How Does Light Scattering Affect Luminescence? Fluorescence


Nov 1, 2002 - Fluorescence quantum yields and luminescence spectra for solid samples are presented and interpreted. Re-absorption of the emitted light...
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How Does Light Scattering Affect Luminescence? Fluorescence Spectra and Quantum Yields in the Solid Phase M. Gabriela Lagorio* and Enrique San Román INQUIMAE, Departamento de Química Inorgánica, Analítica y Química Física, Universidad de Buenos Aires, Buenos Aires, Argentina; *[email protected]

Many articles connected with the topic of molecular fluorescence in solution have been published in the educational literature. Helpful papers for teaching purposes may be found in this Journal (1–6). However, no information about spectral analysis and quantum yield determinations in the presence of light scattering is found. This situation usually appears when dealing with most solid materials. Despite the increasing importance that the luminescence of solids has in our daily life (in textiles, printings, paints, etc.), it usually remains unclear how to elucidate fluorescence data from such systems. As a general rule, students are far more familiar with solution physical chemistry than with solid-state physical chemistry. Concerning photochemistry, this probably results from the complexity that arises when light scattering is introduced. This article attempts to fill this vacancy by explaining how to work with such systems and showing quantitative corrections to account for light re-absorption and re-emission processes. For didactical reasons we present the approach for scattering media compared to the well-known treatment for non-scattering materials. This presentation is suitable for a graduate-level course in fluorescence as well as for a spectroscopy course for undergraduate students in the last year of their university study. Experimental details for obtaining true emission and excitation spectra are presented. Frequent artifacts and misinterpretations are also discussed. The analysis follows closely a treatment developed in our laboratory (7). Transparent Samples (Liquid or Solid)

Light Absorption and Emission Assuming one absorbing species, the rate of emission of fluorescence (Je) is equal to the rate of light absorption by the fluorophore (Ia) multiplied by the fluorescence quantum yield (f) (8, 9): J e = I a φf

(1)

If we consider a parallel beam of light of intensity I0 directed on a sample, we can write eq 2 for the energy balance, I 0 = IR + I a + I T

(2)

where IR is the amount of exciting light (I0) reflected and scattered by the sample, and IT and Ia are the amounts of light transmitted and absorbed respectively. For a transparent medium (nonscattering liquid or solid) IR equals zero and IT = I 0 10 − A (λ 0) = I 0 10 − α( λ 0) b c

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(3)

where A(0) and (0) (mol1cm2) are the absorbance and the absorption coefficient at excitation wavelength (0) respectively, b is the optical pathlength, and c is the fluorophore concentration. Combining eqs 1, 2, and 3,

(

Je = φf I0 1 − 10 − α (λ ) b c 0

)

(4)

Transparent medium (Liquid or solid)

Je is calculated as the integrated emission area. The fluorescence quantum yield (f) of a sample is related to that of a reference (r) by eq 5 (10),

( (

) )

−α( ) b c 2 I0 r 1 − 10 λ Je r n φf = φ fr Je r I0 1 − 10 − α (λ ) b c n 0 2 0

0

(5)

Transparent medium (Liquid or solid)

where n and n0 are the refractive indexes for sample and standard respectively at the sodium D line and at the temperature of the emission measurement. Even when the excitation wavelengths are different for sample and reference, the ratio I0r/I0 is usually set to unity by the instrument because of an internal correction of the excitation beam (using a quantum counter). This correction is usually required in fluorometers to correct for variations in lamp intensity with both wavelength and time (6). Concerning this point, it is important to know exactly the wavelength range where the correction is valid. Using rhodamine B as a quantum counter excitation is corrected up to about 630 nm. With HITC basic blue (1,1´,3,3,3´,3´-hexamethylindotricarbocyanine iodide) the range may be extended up to 800 nm (6). To allow a correct comparison between sample and reference a further adjustment is needed to compensate for the wavelength dependence of the detector response. For this purpose, the emission spectra of a dye of known absolute spectrum (i.e., cresyl violet in methanol, ref 11) is recorded and the correction factor is calculated by dividing the absolute spectrum and the spectrum experimentally obtained for this dye. The experimental emission spectrum should be multiplied by this factor to obtain the true spectrum. New spectrofluorometers usually have this correction function already included in their software. For transparent samples, the choice of a standard is easy and wholly described in the literature (ref 5, 10, and references therein) and we will not address this point here.

Journal of Chemical Education • Vol. 79 No. 11 November 2002 • JChemEd.chem.wisc.edu

Research: Science and Education

Excitation and Absorption Spectra Excitation spectra are obtained by recording emission intensity (at a given emission wavelength) for different excitation wavelengths. If correction for differences in excitation light intensity with wavelength is performed,1 then the excitation spectrum is called the true fluorescence excitation spectra. For a weakly absorbing medium, (bc < 0.05, ref 5), in the absence of scattering, eq 4 may be rewritten as: Je = I0 2.3 A φf = I 0 (2.3 α b c ) φf

(6)

strongly absorbing transparent systems front face illumination (Figure 1b) is used. Even when this geometry reduces inner filter effects, distortions in emission spectra are usually observed (see ref 8). Fluorescence re-absorption is one of the main problems leading to erroneous conclusions in interpreting luminescence data. In liquid solution it has been extensively described in the literature (4, 8). Scattering Samples

Under these conditions, assuming I0 and f as constants, the excitation spectrum should be proportional to the fluorophore absorbance spectrum (in the absence of the inner filter or reabsorption effect, ref 8). Knowledge of the fraction of absorbed light is needed to calculate fluorescence quantum yields (see eq 5). For transparent samples, this fraction is calculated as [1  10A(˚)]. The absorbance A is recorded using a standard spectrophotometer.

Light Absorption and Emission Equations 1 and 2 are also valid in the presence of light scattering. Fluorescence quantum yields may be easily obtained, in this case, for a thick layer such that no light is transmitted through the layer (IT equal to zero). In this system Ia = I0 − IR

(7)

Geometrical Arrangement for Emission Measurements Right angle illumination (Figure 1a) is suitable for weakly absorbing transparent samples. This geometry minimizes interference by excitation light reflected at the cell faces. For

Je = (I0 − IR ) φf = I 0 (1 − R λ 0 ) φ f

(8)

and from eq 1,

Scattering medium Optically thick layer

where R0 is the sample total reflectance at the excitation wavelength (0), that is, the fraction of incident light that is reflected. To obtain the unknown fluorescence quantum yield of a solid sample, its emission spectrum should be compared with that of a reference to yield:

a Excitation beam

φf =

detector

Excitation beam

sample

30°

(9)

Scattering medium Optically thick layer

The same considerations discussed previously for the ratio I0r/I0 and for corrections in Je due to the detector response should be taken into account. Usually for a powdered sample, a thickness from one to three mm is enough to assure IT is equal to zero. In the presence of light scattering, the choice of an emission standard is far more complex than for a transparent medium. A reference dye to which a unity fluorescence quantum yield may be assigned in the solid phase is preferred. Rhodamine 101 (f equal to one) adsorbed on cellulose is cited in the literature as a suitable reference (7, 12). The dye amount in the solid sample used as standard should be low enough to assure no dye aggregation is present (12).

sample

b

I0 (1 − R λ 0 ) r Je φ fr r J er I0 (1 − R λ 0 )

detector filter

Figure 1. Geometrical arrangement for measurements (a) right angle illumination and (b) front face illumination.

Excitation and Absorption Spectra The approach usually followed to describe the absorption of light in scattering media is the Kubelka–Munk theory (7, 13). Within this approach, two light fluxes—I (the flux in the direction of the incident light) and J (the flux in the direction of the reflected light)—are considered to travel in opposite directions perpendicular to the irradiated surface. The attenuation of both fluxes is given by

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d I ( x ) = − I ( x ) ( K + S ) d x + J( x )S d x

(10)

− d J ( x ) = − J ( x ) ( K + S ) d x + I( x ) S d x

(11)

where K and S are the absorption and scattering coefficients of the sample respectively. The diffuse reflectance is, R =

J0 I0

(12)

where I0 is the incident flux and J0, the reflected flux at the front surface. Solving eqs 10 and 11 for an optically thick layer of scattering material, a function F(R), the remission function, relating the measured reflectance with the absorption and scattering coefficients, is obtained:

F (R ) =

(1 − R )2 2R

=

K S

(13)

This quantity is proportional to the chromophore concentration when the scattering coefficient is kept constant (13). Therefore, for a thick layer of scattering solid, absorption spectra are represented by F(R) as a function of wavelength. Thus, as opposed to solution’s behavior, the excitation spectrum is no longer proportional to the absorption spectrum but to the quantity, 1R0 (in the absence of the inner filter effect). This may be deduced from eq 8, assuming constant I0, and f.

Estimation of the Fraction of Absorbed Light The fraction of absorbed light is needed to calculate f in eq 9. For optically thick samples, the reflectance at the excitation wavelength should be known to calculate the fraction of absorbed photons as (1R). A conventional spectrophotometer equipped with a diffuse reflectance attachment is used to measure R. However, errors may arise when measuring reflectance for highly fluorescent materials. This results because the monochromator is placed between the light source and the sample, and upon excitation in an absorption band, the light reaching the detector is no longer monochromatic (it is composed of reflected and emitted radiation). To exclude fluorescence emission from reaching the detector short-wavelength-pass filters should be placed before the detector. For instance, a Corion LS-600 filter (cut-on wavelength 600 ± 5 nm, with a minimum spectral transmittance range: 415–590 nm) may be used for samples absorbing at wavelengths lower than 600 nm and emitting mostly at wavelengths higher than 600 nm. The calibration of the system is performed using barium sulfate as a perfect reflector (reflectance is one). The reflectance, R, for a solid sample is then obtained as a function of excitation wavelength (9, 14). Geometrical Arrangement for Emission Measurements For solid samples a front face attachment (Figure 1b) is used. In this case the emission beam should pass through a suitable filter to avoid the excitation beam reaching the detector (e.g., an orange Schott OG 550 filter may be used when exciting at 540 nm). 1364

Re-absorption and Re-emission Processes: Avoiding Artifacts and Usual Mistakes Theoretical Approach In the solid phase, fluorescence re-absorption processes are actually far more important than in solution, even for low fluorophore concentrations. Let us assume a fluorophore with a fluorescence quantum yield, , is irradiated in its absorption band. A fraction  of the absorbed light will be emitted. A fraction of the emitted photons may be re-absorbed (before reaching the detector) and subsequently another fraction may be re-emitted. From these processes, two consequences arise: distortion in emission spectra (decrease in luminescence intensity in the region where absorption and emission spectra overlap) and the experimentally observed obs will be lower than the true . Let us define Ia as the number of incoming photons absorbed by the sample per unit time and P1 as the probability of re-absorption of a primarily emitted photon. Then, from the emitted photons Ia, a quantity IaP1 will be re-absorbed and Ia(1P1) will emerge out of the system. The re-absorbed fraction will lead also to emission and a quantity Ia2P1 will be re-emitted again. These photons will be partially re-absorbed in a quantity Ia2P1P2, a quantity Ia2P1(1  P2) will emerge and so forth. The observed fluorescence quantum yield, obs, may be written as the sum of all emerging photon flows divided by Ia: ∞

n −1

n=2

i =1

φobs = φ (1 − P1 ) + ∑ φn (1 − Pn ) ∏ Pi

(14)

Assuming that all re-absorption probabilities, P, are equal and rearranging eq 14, a relation between the observed fluorescence quantum yield, obs, and the true emission quantum yield, , is found (7, 15): φ =

φobs 1 − P (1 − φobs )

(15)

It is clear from eq 15 that  is equal to obs, either when the probability of re-absorption is zero or  is equal to 1. Within the model we present here, P is related to the absorption of light by the sample. To find this relation, emission in a scattering material is decomposed into two photon flows, i()(1) and j()(1). Following arguments similar to those for eqs 10 and 11, we can write



di (1) = − (K + S ) i (1) + S j (1) + dx

1 2

f (λ ) φ

d I a(0) (16) dx

d j (1) = − ( K + S ) j (1) + Si (1) + dx

1 2

f (λ ) φ

d I a(0) (17) dx

where ƒ() is the normalized spectral emission, ∫ f (λ ) dλ = 1

λ

and the factor 1/2 in the emission terms takes into account

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that half of the radiation is emitted in the positive direction and the other half in the other direction. After calculation of dIa(0)/dx and some algebraic manipulation under suitable boundary conditions, eq 18 is obtained (for a detailed derivation of formulas, see ref 7), f (λ) γ (λ ,λ 0) d λ

(18)

λ

where (, 0) is a function of excitation (0) and emission () wavelengths that can be calculated from reflectance data as

1+

F (Rλ ) F (Rλ ) + 2

×

1

1+

F (Rλ ) (F ( Rλ ) + 2)

(

F (Rλ ) F ( Rλ0 ) + 2

(19)

)

where F(R) and F(R0) are the remission functions (see eq 13) at the emission and excitation wavelengths respectively. It may be shown that by dividing the experimental emission spectrum by the corresponding gamma function, correction for light re-absorption in the spectrum shape is achieved (7). Gamma is one when no re-absorption is present and decreases towards zero as re-absorption becomes more important. Accordingly, the probability of re-absorption, P (eq 18) is zero when  is equal to one, and increases as  values decrease. In eq 15,  stands for the fraction of absorbed light that is emitted as luminescence from the fluorophore and obs represents the fraction of absorbed light that actually reaches the fluorometer detector. It is worth noting that, depending on the particular case, one can be interested in either of these two quantities. So, for instance, to know how fluorescent a solid specimen would appear to our eyesight, obs should be considered but to get information about the fluorophore photophysical behavior in the solid phase  should be calculated. If the fluorophore’s f value is one, no corrections in the fluorescence quantum yield, due to re-absorption and re-emission, are needed because every re-absorbed photon is re-emitted. When  is different from unity, re-absorption processes may lead to misunderstanding. We will show an experimental example for the analysis of dye fluorescence in the solid phase. The scope of this example is to illustrate: How to obtain a true emission spectrum in the solid phase. How to analyze whether changes observed by varying excitation wavelengths are due to excimer emission or to re-absorption processes. How to calculate and interpret experimental and true fluorescence quantum yields.

0.008

0.006

F (R)

1

γ ( λ, λ0 ) =

0.004

0.002

0.000 500

600

700

800

Wavelength / nm Figure 2. Absorption spectrum for rhodamine B on cellulose (2.3 × 108 mol/g) obtained for a thick layer (3 mm) of the sample.

Fluorescence Intensity (arb u)

P = 1−

Experimental A sample of rhodamine B on microcrystalline cellulose (concentration 2.3 × 108 mol/g) was prepared in the following way: a known amount of a rhodamine B (Aldrich) solution in ethanol (Mallinckrodt, analytical grade) was added to a weighed mass of microcrystalline cellulose (Aldrich, average particle size: 20 m) and the solvent was evaporated in a rotavap system. To remove any final traces of solvent, the sample was dried at room temperature under vacuum for 24 h. The diffuse reflectance spectrum for an optically thick sample (3 mm) was then recorded on a Shimadzu 3101 PC spectrophotometer equipped with an integrating sphere. Barium sulfate was used as a white standard to adjust 100% reflectance level. The remission function, F(R) as a function of wavelength (absorption spectrum), was obtained from reflectance data using eq 13 (Figure 2). At this concentration no aggregation of the dye is present. In Figure 3, emission spectra for a thin layer (where almost no re-absorption takes place) and for a thick layer (3 mm) of the sample are presented. The thin layer was

1

0 550

600

650

700

Wavelength / nm Figure 3. Emission spectra for rhodamine B on cellulose (2.3 × 108 mol/g). Excitation wavelength: 530 nm. Solid line: 3 mm thick layer. Dashed line: ~0.1 mm thin layer. Points: thick layer corrected for light reabsorption. Spectra were normalized at their respective emission maxima.

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prepared on squares of double-sided fixing tape (1 cm × 1 http://www.saveyoursmile.com/toothpaste/toothpaste-a.htmlcm) attached to a glass plate. The powdered sample containing the dye was homogeneously distributed on the free side of the fixing face. The thick layer was prepared by pressing the solid on a front face holder. Division of the experimental spectrum for the thick layer by the gamma function (eq 19) allows correction for luminescence re-absorption. In Figure 3 it is shown that very good agreement between thin layer and gamma corrected spectra exists (spectra were normalized at emission maxima to allow a better comparison). Emission spectra recorded for a thick layer at two different excitation wavelengths, 500 and 550 nm, show different maxima positions (Figure 4a). At 500 nm the dye absorption is lower than at 550 nm (Figure 2), so in the first case, the light penetrates deeper into the solid and the reabsorption of luminescence is higher. The net result is a relative decrease in the luminescence intensity at the shorter emission wavelengths. For excitation at 500 nm, there is more re-absorption of luminescence at short wavelengths relative to longer wavelengths because the dye absorbs more

strongly at these wavelengths (560–580 nm) than at longer wavelengths (>595 nm) (see Figure 2). This result may be easily misinterpreted as excimer emission in many cases. These effects should be carefully taken into account when working in the solid phase. To decide whether changes in emission spectra with varying wavelengths are due to different emission species or only to the re-absorption process, quantitative correction of luminescence spectra should be performed. In Figure 4b we can see the superimposition (within experimental error) of both spectra after re-absorption correction. The gamma corrected spectrum may be considered as the true fluorescence spectrum. To obtain the fluorescence quantum yield, emission spectra were obtained for a thick layer of the sample and of the reference (rhodamine 101 on cellulose, 2 × 108 mol/g) at the same excitation wavelength (520 nm). The fluorescence intensity was calculated as the integrated area under the emission spectra. The experimental fluorescence quantum yield (obs) was thus obtained from eq 9 following the details described above. A value of 0.82 ± 0.03 was obtained in this case. The fluorescence distribution for a thin layer of the sample was normalized to satisfy: ∫ f (λ ) dλ = 1

a Fluorescence Intensity (arb u)

λ 1

excitation at 500 nm

excitation at 550 nm

0 540

560

580

600

620

640

660

680

P was then obtained from eq 18 and finally a value of  = 0.89 ± 0.03 was obtained from eq 15. These results mean that 89% of the light absorbed by the sample is emitted as fluorescence but due to re-absorption processes only 82% reaches the fluorometer detector. It may be seen that even at high fluorescence quantum yields, correction is needed. The correction is far more important when the emission quantum yield is lower. A detailed account of the correction procedure in the solid phase even in the presence of dye aggregation (a case that was not considered here) may be found in reference 7.

700

Conclusions

Wavelength / nm

We showed that scattering leads to important light reabsorption processes which: Fluorescence Intensity (arb u)

b

1. Decrease the observed fluorescence quantum yield.

1

2. Produce spectral distortion in emission (maxima shift to longer wavelengths). This distortion is dependent on: (a) the layer thickness of the fluorescent material, (b) the sample absorption at the excitation and emission wavelengths, and (c) the excitation wavelength.

0 540

The spectral distortion may be easily misinterpreted as caused by different emitting species (excimer emission for instance), so quantitative corrections are necessary for accurate data analysis. By application of the correction model we presented here, we were able to: 560

580

600

620

640

660

680

700

Wavelength / nm Figure 4. Emission spectra for rhodamine B on cellulose at two excitation wavelengths: 500 nm (points) and at 550 nm (solid line). (a) experimental spectra, (b) spectra corrected for light reabsorption. Spectra were normalized at their respective emission maxima.

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1. Obtain true emission spectra and true fluorescence quantum yields. 2. Distinguish between the observed fluorescence quantum yield (useful for industrial applications in textiles, printings, etc.) and the true fluorescence quantum yield (necessary to understand the fluorophore behavior in the solid).

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Note 1. This is usually set internally in the instrument by means of a fluorescence quantum counter.

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1992, 69, A8–A12. 7. Lagorio, M. G.; Dicelio, L. E.; Litter, M.; San Román, E. J. Chem. Soc., Faraday Trans. 1998, 94, 419–425. 8. Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Kluwer Academic Publishers: New York, 1999. 9. Vieira Ferreira, L. F.; Netto-Ferreira, J. C.; Khmelinskii, I. N.; Garcia, A. R.; Rosário Freixo, M.; Costa, S. M. B. J. Chem. Soc., Faraday Trans. 1993, 89, 1937–1944. 10. Eaton, D. F. Pure Appl. Chem. 1988, 60, 1107–1114. 11. Magde, D.; Brannon, J. H.; Cremers, T. L.; Olmsted, J., III J. Phys. Chem. 1979, 83, 696–699. 12. Vieira Ferreira, L. F.; Rosário Freixo, M.; García, A. R.; Wilkinson, F. J. Chem. Soc., Faraday Trans. 1992, 88, 15–22. 13. Lagorio, M. G. J. Chem. Educ. 1999, 76, 1551–1554. 14. Vieira Ferreira, L. F.; Oliveira, A. S.; Wilkinson, F.; Worrall, D. J. Chem. Soc., Faraday Trans. 1996, 92, 1217–1225. 15. Birks, J. B. Phys. Rev. 1954, 94, 1567–1573.

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