Improved Method of Fluorescence Quantum Yield Determination

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An improved method of fluorescence quantum yield determination. Krzysztof Nawara, and Jacek Waluk Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b02013 • Publication Date (Web): 31 Jul 2017 Downloaded from http://pubs.acs.org on July 31, 2017

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Analytical Chemistry

An improved method of fluorescence quantum yield determination. Krzysztof Nawara1*, Jacek Waluk1,2 1

Faculty of Mathematics and Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01815 Warsaw, Poland 2 Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warsaw, Poland

*

Correspondence to: [email protected]

Abstract In the most widely used procedure for luminescence quantum yield determination, absorption and emission spectra are measured on two different instruments. This leads to errors caused by wavelength misalignment and different monochromator characteristics of the spectrophotometer and the spectrofluorometer. These errors can be avoided using a method for fluorescence quantum yield determination that relies on simultaneous absorption and fluorescence emission (SAFE) measurement using a single commercial spectrofluorometer. The method’s performance is compared with the standard routinely used procedure for the relative quantum yield determination. The advantages of SAFE measurement are discussed. The proposed novel approach eliminates a number of potential errors in quantum yield determination protocol and provides higher accuracy.

Introduction Fluorescence quantum yield is the primary parameter characterizing emissive properties of a chromophore in its environment. It is defined as the ratio of the number of photons emitted per the total number of photons absorbed by the sample.1,2 In recent years, the number of reported fluorescence quantum yield values increased remarkably. Several reviews of methods currently used for quantum yield determination have been published3–6. Unfortunately, quite often quantum yields are still inaccurately measured and reported.7 This creates an urgent need to develop procedures, methods, and standards facilitating proper quantum yield determination.6,7 Here our goal is to present a useful improvement of the most widely used procedure of quantum yield determination, which is the relative method. In this approach, the emission of an unknown sample is compared with the emission of a well-known standard (a reference sample with the reported quantum yield). The exact formula for quantum yield determination is given by: మ ௙೔೙೟೐೒ೝೌ೗షೣ ௡ೣ మ ஺ ௡ ೑ೌ೎೟೚ೝషೣ ೔೙೟೐೒ೝೌ೗షೃ ೃ

஺

ܻܳ௫ = ܻܳோ ௙ ೑ೌ೎೟೚ೝషೃ

( 1)

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Where QYR is the reference quantum yield value, Afactor denotes the absorption factor, fintegral is the integrated emission intensity, n is the refractive index of the medium, and the subscripts R and x refer to the reference and the measured sample, respectively. This method requires determination of emission integrals for both unknown and reference samples, as well as the corresponding absorption factors. The latter are defined as: Afactor= 1- T-λ1 or Afactor= 1-10-A

(2)

Where T is the sample transmittance and A is the absorbance. A more precise determination of absorption factors is achieved if the spectral profile of excitation is taken into account, as expressed by: భ మ భ ఒబ ିమ∆ఒ

‫ܣ‬௙௔௖௧௢௥ = ‫׬‬

ఒబ ା ∆ఒ

1 − 10ି஺ഊ ݀ߣ

(3)

Where λ0 denotes the center of the excitation band, ∆λ is the excitation bandpass, and Aλ is the absorbance measured at λ. The relative method requires the measurements of both fluorescence emission and absorption spectra. These are recorded on two different instruments: spectrofluorometer and spectrophotometer, respectively. Therefore, any misalignment between these two instruments could remarkably affect the determined value of the quantum yield. For this reason, special care must be taken to control the performance of monochromators in both instruments. For the spectrophotometer, a holmium oxide filter and for the spectrofluorometer a calibrated mercury argon lamp can be used for quality control and monochromator tuning. Nevertheless, even for such properly calibrated instruments the precision of measurements is limited by the monochromator wavelength accuracy and repeatability. A spectrophotometer, in this respect, performs much better than a spectrofluorometer. The wavelength repeatability of all major spectrofluorometers present on the market is around 0.5 nm. The value of the excitation monochromator is of primary concern for the spectrofluorometer, as the quantum yield is determined based on the absorption factor and the emission integral obtained for exactly the same wavelength. But even for an ideal case of perfectly matching wavelengths, the absorption factors determined on the two instruments need not be the same, because of different monochromator characteristics. Thus, quantum yield determination based on using the absorbance values measured with a spectrophotometer always contains an inherent error. In order to eliminate this source of errors, we describe a method of simultaneous absorbance and fluorescence measurement (SAFE) for quantum yield determination using a single commercial spectrofluorometer. This is a useful upgrade of the relative method, which solves the issue of misalignment between the spectrophotometer and the spectrofluorometer. Moreover, if the sample and reference are measured using the same excitation wavelength, it also eliminates the necessity of calculating integrals of absorption factors over the bandwidth, as both fluorescence and absorbance are measured under exactly the same experimental conditions. Overall, our approach allows for determination of fluorescence quantum yield with higher accuracy as compared to the standard relative method. 2 ACS Paragon Plus Environment

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We compare the SAFE approach with the standard relative method for fluorescence quantum yield determination1,2,6. Both procedures are evaluated in terms of accuracy. The accuracy is checked with respect to three well-established quantum yield standards7: quinine sulfate in 0.05M sulfuric acid solution, fluorescein in 0.1M sodium hydroxide solution, and rhodamine 6G water solution. We also compare quantum yields determined using both methods for anthracene in ethanol, a challenging case where remarkable changes in absorbance values are observed for slight variations of excitation wavelength.

Materials and methods Fluorescent dyes were of the highest available purity: quinine sulfate, fluorescein, rhodamine 6G, anthracene. Sulfuric acid, and sodium hydroxide were of analytical grade, ethanol (spectral grade). All the chemicals were from Sigma-Aldrich (Poland), Exciton (US), POCH (Poland) and Merck (Poland). Water of “type 1” (18.2 MΩ·cm) from MiliQ filtration system was used to prepare solutions. All the dye solutions were prepared freshly before the measurement. The values of fluorescence quantum yields of well-established standard solutions were taken from the IUPAC technical report7 and are equal to 0.52 for quinine sulfate in 0.05M sulfuric acid solution in water,8,9 0.95 for fluorescein in 0.1M NaOH water solution,10 and 0.92 for rhodamine 6G in water.11 Absorption spectra were recorded on a Shimadzu UV 2700 double beam spectrophotometer with monochromator wavelength accuracy of 0.3 nm and repeatability of 0.05nm (values declared by the producer). All spectra were collected with 1nm bandpass in a slow scanning mode using 10x10 mm pathlength Spectrosil quartz cuvettes (Starna). In order to minimize inner filter effects the absorbance of the samples did not exceed 0.04. Prior to measurements, quartz cuvettes were washed with piranha solution (mixture of 30% H2O2 and concentrated sulfuric acid), washed several times with distilled water, spectral grade methanol, and dried. The instrumental baseline was registered each time prior to the measurement with the cuvette filled with pure solvent. Fluorescence was recorded on an FS5 spectrofluorometer (Edinburgh Instruments), equipped with three standard detectors: (i) a single-photon counting detector for steady-state emission measurements; (ii) a reference detector (silicon photodiode) for light intensity correction, and (iii) a transmission detector (silicon photodiode) for absorbance measurements. The declared monochromator wavelength accuracy and repeatability are 0.5 and 0.3 nm, respectively, and the dispersion is 3.5nm/mm. For the accurate absorbance and transmittance measurements it is of primary importance to achieve a stable response signal from all the detectors. This task could be achieved by running a blank (without sample) kinetic scan for any arbitrary wavelength, monitoring signals from all the detectors. As there is no sample present, the (fluorescence) emission signal should stabilize at a very low constant value of dark current, the reference (lamp intensity) signal should reach a constant value when the lamp is properly warmed up (it takes usually 0.5 h from turning on the xenon lamp), and the transmittance 3 ACS Paragon Plus Environment


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detector must also reach a constant value. From our observation the proper warm-up period for the transmittance detector is the longest one and takes from 1.5 to 2 hours. Once the signal of the transmittance detector is parallel to the reference signal over time the spectrofluorometer is ready for simultaneous absorbance and fluorescence measurements. It is important to remember for the transmittance detector that its warming up period cannot be achieved with the closed shutters. The transmittance detector must be exposed to the photon flux prior to measurements. All steady-state fluorescence spectra were registered with both excitation and emission spectral bandpass equal to 1 nm and without polarizers, as the emission of the studied samples is isotropic. The emission spectra were dark current subtracted, and corrected for the emission (wavelength-dependent detector sensitivity) and excitation light intensity signals (including the measured reference signal and the silicon photodiode response curve). The emission correction curve was periodically checked using the set of secondary emission standards.12 The wavelength accuracy of the monochromators was checked with a mercury argon calibration lamp (Ocean Optics). Determination of the absorption factor from spectrofluorometer measurements For the determination of the sample absorbance the signals of both reference and transmittance detectors were used. All the signals were averaged over the time of each emission measurement. The blank samples (cuvettes with pure solvent) data were used to determine the beam splitting coefficient, an important instrumental factor that has to be determined in order to measure the sample absorbance. It is defined as the ratio of signals reaching the transmission detector vs the reference detector for the blank sample. It is further used to calculate the intensity of incident light for the determination of transmittance. The beam splitting coefficient (BS) was determined by dividing the averaged transmission detector signal (Transav-blank-λ1) by the averaged reference detector signal (Refav-blank-λ1). BS=(Transav-blank-λ1)/ (Refav-blank-λ1)

(4)

The calculated beam splitting coefficient for a given wavelength (λ1) was then multiplied by the reference detector signal of a dye sample solution (Refav-sample-λ1), registered at the same wavelength. This operation gives the incident light intensity (Izero-λ1) for the absorbance measurement. Izero-λ1= BS × (Refav-sample-λ1)

(5)

By dividing the averaged transmission detector signal of the dye sample (Transav-sample-λ1) by the incident light intensity of the sample, the value of transmittance is obtained (T-λ1). All calculations must be done for the same wavelength (λ1). T-λ1= (Transav-sample-λ1)/ (Izero-λ1)

(6)

The absorbance (A) is then calculated: A=log(1/ T-λ1)

(7)


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For the quantum yield calculations there is no need to convert transmittance (T-λ1) into absorbance (A), as we are interested in the absorption factor (Afactor) determined from equation 2.

Fluorescence quantum yield determination for the samples with a common absorption wavelength range The spectrophotometer absorbance measurement for anthracene in ethanol solution and quinine sulfate in 0.05M sulfuric acid water solution were measured as described above in the absorbance measurement section. All spectra were measured three times and did not show any variation with respect to signal intensity or wavelength shift. From these spectra four wavelength values corresponding to equal absorbances were selected for quantum yield determination studies. These were 337.9, 340.5, 351.9, and 360 nm. The spectrofluorometer was used to measure simultaneously absorbance and fluorescence emission. The spectra were collected for the excitation wavelengths equal to 337.9, 340.5, 351.9, and 360 nm (as determined previously) and each emission spectrum was collected from 365 to 700nm with 0.5nm step and 0.5 s dwell time. The signals from the reference and transmittance detectors were collected during the emission scan. The total acquisition time for each spectrum was 335 s, thus the reference and transmittance signals were averaged over this time period. Both quinine sulfate and anthracene solutions were measured for exactly the same excitation wavelength: once the excitation monochromator was set to 337.9 nm, the anthracene and quinine solutions were measured. Next, the monochromator was set to 340.5nm, where again both solutions were measured, and the same procedure was applied for all other wavelengths. After collecting all the spectra, the entire procedure was repeated two times, so that the set of three independent values could be compared. After the measurements the dye solutions were discarded, the cuvettes washed several times with pure solvent and filled with pure solvent for the blank sample measurement. Exactly the same cuvettes were used for the blank as for the dye sample measurement. In the case of anthracene and quinine sulfate solutions, the blank samples did not show any emission, so there was no need to correct the emission spectra. The blank samples were measured in an excitation monochromator scanning mode. The blank spectra of pure ethanol and 0.05M sulfuric acid water solution were recorded from 335 to 362nm with 0.5 nm step and dwell time of 1 s, repeated 20 times (reference and transmittance detector signals were collected). For the SAFE method the absorption factor was calculated as described in the previous section, while for the standard comparative method the absorbance data measured by means of spectrophotometer the absorption factor was calculated from equation 2 and the quantum yield for a given compound (QYx) was obtained using equation 1. The standard deviation of the measurement was calculated from multiple measurements. All the spectral calculations and the error analysis were done using OriginPro2017 software (OriginLab).



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Fluorescence quantum yield determination for the samples with different absorption wavelength ranges The fluorescence emission maps (with simultaneous reference and transmission signals) were recorded for each sample solution and blank (pure solvent) sample. For quinine sulfate solution in 0.05M sulfuric acid the emission spectra were recorded from 380 to 650 nm with 0.5 nm step and 0.5 s dwell time for the following excitation wavelengths: 285, 295, 305, 315, 325, 335, 345, and 355 nm. For fluorescein in 0.1M NaOH solution the emission spectra were recorded from 480 to 670nm with 0.5 nm step and 0.5 s dwell time for the following excitation wavelengths: 455, 465, and 475 nm. For rhodamine 6G in water solution the emission spectra were recorded from 510 to 750 nm with 0.5nm step and 0.5 s dwell time for the following excitation wavelengths: 465, 475, 485, 495, and 505 nm. The same set of spectra was collected for pure solvents measured in exactly the same cuvettes. The absorption factor was calculated for each spectrum as described in the previous section. For the comparison with the standard comparative method the absorption factor was calculated from the absorbance spectra obtained using the spectrophotometer. For each excitation wavelength, the integrated surface area of the emission spectrum was calculated. For each sample the plot of its absorption factor with respect to the fluorescence integral was plotted and the data were fitted with the straight line, the value of Afactor /fintegral ratio. Both the slope value and the standard deviation were calculated from the best fit curve. The Afactor /fintegral ratio was calculated for each sample and further used for quantum yield determination. Each of the three fluorescence standard solutions has been used to determine the fluorescence quantum yield of the other two standards, in order to evaluate the consistency of all data and the accuracy. An example of fluorescence quantum yield determination for the samples with different absorption wavelength ranges is shown in the supporting information.

Results and discussion The accuracy of both methods has been evaluated with respect to the three well-established quantum yield standards.7 We have determined: (i) the value of quinine sulfate quantum yield based on both fluorescein and rhodamine 6G solutions; (ii) the value of fluorescein quantum yield based on both quinine sulfate and rhodamine 6G solutions, and (iii) the value of rhodamine 6G quantum yield based on both fluorescein and quinine sulfate solutions. In an ideal case all of the determined values would point to the exactly the same quantum yield, which should be equal to the reference value known from the literature3,7. The comparison of all of these standards is not an easy task, as they show absorption and emission in different spectral regions [Figure 1]. There is no single wavelength which could be found to excite all of these chromophores for comparison. The most remarkable spectral difference is exhibited by quinine sulfate, as it absorbs in the UV region. The absorption spectra of fluorescein and rhodamine 6G do overlap; however, both emit with small Stokes shifts. For this reason the 6 ACS Paragon Plus Environment

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excitation wavelength has to be blue shifted from the absorption maximum. The suitable value of excitation wavelength for fluorescein quantum yield determination falls in the region where the absorption value of rhodamine 6G is difficult to be determined, as it is very close to zero. These reasons led us to compare all the standards using multipoint analysis. In this approach, each of the chromophores is excited in the region of its absorption at several different wavelengths. For each excitation wavelengths both the sample absorption value and the emission spectrum is collected. We have chosen to change the excitation wavelength by 10 nm (as described in the materials and methods section). For each studied compound the set of absorption factors and emission integrals was calculated. All the data were fitted to the straight line, as the fluorescence intensity is proportional to the number of absorbed photons for diluted solutions13. The slope of the fitted curve is the ratio of the absorption factor to the emission integral. The lower the slope value, the higher is the value of fluorescent quantum yield. The obtained values were substituted into the equation for quantum yield determination. While for the SAFE method the value of absorption factor was determined in a single experiment, for the standard method the value of absorption factor was calculated from the absorbance spectrum registered on the spectrophotometer. The list of the obtained fluorescence quantum yield values and their absolute uncertainties is presented in Table 1. For ease of comparison we have presented these data in a set of three plots showing distribution of probability functions for different experiments around the literature reference value [Figure 2]. Each of the three plots shows the fluorescence quantum yield values determined for each compound. In general, both methods provide reliable results for all three standards, where the literature reference value lies in a 3 times uncertainty region (which accounts for the 99.7% probability) from the mean. The difference between the methods starts to appear if we narrow the region around the mean. In the region mean ± absolute uncertainty, all the data obtained using the SAFE approach match the literature reference values, whereas this is true for only two results that were obtained from the standard comparative method (the fluorescein quantum yield measured based on the quinine sulfate standard and quinine sulfate quantum yield based on the fluorescein standard). The differences in the mean fluorescence quantum yield value determined by the two different standards do not exceed 1%, while for the standard comparative method they range from around 2.5% (for quinine sulfate and rhodamine 6G) up to 3,5% (for fluorescein). This shows that the accuracy of the SAFE method is higher compared to the standard comparative method. The accuracy of both methods has been further evaluated using another data set. We compared the fluorescence quantum yield of anthracene in ethanol with respect to quinine sulfate in 0.05M sulfuric acid solution. Both anthracene and quinine sulfate absorb light in the same spectral region, which allows quantum yield determination for the same excitation wavelength [Figure 3]. Anthracene is a very challenging compound for quantum yield determination as its absorption spectrum consists of several peaks and minima with very steep slopes in-between. For this reason any mismatch of the excitation wavelength between absorption and emission measurement would result in a large difference in the value of quantum yield. The literature quantum yield value of anthracene in ethanol is 0.27 8,14 for 7 ACS Paragon Plus Environment


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degassed solution. The quantum yield of anthracene in ethanol is heavily dependent on the presence of oxygen and temperature. Our goal was the comparison of the two methods, thus we worked with undegassed anthracene solutions, which are easier to prepare. For this reason the values of obtained quantum yields of anthracene were affected by oxygen quenching. We performed the measurements for four different excitation wavelength (337.9, 340.5, 351.9, and 360 nm), where the absorbances of both compounds were equal [Figure 3]. It should also be mentioned that quinine sulfate cannot be used as a reference compound for the excitation red-shifted from 360 nm, as its emission spectrum is shifted under these conditions.15 Therefore our measurements were limited to four crossing points. In the comparative method it is recommended to choose the points of equal absorbance in the region where absorbances cross smoothly. Our case is opposite to this rule, as the spectra are very steep at the crossing points. This is an additional challenge which makes anthracene a good sample for the comparison of both methods. The determined quantum yields with absolute uncertainties are summarized for anthracene in [Figure 4]. The plot on the left shows the quantum yield values determined using the SAFE method. It shows very similar quantum yields values for all excitation wavelengths. The values obtained for the standard relative method show quantum yield variation with respect to the excitation wavelength (the plot on the right). The difference in the determined values is obvious, and for each excitation wavelength a different value of quantum yield is obtained. Even though both methods show similar average results, the advantage of SAFE method is evident. It provides higher accuracy as compared to the standard relative method.

Summary In this work we propose a new approach for the relative quantum yield determination that relies on simultaneous absorbance and fluorescence emission (SAFE) measurements using a single commercial instrument. This approach solves an issue of wavelength misalignment between the spectrophotometer and spectrofluorometer monochromators. The SAFE method eliminates also the necessity of calculating the integrals of absorption factors with respect to the measured bandwidth, as both fluorescence and absorbance are measured under exactly the same experimental conditions. The simultaneous measurement might produce absorption spectrum that is of lower quality than that registered by the spectrophotometer, but for the quantum yield determination it is of primary importance that both absorbance and emission spectrum are collected at the same time and geometry with exactly the same position of the cuvette in the sample holder. Even though the absorbance spectrometers produce spectra of much higher quality with higher signal to noise ratios and wavelength accuracy, it is recommended to use simultaneous absorbance and fluorescence measurement for quantum yield determination. This approach may also eliminate trivial sources of error that result from improper sample handling between absorbance and fluorescence measurement, such as solvent evaporation, sample dissolution, or temperature variations. Overall, the SAFE approach allows for determination of fluorescence quantum yield with higher accuracy as 8 ACS Paragon Plus Environment

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compared to the standard relative method. It is a safe method, as it limits a number of potential errors in the quantum yield determination protocol. Acknowledgements The work was supported by the grant DEC-2013/10/M/ST4/00069 from the Polish National Science Centre.



Table 1

Quantum yield value and absolute uncertainty determined for: Quinine sulfate

SAFE method

Quinine sulfate as reference

Standard comparative method

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Fluorescein

Rhodamine 6G

-

0,958±0,020

0,919±0,028

Fluorescein as reference

0,516±0,011

-

0,911±0,015

Rhodamine 6G as reference

0,521±0,017

0,959±0,016

-

-

0,963±0,019

0,890±0,025

Fluorescein as reference

0,512±0,010

-

0,877±0,017

Rhodamine 6G as reference

0,538±0,015

0,996±0,019

-

0.52

0.95

0.92

(relative method and direct integrating sphere method)

(thermal blooming)

(thermal blooming)

Quinine sulfate as reference

Literature reference value7


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Figure 1

0,040 1,0

0,8

0,030 0,025

0,6 0,020 0,4

0,015 0,010

0,2

normalized fluorescence

0,035

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0,005 0,000

0,0 300 350 400 450 500 550 600

wavelength

400 450 500 550 600 650 700 750

wavelength /nm



Figure 2

probability density function

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1,0 0,8 0,6 0,4 0,2 0,0 1,0 0,8 0,6 0,4 0,2 0,0 1,0 0,8 0,6 0,4 0,2 0,0

48

49

90

91

84

85

50

92

86

93

87

51

94

88

52

95

96

89

90

53

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54

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91

55

56

57

58

99 100 101 102 103 104 105

92

93

94

95

96

97

98

quantum yield %


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Figure 3

0,045 1,0

0,035

0,8

0,030 0,6

0,025 0,020

0,4 0,015 0,010

0,2

normalized fluorescence

0,040

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0,005 0,000

0,0 280 300 320 340 360 380 400 420

wavelength /nm

400 450 500 550 600 650 700

wavelength /nm

Figure 4 13 ACS Paragon Plus Environment

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Quantum yield %


11,2

11,2

11,0

11,0

10,8

10,8

10,6

10,6

10,4

10,4

10,2

10,2

10,0

10,0

9,8

9,8

9,6

9,6 337,9

340,5

351,9

360

337,9

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340,5

351,9

360


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Captions:

Figure 1: The absorbance and normalized emission spectra of quinine sulfate in 0.05M sulfuric acid (red), fluorescein in 0.1M sodium hydroxide water solution (blue) and rhodamine 6G in water solution (green).

Figure 2: The probability density function for the quantum yields determined for quinine sulfate in 0.05M sulfuric acid solution (upper plot), fluorescein in 0.1M sodium hydroxide water solution (middle) and rhodamine 6G water solution (bottom). The colors indicate the reference compound which was used for quantum yield determination: red for quinine sulfate, blue for fluorescein, and green for rhodamine 6G. The solid line represents the data obtained using SAFE method, while the dashed lines represents the data obtained by the standard comparative method. The black vertical lines indicate the literature reference values of quantum yields.

Figure 3: The absorbance and normalized emission spectra of quinine sulfate in 0.05M sulfuric acid (red) and anthracene in ethanol solution (black). The arrows indicate four points of equal absorbance that were used for quantum yield determination.

Figure 4: The values of fluorescence quantum yield determined for anthracene in ethanol solutions and standard deviations for each excitation wavelength. The figure on the left presents the results obtained by SAFE method. The plot on the right shows the data obtained using the standard comparative method.



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(2)

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(3)

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(4)

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(5)

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(6)

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(7)

Brouwer, A. M. Pure Appl. Chem. 2011, 83, 2213–2228.

(8)

Suzuki, K.; Kobayashi, A.; Kaneko, S.; Takehira, K.; Yoshihara, T.; Ishida, H.; Shiina, Y.; Oishi, S.; Tobita, S. Phys. Chem. Chem. Phys. 2009, 11, 9850–9860.

(9)

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(10)

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Improved Method of Fluorescence Quantum Yield Determination

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