Spatial fluorescence profiles in multiple light scattering systems

JOURNALOE

LUMINESCENCE

--

ELSEVIER

Journal of Lum~nescenccôO&61

1994) 422 42~

Spatial fluorescence profiles in multiple light scattering systems Dieter Oelkrug*, Manfred Brun, Ulrike Mammel Insiitutc of

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Abstract The intensities of forward and backward fluorescence in multiple scattering samples and the radial fluorescence profiles under point irradiation are investigated theoretically and experimentally. Calculations are carried out with the model of radiative transfer using the Kubelka Munk approximation. the P 1 -method, and the MonteCarlo procedure. Experiments are carried out with silica gel as scattering substrate loaded with pvrene as fluorophore.

1. Introduction Many fluorescent sampies of practical interest are strongly light scattering. It is possible nowadays to investigate the photophysics and photochemistry of those samples very sensitively by fluorimetrie methods [1,2], but it is still a significant problem to quantify the spectral and spatial distribution of the emitted light fluxes correctly. In the following we present some theoretical and experimental results of the fluorescence intensity distribution in multiple scattering fluorescent layers considering especially the influences of penetration depth, sample thickness, reabsorption, and inner filter effects.

d. One surface of the layer is irradiated monochromatically at ,~. with intensity 1~. Inside the layer the light is partly absorbed by the fluorophore I + background) with absorption coefficient ic,( I + ic~)and partly scattered from its original direction by the substrate with scattering coefficient a,~ Both coefficients are defined per unit length of the propagating light in arbitrary direction inside the sample. The absorbed light is isotropically emitted at ).~by fluorescence with the emission coefficient q~= ~ where ~ is the spectral fluorescence quantum yield of the fluorophore. Experimentally. the following photometric quantities are accessible from the irradiated (x = U) and nonirradiated = d) surface at i.. and ),~: reflectance R.~= J~ l~. R~= .J~ I~>.

2. Results and discussion

.

transmittance T

2.1. Calculations The samples are modeled by multiple scattering and fluorescent planar layers of arbitrary thickness

=

1

., l~. Te

backward fluorescence F5 = forward fluorescence F1

=

=

j~

‘ii.

j~j.(

1~l~.

2.1.1. E.vte,id~larc’cl ot irradiation In this case the Kubelka-Munk (KM)formalism

*

Corresponding auihor.

[2]

0022-23t3/94/$07.OO c~ 994 Elsevier Science 13V. All rights reserved SSL)JOO22-23t3)93)EO33~-tJ

can be successfully used to calculate the

D. Oelkrug et al. / Journal of Luminescence 6O&61 (1994) 422—425

423

I.0 1.0

-

—

F~ 0.5 ,~a(P) ~

/Fb(p)~

_________________________

0.5 0 0

Fb

0.0

0

tOO

200

p/~.sm

0.0 -2

-l

0 logK~

1

2

Fig. I. Forward and backward fluorescence (Ff,Fh), diffuse reflectance (R,), and diffuse transmittance (Tj of a multiple scattering layer (d = 1cm, S~= S~= 50cm~, K~= Kb = 0) as a function of the absorption coefficient logK~ of the fluorophore. The values are normalized to their maxima,

Fig. 2. Calculated radial distributions of R,(p),F~(p), and 1,ic~ = Ff(p). Parameters = 300cm~ lSOcm’, ,c~= 0. are d = 200pm, a~=

(Ke > 0) also Fb.

reduces Ff extremely, and to some extent These facts have to be considered when fluorescence yields are determined. 2.1.2. “Point” irradiation with a focussed laser

experimental photometric quantities. The optical coefficients are replaced by formal absorption and scattering constants K = 2K and S = 3u(1 K/4 that are defined per unit length parallel to the normal of the sample surface. The quantity 1 ~ g ~ + 1 considers the anisotropy of scattering. Using expressions for R and T from the KM theory [3], a lengthy calculation leads to the fluorescence intensities q~ Fb = 2 (Ka + Kb)Va KeVe 1~Va+ Ve)(Re Ra) —

—

—

—

+

Ff

(Va

—

Ve)(I

—

—

RaRe

—

KeVe ~

—

Ta Te)],

q~ =

2(Ka + Kb)Va

—

(Ca

—

+ Ve)(Te

—

Ta)

beam

In this case we calculate the radial distribution of fluorescence emerging from the surface, Fb(p) and Ff(p), with the Monte-Carlo formalism and with the theory of radiative transfer [4] using the rigorous PL-method of series expansion into spherical harmonics up to L = 5. By these methods we obtain theoretical point spread functions of the fluorescence and of the incident laser beam that fit the experiments very well [2]. Figure 2 shows typical radial distribution functions of a scattering layer that is irradiated with a Gaussian laser profile of e2-half-width = 12.5 ~.tm. Because of Ka>~l’/e, the fluorescence diffuses much farther from the point of incidence than the reflected primary radiation. This result may be of consequence to the resolution of fluorescence images of microscopic preparations.

Ve)(Ra’Te + Re’Ta)],

where Va = Ka + Kb + 2Sa, Ce Ke + 2Se. These equations consider background absorption and fluorescence reabsorption but not fluorescence reemission. Figure 1 illustrates some aspects of these equations. With the exception of Sd 0, the forward fluorescence is always weaker than the backward fluorescence. It is, however, not easy to suppress Ff completely by increasing the layer thickness or Ka. Fluorescence reabsorption —÷

2.1.3. Spectrofluorimetric measurements

The situation of Fig. I is verified with pyrene as model fluorophore that has been adsorbed on microdisperse, strongly scattering metal oxide powders [1]. Figure 3 presents low loaded silica gel (specific surface area = 500m2 g I) where pyrene is exclusively physisorbed as nonaggregated monomers. In the excitation spectra, left, the absorption

424

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Journal of 1_undncsccncc O0&O/ (1994 422 425

I—

1.0/

\//~

--

~

0.5

-\

‘~

A -

N

F~\

-

\

-

-, ~

,-—~~-

280

_~---~-,

I

-

~

~./

~,

\~)/~~

F1-

eniission

‘

380

Fig. 3 Fluorescence excitation (left) and emission (right) spectra of pyrene on silica gel ~ ~ec test

I I

I

I

thick layer

‘F

I

; -- -

Pt

-- ~

Pa -

--

--

-

-

-

-

-

--

-

-

--

--

-

~

thin layer --

Pt

--

~

--

-

-

--

p

--

---

-

I 250

300

350

,Jnm

Fig. 4 Fluorescence excitation spectra of monomers (Pd and aggregaies (P,,( of pyrene on silica gel (c ,,,,,. = 29 x I)) molg).

coefficient varies widely from K~ 0.2cm IS1band. 350—370nm) to Ka 50cm~ (S2band, ~‘a 290—340 nm), and the intensity of F5(Ka) follows the raising curve of Fig. I. The intensity of Ff(Ka), however, passes through a maximum so that excitation into the weakly absorbing Si-band yields almost the same forward fluorescence intensity as the strongly absorbing ,~..

‘-~

-~

360 2Jnm

320

FN

/

-

excitation

0.0

~

‘ --

420 ~Jnm —

~

I)) -

niol g. 1

I cm) For detaik

S2-band. Moreover. S, extends to the region of negative slope so that the highest vibronic absorption maxima appear as minima in the forward fluorescence excitation spectrum. The shape of the emission spectra, Fig. 3 right, is nearly undistorted in backward direction, whereas the forward cornponent is almost completely suppressed by reabsorption in the region of overlap with the S1absorption peak and even with the very weak hot side-bands. It should be noticed that also the backward spectrum becomes strongly distorted when K~of the fluorophore increases [2]. Finally, the influence of background absorption. K 5~j. is demonstrated with a system similar to Fig. 3. but with a five times higher surface loading. Pyrene is now partly adsorbed as aggregates that emit the well-known unstructured excimer spectrum at )~‘ 475nm. The magnitude of the aggregates is discussed controversially ranging from dimers to microcrystallites. The fluorescences cxcitation spectrum taken in conventional way, Fig. 4 upper. brings the question not to decision since the spectrum is completely distorted by the monomeric majority that acts as an inner filter with wavelength-dependent absorption coefficient K5(,~.a):maxima of the monomer appear as minima in the excitation spectrum of the excimer. The best way to reduce this undesired effect is to investigate “infinitesimally” thin layers or. in praxi, only a few granula of the loaded adsorbent. Now the “real” spectrum of the aggregates is measured, Fig. 4 lower, that is red-shifted by only 500 cm against =

.

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0. Oelkrug et at.

/

Journal of Luminescence 60&61 (1994) 422—425

the monomer, i.e. much less than in the crystal, so that the aggregates on the surface must be very small. Acknowledgements

This work was supported by the Deutsche For-

schungsgemeinschaft, Oe 57/12, and by the Fonds der Chemischen Industrie.

425

References [1] D. Oelkrug, W. Flemming, R. Füllemann, R. Gunther, W. Honnen, G. Krabichler, M. Schafer and S. UhI, Pure Appi. Chem. 58 (1986) 1207. [2] D. Oelkrug, U. Mammel, M. Brun, R. Gunther and S. Uhi, in: Fluorescence Spectroscopy, New Methods and Applications, ed. OS. Wolfbeis (Springer, Berlin, 1993) pp. 65—78. [3] P. Kubelka, J. Opt. Soc. Am. 35 (1948) 448. [4] B. Davison, Neutron Transport Theory (Clarendon Press, Oxford 1957) pp. 116-171.