and optimization of the efficiency is of major importance. The experimental determination of the transfer quantum efficiency in terms of the donor luminescence lifetime has been critically compared with that in terms of the donor luminescence intensities [19]. The simplest expression for energy transfer efficiency involves the comparison of the lifetimes of the donor without the presence of the acceptor (τD) and with the presence of the acceptor (τDA), assuming single exponential decay in each case [20]:
(13)
This method allows one to test two aspects that often bias quantum yield determinations: dissociation of the sample (particularly in the case of metal complexes) and aggregation of the sample (particularly in the case of polyaromatic molecules). In both cases, the plots are not linear and suitable corrections have to be made.
ηET ¼ 1
3.2.2. Measurement of quantum yield for powders using a relative method The technique above can be adapted for powders [14], since several standards exist. Sodium salicylate is often employed but we note that its reported quantum yield varies from 40 to 60%, so that it is not an ideal reference compound. The blue lamp phosphor BAM, BaMgAl10O17:Eu2þ, is better characterized. The quantum yield is close to 90% (92% and 85% for Eu2þ concentration of 11.6 and 15%) [15]. The quantum yields of such phosphors depend on the granulometry, temperature, excitation wavelength, and activator concentration. It is also very sensitive to the synthesis protocol so that the latter should be carefully described, along with the origin and purity of the reactants.
τDA τD
(15)
3.2.5. Measurement of quantum yield using lifetimes If the radiative lifetime τr is known, measuring the luminescence decay curve and determining the corresponding lifetime is a method of accessing the quantum yield (see eq. (7)). This method is exemplified below for lanthanides. 3.2.6. Quantum yield of nanoparticles Most determinations of quantum yield of nanoparticles have employed the above relative solution methods. The solutions are dilute and transparent and usually the nanoparticles of uniform size are surface passivated. Assuming that the dilute solutions are photostable and that the appropriate choice of standard and photoexcitation wavelength has been made, difficulties may arise if the ensembles, such as quantum dots, exhibit an increase in emission upon illumination (photo brightening); aggregate at the concentration employed; or weaklybound shell ligands desorb at low concentrations, leaving “naked” nanoparticles. It is therefore important to investigate the concentration-
3.2.3. Measurement of quantum yield by an absolute method using an integrating sphere With an accuracy of (10–15%), quantum yields can be determined for luminescent materials with the use of an integrating sphere and with good statistics (3–5 measurements at least): see Box 1 for an example and refer to the literature for details [17,18]. 5
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dependence of the quantum yield [21]. A cost-effective set-up for measuring the quantum yield of upconverting nanoparticles has recently been proposed [22].
3.2.10. Use of quantum yield measurement The rationale of quantum yield measurement has been that it gives an indication of the usefulness of the material as an emitter, considering instrument characteristics, doping concentration, temperature and temporal stability and effects such as self-absorption and scattering. Numerous studies have therefore set out to optimize the quantum yield of a given system, for example by adjusting the dopant concentration, growing a protective shell on a nanoparticle core, tailoring coordinated ligands, adjusting the site symmetry of an activator or its local field, etc. However, one item has been less often considered. Is quantum yield really the most important factor for characterizing light emission? Isn’t “brightness” more relevant? We want the brightest phosphor, not the phosphor that only absorbs a few incident photons and wastes the remainder. For instance, a recent paper discusses the influence of dopant concentrations on the quantum yield, the luminescence decay kinetics, and brightness of upconverting nanoparticles [32]. In the following section, we identify how brightness is perceived in the various fields of photonics and propose a measurement method for solid-state samples.
3.2.7. Quantum yield of single molecules Determination of the quantum yield of a single molecule is achiev able by an absolute method involving a tunable optical resonator. Variation of the cavity length changes the local electromagnetic field, which in turn modifies the coupling of the emitting molecule to that field. Monitoring the luminescence lifetime versus the coupling strength and applying a theoretical model enables the extraction of both the quantum yield and the radiative lifetime. A test on an perylene deriva tive, N-(2,6-diisopropylphenyl)-perylene-3,4-dicarboxymide, yielded Φint ¼ 0.7 and τr ¼ 4.1 ns [23]. 3.2.8. Intrinsic quantum yields of lanthanide compounds Intrinsic quantum yields for lanthanide ions in compounds are often very difficult to determine by direct excitation into a 4fN energy level because the corresponding transition may have a small oscillator strength, and/or it is commonly obscured by a more intense transition from the matrix or the ligands. A solution is to use the last part of eq. (7): Φint ¼ τobs/τr. The lifetime is usually easy to measure. The radiative lifetime depends on the chemical and physical environment of the lanthanide ion as well as on the nature of the emitting level. Therefore, it has to be determined experimentally, or calculated from the transition oscillator strengths. Relying on published values for other compounds may lead to substantial errors. There are various ways of determining τr depending on the lantha nide ion. The first, general one relies on Judd-Ofelt (JO) parameters determined from absorption spectra. Emission probabilities can then be calculated with these JO parameters and the radiative lifetime is simply the inverse of the sum of emission probabilities from the excitation state. In lieu of the absorption spectrum, it is feasible to use the excitation or emission spectrum [24]. For two-level systems, e.g. Yb3þ, the radiative lifetime can be esti mated from the integrated absorption spectrum: Z 1 8πcn2 ν2 ð2J þ 1Þ ¼ 2302 � εðe ν Þd~ν (16) NA ð2J ’ þ 1Þ τr
4. Brightness Quantum yield is dimensionless and is not related to visual percep tion. What about brightness? In fact, we are unsure how to quantify “brightness”. The IUPAC Gold Book [6] states: “Obsolete term. This term is reserved for non-quantitative reference to physiological perception of light and is not recommended as a quantitative measure of the radiance of an emitting device, e.g., a lamp.” In other words: do not confuse photometry and radiometry! Nevertheless, the Gold Book proposes a more precise definition of brightness (see below). In his listing of six parameters important to the perception of light, Halsted describes brightness as a non-measurable but “perceivable” quantity with the corresponding quantitative parameter being luminance [33]. However, the United States Federal Trade Commission [34] has assigned two meanings of brightness: for light bulb packages, brightness means lu minous flux (cd sr), while in other contexts it means luminance (cd m-2). On the other hand, the Green Book [2] states that radiance is a normalized measure of the brightness of a source; it is the power emitted per area of the source per solid angle of the beam from each point of the source.
c is the speed of light in vacuum, n the refractive index of the absorbing medium, ~ν , wavenumber, is the inverse of wavelength (1/λ, cm-1), ν is the barycenter of the transition, J and J’ are the total angular mo mentum quantum numbers for the ground and excited state, respec tively, and NA is Avogadro’s number. The integral represents the integral of the absorption spectrum expressed in molar absorption coefficient versus wavenumbers. More accurately, the detailed crystal field level structures of the J-manifolds need to be considered. In the case of emission from the 5D0 level of Eu3þ, the value of radiative lifetime can be simply gained from the emission spectrum: � � 1 Ftot ¼ 14:65 � n3 � (17) τr FMD
4.1. Photophysical definition The photophysical definition of brightness B given in the Gold Book [6] is the product of the luminescence quantum yield Φ(λ) (Eq. (4)) and the molar absorption coefficient at the excitation wavelength, ε(λ): B ¼ ΦðλÞ � εðλÞ
(18a)
In this case brightness has the units of M-1 cm-1 or m2 mol-1 since the coefficient ε(λ) is given by Ref. [6]: � 0� 1 P AðλÞ (18b) εðλÞ ¼ log10 λ ¼ cL cL Pλ where c (M or mol dm-3) is molarity, L is the absorption path length (cm), P0λ and Pλ are the incident and transmitted spectral radiant power at wavelength λ per unit wavelength interval (W nm-1) and A(λ) is the absorbance. It is assumed that emission intensity has reached steady state after switching on the light source: that is, the number of photons emitted by the sample per unit time is constant. This definition of brightness is best suited for solutions for which measuring ε(λ) is easy, while Φ(λ) can be measured by either the relative method or the absolute method (integrating sphere) described above. Later we recommend another interpretation aimed at proposing a practical definition for solid samples. In the case of pulsed excitation when time-resolved detection is used for suppressing the autofluorescence of a biological sample (for instance
with Ftot and FMD being the integrated (and corrected) total emission spectrum (5D0→7FJ, J ¼ 0–6) and the integrated magnetic dipole tran sition (5D0→7F1). Note that transitions to J ¼ 5–6 extend up to 850 nm and are not often taken into account in the literature. The validity of the various formulae given above has been success fully tested [25]. 3.2.9. Other measurement techniques Other techniques of quantum yield measurement have employed, for example, photoacoustic spectroscopy [26], the thermal lens effect [27], and calorimetry [28]. The incident intensity-dependence of quantum yield has received attention [29], just as the temperature [30] and wavelength [31] dependences. 6
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in luminescence microscopy), the number of photons emitted after the end of the excitation pulse decreases exponentially with time. Therefore, a sample with a very short lifetime (e.g., ns) will appear brighter compared to one with a longer lifetime (e.g., ms or s). The latter will shine longer but with weaker intensity. The same occurs with a long persistent phosphor that can emit light for hours but at a usually low intensity level. This situation renders the comparison of brightness be tween different phosphors more difficult and one solution could be to divide Eq. (18a) by the lifetime: B ¼ ΦðλÞ � εðλÞ=τobs
with a defined acceptance angle and a minimum measurement area, are commercially available from the lowest range of about 1 mcd m-2. 4.3.3. Astronomy In astronomy, the brightness of a star is defined by the magnitude, a unitless measure with a logarithmic scale. It is defined such that one step of magnitude difference corresponds to an approximately 2.51-fold change in brightness. Sky brightness is measured, for example, by cali brated consumer digital cameras with fisheye lenses, or by a sky brightness photometer, in units of mag arcsec-2 (magnitude per square arcsecond: squims). These units are related to luminance by the equation: h i� � mag � � 0:4� value in 2 arcsec2 5 value in cd m ¼ 1:08 � 10 � 10 (20)
(19)
This is open to debate. As a complicating factor, the decay rate of a persistent luminescence phosphor decreases with time. 4.2. Physiological complications
4.3.4. Flow cytometry, biophysics and microscopy In flow cytometry, the brightness of fluorophores is measured in MESF units, molecules of equivalent soluble fluorophore. This is ach ieved by comparing the integrated fluorescence intensity FS of a sample of concentration CS across the entire emission spectrum, with that of a standard fluorophore (FDYE, over the same spectral range) of concen tration CDYE:
Brightness is experienced differently by humans and light detectors. It also means different things to an emitter or a detector. The human eye is only sensitive in the region from ca. 380–740 nm under well-lit con ditions and its response varies within this region, with a maximum in the green spectral region at 555 nm. This phototopic response of our eyes, V (λ), to different wavelengths has been displayed in Fig. 1a. Light de tectors measure radiance and not luminance. Luminance and radiance both denote power per unit area per unit solid angle, but the former is with respect to our phototopic response. Thus, brightness is an attribute of visual perception and is based upon, but not necessarily proportional to luminance [35], as shown in Fig. 1b [5]. Our perception of brightness is complicated by time-dependent light and dark adaptation, simulta neous contrast, lateral inhibition, dazzle, and color – i.e., the visual context [33]. Furthermore, the phototopic response V(λ) misrepresents the spectral sensitivity of important visual sensations such as brightness perception and a more universal luminous efficiency function U(λ) should be used instead [4].
B¼
FS CDYE � CS FDYE
(21)
so that the value is independent of the measurement instrument or method. The method is valid for nanoparticles (NPs), as shown for highly fluorescent quantum dots made of cellulose acetate; then equa tion (21) allows one to calculate the brightness of a single nanoparticle if the size of the NPs and their exact composition are known [40]. In microscopy, regardless of the imaging mode, not only the light source, the emission spectrum of the fluorescent antibody, the sensi tivity of the detector, but also the aperture and magnification of the objective lens are critical components of image brightness. In some cases, brightness (or normalized brightness) has been equated with fluorescence image intensity, or average counts per second, particularly using z-scan fluorescence fluctuation spectroscopy to characterize sample geometry and correct for bias of thin samples. The analysis of concentration-dependent brightness has been employed to distinguish monomer-oligomer transitions of proteins. Number and brightness analysis is a moment analysis capable of measuring the apparent average number of molecules and their oligo merization state in each pixel from a series of fluorescence microscopy images [41]. The apparent brightness, Bapp, which represents the mo lecular oligomerization level, is calculated as the ratio of variance (the second moment: σ2) to average intensity (the first moment: k) of the images:
4.3. How to quantify brightness? There are various approaches to measure brightness, depending upon the field of study. Hence, it is not surprising that different authors working in different fields have employed different definitions and metrics to characterize “brightness” in their reports. 4.3.1. Light sources For lamps (particularly LEDs), the brightness appearing on the packages refers in fact to either luminous flux (lm) or luminance (cd m2 ). Sometimes scientists define it as being the averaged red-green-blue (RGB) CIE coordinates, (R þ G þ B)/3. Another way of characterizing the brightness of a lamp is to give the temperature in K of a blackbody, the emission of which has the same brightness as the lamp. However, brightness is often confused with radiance. For instance, a record brightness of 9.3 � 1011 W m-2 sr-1 was reported for a 1450 nm laser array in a wavelength-beam-combining cavity [36].
Bapp ¼ σ2/k
(22)
whereas the average apparent number of molecules, N, is given by: N ¼ k2/σ2
4.3.2. Persistent luminescence Persistent phosphors emit light after excitation has ceased, due to the thermal emptying of traps. Xu and Tanabe [37] have expressed the “brightness” of persistent phosphors as luminance, in mcd m-2. The duration of a persistent phosphor is often defined as the time when the luminance has decayed to 0.32 mcd m-2: roughly 100 times the sensi tivity of the dark-adapted human eyes. This research group also stated that radiance is more appropriate than luminance to quantify the brightness of red to near-infrared persistent phosphors to which the eye is insensitive [38]. For example, the radiances of the persistent phosphor Y3Al2Ga3O12:Cr3þ were reported (in units of mW sr-1 m-2) as 6.59 � 10-1 and 0.67 � 10-1 after 5 min and 1 h, respectively, after ceasing excitation [39]. Computer-controlled brightness meters, measuring luminance
(23)
This analysis is performed for all the pixels of an image, each with a volume of ~ (1–2)x10-3 μm3, providing oligomerization maps of entire cells on a pixel-by-pixel basis. The diffusion rate of the proteins and the temporal capability and dynamic range of the acquisition device determine oligomerization heterogeneity [41]. The technique has also been employed using total internal reflection microscopy. It is essential to correlate optical measurements of isolated particles with electron microscope images that clearly resolve the particle size in order to confirm that the emission is from an individual particle and not a cluster of particles. These measurements must be able to determine how the distribution in particle brightness correlates with the distribu tion of particle size and quality [42]. 7
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However, in the literature brightness is also described by Eq. (18), so that for a fluorophore-labeled molecule, the brightness of a stained section under a given illumination intensity is given by the product of the molar absorption coefficient and quantum yield. The brightness depends upon the dye concentration within stained sections of the specimen, the thickness of the specimen, and the amount of stained material actually present within the field of view of the microscope. For example, fluorescein and Cy5™ have quantum yields of 0.9 and 0.3, respectively, molar absorption coefficients of 7 � 104 and 2 � 105 M1 cm-1, respectively, and are very bright fluorochromes with B ¼ 6.3 � 104 and 6 � 104 M-1 cm-1. With a slightly different definition from Eq. (18a), brightness, B has been defined and investigated at the single molecule level [43] by Tian et al.: B¼
N Ck σ Φ ¼ ¼ η Iex Iex hν det
� 2 cm W
1
s
1
�
quantum yield) can be measured. 4.4. Alternative description of brightness and examples Seeking to define a dimensionless quantity, we propose the following definition for brightness (previously called external quantum yield [20]) that would apply to both solutions and solids: Brightness; B ¼
B¼
ðnumber of photons emittedÞ ðnumber of incident photonsÞ
(25)
number of photons emitted number of photons absorbed � number of photons absorbed number of incident photons
¼ ΦðλÞ � ξabs
(26)
where ξabs is the absorption efficiency:
(24)
ξabs ¼
where N (s-1) is the number per second of experimentally detected photons and Iex is the excitation power density (W cm-2); C is the measured charge coupled device counts and k is the conversion factor which changes counts into detected photons. The final part of the equation employs the absorption cross-section (σ , cm2), the fluorescence quantum yield, Φ, the photon energy (hν, J), and the light detection efficiency of the setup (ηdet). Notice that Eq. (24) differs from Eq. (18a) in measure ment units but it similarly involves absorption and quantum yield components. Many factors influence the measurement of single mole cule emission intensity, including the orientation of the molecule rela tive to the polarization plane of the incident photons and the optic axis of the objective lens. Single molecule absorption measurements are problematic and as an alternative to quantum yield measurements, the fluorescence excitation cross-section (¼ absorption cross-section �
number of photons absorbed number of incident photons
(27)
and ξabs is also a dimensionless quantity readily obtainable in an inte grating sphere measurement, as in Box 1. Brightness is then a dimen sionless quantity not related to the sensitivity of the human eye. This definition applies to both solid-state samples and solutions but requires the use of an integrating sphere for solutions too. Box 2, left hand side, displays a typical measurement of brightness by the integrating sphere method for a cyclamEu-phen (phen ¼ 1,10-phe nanthroline; cyclam ¼ substituted 1,4,7,10-tetrazacyclododecane) complex as a powder [44]. The overall quantum yield is 4.4% and the brightness is 0.032, with 5–10% error. Interestingly, the brightness is about ten times smaller for the complex cyclamEu-phLa (ph ¼ phen (pdtc)3, pdtc ¼ pyrrolidine-1-carbodithioate), where the absorption, internal quantum efficiency and Eu(5D0) decay lifetime are all similar to
Box 2 Comparison of brightness for a powder sample (left [44]) and solutions (right). Concentration for solutions: 7.5 � 10-5 M (dipicolinate [45]) and 1.5 � 10-5 M (helicate [46]).
8
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Journal of Luminescence 224 (2020) 117256
Table 2 Recommended definitions in the field of photophysics; ε(λ) ¼ molar absorption coefficient, ξabs ¼ fraction of absorbed photons (absorption efficiency). Quantity
Symbol
Definition
Units
Sample
Comment
Quantum yield
Φ(λ)
dimensionless
any
Recommended
Quantum efficiency
η
dimensionless
any
Recommended
Brightness
B B
number of photons emitted number of photons absorbed energy output energy input B ¼ Φ(λ) � ε(λ) B ¼ Φ(λ) � ξabs
M-1 cm-1 dimensionless
solutions solids, solutions
Recommended Recommended
Basic parameters
Other definitions of quantum yields (QY) for doped materials or coordination compounds Quantity
Symbol
Definition
Comment
Internal QY
Φint(λ)
Same as Φ(λ) above
Intrinsic QY
Φint(λ)
Same as Φ(λ) above
External QY
Φext(λ)
Overall QY
Φovl(λ)
number of photons emitted number of incident photons Same as Φ(λ) above
Excitation into the Not recommended Excitation into the Recommended Excitation into the Not recommended Excitation into the Recommended
those of a cyclamEu-phen, but the sensitization efficiency and overall quantum yield are both about an order of magnitude smaller. The maximum values of brightness to be expected for useful phosphors – for example, with an overall quantum yield of 80% and ξabs about 0.5 – would be more than ten times greater than for cyclamEu-phen. In the case of solid samples, e.g., powders, measuring the diffuse reflection spectrum of a thick layer is an alternative since this spectrum can then be used to determine the fraction of light absorbed by the sample at the excitation wavelength. Combined with quantum yield determination, this gives access to the brightness. The right hand side of Box 2 shows the calculation of brightness according to Eq. (18) for two cases: europium(III) tris(dipicolinate), with the quantum yield determined by a the comparative method [45], and the dinuclear europium(III) triple-stranded helicate [Eu2(LC2)3] in aqueous solution, with the quantum yield determined by both compar ative and absolute methods [46]. These two europium complexes have almost the same overall quantum yields but their brightness differs 28-fold because the helicate has a far larger molar absorption coefficient at the excitation wavelength. As far as we know, the Eu3þ complexes with highest brightness in water have been reported by Parker’s group: they feature a triaza-cyclononane anchor decorated with various an tenna substituents. Their quantum yield is in the range 24–37% and their brightness in the range 5.65–5.8 � 104 M-1 cm-1 with excitation wavelengths in the range 322–332 nm [47]. Aryl-substituted pyr azolecarboxylic acids have values ε ~ 2 � 104 M-1 cm-1 for wavelengths in the range 240–280 nm and the Tb3þ complex of 1-methyl-5-phe nyl-1H-pyrazole-3-carboxylic acid has the reported quantum yield of 100% [48]. Note that the nature of the solvent has a remarkable effect upon the brightness of a chromophore. Acridine has the fluorescent brightness <27 M-1 cm-1 when dissolved in benzene (Φ(fl) < 10-3, ε ¼ 2.7 � 104 M-1 cm-1), but has the reported value of 7030 M-1 cm-1 in aqueous solution (Φ(fl) ¼ 0.37, ε ¼ 1.9 � 104 M-1 cm-1) [49].
activator/metal ion activator/metal ion matrix/metal ion matrix/metal ion
1. Quantum yield and brightness are both useful concepts. High quantum yields are essential for lighting phosphors. For bioprobes and bionanoprobes the quantum yield may be low but the massive molar absorption coefficient can lead to high brightness. 2. The measurements of quantum yield and brightness depend upon many factors [50] that have to be clearly documented in the exper imental report, such as experimental procedure, excitation wave length, temperature, and exact composition of the sample and standard. 3. For solids, the definition of brightness described by Eq. (26) should be used while for solutions both Eqs. (18) and (26) can be used provided the quantum yield measurement is made with an inte grating sphere. Both methods illustrated in Box 2 provide a measure of outgoing photons to incoming photons. The definition Eq. (18a) has previously been employed in studies of nanoparticles, quantum dots and fluorescent dyes [18,32,51]. 4. Care should be taken to clearly state the definition of a term related to brightness, and with respect to quantum yield and quantum effi ciency. Clear definitions have been provided for intrinsic and overall quantum yield (See Table 2) and we recommend the use of these two. 5. A solid sample with given particle size and activator doping con centration or a solution with a given concentration could be both QY and brightness standards. We are taking steps in this direction. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements J.-C. B thanks HKBU for the Dr Kennedy Wong Distinguished Visiting Professorship (2017-2019). K.-L. W. and J.-C. B. thank the CAS-Croucher Funding Scheme for Joint Laboratories (CAS 18204). We are grateful to Professor Setsuhisa Tanabe for correspondence regarding LEDs.
5. Summary and recommendations ‘Brightness’ has different definitions and is measured in different ways in different areas of science - usually based upon luminance or radiance. Some measurements of brightness have been summarized and the relevance to our perception has been included. Other factors besides luminance affect our perception, from dim to bright, of brightness. Some observations concerning two methods of measuring brightness are given in bullets at the foot of Box 2. The following comments and recommendations are made from our study.
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Journal of Luminescence journal homepage: http://www.elsevier.com/locate/jlumin
Review
Quantum yield and brightness Ka-Leung Wong a, Jean-Claude G. Bünzli a, b, Peter A. Tanner a, * a b
Department of Chemistry, Hong Kong Baptist University, Waterloo Road, Kowloon Tong, Hong Kong, S.A.R., PR China Institute of Chemical Sciences and Engineering, Swiss Federal Institute of Technology, Lausanne, Switzerland
A R T I C L E I N F O
A B S T R A C T
Keywords: Brightness Quantum yield Radiance Luminance luminescent materials
Brightness has different meaning in different contexts and some of these are reviewed. The scientific definition of brightness does not represent our perception. The current definition is that from the IUPAC Gold Book and is mainly restricted to solutions. We propose a definition for solids that requires the use of an integrating sphere. Terms related to quantum yield and efficiency are clarified as well as those characterizing light properties.
1. Introduction A search for “luminescence” and associated terms in any biblio graphic database or web search engine typically returns hundreds of thousands of articles, pointing to the importance of this phenomenon. Indeed, applications as diverse as lighting, lasers, displays, telecom munications, road and security marking, bioanalysis or bioimaging rely on luminescent materials and probes. The search for efficient and highly luminescent materials is an on-going process that has been greatly stimulated by the advent of nanomaterials. While a colored material is optically characterized by its refractive index and molar absorption coefficient (abbreviated to absorption coefficient in the following), luminescent substances are more difficult to describe precisely. There are several reasons for this. Firstly, luminescent materials convert excitation energy into photons and this conversion is usually not 100% efficient due to various losses occurring through alternative deactivation paths. Therefore, two addi tional parameters have to be defined, the quantum yield and the quan tum (energy) efficiency [1]. Exact definitions are provided below (Section 3). Typically, if we refer to photoluminescence, the luminescent substance is acting as a wavelength-converting material by transforming the excitation photons into (commonly) lower energy photons. There fore, even if the quantum yield is 100% (1 photon produced per photon absorbed), the quantum efficiency will be lower since the emitted photons have lower energy (longer wavelength). In addition, if the excitation is not direct, e.g., if the luminescent material consists of a matrix doped with a luminescent activator, or a metal complex, the activator is excited through an energy transfer process in which the
matrix (and not the activator) is absorbing light, then the definition of the quantum yield has to be refined. The phenomenon outlined above (i. e., λem > λexc) is called “downshifting” but the concept of quantum yield is also valid for other types of wavelength-converting materials exhib iting downconversion in which a higher energy photon is converted into several lower energy ones, or upconversion in which several lower en ergy photons are combined to yield a higher energy photon, see Scheme 1. Several different definitions are used in the literature to describe these processes and we attempt to clarify them in this paper. Secondly, scientists developing luminescent materials very often mainly focus on getting a high quantum yield. However, when one looks at a luminescent substance, what is important is the number of photons it emits per area and per second: i.e., both absorption of light and quantum yield are important since a high quantum yield coupled with low absorption of light will yield a poorly luminescent material. The concept of brightness - sometimes also referred to as luminosity - is meant to reflect this interplay and is particularly useful when comparing different luminescent materials or probes. Brightness is easy to define from a (photo)physical point of view, namely the product of absorption coefficient and quantum yield, but the reality of practical applications is often much more complex in that the physiological perception of light depends on wavelength. In addition, a score of different concepts and specific units is in use when it comes to quantify light and light sources, such as luminous flux, luminance and radiance. The purpose of this commentary is to give fresh and systematic insight into these parameters and to provide researchers active in the synthesis and characterization of luminescent materials a clear view of the concepts and definitions used across the literature, with
* Corresponding author. E-mail address: [email protected] (P.A. Tanner). https://doi.org/10.1016/j.jlumin.2020.117256 Received 19 February 2020; Received in revised form 26 March 2020; Accepted 26 March 2020 Available online 2 April 2020 0022-2313/© 2020 Elsevier B.V. All rights reserved.
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Journal of Luminescence 224 (2020) 117256
Scheme 1. Simplified schematic representation of resonant emission, downshifting (see text), downconversion, and upconversion; Φ is the quantum yield and η the quantum efficiency (see Section 2); ic means internal conversion.
recommendations as to which ones are the most adequate.
3. Quantum yield
2. Parameters characterizing light
3.1. Definitions and concept
Light is an electromagnetic wave (or radiation) consisting of photons and can be characterized in a medium by wavelength (λ, unit: m) and speed s (unit: m s-1), where the latter is equal to:
Rubin and Braslavsky [1] have described the history of the term quantum yield and the nomenclature employed prior to its first use in 1925. The IUPAC definition of (integral) quantum yield, Φ(λ) is [6]:
s ¼ c=n; with n ¼ λ0 =λ;
(1)
ΦðλÞ ¼
where n is the refractive index of the medium; wavelengths λ and λ0 are those in the medium and in vacuum, respectively (n ¼ 1 for vacuum), and c is the speed of light in vacuum (2.998 � 108 m s-1). The photon energy (in Joules, J) is given by: E ¼ hν ¼ hc=nλ
number of events number of photons absorbed
(3)
where Φ(λ) can be used for photophysical processes (such as intersystem crossing, luminescence, ejection of electrons in the case of photo multipliers, or photochemical reactions). More usually, it is written for emission of light:
(2)
where ν (unit: s-1 or Hz) is the frequency and h is Planck’s constant (6.626 � 10-34 J s). Since a light wave comprises photons, one has to define other quantities to characterize its actual energy and the way it is perceived, see Table 1. When the light source is polychromatic, the problem be comes more complicated as the number of emitted photons and their energy depend on the wavelength. Therefore, new parameters are defined per unit of wavelength interval (λ) or per unit of frequency in terval (ν) and prefixed by “spectral”. Finally, since the physiological response of the human eye is a function of the wavelength, two new SI units have been defined for quantifying the emission of a light source: the candela (cd) and the lumen (lm). The candela (cd) is the luminous intensity, in a given di rection, of a source that emits monochromatic radiation of frequency 5.40 � 1014 Hz (a wavelength of 555 nm in standard air, corresponding to the maximum sensitivity of the human eye) and that has a radiant intensity in that direction of (1/683) W sr-1 [2]. The luminous flux is given in lumen, 1 lm ¼ 1 cd sr [3]. The physiological parameter called luminous intensity differs from the radiant intensity in that it is the radiant intensity weighted by the standard luminosity function of the human eye V(λ) (Fig. 1a). Recent progress in neuroscience and vision however has shown V(λ) being biased in the short wavelength range and a new “universal luminous efficiency function” U(λ), comprising all wavelengths to which the retina is sensitive, has been proposed [4]; it is also shown on Fig. 1a. Luminance is the luminous intensity per unit area (cd m-2) and illuminance is the luminous flux incident upon a surface per unit area (lm m-2). The latter composite unit is called lux. The perception of the luminance of an object by the human eye also depends upon the background in which this object is represented, adding to the complexity of the problem (Fig. 1b).
Table 1 Quantities characterizing light [2,3]. Ω is the solid angle and A the area of the light source. Note that radiant flux (power) and quantum yield (see Section 3) are both represented by the same symbol Φ. The subscript v stands for visual: do not confuse with ν. Quantity
Symbol Definition
Units
Radiant energy Radiant flux (power)
Q Φ
J (kg m2 s-2) W ¼ J s-1 (kg m2 s-3)
Radiant intensity
I
Irradiance (flux density)
E
Radiance
L
Spectral flux (power)
Φλ Φν
Spectral intensity
Iλ Iν
Spectral radiance
Eλ Eν
Luminous intensity Luminous flux Luminance
Iv Φv Lv
Illuminance Ev Luminous efficacy of a light source η
2
dQ Φ ¼ dt dΦ I ¼ dΩ dΦ E ¼ dA
d2 Φ dΩ dAsource dΦ Φλ ¼ dλ dΦ Φν ¼ dν d2 Φ Iλ ¼ dΩ dλ d2 Φ Iν ¼ dΩ dν d3 Φ Eλ ¼ dΩ dA dλ d3 Φ Eν ¼ dΩ dA dν See text Φv ¼ Iv dΩ
L ¼
dIv dA See text Lv ¼
dt η ¼ dΦv dQ
W sr-1 W m-2 W sr-1 m-2 W m-1 W s-1 W sr-1 m-1 W sr-1 s-1 W sr-1 m-3 W sr-1 m-2 s-1 cd lm (¼ cd sr) cd m-2
lm m-2 (lux) lm W-1
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The term quantum efficiency η refers to energy and not to the number of photons [6]:
η¼
number of photons emitted number of photons absorbed
3.1.1. Doped phosphors and metal complexes In an emissive material consisting of an activator doped into a ma trix, e.g., the red phosphor YVO4:Eu3þ (3–5%), or of a coordination compound, e.g. Cs3[Eu(dpa)3] where dpa ¼ pyridine-2,6-dicarboxylate, the matrix or the organic ligand acts as an antenna, absorbing light and then transferring energy onto the activator (or metal ion). The process within the antenna involves at least one donor state that can be any type of state but is often a triplet or a charge transfer state (Fig. 2). In reality, several states can be involved, as well as several mechanisms [7]. First, considering direct excitation into a luminescent level of the activator or metal ion (E), the intrinsic quantum yield is defined as:
(4)
The wavelength λ refers to that of the photons absorbed and other variables such as temperature, the form under which the sample is measured, the irradiance (particularly relevant for upconverting nano particles), or the emission wavelength range considered should be cited when reporting quantum yield data. As written, the equation is not time dependent. The quantum yield therefore reflects the relative importance of radiative and nonradiative processes in the chromophore: kr P ΦðλÞ ¼ kr þ knr
(6)
It is only equal to quantum yield for a primary photochemical process, e. g., resonant luminescence from a two-level system (Scheme 1). When the emitting entity is not excited directly into one of its energy levels, there is need for defining two different quantum yields, the intrinsic quantum yield and the overall quantum yield. However, different meanings are sometimes assigned to these parameters in the literature, depending on the field of study. These are clarified in the following sections.
Fig. 1. (a) Normalized luminous efficiency of the human eye, V(λ) (black: data downloaded from http://www.cvrl.org/lumindex.htm) and universal luminous efficiency function, U(λ) (red: data from Ref. [4]); (b) To the eye, the central, constant luminance, rectangle appears to be brighter on the left hand side when it is inside the non-uniform background. However, it appears to be equally bright when it is outside. (Figure adapted from Ref. [5]).
ΦðλÞ ¼
energy output energy input
Φint ¼
Nem ðmetalÞ kr τobs ¼ ¼ Nabs ðmetalÞ kr þ knr τr
(7)
where N is a number of photons per unit time, τobs is the measured decay lifetime and τr is the radiative lifetime of the relevant state. Hence Φint represents the probability that a photon is emitted after the system has been excited to its emitting state E. The rate constants kr and knr are those of radiative and nonradiative decay pathways of E. The latter is usually a sum of rate constants since several quenching mechanisms can be operating. In addition, if the metal ion is not directly excited into the luminescent level E, but into a higher accepting level A, one would have to take nonradiative internal conversions into consideration (kic nr). In ternal conversions between levels close in energy are fast and often nearly quantitative. However, the situation may be more complex, for instance if the excited levels are much higher in energy, also emissive, and/or subject themselves to nonradiative deactivations (e.g., via interaction with charge transfer states). Hence, if the direct sensitization pathway to state E (dashed arrow in Fig. 2) is not operative, then the
(5)
where kr and knr are the first-order rate constants for emission (radia tive) decay and nonradiative processes (intersystem crossing, energy transfer, multiphonon relaxation, etc.). The quantum yield for down shifting processes is often smaller than 100% and this value can only be attained in a resonance situation (Scheme 1) or if the excited level transfers its energy quantitatively to the emitting level. Note that luminescence is a generic term. When the implied transition occurs without spin change (ΔS ¼ 0) it is named “fluorescence” whereas when ΔS > 0, the phenomenon is termed “phosphorescence”. Fluorescence is allowed by the spin rule whereas phosphorescence is not, explaining why the former is a much faster process.
Fig. 2. Simplified schematic representation of (left) the antenna effect in a transition metal chelate and (right) the energy transfer scheme, with corresponding definitions. Key: N ¼ number of absorbed (A) or emitted (E) photons per unit time; D ¼ donor, A ¼ acceptor, and E ¼ emissive state; k’s are first-order rate constants and η’s are the components of the sensitization efficiency, while Φ’s are quantum yields (see text). A real metal chelate comprises many more ligand singlet and triplet states. 3
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sensitization efficiency would contain an additional term referring to the efficiency of the conversion between the excited and the luminescent level, η3. We also note that several authors use the term “internal quantum yield” for Φint but since this adjective is used in other fields with slightly different definitions, we prefer to keep to the term “intrinsic”. The overall quantum yield (i.e., number of photons emitted/number of photons absorbed by the matrix/ligand), Φovl, is given by: Nem ðmetalÞ Φovl ¼ ¼ ηsens � Φint ¼ η1 � η2 � η3 � Φint Nabs ðmatrix=ligandÞ
Φext ðor EQYÞ ¼
¼ Φint � ηinjection � ηextraction Φint ðor IQYÞ ¼
(8)
(11b)
3.2. Measurement of quantum yield It has become the norm to list measurements of quantum yield when discussing luminescent materials. Between 1960 and the end of 2019, this term was used in 78,839 scientific documents, Fig. 3, with most of these concerning chemistry. 3.2.1. Measurement of quantum yield for solutions using a relative method Early measurements of quantum yield for an optically dilute solution (Φx), with particular attention to experimental errors and sample purity, involved the comparison of the integrated emission spectrum of the sample (x) with that of a standard (s) with quantum yield Φs, such as quinine sulphate, or with a scatterer [12]:
3.1.2. Quantum yield of downconversion processes The quantum yield of downconversion (quantum cutting) processes can be larger than 100% since more photons are emitted than absorbed. Its maximum value is n � 100% where n is the number of lower energy photons produced per absorbed photon. The quantum yield of photon cutting processes has been estimated from measurements of branching ratios [8], with neglect of nonradiative processes, or by assuming unit quantum yield for the high-energy feeder level.
Φx ¼ Φs �
EðexÞs AðexÞs Fx n2x � � � EðexÞx AðexÞx Fs n2s
(12)
where E(ex) is the excitation irradiance, A(ex) the absorbance at the excitation wavelength, and Fx, Fs are the integrated emission spectra (corrected for the instrumental function) of sample and standard, respectively, in units of photons; ni (i ¼ x,s) are the refractive indices [13]. Linearity between the concentration and emission intensity is only maintained if A(ex) < 0.05, so that care must be taken to keep the so lutions dilute enough. If not possible, the terms A(ex) in Eq. (12) should then be replaced with (1-10-A(ex)). If λ(ex)s ¼ λ(ex)x then the terms E(ex) can be neglected and absorbance can be as large as 0.5 without intro ducing distortions. If the same solvent is used for sample and standard, then the refractive indices can be neglected since the solutions are dilute. A good protocol for precise determination of solution quantum yields
3.1.3. Quantum yield of upconversion processes The quantum yield of upconversion processes can be determined by careful measurements of photons emitted and absorbed, which is not easy a task since the quantum yields tend to be small and high laser power is used for excitation. Its maximum value is 100%/n where n is the number of summed up photons. If n ¼ 2, then Φmax ¼ 50%. We draw the attention of the readers to the fact that when triplet-triplet annihi lation (TTA) is considered for upconverting light, it is common practice to scale up the observed quantum yield by the factor two; this has to be avoided since it does introduce an unwanted distortion of data! A dis cussion of the efficiency of photon upconversion is provided in Ref. [9]. 3.1.4. The special cases of solar cells and light emitting diodes In the literature regarding solar cells, the term quantum efficiency is often used both for energy efficiency and for quantum yield. To be consistent with our definitions, the quantum yield of a solar cell is: number of electrons produced number of photons at reactive surface
number of emitted photons number of electron-hole recombinations
(11a)
where ηinjection represents the proportion of electrons passing through the device that are injected into the active region (i.e., electron current/ total current) and ηextraction is the proportion of photons produced that escape the device [10], since there are, for example, Fresnel and critical angle losses. IQY represents radiative recombination yield. The external quantum efficiency of a LED is defined as the total power of output photons (J s-1 ¼ W)/{input electric power, (V � A ¼ W)}, which matches the definition of Eq. (6).
here ηsens is the overall energy transfer efficiency from the ligand to the activator/metal ion luminescent state E; if the donor state is a triplet state, η1 includes the intersystem crossing S → T. The efficiency of the internal nonradiative process (η3 ) is usually overlooked, or assumed to be unity, but care should be exercised (see above). It is also important to stress that Φovl � Φint. The overall quantum yield is sometimes referred to as “external quantum yield” but, again, this may be confusing in view of other def initions of this parameter. Therefore, we suggest keeping to Φovl. Since all this terminology may be unclear when applied to phosphors, it is essential that the reported parameters should always be defined by an equation. Sometimes “internal” and “external” have been applied with reference to absorbed and incident photons, respectively.
ΦðλÞ ¼
number of emitted photons number of electrons passing into the device
(9)
The quantum yield falls to zero above λ ¼ hc/Ebg where Ebg is the bandgap energy of the semiconductor. For practical devices, and for the sake of comparison, the efficiency of solar cells is defined as the fraction of incident power converted into electrical power (under AM 1.5 illu mination and at 25 � C); it is expressed as:
ηext ðor EQEÞ ¼
Pm PS � A
(10)
with Pm (W) being the maximum cell power output (i.e., for maximum output voltage), PS the surface input power (W m-2), and A the cell area (m2). For light emitting diodes, the quantum yields are defined as:
Fig. 3. Number of publications per year concerning quantum yield. The red fit uses a first order exponential growth function, R2adj ¼ 0.9915. Data from Ref. [11].
4
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Box 1 Measurement of quantum yield of a powder using the integrating sphere. (Figures adapted from Ref. [16] for Cs3[Tb(dpa)3]).
is to prepare several solutions with different absorbances (<0.05) and to plot integrated emission versus absorbance. The gradients G of the ob tained linear dependences can be used to calculate the quantum yield: Φx ¼
Gx n2x Φs Gs n2s
3.2.4. Quantum efficiency in energy transfer The process of energy transfer between donor and acceptor species has been extensively studied both experimentally and theoretically, and optimization of the efficiency is of major importance. The experimental determination of the transfer quantum efficiency in terms of the donor luminescence lifetime has been critically compared with that in terms of the donor luminescence intensities [19]. The simplest expression for energy transfer efficiency involves the comparison of the lifetimes of the donor without the presence of the acceptor (τD) and with the presence of the acceptor (τDA), assuming single exponential decay in each case [20]:
(13)
This method allows one to test two aspects that often bias quantum yield determinations: dissociation of the sample (particularly in the case of metal complexes) and aggregation of the sample (particularly in the case of polyaromatic molecules). In both cases, the plots are not linear and suitable corrections have to be made.
ηET ¼ 1
3.2.2. Measurement of quantum yield for powders using a relative method The technique above can be adapted for powders [14], since several standards exist. Sodium salicylate is often employed but we note that its reported quantum yield varies from 40 to 60%, so that it is not an ideal reference compound. The blue lamp phosphor BAM, BaMgAl10O17:Eu2þ, is better characterized. The quantum yield is close to 90% (92% and 85% for Eu2þ concentration of 11.6 and 15%) [15]. The quantum yields of such phosphors depend on the granulometry, temperature, excitation wavelength, and activator concentration. It is also very sensitive to the synthesis protocol so that the latter should be carefully described, along with the origin and purity of the reactants.
τDA τD
(15)
3.2.5. Measurement of quantum yield using lifetimes If the radiative lifetime τr is known, measuring the luminescence decay curve and determining the corresponding lifetime is a method of accessing the quantum yield (see eq. (7)). This method is exemplified below for lanthanides. 3.2.6. Quantum yield of nanoparticles Most determinations of quantum yield of nanoparticles have employed the above relative solution methods. The solutions are dilute and transparent and usually the nanoparticles of uniform size are surface passivated. Assuming that the dilute solutions are photostable and that the appropriate choice of standard and photoexcitation wavelength has been made, difficulties may arise if the ensembles, such as quantum dots, exhibit an increase in emission upon illumination (photo brightening); aggregate at the concentration employed; or weaklybound shell ligands desorb at low concentrations, leaving “naked” nanoparticles. It is therefore important to investigate the concentration-
3.2.3. Measurement of quantum yield by an absolute method using an integrating sphere With an accuracy of (10–15%), quantum yields can be determined for luminescent materials with the use of an integrating sphere and with good statistics (3–5 measurements at least): see Box 1 for an example and refer to the literature for details [17,18]. 5
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dependence of the quantum yield [21]. A cost-effective set-up for measuring the quantum yield of upconverting nanoparticles has recently been proposed [22].
3.2.10. Use of quantum yield measurement The rationale of quantum yield measurement has been that it gives an indication of the usefulness of the material as an emitter, considering instrument characteristics, doping concentration, temperature and temporal stability and effects such as self-absorption and scattering. Numerous studies have therefore set out to optimize the quantum yield of a given system, for example by adjusting the dopant concentration, growing a protective shell on a nanoparticle core, tailoring coordinated ligands, adjusting the site symmetry of an activator or its local field, etc. However, one item has been less often considered. Is quantum yield really the most important factor for characterizing light emission? Isn’t “brightness” more relevant? We want the brightest phosphor, not the phosphor that only absorbs a few incident photons and wastes the remainder. For instance, a recent paper discusses the influence of dopant concentrations on the quantum yield, the luminescence decay kinetics, and brightness of upconverting nanoparticles [32]. In the following section, we identify how brightness is perceived in the various fields of photonics and propose a measurement method for solid-state samples.
3.2.7. Quantum yield of single molecules Determination of the quantum yield of a single molecule is achiev able by an absolute method involving a tunable optical resonator. Variation of the cavity length changes the local electromagnetic field, which in turn modifies the coupling of the emitting molecule to that field. Monitoring the luminescence lifetime versus the coupling strength and applying a theoretical model enables the extraction of both the quantum yield and the radiative lifetime. A test on an perylene deriva tive, N-(2,6-diisopropylphenyl)-perylene-3,4-dicarboxymide, yielded Φint ¼ 0.7 and τr ¼ 4.1 ns [23]. 3.2.8. Intrinsic quantum yields of lanthanide compounds Intrinsic quantum yields for lanthanide ions in compounds are often very difficult to determine by direct excitation into a 4fN energy level because the corresponding transition may have a small oscillator strength, and/or it is commonly obscured by a more intense transition from the matrix or the ligands. A solution is to use the last part of eq. (7): Φint ¼ τobs/τr. The lifetime is usually easy to measure. The radiative lifetime depends on the chemical and physical environment of the lanthanide ion as well as on the nature of the emitting level. Therefore, it has to be determined experimentally, or calculated from the transition oscillator strengths. Relying on published values for other compounds may lead to substantial errors. There are various ways of determining τr depending on the lantha nide ion. The first, general one relies on Judd-Ofelt (JO) parameters determined from absorption spectra. Emission probabilities can then be calculated with these JO parameters and the radiative lifetime is simply the inverse of the sum of emission probabilities from the excitation state. In lieu of the absorption spectrum, it is feasible to use the excitation or emission spectrum [24]. For two-level systems, e.g. Yb3þ, the radiative lifetime can be esti mated from the integrated absorption spectrum: Z 1 8πcn2 ν2 ð2J þ 1Þ ¼ 2302 � εðe ν Þd~ν (16) NA ð2J ’ þ 1Þ τr
4. Brightness Quantum yield is dimensionless and is not related to visual percep tion. What about brightness? In fact, we are unsure how to quantify “brightness”. The IUPAC Gold Book [6] states: “Obsolete term. This term is reserved for non-quantitative reference to physiological perception of light and is not recommended as a quantitative measure of the radiance of an emitting device, e.g., a lamp.” In other words: do not confuse photometry and radiometry! Nevertheless, the Gold Book proposes a more precise definition of brightness (see below). In his listing of six parameters important to the perception of light, Halsted describes brightness as a non-measurable but “perceivable” quantity with the corresponding quantitative parameter being luminance [33]. However, the United States Federal Trade Commission [34] has assigned two meanings of brightness: for light bulb packages, brightness means lu minous flux (cd sr), while in other contexts it means luminance (cd m-2). On the other hand, the Green Book [2] states that radiance is a normalized measure of the brightness of a source; it is the power emitted per area of the source per solid angle of the beam from each point of the source.
c is the speed of light in vacuum, n the refractive index of the absorbing medium, ~ν , wavenumber, is the inverse of wavelength (1/λ, cm-1), ν is the barycenter of the transition, J and J’ are the total angular mo mentum quantum numbers for the ground and excited state, respec tively, and NA is Avogadro’s number. The integral represents the integral of the absorption spectrum expressed in molar absorption coefficient versus wavenumbers. More accurately, the detailed crystal field level structures of the J-manifolds need to be considered. In the case of emission from the 5D0 level of Eu3þ, the value of radiative lifetime can be simply gained from the emission spectrum: � � 1 Ftot ¼ 14:65 � n3 � (17) τr FMD
4.1. Photophysical definition The photophysical definition of brightness B given in the Gold Book [6] is the product of the luminescence quantum yield Φ(λ) (Eq. (4)) and the molar absorption coefficient at the excitation wavelength, ε(λ): B ¼ ΦðλÞ � εðλÞ
(18a)
In this case brightness has the units of M-1 cm-1 or m2 mol-1 since the coefficient ε(λ) is given by Ref. [6]: � 0� 1 P AðλÞ (18b) εðλÞ ¼ log10 λ ¼ cL cL Pλ where c (M or mol dm-3) is molarity, L is the absorption path length (cm), P0λ and Pλ are the incident and transmitted spectral radiant power at wavelength λ per unit wavelength interval (W nm-1) and A(λ) is the absorbance. It is assumed that emission intensity has reached steady state after switching on the light source: that is, the number of photons emitted by the sample per unit time is constant. This definition of brightness is best suited for solutions for which measuring ε(λ) is easy, while Φ(λ) can be measured by either the relative method or the absolute method (integrating sphere) described above. Later we recommend another interpretation aimed at proposing a practical definition for solid samples. In the case of pulsed excitation when time-resolved detection is used for suppressing the autofluorescence of a biological sample (for instance
with Ftot and FMD being the integrated (and corrected) total emission spectrum (5D0→7FJ, J ¼ 0–6) and the integrated magnetic dipole tran sition (5D0→7F1). Note that transitions to J ¼ 5–6 extend up to 850 nm and are not often taken into account in the literature. The validity of the various formulae given above has been success fully tested [25]. 3.2.9. Other measurement techniques Other techniques of quantum yield measurement have employed, for example, photoacoustic spectroscopy [26], the thermal lens effect [27], and calorimetry [28]. The incident intensity-dependence of quantum yield has received attention [29], just as the temperature [30] and wavelength [31] dependences. 6
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in luminescence microscopy), the number of photons emitted after the end of the excitation pulse decreases exponentially with time. Therefore, a sample with a very short lifetime (e.g., ns) will appear brighter compared to one with a longer lifetime (e.g., ms or s). The latter will shine longer but with weaker intensity. The same occurs with a long persistent phosphor that can emit light for hours but at a usually low intensity level. This situation renders the comparison of brightness be tween different phosphors more difficult and one solution could be to divide Eq. (18a) by the lifetime: B ¼ ΦðλÞ � εðλÞ=τobs
with a defined acceptance angle and a minimum measurement area, are commercially available from the lowest range of about 1 mcd m-2. 4.3.3. Astronomy In astronomy, the brightness of a star is defined by the magnitude, a unitless measure with a logarithmic scale. It is defined such that one step of magnitude difference corresponds to an approximately 2.51-fold change in brightness. Sky brightness is measured, for example, by cali brated consumer digital cameras with fisheye lenses, or by a sky brightness photometer, in units of mag arcsec-2 (magnitude per square arcsecond: squims). These units are related to luminance by the equation: h i� � mag � � 0:4� value in 2 arcsec2 5 value in cd m ¼ 1:08 � 10 � 10 (20)
(19)
This is open to debate. As a complicating factor, the decay rate of a persistent luminescence phosphor decreases with time. 4.2. Physiological complications
4.3.4. Flow cytometry, biophysics and microscopy In flow cytometry, the brightness of fluorophores is measured in MESF units, molecules of equivalent soluble fluorophore. This is ach ieved by comparing the integrated fluorescence intensity FS of a sample of concentration CS across the entire emission spectrum, with that of a standard fluorophore (FDYE, over the same spectral range) of concen tration CDYE:
Brightness is experienced differently by humans and light detectors. It also means different things to an emitter or a detector. The human eye is only sensitive in the region from ca. 380–740 nm under well-lit con ditions and its response varies within this region, with a maximum in the green spectral region at 555 nm. This phototopic response of our eyes, V (λ), to different wavelengths has been displayed in Fig. 1a. Light de tectors measure radiance and not luminance. Luminance and radiance both denote power per unit area per unit solid angle, but the former is with respect to our phototopic response. Thus, brightness is an attribute of visual perception and is based upon, but not necessarily proportional to luminance [35], as shown in Fig. 1b [5]. Our perception of brightness is complicated by time-dependent light and dark adaptation, simulta neous contrast, lateral inhibition, dazzle, and color – i.e., the visual context [33]. Furthermore, the phototopic response V(λ) misrepresents the spectral sensitivity of important visual sensations such as brightness perception and a more universal luminous efficiency function U(λ) should be used instead [4].
B¼
FS CDYE � CS FDYE
(21)
so that the value is independent of the measurement instrument or method. The method is valid for nanoparticles (NPs), as shown for highly fluorescent quantum dots made of cellulose acetate; then equa tion (21) allows one to calculate the brightness of a single nanoparticle if the size of the NPs and their exact composition are known [40]. In microscopy, regardless of the imaging mode, not only the light source, the emission spectrum of the fluorescent antibody, the sensi tivity of the detector, but also the aperture and magnification of the objective lens are critical components of image brightness. In some cases, brightness (or normalized brightness) has been equated with fluorescence image intensity, or average counts per second, particularly using z-scan fluorescence fluctuation spectroscopy to characterize sample geometry and correct for bias of thin samples. The analysis of concentration-dependent brightness has been employed to distinguish monomer-oligomer transitions of proteins. Number and brightness analysis is a moment analysis capable of measuring the apparent average number of molecules and their oligo merization state in each pixel from a series of fluorescence microscopy images [41]. The apparent brightness, Bapp, which represents the mo lecular oligomerization level, is calculated as the ratio of variance (the second moment: σ2) to average intensity (the first moment: k) of the images:
4.3. How to quantify brightness? There are various approaches to measure brightness, depending upon the field of study. Hence, it is not surprising that different authors working in different fields have employed different definitions and metrics to characterize “brightness” in their reports. 4.3.1. Light sources For lamps (particularly LEDs), the brightness appearing on the packages refers in fact to either luminous flux (lm) or luminance (cd m2 ). Sometimes scientists define it as being the averaged red-green-blue (RGB) CIE coordinates, (R þ G þ B)/3. Another way of characterizing the brightness of a lamp is to give the temperature in K of a blackbody, the emission of which has the same brightness as the lamp. However, brightness is often confused with radiance. For instance, a record brightness of 9.3 � 1011 W m-2 sr-1 was reported for a 1450 nm laser array in a wavelength-beam-combining cavity [36].
Bapp ¼ σ2/k
(22)
whereas the average apparent number of molecules, N, is given by: N ¼ k2/σ2
4.3.2. Persistent luminescence Persistent phosphors emit light after excitation has ceased, due to the thermal emptying of traps. Xu and Tanabe [37] have expressed the “brightness” of persistent phosphors as luminance, in mcd m-2. The duration of a persistent phosphor is often defined as the time when the luminance has decayed to 0.32 mcd m-2: roughly 100 times the sensi tivity of the dark-adapted human eyes. This research group also stated that radiance is more appropriate than luminance to quantify the brightness of red to near-infrared persistent phosphors to which the eye is insensitive [38]. For example, the radiances of the persistent phosphor Y3Al2Ga3O12:Cr3þ were reported (in units of mW sr-1 m-2) as 6.59 � 10-1 and 0.67 � 10-1 after 5 min and 1 h, respectively, after ceasing excitation [39]. Computer-controlled brightness meters, measuring luminance
(23)
This analysis is performed for all the pixels of an image, each with a volume of ~ (1–2)x10-3 μm3, providing oligomerization maps of entire cells on a pixel-by-pixel basis. The diffusion rate of the proteins and the temporal capability and dynamic range of the acquisition device determine oligomerization heterogeneity [41]. The technique has also been employed using total internal reflection microscopy. It is essential to correlate optical measurements of isolated particles with electron microscope images that clearly resolve the particle size in order to confirm that the emission is from an individual particle and not a cluster of particles. These measurements must be able to determine how the distribution in particle brightness correlates with the distribu tion of particle size and quality [42]. 7
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However, in the literature brightness is also described by Eq. (18), so that for a fluorophore-labeled molecule, the brightness of a stained section under a given illumination intensity is given by the product of the molar absorption coefficient and quantum yield. The brightness depends upon the dye concentration within stained sections of the specimen, the thickness of the specimen, and the amount of stained material actually present within the field of view of the microscope. For example, fluorescein and Cy5™ have quantum yields of 0.9 and 0.3, respectively, molar absorption coefficients of 7 � 104 and 2 � 105 M1 cm-1, respectively, and are very bright fluorochromes with B ¼ 6.3 � 104 and 6 � 104 M-1 cm-1. With a slightly different definition from Eq. (18a), brightness, B has been defined and investigated at the single molecule level [43] by Tian et al.: B¼
N Ck σ Φ ¼ ¼ η Iex Iex hν det
� 2 cm W
1
s
1
�
quantum yield) can be measured. 4.4. Alternative description of brightness and examples Seeking to define a dimensionless quantity, we propose the following definition for brightness (previously called external quantum yield [20]) that would apply to both solutions and solids: Brightness; B ¼
B¼
ðnumber of photons emittedÞ ðnumber of incident photonsÞ
(25)
number of photons emitted number of photons absorbed � number of photons absorbed number of incident photons
¼ ΦðλÞ � ξabs
(26)
where ξabs is the absorption efficiency:
(24)
ξabs ¼
where N (s-1) is the number per second of experimentally detected photons and Iex is the excitation power density (W cm-2); C is the measured charge coupled device counts and k is the conversion factor which changes counts into detected photons. The final part of the equation employs the absorption cross-section (σ , cm2), the fluorescence quantum yield, Φ, the photon energy (hν, J), and the light detection efficiency of the setup (ηdet). Notice that Eq. (24) differs from Eq. (18a) in measure ment units but it similarly involves absorption and quantum yield components. Many factors influence the measurement of single mole cule emission intensity, including the orientation of the molecule rela tive to the polarization plane of the incident photons and the optic axis of the objective lens. Single molecule absorption measurements are problematic and as an alternative to quantum yield measurements, the fluorescence excitation cross-section (¼ absorption cross-section �
number of photons absorbed number of incident photons
(27)
and ξabs is also a dimensionless quantity readily obtainable in an inte grating sphere measurement, as in Box 1. Brightness is then a dimen sionless quantity not related to the sensitivity of the human eye. This definition applies to both solid-state samples and solutions but requires the use of an integrating sphere for solutions too. Box 2, left hand side, displays a typical measurement of brightness by the integrating sphere method for a cyclamEu-phen (phen ¼ 1,10-phe nanthroline; cyclam ¼ substituted 1,4,7,10-tetrazacyclododecane) complex as a powder [44]. The overall quantum yield is 4.4% and the brightness is 0.032, with 5–10% error. Interestingly, the brightness is about ten times smaller for the complex cyclamEu-phLa (ph ¼ phen (pdtc)3, pdtc ¼ pyrrolidine-1-carbodithioate), where the absorption, internal quantum efficiency and Eu(5D0) decay lifetime are all similar to
Box 2 Comparison of brightness for a powder sample (left [44]) and solutions (right). Concentration for solutions: 7.5 � 10-5 M (dipicolinate [45]) and 1.5 � 10-5 M (helicate [46]).
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Journal of Luminescence 224 (2020) 117256
Table 2 Recommended definitions in the field of photophysics; ε(λ) ¼ molar absorption coefficient, ξabs ¼ fraction of absorbed photons (absorption efficiency). Quantity
Symbol
Definition
Units
Sample
Comment
Quantum yield
Φ(λ)
dimensionless
any
Recommended
Quantum efficiency
η
dimensionless
any
Recommended
Brightness
B B
number of photons emitted number of photons absorbed energy output energy input B ¼ Φ(λ) � ε(λ) B ¼ Φ(λ) � ξabs
M-1 cm-1 dimensionless
solutions solids, solutions
Recommended Recommended
Basic parameters
Other definitions of quantum yields (QY) for doped materials or coordination compounds Quantity
Symbol
Definition
Comment
Internal QY
Φint(λ)
Same as Φ(λ) above
Intrinsic QY
Φint(λ)
Same as Φ(λ) above
External QY
Φext(λ)
Overall QY
Φovl(λ)
number of photons emitted number of incident photons Same as Φ(λ) above
Excitation into the Not recommended Excitation into the Recommended Excitation into the Not recommended Excitation into the Recommended
those of a cyclamEu-phen, but the sensitization efficiency and overall quantum yield are both about an order of magnitude smaller. The maximum values of brightness to be expected for useful phosphors – for example, with an overall quantum yield of 80% and ξabs about 0.5 – would be more than ten times greater than for cyclamEu-phen. In the case of solid samples, e.g., powders, measuring the diffuse reflection spectrum of a thick layer is an alternative since this spectrum can then be used to determine the fraction of light absorbed by the sample at the excitation wavelength. Combined with quantum yield determination, this gives access to the brightness. The right hand side of Box 2 shows the calculation of brightness according to Eq. (18) for two cases: europium(III) tris(dipicolinate), with the quantum yield determined by a the comparative method [45], and the dinuclear europium(III) triple-stranded helicate [Eu2(LC2)3] in aqueous solution, with the quantum yield determined by both compar ative and absolute methods [46]. These two europium complexes have almost the same overall quantum yields but their brightness differs 28-fold because the helicate has a far larger molar absorption coefficient at the excitation wavelength. As far as we know, the Eu3þ complexes with highest brightness in water have been reported by Parker’s group: they feature a triaza-cyclononane anchor decorated with various an tenna substituents. Their quantum yield is in the range 24–37% and their brightness in the range 5.65–5.8 � 104 M-1 cm-1 with excitation wavelengths in the range 322–332 nm [47]. Aryl-substituted pyr azolecarboxylic acids have values ε ~ 2 � 104 M-1 cm-1 for wavelengths in the range 240–280 nm and the Tb3þ complex of 1-methyl-5-phe nyl-1H-pyrazole-3-carboxylic acid has the reported quantum yield of 100% [48]. Note that the nature of the solvent has a remarkable effect upon the brightness of a chromophore. Acridine has the fluorescent brightness <27 M-1 cm-1 when dissolved in benzene (Φ(fl) < 10-3, ε ¼ 2.7 � 104 M-1 cm-1), but has the reported value of 7030 M-1 cm-1 in aqueous solution (Φ(fl) ¼ 0.37, ε ¼ 1.9 � 104 M-1 cm-1) [49].
activator/metal ion activator/metal ion matrix/metal ion matrix/metal ion
1. Quantum yield and brightness are both useful concepts. High quantum yields are essential for lighting phosphors. For bioprobes and bionanoprobes the quantum yield may be low but the massive molar absorption coefficient can lead to high brightness. 2. The measurements of quantum yield and brightness depend upon many factors [50] that have to be clearly documented in the exper imental report, such as experimental procedure, excitation wave length, temperature, and exact composition of the sample and standard. 3. For solids, the definition of brightness described by Eq. (26) should be used while for solutions both Eqs. (18) and (26) can be used provided the quantum yield measurement is made with an inte grating sphere. Both methods illustrated in Box 2 provide a measure of outgoing photons to incoming photons. The definition Eq. (18a) has previously been employed in studies of nanoparticles, quantum dots and fluorescent dyes [18,32,51]. 4. Care should be taken to clearly state the definition of a term related to brightness, and with respect to quantum yield and quantum effi ciency. Clear definitions have been provided for intrinsic and overall quantum yield (See Table 2) and we recommend the use of these two. 5. A solid sample with given particle size and activator doping con centration or a solution with a given concentration could be both QY and brightness standards. We are taking steps in this direction. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements J.-C. B thanks HKBU for the Dr Kennedy Wong Distinguished Visiting Professorship (2017-2019). K.-L. W. and J.-C. B. thank the CAS-Croucher Funding Scheme for Joint Laboratories (CAS 18204). We are grateful to Professor Setsuhisa Tanabe for correspondence regarding LEDs.
5. Summary and recommendations ‘Brightness’ has different definitions and is measured in different ways in different areas of science - usually based upon luminance or radiance. Some measurements of brightness have been summarized and the relevance to our perception has been included. Other factors besides luminance affect our perception, from dim to bright, of brightness. Some observations concerning two methods of measuring brightness are given in bullets at the foot of Box 2. The following comments and recommendations are made from our study.
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