# Quantum yeild

## Recording Fluorescence Quantum Yields

Measurement of the absolute photoluminescence quantum yield (PLQY) of thin films is a more complex procedure than the corresponding solution measurement. This is due to the fact that films are a high refractive index medium, which in turn results in substantial waveguiding of the luminescence. To overcome the angular dependence of the emission from films, integrating spheres are generally used to collect the emitted light. The use of integrating spheres has usually required a laser as the excitation source in combination with a fibre coupled CCD camera or a calibrated photodiode as the luminescence detectors. We can however, fit an integrating sphere into the sample chamber of both the FluoroLog and FluoroMax Spectrofluorometers to measure solid state photoluminescence quantum yields of films. This approach significantly simplifies the experimental method as the need for special equipment on the excitation and detection side is relaxed.

The results are rewarding since it shows that PLQYs can be determined in an easy way with an instrument that has additional flexibility compared to the experimental set-ups that are generally used, and will be found in very many laboratories. This should make PLQY measurements accessible to a large number of groups with the minimum of cost.

We gratefully acknowledge the help of Dr L Palsson, Dr A Monkman and Dr A Beeby (University of Durham, UK) for the Fluorescence Quantum Yield information provided on this page.

Sours: https://www.horiba.com/

### Abstract

The mechanisms underlying the wavelength dependence of the quantum yield for CO2 fixation (α) and its acclimation to the growth-light spectrum are quantitatively addressed, combining in vivo physiological and in vitro molecular methods. Cucumber (Cucumis sativus) was grown under an artificial sunlight spectrum, shade light spectrum, and blue light, and the quantum yield for photosystem I (PSI) and photosystem II (PSII) electron transport and α were simultaneously measured in vivo at 20 different wavelengths. The wavelength dependence of the photosystem excitation balance was calculated from both these in vivo data and in vitro from the photosystem composition and spectroscopic properties. Measuring wavelengths overexciting PSI produced a higher α for leaves grown under the shade light spectrum (i.e., PSI light), whereas wavelengths overexciting PSII produced a higher α for the sun and blue leaves. The shade spectrum produced the lowest PSI:PSII ratio. The photosystem excitation balance calculated from both in vivo and in vitro data was substantially similar and was shown to determine α at those wavelengths where absorption by carotenoids and nonphotosynthetic pigments is insignificant (i.e., >580 nm). We show quantitatively that leaves acclimate their photosystem composition to their growth light spectrum and how this changes the wavelength dependence of the photosystem excitation balance and quantum yield for CO2 fixation. This also proves that combining different wavelengths can enhance quantum yields substantially.

### INTRODUCTION

For well over half a century, it has been known that the energy conversion efficiency of incident photons to chemical energy by leaves is wavelength dependent (Hoover, 1937). This is due to several processes that can be divided into two classes. First, the absorption of incident irradiance by a leaf is wavelength dependent due to the different absorptance spectra of the different leaf pigments. Second, even on an absorbed light basis, different wavelengths have different quantum yields for CO2 fixation or O2 evolution: Red light (600 to 640 nm) has the highest quantum yield, whereas blue and green light (400 to 570 nm) are considerably less efficient in driving photosynthesis (McCree, 1972b; Inada, 1976; Evans, 1987). Maximum quantum yields for C3 leaves were found to be close to 0.093 mol CO2 fixed (Long et al., 1993) or 0.106 mol O2 evolved (Björkman and Demmig, 1987) per mol absorbed photons.

Three major causes for the wavelength dependence of the quantum yield for absorbed photons have been identified (i.e., absorption by photosynthetic carotenoids, absorption by nonphotosynthetic pigments, and an imbalanced excitation of the two photosystems) (Terashima et al., 2009). Photosynthetic carotenoids have absorption maxima for blue wavelengths and differ in their efficiency (35 to 90%) for excitation energy transfer to chlorophylls, depending on the type of carotenoid and its position within the photosynthetic apparatus, whereas the energy transfer efficiency in the antenna complexes from chlorophyll to chlorophyll is 100% (Croce et al., 2001; de Weerd et al., 2003a, 2003b; Caffarri et al., 2007). Nonphotosynthetic pigments, such as flavonoids and free carotenoids, also absorb light, predominantly in the UV region but also in the blue and green part of the spectrum (e.g., anthocyanins). Nonphotosynthetic pigments do not transfer any absorbed energy to the photosynthetic apparatus. Finally, the pigment composition and absorbance properties differ for photosystem I (PSI) and photosystem II (PSII); consequently, the balance of excitation between the two photosystems is wavelength dependent (Evans, 1986, 1987; Chow et al., 1990; Melis, 1991; Walters and Horton, 1995). Any imbalance in excitation of the two photosystems results in quantum yield losses (Pfannschmidt, 2005). However, a quantitative understanding of the relative contribution of each of these factors causing quantum yield losses is still lacking.

Plants are continuously exposed to spectral changes, in the short term due to changes in weather and sun angle and in the longer term when leaves become shaded by other leaves or when shaded leaves become exposed to full sun (e.g., after canopy gap formation). The degree of shading by other vegetation strongly affects both the light intensity and spectrum to which a leaf is exposed. Spectral changes can directly alter the photosynthetic quantum yield via changes in the relative absorbance by the different pigments and via changes in photosystem excitation balance. Acting on a time scale of minutes, state transitions are believed to redirect excitation energy from one photosystem to another (Haldrup et al., 2001), although in intact leaves no subsequent increase in the quantum yield for CO2 fixation has been found (Andrews et al., 1993). In the longer term, photosynthetic organisms can adapt to spectral changes by altering the relative size of the two photosystems, thus, at least partly restoring the excitation balance between them (Chow et al., 1990; Melis et al., 1996; Fujita, 1997). In leaves, acclimation to the spectral environment resulted in an increase in the quantum yield for CO2 fixation and linear electron transport (Walters and Horton, 1995) and an altered PSI:PSII ratio (Chow et al., 1990). However, the consequences of acclimation of the photosystem composition to the spectral environment for the wavelength dependence of the photosystem efficiency balance and how this relates quantitatively to the quantum yield for CO2 fixation have so far not been explored.

Combined in vivo chlorophyll fluorescence and 820-nm absorbance change (ΔA820) measurements (Baker et al., 2007) can be used to estimate the functional photosystem efficiency balance (Eichelmann and Laisk, 2000). The spectroscopic properties of isolated pigment-protein complexes (i.e., in vitro) can likewise be used to estimate the photosystem excitation balance (Evans and Anderson, 1987). Due to inefficiencies in excitation energy transfer and charge separation and nonlinear electron transport processes, such as cyclic electron transport, back-reactions, or transfer to O2, the relationship between excitation balance, absorbance balance, and a more functional photosystem efficiency balance is not simple.

In this study, we explore the relationship between the wavelength dependence of the in vitro photosystem absorbance balance and the in vivo photosystem efficiency balance and how this balance relates to the quantum yield for CO2 fixation. We also show how the growth spectrum affects the wavelength dependence of the quantum yield for CO2 fixation in leaves. Cucumber (Cucumis sativus) was grown under an artificial sunlight spectrum, blue light, and an artificial shade light spectrum, the latter containing a stronger intensity at wavelengths >680 nm, thus preferentially exciting PSI. The blue growth spectrum (∼445 nm) used is expected to excite the photosystems in a similar ratio as the sunlight (Evans and Anderson, 1987) but has earlier been shown to produce some distinct physiological effects (e.g., sun-type photosynthetic characteristics and a shade-type phytochrome equilibrium; Hogewoning et al., 2010c). By combining both an in vitro and in vivo approach we unambiguously show how acclimation to growth spectrum results in changes in the relative absorptance of the two photosystems, which are directly linked to changes in photosystem excitation balance and quantum yield for CO2 fixation.

### Quantum Yield for CO2 Fixation

The wavelength dependence of the quantum yield for CO2 fixation under nonphotorespiratory conditions (0.038% CO2; 2% O2) was measured on cucumber leaves developed under three different growth-light spectra (sunlight spectrum, shade light spectrum, and blue light; Figure 1). All measurements were performed under light-limited conditions as indicated by the fact that the assimilation-irradiance response was typically highly linear (R2 ≥ 0.997; see Supplemental Figure 1 online). The quantum yield for CO2 fixation on an incident irradiance basis, which is an ecophysiologically relevant parameter, was highest in the range 620 to 680 nm in all three treatments (Figure 2A; see Supplemental Table 1 online). From 427 to 560 nm, the yield changed relatively little and was ∼70% of the highest yield measured, while at 400 nm, the yield was higher than in the range 427 to 560 nm (P < 0.05 for sunlight and shade light spectrum, but for blue light not at all wavelengths). Above 680 nm, the yield declined rapidly down to zero at 736 nm. Differences in the absorptance spectra of the leaves from the three different growth conditions were small (Figure 3). The maximum value for the quantum yield for CO2 fixation on an absorbed light basis (α), which is more relevant than the yield on an incident light basis with respect to our research objectives, was 0.093 CO2 fixed per absorbed photon at 620 to 640 nm (Figure 2B; see Supplemental Table 2 online). Compared with the quantum yield for CO2 fixation on an incident light basis, the wavelength range producing the highest values of α (580 to 640 nm) was found at shorter wavelengths (Figure 2). In the green region (520 to 580 nm) and far-red (FR) region (≥700 nm), the differences between quantum yield on an incident (Figure 2A) and absorbed (Figure 2B) light basis are greatest due to the relatively low absorptance of these wavelength ranges.

Figure 1.

Growth-Light Spectra.

Spectral distribution of the artificial sunlight spectrum (thick solid line), the artificial shade light spectrum (dotted line), and blue light (thin solid line) used as growth light sources during leaf development.

Figure 1.

Growth-Light Spectra.

Spectral distribution of the artificial sunlight spectrum (thick solid line), the artificial shade light spectrum (dotted line), and blue light (thin solid line) used as growth light sources during leaf development.

Figure 2.

Wavelength Dependence of Photosynthetic Quantum Yield.

The quantum yield for CO2 fixation for 19 different wavelengths on an incident light (A) and absorbed light (B) basis of cucumber leaves developed under a sunlight spectrum (open circles), a shade light spectrum (closed circles), and blue light (open squares). Error bars through data points represent the se; the error bar in the top right corner represents Fisher's LSD (P < 0.05, n = 3) of the significant interaction between the means of growth light spectrum and measuring light spectrum effects.

Figure 2.

Wavelength Dependence of Photosynthetic Quantum Yield.

The quantum yield for CO2 fixation for 19 different wavelengths on an incident light (A) and absorbed light (B) basis of cucumber leaves developed under a sunlight spectrum (open circles), a shade light spectrum (closed circles), and blue light (open squares). Error bars through data points represent the se; the error bar in the top right corner represents Fisher's LSD (P < 0.05, n = 3) of the significant interaction between the means of growth light spectrum and measuring light spectrum effects.

Figure 3.

Leaf Absorptance Spectra.

Absorptance spectra of green cucumber leaves grown under a sunlight spectrum (middle solid line), shade light spectrum (bottom solid line), and blue light (top solid line) spectrum and the absorptance spectrum of albino cucumber leaves (dotted line).

Figure 3.

Leaf Absorptance Spectra.

Absorptance spectra of green cucumber leaves grown under a sunlight spectrum (middle solid line), shade light spectrum (bottom solid line), and blue light (top solid line) spectrum and the absorptance spectrum of albino cucumber leaves (dotted line).

The overall wavelength response pattern of α (Figure 2B) is similar to that observed in previous studies (McCree, 1972b; Inada, 1976). However, the growth light spectrum affected α to a considerable extent. At wavelengths >680 nm, which are usually considered as PSI light, the leaves grown under a shade light spectrum produced a higher α than those grown under a sunlight spectrum or blue light (Figure 2B; P < 0.05 at 700 nm for the shade light spectrum versus the sunlight spectrum and the blue light, P < 0.05 at 710 nm for the shade light spectrum versus blue light). Below 680 nm, which is usually considered to be PSII light, α of leaves grown under the sunlight spectrum and the blue light was higher than α of leaves grown under the shade light spectrum in the range 480 to 600 nm (except at 520 nm) and at 660 nm (P < 0.05 for shade light spectrum versus sunlight spectrum and/or blue light). However, <460 nm, at 520 nm and at 620 to 640 nm, α did not differ significantly for the leaves grown under the three different spectra. Across the spectrum, no significant difference between α of the sunlight spectrum and the blue light grown leaves was found.

### Quantum Yield for Electron Transport through PSI and PSII

The quantum yield for CO2 fixation was strictly light limiting for the actinic light intensity range used (see Supplemental Figure 1 online). However, the quantum yield for electron transport through PSII (ΦPSII) decreased with increasing irradiance at those wavelengths where PSII was overexcited (i.e., ΦPSII < 0.8; Figure 4). Possibly alternative electron sinks on the PSII acceptor side played a significant role at very low irradiances (see Discussion). Therefore, it appeared most reasonable to use the ΦPSI and ΦPSII values associated with the highest light-limited irradiance for the calculation of the photosystem efficiency balance in vivo (see below). The efficiency of the electron transport by open PSII traps (Fv′/Fm′) was consistently close to 0.8. This, together with the linear relationship between ΦPSII and the PSII efficiency factor (qp; Figure 5), implies that within the light-limited irradiance range used, the loss of ΦPSII was wholly due to decreases in qp, with no contribution from nonphotochemical quenching. While qp indicates the fraction of photochemical quenching, qL provides an estimate of the fraction of open PSII centers (with primary electron accepting plastoquinone of PSII [QA] oxidized) following the lake model for PSII (Kramer et al., 2004). The relationship of qL with ΦPSII was curvilinear (Figure 5C). The low values of qL (i.e., <0.4) show how reduced QA can become even at light-limited irradiances in the case of PSII overexcitation (Figures 4A and 5C).

Figure 4.

Responses of a Range of Photosynthetic Parameters to Irradiance Preferentially Exciting Either PSI (700 nm) or PSII (480 nm), or Exciting Both Photosystems nearly Equally (620 nm).

Response of the photosynthetic parameters ΦPSI and ΦPSII (top), qp and Fv′/Fm′ (middle), and qL (bottom) for cucumber leaves grown under a sunlight spectrum (open circles), shade light spectrum (closed circles), and blue light (squares) to absorbed actinic irradiance (light-limited range) of 480 nm (A), 620 nm (B), and 700 nm (C).

Figure 4.

Responses of a Range of Photosynthetic Parameters to Irradiance Preferentially Exciting Either PSI (700 nm) or PSII (480 nm), or Exciting Both Photosystems nearly Equally (620 nm).

Response of the photosynthetic parameters ΦPSI and ΦPSII (top), qp and Fv′/Fm′ (middle), and qL (bottom) for cucumber leaves grown under a sunlight spectrum (open circles), shade light spectrum (closed circles), and blue light (squares) to absorbed actinic irradiance (light-limited range) of 480 nm (A), 620 nm (B), and 700 nm (C).

Figure 5.

Relationship between Fv′/Fm′, Photochemical Quenching, the Fraction of Oxidized QA, and the Relative Quantum Yield of PSII.

Relationship of the chlorophyll fluorescence derived parameters Fv′/Fm(A), qp(B), and qL(C) with ΦPSII. The data corresponding with all wavelengths of actinic light used (380 to 740 nm), and all different light intensities used per wavelength, are plotted for the three different growth light treatments (sunlight spectrum, open circles; shade light spectrum, closed circles; blue light, squares).

Figure 5.

Relationship between Fv′/Fm′, Photochemical Quenching, the Fraction of Oxidized QA, and the Relative Quantum Yield of PSII.

Relationship of the chlorophyll fluorescence derived parameters Fv′/Fm(A), qp(B), and qL(C) with ΦPSII. The data corresponding with all wavelengths of actinic light used (380 to 740 nm), and all different light intensities used per wavelength, are plotted for the three different growth light treatments (sunlight spectrum, open circles; shade light spectrum, closed circles; blue light, squares).

The wavelength dependence of ΦPSI and ΦPSII is shown in Figure 6A. Overall ΦPSI is close to 1.0 at wavelengths <680 nm, whereas it drops progressively at ≥680 nm, which, as expected, indicates that the longer wavelengths overexcited PSI. However, a slight overexcitation of PSI was also found for the sunlight spectrum and the blue light–grown leaves at 380 to 400 nm and at 520 nm, where ΦPSI was smaller (P < 0.05) than at 460 to 500nm at which PSII is overexcited. Maximum values for ΦPSII (∼0.8) were measured >680 nm for all growth light treatments and for the sunlight spectrum and the blue light grown leaves at wavelengths below 460 nm and at 520 nm. The lowest ΦPSII values were measured around 480, 560, and at 660 nm, indicating significant overexcitation of PSII. Overall for the shade light spectrum–grown leaves, ΦPSII was lower at wavelengths <680nm, whereas ΦPSI was higher at wavelengths >680 nm, compared with the sunlight spectrum and blue light–grown leaves (Figure 6A), which is similar to the pattern found for α (Figure 2B).

Figure 6.

Wavelength Dependence of ΦPSI, ΦPSII, and the Development of State Transitions.

(A) Wavelength dependence of ΦPSI (dashed lines) and ΦPSII (solid lines) of leaves exposed to an irradiance just below an intensity high enough to be no longer light-limited (in the range 50 to 55 µmol m−2 s−1 for most wavelengths). The open circles, closed circles, and squares correspond to sunlight spectrum–, shade light spectrum–, and blue light–grown cucumber leaves, respectively. The inset shows the relationship between ΦPSI and ΦPSII found for sunlight spectrum leaves for the wavelengths that produced values of ΦPSI within the efficiency range of 0.94 to 0.98.

(B) Wavelength dependence of the ratio of light-adapted minimum fluorescence (F0′) and dark-adapted minimum fluorescence (F0), as an indicator of state transitions induced by the actinic measuring light (F0′/F0 = 1 indicates state 1; symbols are as in (A).

Error bars through data points represent the se; the error bars in the top right corner in (A) and top middle in (B) represent Fisher's LSD (P < 0.05, n = 3) of the significant interaction between the means of growth light spectrum and measuring light spectrum effects.

Figure 6.

Wavelength Dependence of ΦPSI, ΦPSII, and the Development of State Transitions.

(A) Wavelength dependence of ΦPSI (dashed lines) and ΦPSII (solid lines) of leaves exposed to an irradiance just below an intensity high enough to be no longer light-limited (in the range 50 to 55 µmol m−2 s−1 for most wavelengths). The open circles, closed circles, and squares correspond to sunlight spectrum–, shade light spectrum–, and blue light–grown cucumber leaves, respectively. The inset shows the relationship between ΦPSI and ΦPSII found for sunlight spectrum leaves for the wavelengths that produced values of ΦPSI within the efficiency range of 0.94 to 0.98.

(B) Wavelength dependence of the ratio of light-adapted minimum fluorescence (F0′) and dark-adapted minimum fluorescence (F0), as an indicator of state transitions induced by the actinic measuring light (F0′/F0 = 1 indicates state 1; symbols are as in (A).

Error bars through data points represent the se; the error bars in the top right corner in (A) and top middle in (B) represent Fisher's LSD (P < 0.05, n = 3) of the significant interaction between the means of growth light spectrum and measuring light spectrum effects.

Notably, besides wavelengths producing a ΦPSI or ΦPSII close to maximal (1.0 and 0.8, respectively), there was a range of wavelengths where neither ΦPSI nor ΦPSII was at its maximum. At the narrow range of efficiencies associated with these wavelengths (i.e., 0.94 < ΦPSI < 0.98), ΦPSI and ΦPSII changed proportionately and inversely (Figure 6A, inset). This phenomenon may be related to differences in the photosystem stoichiometry of cell layers through the leaf cross section due to the spectral changes of light penetrating into the leaf. Nevertheless, no consistent pattern of differences in ΦPSII measured with red and green (deeper leaf penetration) excitation wavelengths was found. The high values of ΦPSII at very low irradiances, as described above, make further analysis of these results speculative.

The measurements of ΦPSII (Figure 6A) were taken after the leaf was exposed to the actinic light for sufficient time to allow for possible state transitions (≥15 min). The ratio of F0′ and F0 can be used as an indicator for state transitions in the absence of nonphotochemical quenching (Allen, 1992; Samson and Bruce, 1995). At those wavelengths where ΦPSII is well below its maximum of 0.8 and, therefore, PSII is excited more than PSI, F0′ was almost 10% lower than F0, consistent with the development of a state transition, whereas at wavelengths overexciting PSI, F0′ and F0 were similar (Figure 6B). Notably, the ratio of F0′ and F0 is at its lowest value over a broader range of wavelengths in the shade light spectrum–grown leaves than in the sunlight spectrum– and blue light–grown leaves, which is consistent with the broader range of wavelengths overexciting PSII in the shade light spectrum leaves (Figure 6).

### Photosystem Composition and Excitation Balance

To relate the in vivo parameters to the molecular composition of the photosynthetic apparatus, the pigment and protein composition of the leaves developed under the three growth light spectra was determined. The chlorophyll a:b ratio was lowest in the leaves grown under the shade light spectrum and slightly lower in the sunlight spectrum–grown leaves compared with the blue light–grown leaves (Table 1). This difference in chlorophyll a:b ratio can have two origins: (1) a change in the antenna size of PSII or (2) a change in the PSI/PSII ratio. To discriminate between these two possibilities, the protein composition of the thylakoid membranes was analyzed by SDS-PAGE and protein quantification (see Methods). The sunlight– and shade light spectrum–grown leaves showed a virtually identical PSII antenna size (Tables 1 and 2; see Supplemental Figure 2 online), while the PSI:PSII ratio was significantly lower for the shade light spectrum leaves. In the blue light–grown leaves, a slightly reduced amount of light-harvesting complex II (LHCII) was observed, while the PSI:PSII ratio was identical to that of the sunlight spectrum–grown leaves. The lower PSI:PSII ratio found for the shade light spectrum–grown leaves compared with the sunlight spectrum– and blue light–grown leaves was confirmed by protein immunoblot analysis (see Supplemental Figure 3 online). The two methods produced similar relative differences between the PSI/PSII ratios of the leaves grown under the different light spectra.

#### Effect of Growth-Light Spectrum on Photosystem Composition

Table 1.

Effect of Growth-Light Spectrum on Photosystem Composition

Growth Light . Sun . Shade . Blue .
Chlorophyll a:b2.98b2.67c3.10a
LHCII per PSII core 3.61ab3.72a3.29b
RC ratio PSI/PSII0.90a0.64b0.90a
RC ratio PSII/(PSII+PSI) 0.53b0.61a0.53b
Growth Light . Sun . Shade . Blue .
Chlorophyll a:b2.98b2.67c3.10a
LHCII per PSII core 3.61ab3.72a3.29b
RC ratio PSI/PSII0.90a0.64b0.90a
RC ratio PSII/(PSII+PSI) 0.53b0.61a0.53b

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Table 1.

Effect of Growth-Light Spectrum on Photosystem Composition

Growth Light . Sun . Shade . Blue .
Chlorophyll a:b2.98b2.67c3.10a
LHCII per PSII core 3.61ab3.72a3.29b
RC ratio PSI/PSII0.90a0.64b0.90a
RC ratio PSII/(PSII+PSI) 0.53b0.61a0.53b
Growth Light . Sun . Shade . Blue .
Chlorophyll a:b2.98b2.67c3.10a
LHCII per PSII core 3.61ab3.72a3.29b
RC ratio PSI/PSII0.90a0.64b0.90a
RC ratio PSII/(PSII+PSI) 0.53b0.61a0.53b

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The stoichiometry between the complexes was used to scale their absorbance spectra (spectra for PSII supercomplex, PSI-light-harvesting complex I (LHCI), and LHCII in Supplemental Figure 4 online), thus allowing calculation of an estimate of the wavelength dependence of the excitation balance of the two photosystems. A comparison of this in vitro photosystem excitation balance with the in vivo photosystem efficiency balance (i.e., derived from ΦPSI and ΦPSII at the highest actinic light intensity used at each wavelength) revealed a strong linear relationship (Figure 7). Note that the linearity (Figure 7B) is improved if the data corresponding with the wavelengths 460 and 500 nm, which are dominated by carotenoid absorption, are not taken into account (see Supplemental Figure 5 online). Excitation in vitro at those wavelengths overexciting PSII (i.e., PSII light) appears to be more imbalanced than in vivo, where state transitions play a role. For PSI light, the two approaches produce similar results. The apparently stronger overexcitation of PSII in vitro is illustrated by the different slopes of the relationship between the two approaches for the data points corresponding with PSI light and PSII light (Figure 7B).

Figure 7.

Wavelength Dependence of the Excitation Balance between PSI and PSII.

(A) Wavelength dependence of the excitation balance of the two photosystems calculated as absorption by PSII divided by absorption of both PSI and PSII using an in vitro (connected lines) and in vivo (unconnected data points) approach. The left y axis corresponds to the in vitro approach (sunlight spectrum, dashed line; shade light spectrum, top solid line; blue light, bottom solid line) and the right y axis with the in vivo approach (sunlight spectrum, open circles; shade light spectrum, closed circles; blue light, squares). Note that the scale is different for the two y axes.

(B) Relationship between the excitation balances obtained via the in vitro and in vivo approach. The data in the top right corner, which are the data in plot (A), are presented in more detail in Supplemental Figure 5 online. Note that for values of PSII/(PSII+PSI) < 0.4, which correspond with wavelengths preferentially exciting PSI, both the in vitro and in vivo methods produce similar results. At values of PSII/(PSII+PSI) > 0.5, which correspond with wavelengths preferentially exciting PSII, the overexcitation of PSII appears to be stronger in vitro.

Figure 7.

Wavelength Dependence of the Excitation Balance between PSI and PSII.

(A) Wavelength dependence of the excitation balance of the two photosystems calculated as absorption by PSII divided by absorption of both PSI and PSII using an in vitro (connected lines) and in vivo (unconnected data points) approach. The left y axis corresponds to the in vitro approach (sunlight spectrum, dashed line; shade light spectrum, top solid line; blue light, bottom solid line) and the right y axis with the in vivo approach (sunlight spectrum, open circles; shade light spectrum, closed circles; blue light, squares). Note that the scale is different for the two y axes.

(B) Relationship between the excitation balances obtained via the in vitro and in vivo approach. The data in the top right corner, which are the data in plot (A), are presented in more detail in Supplemental Figure 5 online. Note that for values of PSII/(PSII+PSI) < 0.4, which correspond with wavelengths preferentially exciting PSI, both the in vitro and in vivo methods produce similar results. At values of PSII/(PSII+PSI) > 0.5, which correspond with wavelengths preferentially exciting PSII, the overexcitation of PSII appears to be stronger in vitro.

### The Impact of Photosystem Excitation Balances on the Quantum Yield for CO2 Fixation: Significance of Enhancement Effects

The photosystem efficiency balances in vivo (Figure 7A) were used to estimate a corresponding wavelength dependency of the quantum yield for CO2 fixation (i.e., αest; see Methods). In this calculation, quantum yield losses attributable to light absorption by photosynthetic carotenoids and nonphotosynthetic pigments are not taken into account. The values of the in vivo α calculated from gas exchange measurements (as in Figure 2B) were similar to the values of αest at wavelengths ≥580 nm (Figure 8), except at 700 nm and at 680 nm (shade light spectrum–grown leaves). However, while the photosystem efficiency balance apparently determined the wavelength dependency of α at wavelengths ≥580 nm, it did not at wavelengths ≤560nm where photosynthetic carotenoids and nonphotosynthetic pigments absorb. At these shorter wavelengths, αest overestimated α considerably (up to 50% in the range 420 to 460 nm). The absorptance spectrum of the albino leaves, which had a visually white appearance and were largely free of chlorophyll and carotenoids, is shown as a qualitative illustration of an absorptance spectrum by nonphotosynthetic leaf pigments (Figure 3). The albino leaves absorbed substantially at wavelengths <520 nm, whereas at longer wavelengths, absorptance was close to zero.

Figure 8.

Wavelength Dependence of Quantum Yield Losses due to Absorption by Carotenoids and Nonphotosynthetic Pigments.

Quantum yield for CO2 fixation for 18 different wavelengths (400 to 720 nm) calculated from gas-exchange measurements (i.e., measured values of α as in Figure 2B; solid lines) and from the in vivo efficiency balance between the two photosystems as shown in Figure 7A (αest; dotted lines). Note that light absorption by carotenoids and nonphotosynthetic pigments has not been taken into account in the calculation of αest. Graphs (A), (B), and (C) correspond to leaves grown under the sunlight spectrum, the shade light spectrum, and the blue irradiance, respectively. Error bars indicate the se (n = 3).

Figure 8.

Wavelength Dependence of Quantum Yield Losses due to Absorption by Carotenoids and Nonphotosynthetic Pigments.

Quantum yield for CO2 fixation for 18 different wavelengths (400 to 720 nm) calculated from gas-exchange measurements (i.e., measured values of α as in Figure 2B; solid lines) and from the in vivo efficiency balance between the two photosystems as shown in Figure 7A (αest; dotted lines). Note that light absorption by carotenoids and nonphotosynthetic pigments has not been taken into account in the calculation of αest. Graphs (A), (B), and (C) correspond to leaves grown under the sunlight spectrum, the shade light spectrum, and the blue irradiance, respectively. Error bars indicate the se (n = 3).

At the red wavelengths (620 to 640 nm) that produced the highest values of α (i.e., 0.093 for the sunlight spectrum and blue light, and 0.088 for the shade light spectrum–grown leaves; Figure 2B), PSII was also overexcited. This overexcitation was minor for the sunlight spectrum– and blue light–grown leaves (ΦPSII = 0.76 and 0.74, respectively) but more considerable for the shade light spectrum leaves (ΦPSII = 0.67; Figure 6A). A correction for the fraction of quantum yield loss due to these photosystem efficiency imbalances (see Methods) resulted in a calculated mean maximum quantum yield for CO2 fixation of 0.0955 ± 0.0004 for all three growth light treatments. This maximum quantum yield would apply in the case of perfectly balanced photosystem efficiency.

Additional evidence that the photosystem efficiency balance has a strong impact on α is provided by the gas-exchange measurements under broadband light. The quantum yield of both the shade light– and sunlight spectrum–grown leaves was determined for a broadband actinic light spectrum similar to the growth light spectrum over the spectral range 400 to 725nm. The quantum yields were also calculated as the weighted sum of the individual values determined for α at 19 different wavelengths (Figure 2) across the broadband actinic light spectra. For the shade light and sunlight spectrum, α was 21 and 10% higher than the weighted sum of α, respectively (Table 3). The larger enhancement effect found under the shade light spectrum is consistent with the stronger imbalances in photosystem efficiency found at all wavelengths <680 nm for the shade light–grown leaves (Figures 6A and 7).

#### Quantum Yield Enhancement Effect Produced by Combining Wavelengths

Table 3.

Quantum Yield Enhancement Effect Produced by Combining Wavelengths

Light Spectrum . α Measured . α Calculated . Enhancement .
Shade light spectrum 0.085 ± 0.001 0.070 ± 0.001 21%
Sunlight spectrum 0.084 ± 0.001 0.076 ± 0.001 10%
Light Spectrum . α Measured . α Calculated . Enhancement .
Shade light spectrum 0.085 ± 0.001 0.070 ± 0.001 21%
Sunlight spectrum 0.084 ± 0.001 0.076 ± 0.001 10%

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Table 3.

Quantum Yield Enhancement Effect Produced by Combining Wavelengths

Light Spectrum . α Measured . α Calculated . Enhancement .
Shade light spectrum 0.085 ± 0.001 0.070 ± 0.001 21%
Sunlight spectrum 0.084 ± 0.001 0.076 ± 0.001 10%
Light Spectrum . α Measured . α Calculated . Enhancement .
Shade light spectrum 0.085 ± 0.001 0.070 ± 0.001 21%
Sunlight spectrum 0.084 ± 0.001 0.076 ± 0.001 10%

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### Origin of the Wavelength Dependence of Quantum Yield

This study aims to clarify the underlying causes of the wavelength dependence of the quantum yield for CO2 fixation and its adaptation capacity to the light spectrum of the growth environment. Previously, the wavelength dependence of photosynthetic quantum yield has been shown qualitatively (McCree, 1972b; Inada, 1976) and, at less wavelengths, also quantitatively (Evans, 1987). We found an overall similar pattern of wavelength dependence of quantum yield on both an incident and absorbed light basis (Figure 2). In contrast with earlier work, our parallel measurements of quantum yields for PSI and PSII electron transport and photosystem stoichiometry allow further analysis of the causes of this wavelength dependence of quantum yield for CO2 fixation on an absorbed light basis (α).

Within the light-limited irradiance range, which was the case for our measurements (see Supplemental Figure 1 online), ΦPSI and ΦPSII are expected to be independent of irradiance in the absence of any alternative electron sinks for reducing power from PSII or back-reactions between electron acceptors and donors, even in case of an imbalanced photosystem excitation. However, even at wavelengths strongly overexciting PSII (e.g., 480 nm; Figure 6A), ΦPSII was relatively high at very low irradiances (i.e., ∼10 µmol−2 s−1) and decreased with increasing irradiance (Figure 4A1). This phenomenon suggests that an alternative electron acceptor, such as O2 (Pospísil, 2009) or possibly back-reactions (Quigg et al., 2006), are maintaining the QA pool in a relatively oxidized state at low irradiances, despite the insufficiency of electron transport through PSI. Notably, a reduced QA pool is also readily oxidized when actinic light is turned off. Though these alternative routes for oxidation of the QA pool increase ΦPSII at low irradiances, they do not increase CO2 fixation, so they do not appear to result in higher rates of linear electron transport. Whatever the underlying cause, these results show that the linkage between PSII electron transport and metabolism associated with CO2 fixation is flexible under low irradiance.

The low values found for qp and qL (Figures 4A and 5) indicate that even at light-limited irradiance, QA reduction may significantly affect redox signaling (Bräutigam et al., 2009), and PSII may be vulnerable to photodamage (Yamamoto et al., 2008). The independence of ΦPSII on Fv′/Fm′ (Figure 5) implies that no nonphotochemical quenching developed under these strictly light-limiting conditions. As ΦPSII is equivalent to the product of qp and Fv′/Fm′ (Genty et al., 1989), this lack of dependency implies that ΦPSII should be determined solely by changes in qp. The curvilinear relationship between qL and ΦPSII is expected because the lake model of PSII organization allows excitation that encounters a closed PSII trap (i.e., QA) in one photosynthetic unit to migrate to another where it can successfully produce charge separation and electron transport (Kramer et al., 2004 and references therein).

In the wavelength range 580 to 720 nm, the α value obtained by calculating efficiency losses due to imbalances in excitation of the two photosystems (i.e., αest) generally agrees well with α calculated from gas exchange (Figure 8), indicating that the photosystem excitation balance determines the wavelength dependence of α in this spectral range. From 400 to 460 nm and at 520 nm, the photosystem excitation is balanced for the leaves grown under the sunlight spectrum and blue light (or nearly so; Figure 6A), but αest is up to 50% higher than α (Figure 8). Energy losses at wavelengths <580 nm are to be expected due to the presence of carotenoids and nonphotosynthetic pigments in the leaf (Terashima et al., 2009). The energy transfer efficiency from carotenoids to chlorophylls in vivo has not yet been fully elucidated. However, for PSI carotenoids, a transfer efficiency of 70% has been reported for the core (de Weerd et al., 2003b) and for the light-harvesting complex (Wientjes et al., 2011). For PSII, β-carotene associated with the core has been shown to transfer energy with an efficiency of only 35% (de Weerd et al., 2003a). An energy transfer efficiency of 85 to 90% has been reported for lutein and neoxanthin in the antenna complexes of PSII (Croce et al., 2001; Caffarri et al., 2007), while violaxanthin in the loosely bound peripheral site of LHCII was shown not to transfer energy to chlorophylls (Caffarri et al., 2001). Considering that a significant fraction of the shorter wavelengths is absorbed by chlorophylls (Gitelson et al., 2002), that carotenoids still have an average energy transfer efficiency of ∼65%, and that for the blue wavelengths αest is up to 50% higher than α (Figure 8), a considerable proportion of the quantum yield losses at the shorter wavelengths must be attributable to nonphotosynthetic pigments. The absorptance spectrum of the albino cucumber leaves (Figure 3) was similar to that found for albino leaf zones of Arabidopsis thaliana in which a gene encoding a key enzyme in carotenoid synthesis was knocked out by virus-induced gene silencing (Zheng et al., 2010). These absorptance spectra qualitatively indicate that nonphotosynthetic pigments absorbed at wavelengths <520 nm, which is in agreement with the lower values of α than those of αest (Figure 8). However, the albino absorptance spectra are unsuitable for quantitative analysis as the nonphotosynthetic pigment composition may be different for the albino and the green cucumber leaves (Solfanelli et al., 2006). UV and blue light are reported to stimulate the transcription of flavonoid synthesis genes in order to protect plants against photodamage (Kubasek et al., 1992; Jackson and Jenkins, 1995). However, no notable difference between α of the sunlight spectrum– and the blue light–grown leaves was found (Figure 2B), suggesting that in these leaves the synthesis of flavonoids that absorb visible light was either insensitive to blue irradiance or it was saturated by the blue light content of the sunlight spectrum.

### Quantum Yield and Photosystem Stoichiometry Acclimation to Growth Spectrum

Despite the possible discrepancies between photosystem excitation balance in vitro, where only the relative absorbance of the photosystems is taken into account, and the photosystem efficiency balance in vivo, where inefficiencies in excitation energy transfer and charge separation, and cyclic electron transport, back-reactions, or transfer to O2 can play a role, the relationship between the two approaches is highly linear (Figure 7B). This indicates that the impact of these in vivo processes at the highest light-limited actinic irradiances used was small enough to allow the measures of ΦPSII and ΦPSI to be used to estimate a functional excitation balance. The moderate outliers in the relationship between the two approaches (460 and 500 nm; see Supplemental Figure 5 online) are likely due to the strong absorption of these wavelengths by carotenoids, which are associated more with PSII than PSI and which on average have a lower excitation energy transfer yield when associated with PSII than PSI (see section above).

In absolute terms, the overexcitation of PSII was found to be greater in vitro than in vivo (Figure 7). This may have several origins: (1) The in vitro approach using absorbance does not incorporate a correction for losses of excitation transfer efficiency and thus overestimates the relative excitation of PSII at wavelengths where carotenoids absorb. (2) In vivo overexcitation of PSII may have been slightly underestimated due to the bias of the 640-nm measuring light used to determine ΦPSII toward the adaxial leaf layers, whereas in vitro proteins from the whole leaf were measured. (3) State transitions did not play a role in vitro, whereas during the in vivo measurements state transitions partly rebalanced photosystem excitation. Any F0′ quenching accounted for by nonphotochemical quenching (Oxborough and Baker, 1997) can be ruled out in our measurements (Figure 5A). Therefore, the lower F0′ found for PSII light than for PSI light, which produced an F0′ equal to dark-adapted F0, and the broader wavelength range producing minimal ratios of F0′ and F0 for the shade spectrum leaves (Figure 6B), support the proposition that state transitions diminished the overexcitation of PSII in vivo. Our data also show that in the case of strong imbalances in photosystem excitation, state transitions are not capable of fully rebalancing excitation, as in vivo the PSII acceptor side is still reduced substantially over a broad range of wavelengths (Figures 6A and

## 3.5: Quantum Yield of Fluorescence

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The quantum yield ($$\varphi_F$$) is a ratio that expresses the number of species that fluoresce relative to the total number of species that were excited. Earlier we said that anything that reduces the number of excited state species that undergo fluorescence is said to quench the fluorescence. The expression for the quantum yield will depend on the rate constants for the different processes that can occur for excited state species. Referring back to our original drawing of the different processes that can occur, we can write the following expression for the quantum yield, where kF is the rate constant for fluorescence, kIC is the rate constant for internal conversion, kEC is the rate constant for external conversion, kISC is the rate constant for intersystem crossing and kC is the rate constant for any other competing processes and includes photodecomposition of the sample. Excited state species sometimes have sufficient energy to decompose through processes of dissociation or predissociation. In dissociation, the electron is excited to a high enough vibrational level that the bond ruptures. In predissociation, the molecule undergoes internal conversion from a higher electronic state to an upper vibrational level of a lower electronic state prior to bond rupture. When putting a sample into a fluorescence spectrophotometer, it is usually desirable to block the excitation beam until just before making the measurement to minimize photodecomposition.

$\mathrm{\varphi_F = \dfrac{k_F}{k_F + k_{IC} + k_{EC} +k_{ISC} + k_C}}$

Since this is a ratio, the limits of $$\varphi$$F are from 0 to 1. Species with quantum yields of 0.01 or higher (1 out of 100 excited species actually undergo fluorescence) are useful for analysis purposes.

Which method is more sensitive, absorption or fluorescence spectroscopy?

On first consideration it might seem reasonable to think that absorption spectroscopy is more sensitive than fluorescence spectroscopy. As stated above, for some compounds that we measure by fluorescence, only one of the 100 species that is excited undergoes fluorescence emission. In this case, 100 photons are absorbed but only one is emitted. The answer though requires a different consideration.

The measurement of absorption involves a comparison of $$P$$ to $$P_o$$. At low concentrations, these two values are large and similar in magnitude. Therefore, at low concentrations, absorption involves the measurement of a small difference between two large signals. Fluorescence, on the other hand, is measured at 90o to the source. In the absence of fluorescence, as in a blank solution, there ought to be no signal reaching the detector (however, there is still some scattered and stray light that may reach the detector as noise). At low concentrations, fluorescence involves the measurement of a small signal over no background. For comparison, suppose you tried to use your eyes to distinguish the difference between a 100 and 99 Watt light bulb and the difference between complete darkness and a 1 Watt light bulb. Your eyes would have a much better ability to determine the small 1 Watt signal over darkness than the difference between two large 100 and 99 Watt signals. The same occurs for the electronic measurements in a spectrophotometer. Therefore, because emission involves the measurement of a small signal over no background, any type of emission spectroscopy has an inherent sensitivity advantage of one to three orders of magnitude over measurements of absorption. Fluorescence spectroscopy is an especially sensitive analysis method for those compounds that have suitable quantum yields.

Sours: https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Molecular_and_Atomic_Spectroscopy_(Wenzel)/3%3A_Molecular_Luminescence/3.5._Quantum_Yield_of_Fluorescence_((varphi_ce_F))
Kinetics: Quantum Yield \u0026 Jablonski Diagrams

## Quantum yield

The quantum yield (Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system.[1]

### Fluorescence Spectroscopy

The fluorescence quantum yield is defined as the ratio of the number of photons emitted to the number of photons absorbed.[2]

Fluorescence quantum yield is measured on a scale from 0 to 1.0, but is often represented as a percentage. A quantum yield of 1.0 (100%) describes a process where each photon absorbed results in a photon emitted. Substances with the largest quantum yields, such as rhodamines, display the brightest emissions; however, compounds with quantum yields of 0.10 are still considered quite fluorescent.

Quantum yield is defined by the fraction of excited statefluorophores that decay through fluorescence:

where is the fluorescence quantum yield, is the rate constant for radiative relaxation (fluorescence), is the rate constant for all non-radiative relaxation processes. Non-radiative processes are excited state decay mechanisms other than photon emission, which include: Förster resonance energy transfer, internal conversion, external conversion, and intersystem crossing. Thus, the fluorescence quantum yield is affected if the rate of any non-radiative pathway changes. The quantum yield can be close to unity if the non-radiative decay rate is much smaller than the rate of radiative decay, that is .[2]

Fluorescence quantum yields are measured by comparison to a standard of known quantum yield.[2] The quinine salt quinine sulfate in a sulfuric acid solution was regarded as the most common fluorescence standard,[3] however, a recent study revealed that the fluorescence quantum yield of this solution is strongly affected by the temperature, and should no longer be used as the standard solution. The quinine in 0.1M perchloric acid (=0.60) shows no temperature dependence up to 45°C, therefore it can be considered as a reliable standard solution.[4]

Experimentally, relative fluorescence quantum yields can be determined by measuring fluorescence of a fluorophore of known quantum yield with the same experimental parameters (excitation wavelength, slit widths, photomultiplier voltage etc.) as the substance in question. The quantum yield is then calculated by:

where is the quantum yield, Int is the area under the emission peak (on a wavelength scale), A is absorbance (also called "optical density") at the excitation wavelength, and n is the refractive index of the solvent. The subscript R denotes the respective values of the reference substance.[5][6] The determination of fluorescence quantum yields in scattering media requires additional considerations and corrections.[7]

#### FRET Efficiency

Förster resonance energy transfer () is the quantum yield of the energy-transfer transition, i.e. the probability of the energy-transfer event occurring per donor excitation event:

where  is the rate of energy transfer,  the radiative decay rate (fluorescence) of the donor, and  are non-radiative relaxation rates (e.g., internal conversion, intersystem crossing, external conversion etc).[8][9]

#### Solvent and Environmental Effects

A fluorophore's environment can impact quantum yield, usually resulting from changes in the rates of non-radiative decay.[2] Many fluorophores used to label macromolecules are sensitive to solvent polarity. The class of 8-Anilinonaphthalene-1-sulfonic acid (ANS) probe molecules are essentially non-fluorescent when in aqueous solution, but become highly fluorescent in nonpolar solvents or when bound to proteins and membranes. The quantum yield of ANS is ~0.002 in aqueous buffer, but near 0.4 when bound to serum albumin.

### Photochemical Reactions

The quantum yield of a photochemical reaction describes the number of molecules undergoing a photochemical event per absorbed photon:[1]

In a chemical photodegradation process, when a molecule dissociates after absorbing a light quantum, the quantum yield is the number of destroyed molecules divided by the number of photons absorbed by the system. Since not all photons are absorbed productively, the typical quantum yield will be less than 1.

Quantum yields greater than 1 are possible for photo-induced or radiation-induced chain reactions, in which a single photon may trigger a long chain of transformations. One example is the reaction of hydrogen with chlorine, in which as many as 106 molecules of hydrogen chloride can be formed per quantum of blue light absorbed.[10]

In optical spectroscopy, the quantum yield is the probability that a given quantum state is formed from the system initially prepared in some other quantum state. For example, a singlet to triplet transition quantum yield is the fraction of molecules that, after being photoexcited into a singlet state, cross over to the triplet state.

### Photosynthesis

Quantum yield is used in modeling photosynthesis:[11]

### References

1. ^ abBraslavsky, S. E. (2007-01-01). "Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)". Pure and Applied Chemistry. 79 (3): 293–465. doi:10.1351/pac200779030293. ISSN 1365-3075.
2. ^ abcdLakowicz, Joseph R. Principles of Fluorescence Spectroscopy (Kluwer Academic / Plenum Publishers 1999) p.10. ISBN 978-0-387-31278-1
3. ^Brouwer, Albert M. (2011-08-31). "Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report)". Pure and Applied Chemistry. 83 (12): 2213–2228. doi:10.1351/PAC-REP-10-09-31. ISSN 1365-3075.
4. ^Nawara, Krzysztof; Waluk, Jacek (2019-04-16). "Goodbye to Quinine in Sulfuric Acid Solutions as a Fluorescence Quantum Yield Standard". Analytical Chemistry. 91 (8): 5389–5394. doi:10.1021/acs.analchem.9b00583. ISSN 0003-2700.
5. ^Albert M. Brouwer, Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report), Pure Appl. Chem., Vol. 83, No. 12, pp. 2213–2228, 2011. doi:10.1351/PAC-REP-10-09-31.
6. ^Levitus, Marcia (2020-04-22). "Tutorial: measurement of fluorescence spectra and determination of relative fluorescence quantum yields of transparent samples". Methods and Applications in Fluorescence. 8 (3): 033001. doi:10.1088/2050-6120/ab7e10. ISSN 2050-6120. PMID 32150732.
7. ^Lagorio, María Gabriela (2020-10-06). "Determination of Fluorescence Quantum Yields in Scattering Media". Methods and Applications in Fluorescence. 8 (4): 043001. doi:10.1088/2050-6120/aba69c. ISSN 2050-6120.
8. ^dos Remedios, Cristobal G.; Moens, Pierre D.J. (September 1995). "Fluorescence Resonance Energy Transfer Spectroscopy Is a Reliable "Ruler" for Measuring Structural Changes in Proteins". Journal of Structural Biology. 115 (2): 175–185. doi:10.1006/jsbi.1995.1042.
9. ^"Fluorescence Resonance Energy Transfer". Chemistry LibreTexts. 2013-10-02. Retrieved 2020-11-30.
10. ^Laidler K.J., Chemical Kinetics (3rd ed., Harper & Row 1987) p.289 ISBN 0-06-043862-2
11. ^Skillman JB (2008). "Quantum yield variation across the three pathways of photosynthesis: not yet out of the dark". J. Exp. Bot.59 (7): 1647–61. doi:10.1093/jxb/ern029. PMID 18359752.
Sours: https://en.wikipedia.org/wiki/Quantum_yield

## What is Quantum Yield?

The IUPAC definition of quantum yield (Φ) is the number of a certain event occurring per photon absorbed by the system,1

However, it is most commonly written specifically for the emission of light (photoluminescence) by a system,2-5

This narrower definition is often simply called quantum yield; with the emission of light being implicit given the context. However, the terms fluorescence, luminescence and photoluminescence quantum yield are also commonly used. The quantum yield is reported as either a decimal fraction between 0 and 1 or as a percentage. For example, if the system absorbs 100 photons and emits 30, then its quantum yield would be is 0.3 or 30%.

The quantum yield of a system (such as a fluorescent molecule) is determined by the balance between the radiative and non-radiative transition rates within it (Figure 1). The quantum yield can therefore be rewritten in terms of these rates,

The radiative transition rate ($k_r$) denotes radiative (light emitting) processes such as fluorescence and phosphorescence whereas the sum of non-radiative rates ($k{_{nr}}$), includes processes such as internal conversion, intersystem crossing, and energy transfer.6 The quantum yield is therefore the probability that a system in the excited state deactivates through a radiative process to its ground state.

### History of Quantum Yield

The roots of quantum yield can be traced back to the beginning of the 20th century when Einstein’s revolutionary work on the photoelectric effect was published in 1905 (a copy of his paper translated in English can be found in Ref. 7). Einstein introduced the quantisation of light, i.e., a light beam consists of discrete quantum particles (quanta) carrying energy equal to $E&space;=&space;h\nu&space;$, where $h$ is Planck’s constant and $\nu&space;$ the light frequency. A few years later, E. G. Warburg published a series of papers over the period 1912-1921 in which he studied the conversion of ozone molecules into oxygen to acquire the ratio of the molecules produced to quanta absorbed. He later named this procedure “quantum efficiency” and used the Greek letter phi (Φ) to denote it.8 His papers (in German) can be found on the German National Library website.9 In 1924, Vavilov referred to the term “fluorescence yield”, based on Warburg’s earlier work, to calculate the fraction of absorbed rays of light to fluorescent rays of light,10 whereas the term “molecules per quantum light absorbed” appears in a paper published in 1925 by Marshall to describe the photochemical reaction between hydrogen and chlorine.11 By 1930 the term “quantum yield” as we know it today had been widely cited in a large number of textbooks and papers.

### How to Measure Quantum Yield?

Quantum yield is one of the most important photophysical parameters when characterising luminescent molecules and materials. High quantum yields are crucial for a wide range of applications including; displays, lasers, bioimaging and solar cells, and accurate measurement of the quantum yield is therefore important.  Quantum yield measurements can be split into non-optical and optical methods. Non-optical methods include the indirect measurement of the conversion of the excitation energy into heat and its dissipation to the solvent,6, 12 and calorimetric methods, such as photoacoustic spectroscopy (PAS),13 and thermal lensing.14 These methods require specialised setups and are generally reserved for the determination of the quantum yield of important standards. Quantum yields are therefore most commonly measured optically, using either the relative or absolute method.

Relative Quantum Yield Method

In the relative method, the quantum yield of the sample interest is calculated by comparing its photoluminescence emission to that of a reference standard of known quantum yield. In conventional fluorescence spectrometers only a certain fraction of the emitted light is collected and detected; with the size of the fraction depending on numerous factors. These factors include; the angular distribution (solid angle) of the emitted photons, the refractive index of the solvent, wavelength, the scattering properties of the sample and sample geometry.6, 12 The fraction is, therefore, impossible to accurately quantify which prevents direct measurement of the quantum yield. The relative method overcomes this problem by using a reference standard of known quantum yield and similar optical properties to those of the sample. The emission spectra of the sample and reference standard are measured under identical excitation conditions and the ratio of the integrated emission used to calculate the quantum yield of the sample.

Figure 2 FS5 Spectrofluorometer equipped with the SC-05 Standard Cuvette Holder.

The advantage of the relative method is that it can be readily applied using standard commercial absorption and fluorescence spectrometers equipped with a simple cuvette holder (Figure 2). The downside is that a reference standard must exist that emits in a similar wavelength region to the sample, and the sample type is generally limited to transparent liquids.

Absolute Quantum Yield Method

In the absolute method, an integrating sphere is used to capture all light emitted by the sample, avoiding the need for a reference standard. The quantum yield is determined by comparing the number of emitted photons with the number of absorbed photons. The advantage of the absolute method is that no reference standard is required which results in a faster measurement of the quantum yield (since fewer measurements are required) and a broader range of emission wavelengths are accessible that are no longer limited to where reference standards exist. Secondly, the absolute method can also be applied to a much larger range of sample types and is the only reliable method for samples such as scattering solids. The downside is that an integrating sphere is required for the measurement, however, these have become increasingly common and are now available as accessories for benchtop fluorescence spectrometers (Figure 3).

Figure 3 FS5 Spectrofluorometer equipped with the SC-30 Integrating Sphere.

Technical notes on how to measure the absolute quantum yield of liquid and powder samples using the FLS1000’s integrating sphere, and application notes on measuring the temperature-dependent absolute quantum yield of halide perovskites and plant leaves can be found on our website.

### References

1. Compendium of Chemical Terminology, 2nd ed. (the “Gold Book”), Compiled by A. D. McNaught and A. Wilkinson, Accessed August 2021
2. K. -L. Wong, J. -C. G. Bünzli, P. A. Tanner, Quantum yield and brightness, J. Lumin., 2020, 224, 117256
3. D. M. Jameson, Introduction to Fluorescence. 1st ed. CRC Press; 2014
4. Lakowicz JR. Principles of Fluorescence Spectroscopy. 3rd ed. Springer New York; 2006.
5. B. Valeur, M. N. Berberan-Santos. Molecular Fluorescence: Principles and Applications. 2nd ed. Wiley-VCH Verlag GmbH & Co. KGaA; 2012.
6. M. Levitus, Tutorial: Measurement of fluorescence spectra and determination of relative fluorescence quantum yields of transparent samples, Methods Appl. Fluoresc., 2020, 8 033001
7. A. Einstein, On a heuristic point of view concerning the production and transformation of light. Ann. Phys. 1905, 17,English Translation
8. M. B. Rubin, S. E. Braslavsky. Quantum yield: The term and the symbol. A historical search. Photochem. Photobiol. Sci., 2010, 9, 670-674
9. E. Warburg papers, DNB, Katalog der Deutschen Nationalbibliothek.
10. S. J. Wawilow, Die Fluoreszenzausbeute von Farbstofflösungen, Zeitschrift für Phys, 1924, 22, 266-272
11. A. L. Marshall, Mechanism of the Photochemical Reaction between Hydrogen and Chlorine. III, J Phys Chem., 1926, 30, 757-762.
12. C. Würth, M. Grabolle, J. Pauli, M. Spieles, U. Resch-Genger, Relative and absolute determination of fluorescence quantum yields of transparent samples. Nat Protoc. 2013, 8,1535-1550
13. M. G. Rockley, K. M. Waugh, The photoacoustic determination of fluorescence yields of dye solutions, Chem Phys Lett., 1978, 54, 597-599
14. M. Fischer, J. Georges, Fluorescence quantum yield of rhodamine 6G in ethanol as a function of concentration using thermal lens spectrometry, Chem Phys Lett. 1996, 260, 115-118

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Quantum Yield Concept

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