COMPARISON OF RECORDED AND CALCULATED PHOTOACOUSTIC SPECTRA OF DYE SOLUTIONS

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COMPARISON OF RECORDED AND CALCULATED PHOTOACOUSTIC SPECTRA OF DYE SOLUTIONS

S. Schneider, U. Möller

To cite this version:

S. Schneider, U. Möller. COMPARISON OF RECORDED AND CALCULATED PHOTOACOUS-

TIC SPECTRA OF DYE SOLUTIONS. Journal de Physique Colloques, 1983, 44 (C6), pp.C6-407-

C6-412. �10.1051/jphyscol:1983667�. �jpa-00223226�

JOURNAL DE P H Y S I Q U E

Colloque C6, suppl6ment au nD1O, Tome 44, octobre 1983 page C6- 407

COMPARISON O F RECORDED A N D C A L C U L A T E D P H O T O A C O U S T I C SPECTRA O F D Y E S O L U T I O N S

S. Schneider and U. ~aller

Lichten Berg. s t r . , 4 , I n s t . Physical and Tkeor. Ckem., 0-8046 Garching, F.R.G.

R&sum&

-

Les spectres photoacoustiques du vert Malachite et de la Rhodamine 6G en solution dans l'&thanol avec des con- centrations de ~ o - ~ M 5 10 '1.1 sont pr&sent&s. On les compare avec les spectres thgoriques calcul6s avec le mod6le du pis- ton composite.

Abstract

-

Photoacoustic spectra of ethanolic solutions of ma1 chite gr en and rhodamine 6G in the concentration range _{10 M)c)}

-9

_{10 M}

-5

are recorded. They are compared with theoretical spectra (amplitude and phase) calculated on the basis of the

"composite piston model".

Introduction

-

With the technological improvements of recent years, considerable interest has developed in the possibility of using photo- acoustic instead of uv-vis spectroscopy for analytical purposes. The high expectations are based on the belief that the Rosencwaig-Gersho model /1,2/ in conjunction with the refinements by Mc Donald and Wetsel /3/ reliably predicts the intensity and phase of the PA signal in dependence of material parameters and modulation frequency (for a review see e.g. reference 4). The theoretical expressions were dis- cussed, however, only for limiting cases (e.g. optically thin or thick samples), whereas during the scan of a PA spectrum, a frequent swit- ching from one limiting case to another will occur. In addition, the photoacoustic yield,

,

i.e. the efficiency at which the absorbed light is converted to heat

!

y radiationless transitions, varies with exci- tation wavelength. As a consequence, PA spectra of a solute may differ significantly from the corresponding electronic absorption spectra thereby making the identification difficult and sensitive to solute concentration (see fig. 1). The aim of this paper is to demonstrate that by comparison of experimental and calculated PA spectra, informa- tion on concentration and competing radiationless processes can be derived with better accuracy.

Model calculations

-

Starting point for the numerical calculations are the (exact) equations derived by the above mentioned authors for the contributions originating from thermodiffusion /1,2/, qth, and from thermally induced bulk vibrations / 3 / , q

.

For the sake of convenience, we introduced three approximations, whicE are valid in our experi- mental arrangement:

i) assumption of a thermally thick sample, i.e. exp = 0 ii) assumption of low chopping frequency, i.e. k.l<< 1

iii assumption that g = ( k t * a') / (k-a)

<<

¹ (for ethanol-air: g=0.01) (The symbols used here and lateron are in accordance with reference 4 and with a forthcoming publication including more details (Zeitschrift Naturforschung) )

.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983667

JOURNAL DE PHYSIQUE

Pig. 1

-

PA spectra of malachite green in ethanol (f = 36 Hz). Con- centrations are (a

-

g ) : 62, 39, 10, 6.2, 3.6, 1.0, 0.62 mM.

The total photoacoustic response, q = qth + q

,

is best expressed in a form, where real and imaginary part are sepapated:

q = K . (ql + i0q2) (

5 ^(St.?;

⁾

where

K =

-

(p1.~,.~~)/(4.a.~1.a2)

It should be emphasized here that all calculations were performed using the literature-values for the materia~lconstants of ethaqol/air.

-,

Parameter values used are: a = 353 cm

,

^{o< = 3.7 1 0 K}

,

a1=24cm

,

T = 300 K , 1 = 0.9 cm. In the case of mixes solutions, energy transfer from the donor species rhodamine 6G to the acceptor species malachite green is assumed to.obey Forsterrs law. Accordingly, the photoacoustic yield of rhodamine 6G varies with concentration of acceptor species

(for more details see reference 5).

Flg. 2

-

Electronic absorpt&yn(-) FigS 3

-

PA spectrum (---) of 3.6- PA spectrum (---) of 3.9- 10 M 10 M malachite green in comparison malachite green in ethanol (f=36IIz) to theoretical spectrum calculated in comparison to calculated PA on the basis of the simple (a) and spectrum (-)

.

extended Rosencw2 j..qiGersho model

(b: a = 3 - 7 - 1 0 K t -3 -1 c: Wt = 1.1.10 K )

Results and Discussion

-

The influence of signal saturation can clearly be seen in figure I , which shows the P spectra (amplitude and phase) for various concentrations above 6.10-'M. Figure 2 shows that the model calculation very well predicts intensity and phase of the PA signal of the 3.9.10 M' solution

.

In accordance with the simple Rosencwaig-Gersho model, the phase 0 approaches - Z / 2 in those wavelength regions, where saturation occurs. At the long wavelength absorption edge, the experi- mentally recorded phase lies between the theoretical predictions of simple and extended model (composite piston model).

Figure 3, which displays the results of the 3 - 6 . I O - ~ T I solution, demon- strates the effect of thermally induced bulk vibrations (thermoelastic effect). In contrast to the prediction of the simple Rosencwaig-Gersho model, the phase angle 0 never reaches the limiting value of -3-Z/4.

The deviation is the larger, the lower the optical density. Both ampli- tude and phase are, however, well described by the composite piston model. This agreement proves that also for liquid solutions, the thermo- elastic effect is of major importance when samples of low optical den- sity are studied.

The formal discrepancy in the derivation of Rosencwaig /4/, on one hand, and Mc Donald and Wetsel /3/ on the other hand,must be resolved in favor of Rosencwaig. The calculation, which uses the linear (trace b) instead of the volume expansion coefficient (trace c) results in a.

better agreement with the experimental spectrum. The result calculated on the basis of the simpe Rosencwaig-Gersho model (trace a) reflects the absorption spectrum (fig. 2 ) , but does not represent the PA response.

C6-410 JOURNAL DE PHYSIQUE

l , , , , , ,

iC_

^{, , * ,}

a"

LOO 500 600 '0° Xlnm_ LOO 500 600 700 Xlnm

Fig. 4

-

Dependence of recorded PA spectrum on sample length (left hand side) : 3.6.10 5~ malachite green in ethanol, f = 36 Hz.

1 = 3cm (a)

,

^{1 = 2 cm (b) and ls =} 0.9 cm (c)

.

~l?e correspondi~g calculated PA spectra are shown on the right side.

m E

c

- cn =2,6.W-bm d - - - - . r ,, ^{= 5 . ~ ~ ~ r n}

LOO MO MXI lca

Wellenlenga * I n n

Fig. 5 _{(CRh =}

-

7.5.10 M) and malachite green (CM indicated) in ethylene Recor ed

-g

PA spectra of mixed solution of rhodamine.6G glycol (f = 23 Hz).

According to theory, the influence of the thermoelastic effect should increase with sample thickness, but saturate for large values of 1.

In figure 4, this prediction is experimentally verified. The effect is even more pronounced than expected on the basis of the calculations.

In order to study the influence of energy transfer on the appearance of PA spectra, we have recorded these for a series of solutions (see fig. 5), which coggain a fixed concentration of donor molecules (rho- damine 6G, 7.5.10 M) and a variable amount of acceptor molecules (ma- lachite green). It is obvious /5/ that due to energy transfer, the photoacoustic efficiency of light absorbed by rhodamine 6G (>=530 nm) is significantly inceased. Figure 6 demonstrates, how the shape of the PA spectrum, and especially the relative intensity of the signal due to rhodamine 6G absorpticq varies, if the energy transfer constant is varied (O<k /T,&1900 M ) . From the peak intensity ratio, an estimate for kq:Yr0 ( To is the rhodamine 6G fluorescence decay time in the absence of acceptor molecules) can be derived.

Fig. 6

-

Dependence of4PA spectra calculated for the mixed solution of rhodamine 6G (7.5

.

^{10 M )} and malachis? green (2.6~40 M) on eg?rgy transfq parameter k / T o (a: 1900 M

,

b: 1265 M

,

c: 633 M

,

d: 0 M 1 . ^qu

The theoretical PA spectra for the different malach+te concentrations calculated with the same value for k /To = 1900 M resemble very closely the actually observed peak rggios. The difference in each pair of corresponding traces in fig. 7 signals again the effect of thermally induced vibrations. It can be stated, that at a chopping frequency of 23 Hz this effect is important only for B-v$ues below about 10, i.e.

a concentration of malachite green below 10 M. The appearance of the spectra is,however, changed significantly, if the molar absorption coefficent is strongly varying function of wavelength.

JOURNAL DE PHYSIQUE

Fig. 7

-

Calculat~d PA spectra for mixed solutions of figure 5

(k / Y e = 1900 M ) . Lower curve of each pair is calculated according toqgimple, higher curve according to extended Rosencwaig-Gersho theory.

Summary

-

The composite piston model as outlined above is a suffi- ciently good approximation to calculate the PA spectra of dye solu- tions on the basis of the absorption spectra and the material para- meters of the solvent. The phase lag is a very sensitive criterion to prove the importance of thermally induced vibrations.

References

-

1. Rosencwaig A. and Gersho A., Science

190

(1975) 556 2. Rosencwaig A. and Gersho A., J. Appl. Phys.

fl

(1976) 64

3. Mc Donald F.A. and Wetsel G.C. jr., J. Appl. Phys.

49

(1978) 2316 4. Rosencwaiq A.: Photoacoustic and Photoacoustic Spectroscopy

(chemical-~nal~sis, Vol. 57, John Wiley & Sons, New ~ o r k / - - Chichester/ Brisbane/Toronto, 1980)

5. Schneider S. and Coufal H., J. Chem. Phys.

76

(1982) 2919