Journal of Applied Spectroscopy, Vol. 76, No. 5, 2009

QUANTITATIVE LUMINESCENT ANALYSIS METHODS A. P. Voitovich,* V. S. Kalinov, L. P. Runets, and A. P. Stupak

UDC 543.426+535.341.08

We have developed quantitative luminescent analysis methods not requiring the use of reference media with known contents of the analyte components. The methods are based on relations describing re-absorption of luminescence and also on a relation connecting the luminescence intensity and the absorption coefficients of a multicomponent medium. We present equations allowing us to find the absorption coefficients and consequently the concentrations of the components of the medium from the luminescence intensity measured in relative units. In order to determine the concentrations of nonluminescent components, we also propose and demonstrate the use of a luminescent probe. We present the experimental results for determination of the absorption coefficients and the concentrations of substances by the methods we developed. Keywords: luminescence, quantitative analysis, absorption coefficient, concentration of components, luminescent probe. Introduction. In luminescent analysis, the presence and concentration of substances are determined from the luminescence spectrum and intensity. For absorption optical densities that are small compared with unity, the photoluminescence (PL) intensity can be assumed to be proportional to the absorption coefficient k0, which is uniquely connected with the concentration of the corresponding component of the medium. Therefore from the changes in the intensity in such a case, we can judge changes in the concentration of the substance, which allows us to follow the temporal kinetics of various processes such as chemical reactions. If the condition that the optical density be small is not met, then the photoluminescence intensity cannot be assumed to be proportional to the concentration. Intensity measurements are usually made in relative units and within a small solid angle, the size of which often is difficult to determine sufficiently accurately. Therefore even in the most favorable cases, when carrying out quantitative luminescent analysis we need to use reference media with known content of the components. Luminescent study methods are widely used in scientific practice [1–4]. They have high sensitivity. There is a large selection of instruments for such studies. However, quantitative luminescent analysis is practically not used due to difficulties in its implementation. This paper is devoted to development of new quantitative luminescent analysis methods. The fundamental difference between our methods and existing methods is the fact that they do not require reference samples, even though they are based on measurements of the photoluminescence intensity in relative units. We have also developed a luminescent probe method which expands the possibilities for analysis, allowing us to use it for nonluminescent substances. The proposed methods are based on analytical relations connecting the photoluminescence intensity and the absorption coefficient of the medium. Such relations have been obtained recently for photoluminescence and photoluminescence excitation (PLE) spectra. In the first case, equations are used that determine the changes in the photoluminescence intensities as a result of re-absorption of photoluminescence in the analyte medium [5]. In the second case, the methods are based on the dependence of the photoluminescence intensity on the absorption coefficients of a multicomponent medium, [6, 7]. From the relations obtained in [5–7], equations are derived that make it possible to find the absorption coefficients of a medium from the measured intensity. The problem of finding the absorption coefficients according to the procedure outlined above is an inverse problem. In order to properly solve inverse problems with original data obtained experimentally with random errors, ∗

To whom correspondence should be addressed.

B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68 prosp. Nezavisimosti, Minsk 220072; e-mail: [email protected]. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 5, pp. 768–778, September–October, 2009. Original article submitted May 14, 2009. 0021-9037/09/7605-0727 ©2009 Springer Science+Business Media, Inc.

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often we need to draw on additional information about the system and simplify the calculations as much as possible. In this paper, in deriving the relations we draw on information about the contours of the photoluminescence and absorption bands. In all cases, we obtain equations for calculation of the absorption coefficient which are solved uniquely. Knowing the absorption coefficients opens up ways to determine the concentrations of the components [8]. For this purpose, in addition to the absorption coefficient we need data on the shape of the contour in analytical or digital form and on the integrated transition probability or the oscillator strength for absorption. The component concentration can also be determined if we separate the absorption coefficient determined into a specific absorption coefficient or molar absorption coefficient (molar extinction coefficient) characterizing attenuation of radiation in a medium with unit concentration of the absorber. Equations for Determining Absorption Coefficients from Photoluminescence Spectra. Changes in the photoluminescence intensity as a result of re-absorption in the analyte medium depend on the relative orientation of the directions of propagation of the exciting radiation and the detected radiation. The simplest relation for these changes is obtained in the case when photoluminescence is detected at a right angle to the direction of propagation of the exciting radiation [5]: Itrue (ν) = Imeas (ν)

k (ν) l , 1 − exp − k (ν) l]

(1)

where Imeas(ν) is the measured photoluminescence intensity at frequency ν; k(ν) is the absorption coefficient at frequency ν; l is the [path] length of the analyte substance along the photoluminescence detection direction; Itrue(ν) is the photoluminescence intensity which would be measured for k(ν) = 0. Then we call the value of Itrue(ν) the true intensity. Let us assume that we know the contours of the photoluminescence band of a luminescent component ϕL(ν) and the absorption band ϕA,s(ν) of the analyte substance, found simultaneously in the same medium. Then we can write Itrue (ν) = Itrue (ν0,L) ϕL (ν) , k (ν) = k0ϕA,s (ν) , where Itrue(ν0,L) and k0 are the photoluminescence intensity and the absorption coefficient at the frequencies of the maxima ν0,L and ν0,A,s of the photoluminescence and absorption bands. Note that ϕL(ν0,L) = 1 and ϕA,s(ν0,A,s) = 1, while the functions ϕL(ν) and ϕA,s(ν) can be specified in analytical or digital form. Let us measure the photoluminescence intensities Imeas(νi) and Imeas(νm) within the limits of the absorption band. From relation (1), we obtained the transcendental equation: Imeas (νi) Imeas (νm)

=

ϕL (νi) ϕA,s (νm) 1 − exp [− k0lϕA,s (νi)] ϕL (νm) ϕA,s (νi) 1 − exp [− k0lϕA,s (νm)]

The number of such independent equations with the same unknown k0 can be photoluminescence intensities are made for a set of more than two frequencies. sorption coefficient and concentration of the substance. Let us assume that in frequencies at which there is practically no absorption, for example, k(νm) = Itrue(νm), and from relation (1) follows Imeas (νi) Imeas (νm)

=

ϕL (νi) 1 − exp [− k (νi) l] ϕL (νm)

k (νi) l

.

.

(2)

increased if the measurements of the From them we find the unknown abthe photoluminescence band we have 0. Then we can assume Imeas(νm) =

(3)

Transcendental equation (3) allows us to calculate the absorption coefficients at different frequencies in the absorption band. For a known function ϕA,s(ν), the absorption coefficient k0 at the band maximum is determined from them. If the absorption band completely overlaps the photoluminescence band, then the possibility arises of determining both the complete band contour and the absorption coefficient k0 for the analyte substance from measurements of the photoluminescence spectrum. 728

Fig. 1. Functions ϕA,as(ν) (1, 1′) and ϕL(ν) (2, 2′) describing respectively the absorption and photoluminescence contours of methylene blue (1, 2) and rhodamine 6G (1′, 2′) in ethanol.

We should make one comment about relations (2) and (3). In those equations and in the next two equations in this section, the ratio of the frequencies νi and νm should appear, as follows from Eq. (8) derived in [6]. However, if the measurements of the photoluminescence intensities are made in units of the number of photons, then the ratio of the frequencies in Eqs. (2)–(5) should not be used. Let us expand the function exp [–kl(ν)], appearing in Eq. (3), in a Taylor series, taking the initial value of the argument lk(ν) = 0 and limiting ourselves to the first three terms of the series. For lk(ν) = 0.5, the error in determining the function {1 — exp [–lk(ν)]} for the selected expansion is <5%. Substituting the result of the expansion into formula (3) and making the substitution lk(νi) = lk0ϕA,s(νi), we obtain the usual equation with one unknown for determining the absorption coefficient at the frequency of the absorption band maximum: k0l 

2 Imeas (νi) ϕL (νm) ⎤ ⎡ ⎥. ⎢1 − ϕA,s (νi) ⎣ Imeas (νm) ϕL (νi) ⎦

(4)

The approximate Eq. (4) can be used to determine the values of k0l, even equal to a few units, if for the calculations we use measurements at frequencies for which the condition lk0ϕA,s(ν) ≤ 0.5 is satisfied. In this case, the systematic error introduced by the approximation will be no greater than 5%. Equations (2)–(4) are applicable for determining the absorption coefficients of a component for which the photoluminescence and absorption bands overlap. Figure 1 demonstrates the contours of the bands for such components, for the example of a solution of methylene blue and rhodamine 6G in ethanol, which we used to carry out the experimental studies. These same equations can also be used to determine the absorption coefficients of other components of the medium, including nonluminescent components. In such a case, we should measure the luminescence intensity of the substance whose photoluminescence spectrum overlaps the absorption spectrum of the analyte component. In the following, we call such a substance a luminescent probe [5]. In determining the absorption coefficients using a probe, the function ϕL(ν) in Eqs. (2)–(4) should describe the contour of the photoluminescence band of the probe. Note that it is possible to determine the coefficient k0 using the criterion of the least square deviations between the photoluminescence contour ϕL(ν) and the normalized spectrum Itrue(ν) recovered using formula (1) from the measured dependence Imeas(ν). In this case, we should set k(ν) = k0ϕA,s(ν) in formula (1). Up to this point, we have discussed the analysis procedure in the measurement variant when the direction of propagation of the exciting and detected fluxes are perpendicular (right angle illumination). In [5], relations are given describing the changes in the photoluminescence intensity as a result of re-absorption for other measurement variants classified as in-line illumination and frontal illumination. Based on these relations, in analogy with (2), (3), we can obtain transcendental equations allowing us to determine the absorption coefficients. Let us give one such equation for 729

a component with overlapping photoluminescence and absorption spectra, like that shown in Fig. 1. Let us use relation (5) from [5]. It describes the change in photoluminescence intensity as a result of re-absorption for a detection direction in line with the direction of illumination. From the indicated relation, for k(νm) = 0 we obtain the following transcendental equation with one unknown: Imeas (νi) Imeas (νm)

=

ϕA,s (νex) ϕL (νi) 1 − exp [− k0l ϕA,s (νex) − ϕA,s (νi))] , ϕL (νm) [ϕA,s (νex) − ϕA,s (νi)] 1 − exp [− k0l ϕA,s (νex)] exp [k0lϕA,s (νi)]

(5)

wher e νex is the frequency of the radiation exciting the photoluminescence. Again the number of such independent equations with the same unknown k0 can be increased if the measurements of the photoluminescence intensity are made for a set of more than two frequencies. From them, we find the values of the absorption coefficient and the concentration of the component. Equations analogous to (5) can also be derived from relations (8), (9), obtained in [5] and describing the effect of re-absorption on the photoluminescence intensity. We note one more way to determine the absorption coefficients (and band contours) using measurement variants when the directions of the exciting flux and detection of photoluminescence coincide or they are in opposite directions. For these experimental setups, all the relations connecting the values of Imeas(ν) and Itrue(ν) go to Eq. (1) when k(ν)l >> kexl << 1. Therefore when the indicated inequalities are satisfied, in all the measurement variants we can make use of Eqs. (1)–(4) with the procedures and possibility stemming from them. Of course, in this case systematic error arises due to the approximation. The indicated inequalities are easily realized in the method using a luminescent probe. Equations for Determining the Absorption Coefficients from the Photoluminescence Excitation Spectra. Let us consider the problem of determining the absorption coefficients from measurement data for the photoluminescence excitation spectra. The relation describing the connection between the photoluminescence intensity at the frequency νdet, for a substance found in a multicomponent absorbing medium, and the absorption of this medium is given in [6, 7]. Let us rewrite it in the following form for a medium containing two components, one of which can be a luminescent probe: I (νdet, ν) =

Akp (ν) 1 − exp [− (l (kp (ν) + k (ν))] ν [kp (ν) + k (ν)]

.

(6)

In Eq. (6), I(νdet, ν) is the photoluminescence intensity of the probe at the frequency νdet for frequency ν of the exciting radiation; A is a constant factor; kp(ν) and k(ν) are the absorption coefficients of the probe and the analyte substance at the frequency ν. The factor A includes in particular the luminescence quantum yield, which is assumed to be independent of frequency within the limits of the excited photoluminescence band. The results we have presented on the measurements show that this hypothesis is correct. It is assumed that the absorption bands of both components overlap. The analyte substance may be nonluminescent. Let us assume that the conditions k(ν)l >> kp(ν)l << 1 are satisfied. In this approximation, from (6) we obtain an equation similar in structure to Eq. (1): I (ν) 

Akp (ν) 1 − exp [− (lk (ν))] νk (ν)

.

(7)

Just as relation (2) is obtained from (1), a transcendental equation is derived from (7) for determination of the absorption coefficient of the analyte substance: I (νi) I (νm)



ϕA,p (νi) ϕA,s (νm) 1 − exp [− k0l ϕA,s (νi)] . ϕA,p (νm) ϕA,s (νi) 1 − exp [− k0l ϕA,s (νm)]

(8)

The frequencies νi and νm in (8) belong to the radiation exciting the photoluminescence, the function ϕA,p(ν) describes the contour of the absorption band for the probe and is equal to unity at the frequency of the maximum of the con-

730

Fig. 2. The ratio I(νi)/I(νm) vs. k0l for ϕA,s(νi) = 1.0 and ϕA,s(νm) = 0.5 (1) and 0.2 (2).

tour. Let us assume that we can choose such a frequency ν = νm for which k(νm) = 0 and kp(νm) ≠ 0, i.e., only the probe absorbs at this frequency. Then from relation (7), we obtain a transcendental equation analogous to Eq. (3): I (νi) ϕA,p (νi) 1 − exp [− k (νi) l]  . (9) I (νm) ϕA,p (νm) k (νi) l Eq. (9), as is the case for (3), allows us to determine the absorption coefficients at different frequencies. In the case when the absorption band of the analyte substance completely overlaps the photoluminescence excitation band (the absorption band of the probe), using (9) we can find not only the coefficient k0 but also the contour of the absorption band of the substance. Let us consider the possibility of determining the concentration of a component of the medium from its own photoluminescence excitation spectrum. Let us assume that its absorption band does not overlap the absorption bands of other components of the medium. Relation (6) for such a component is rewritten in the form −1

I (νdet, ν) = Aν

1 − exp [− lk (ν)] .

(10)

If k(νdet) = 0, i.e., there is no absorption at the frequency at which the photoluminescence is detected, then for any measurement variants (at a right angle, in-line, frontal), the photoluminescence excitation spectrum is described by function (10). In the case k(νdet) ≠ 0, formula (10) remains valid for measurements of the photoluminescence excitation spectrum only in the variation where the orientation of the direction of excitation is at a right angle to the direction of detection of the photoluminescence. In this case, the factor A in (10) is transformed, but remains constant. From relation (10), we obtain the following transcendental equation for determining the absorption coefficient k0 of the component: I (νi) I (νm)

=

1 − exp [− k0lϕA,s (νi)] 1 − exp [− k0lϕA,s (νm)]

.

(11)

In Eqs. (8), (9), and (11), the factors νi and νm are omitted because during the measurements the number of photons was kept constant in excitation of photoluminescence at different frequencies. For small absorption values, when the condition k0lϕA,s(ν) << 1 is satisfied, from transcendental equation (11) we can obtain the usual equation with one unknown for determining the coefficient k0: k0l 

I (νi) ϕA,s (νm) ⎤ ⎡ ⎥. ⎢1 − I (νm) ϕA,s (νi) ⎦ [ϕA,s (νi) − ϕA,s (νm)] ⎣ 2

(12) 731

In deriving (12), we used three terms of the expansion of the exponential in a Taylor series with respect to the parameter k0lϕA,s(ν), just as in derivation of relation (4), and also the approximation [1 – 0.5k0lϕA,s(νm)]–1 ≈ 1 + 0.5k0lϕA,s(νm). As we see from the equation obtained, for unchanged measurement accuracy for the ratio I(νi)/I(νm), in order to reduce the lower limit for determination of the absorption coefficient, we should select the photoluminescence excitation frequencies so as to ensure the greatest possible difference between the quantities ϕA,s(νi) and ϕA,s(νm). This conclusion does not depend on the approximations made, and is also valid when using transcendental equation (11). The correctness of the conclusion is supported by the dependence of the ratio of the photoluminescence intensities (the right hand side of Eq. (11)) on the quantity k0l (Fig. 2). We see that the sensitivity of determination of the changes in optical density when using Eq. (11) will decrease as its magnitude increases. The range of measurable values is expanded with an increase in the ratio ϕA,s(νi)/ϕA,s(νm), as follows from comparison of curves 1 and 2. Note that for the same approximations for which relation (12) was obtained, from transcendental equation (2) we can derive the usual equation with one unknown for determining the quantity k0l from the measured photoluminescence spectra: k0l 

⎡ ϕL (νi) Imeas (νi) ⎤ ⎥. ⎢ ϕA,s (νi) − ϕA,s (νm) ⎣ ϕL (νm) Imeas (νm) ⎦ 2

(13)

Instrumentation and Objects of Investigation. The photoluminescence and photoluminescence excitation spectra were measured on an SFL-1211 A spectrofluorimeter (SOLAR, Belarus). We used a Cary-500 Scan spectrophotometer (Varian, USA) to record the absorption spectra. The proposed methods, based on measurements of the photoluminescence spectra, were tested with rhodamine 6G and methylene blue, the concentrations and optical densities of which are easily varied. For both compounds, the photoluminescence and absorption spectra overlap. Each substance was dissolved in ethanol. The functions needed for the calculations, ϕL(ν) and ϕA,s(ν), describing the contours of their photoluminescence and absorption bands, were determined in digital form (Fig. 1). The functions were determined from the corresponding photoluminescence and absorption spectra, recorded while satisfying the necessary conditions for elimination of systematic errors. The absorption coefficients were determined from the measured photoluminescence excitation spectra using formulas (11) and (12) with methylene blue and oxazine 17. The photoluminescence excitation spectra were measured for different absorption optical densities. The photoluminescence intensities were recorded at a right angle to the direction of propagation of the exciting radiation at λ = 740 nm and 670 nm respectively for methylene blue and oxazine. At these wavelengths, the absorption coefficients of methylene blue and oxazine themselves are equal to zero. The cuvet thickness was l = 1 mm. The luminescent probe method was tested with rhodamine 6G as the probe and the salts NdCl3, Er(NO3)3 as the analyte substances. The probe and one of the analyte substances were dissolved together in ethanol. We verified that the functions ϕL,p(ν) and ϕA,p(ν) did not vary when rhodamine 6G was dissolved together with the analyte substance. The absorption band of the neodymium salt with maximum at 578 nm overlaps the photoluminescence band of the probe, while the bands for the erbium salt with maxima at 487, 521, and 541 nm overlap its absorption band. This allowed us to determine the absorption coefficients by the luminescent probe method both with measurements of the photoluminescence spectrum and with measurements of the photoluminescence excitation spectrum. The main goal of the experimental studies in this stage was to demonstrate the feasibility and the possibilities of our methods. Analysis Method Using the Photoluminescence Spectra. In [5], for three variants of the relative orientation of the directions of excitation and detection of photoluminescence (right angle illumination, in-line illumination, and frontal illumination), the luminescence spectra were measured for the same rhodamine 6G solution in ethanol. We used the results of these measurements to determine the concentration of rhodamine 6G. The absorption coefficients were calculated from formulas (2), (5) and another formula obtained starting from relations (5) and (8) from [5]. We used the measurement results in the entire region of overlap between the photoluminescence spectrum and the absorption spectrum. From the three average values, each average obtained for one of the three indicated measurement variants, we found the arithmetic mean optical density D0(k0l = 2.3D0) = 1.685 for arithmetic mean error 0.012. Independent measurement of the absorption by the conventional procedure gave the value D0 = 1.695. Thus the pro732

Fig. 3. Measured photoluminescence (1) and optical density (2) spectra of methylene blue for D0 = 1.52 (a), 0.132 (b), 0.062 (c); calculation of the absorption spectra from formula (3) for λm = 730 (•), 725 (䉬), and 715 (䉱) nm. posed method allows us to determine with good accuracy the absorption optical densities from the photoluminescence intensities, measured in relative units. –1 From the value D0 = 1.685, we found the decadic absorption coefficient, equal to 8.425 cm , since l = 0.2 cm. Such an absorption coefficient corresponds to a rhodamine 6G concentration in ethanol of 7.26⋅10−5 mol/L, since the decadic molar extinction coefficient of rhodamine 6G in this solvent at the maximum of the contour is equal to –1 –1 1.16⋅10−5 M ⋅cm [9]. From the photoluminescence spectra, partially overlapping the absorption spectra, we can determine both a portion of the absorption band contour and the concentration of the substance. In order to test these possibilities, we measured the photoluminescence spectra of methylene blue for six values of the optical density D0 in the range 1.52–0.040. All the measurements were made for a relative orientation of the directions of excitation and detection at a right angle. Some of the data obtained are presented in Fig. 3. The photoluminescence intensities are reduced to the values ′ Imeas (λ) = aImeas(λ), where the factor a is found from the equality aImeas(λm) = ϕA,s(λm) for the wavelength λm at ′ which k(λm) = 0. Thus the photoluminescence spectra in Imeas units coincide with the function ϕA,s(λ) in the range in which there is no absorption, and are distorted by absorption in the region where k(λ) ≠ 0. Figure 3 also shows sections of the absorption spectra recorded by the usual procedure, with the aim of comparing with the calculations. For D0 = 1.52, 0.77, 0.50, the optical densities calculated from formula (3) agree well with the absorption band measured by the usual method (Fig. 3a). Discrepancies are observed only in the region of low photoluminescence intensities, where the signal-to-noise ratio is low and we need to average the results of many measurements to more accurately determine the optical densities. Measurements in this region were not used to determine the values of D0. For the three samples indicated above, from the measured photoluminescence spectra we determined the following 733

Fig. 4. Measured photoluminescence excitation spectra of oxazine 17, normalized to the maximum value of the photoluminescence intensity for D0 = 2.34 (1), 1.32 (2), 0.65 (3), 0.20 (4), 0.077 (5). values of the optical densities: D0 = 1.48, 0.74, 0.47. Each of them is the arithmetic mean of nine values calculated for three wavelengths λm, and agrees well with the values measured by the conventional procedure. For moderate and low absorption optical densities (D0 = 0.132, 0.062, 0.040), errors in determination of their values from the photoluminescence spectra increase. From Fig. 3b and c we see that the error in measurement of the intensity Imeas(λm) leads to underestimation or overestimation of all the D(λ) values calculated from formula (3) using this intensity value. The calculations using formula (3) give D0 = 0.127, 0.060, 0.035, averaged as indicated above. The largest difference (13%) between the values of D0 measured by the usual procedure and the calculated values were obtained for its very lowest value, D0 = 0.040. The values of D0 found (l = 0.2 cm) allow us to determine the concentration of the substance. The molar 4 –1 –1 extinction coefficient for methylene blue at the maximum of the absorption contour is equal to 7.4⋅10 M ⋅cm . –4 Consequently, from the measured photoluminescence spectra we determined its concentration in the range 1⋅10 – –6 2.4⋅10 mol/L. Expansion of the range of analyte concentrations is possible. For calculation of the optical densities according to formula (4), we used the results of the photoluminescence measurements for the sample with D0 = 0.062. The calculations were carried out for different λi and λm = 715, 725, and 735 nm, at which k(λm) = 0. We obtained the average value D0 = 0.061, very close to 0.062, which is evidence that the simplified formula (4) is suitable for determining the concentration of a substance from the photoluminescence spectra for moderate values of k(ν)l. Comparison of the optical densities calculated from the photoluminescence spectra and measured from the absorption spectra shows that the two independent methods give identical results within error limits. Analysis Method Using Photoluminescence Excitation Spectra. We measured the photoluminescence excitation spectra of methylene blue and oxazine 17 for different values of D0. For oxazine, some of them (normalized to the maximum value of the photoluminescence intensity) are shown in Fig. 4. We see changes in the spectra as the absorption optical density increases. We calculated the absorption optical density from the measured photoluminescence excitation spectra by several methods. In the first method, data from some of the photoluminescence excitation spectra were used for calculations according to formulas (11) and (12). In the second method, in formula (10), where it was assumed that k(ν)l = k0lϕA,s(ν), we selected the value of k0l for which the curve calculated according to (10) with the least square deviations matches the measured photoluminescence excitation spectrum. Using this method for oxazine 17, we obtained D0 = 2.32, 1.35, 0.68, 0.35, 0.197, 0.072. In this case, the optical densities measured for the same samples from the absorption spectra were D0 = 2.34, 1.32, 0.65, 0.34, 0.199, 0.077. From comparison of the calculated and measured values of D0, it follows that the two quite independent methods for determining the absorption optical densities give identical results within error limits. The same conclusion can be drawn from comparison of calculated values of the absorption optical densities and those measured from the absorption spectra of methylene blue.

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Fig. 5. Photoluminescence (1) and absorption (2) spectra of the system probe + neodymium salt + ethanol, the absorption spectrum (°) calculated from formula (3) for λm = 660 nm (a); (b) the absorption spectra of the neodymium salt calculated from formula (3) for λm = 660 (1), 620 (2) nm and measured according to the conventional procedure (3). Formula (11) was used for calculations of the optical densities of methylene blue from its photoluminescence excitation spectra. The optical densities varied within the range 0.156–1.960. The data obtained agree well with results calculated by the second method, and also those measured from the absorption spectra. The arithmetic mean errors of the values of D0 found vary within the range 8.0%–1.5%. The optical densities were calculated according to formula (12) using the results of measurements of the photoluminescence excitation spectra for a methylene blue sample with D0 = 0.067. From four calculated values, we obtained the arithmetic mean D0 = 0.0685. The arithmetic mean error in this quantity is 0.018. Thus formula (12) is suitable for determining the concentrations of substances from the measured photoluminescence excitation spectra for moderate values of k0lϕA,s(ν). Thus from the photoluminescence excitation spectra we can find the concentrations of substances over a broad range of their variation. Luminescent Probe Method. As noted, Eqs. (2)–(4) can be used to determine the absorption coefficients and concentrations of nonluminescent substances or substances whose absorption and photoluminescence spectra do not overlap. in order to realize this possibility, we should use a luminescent probe whose photoluminescence spectrum overlaps the absorption spectrum of the analyte substance. Figure 5a shows the photoluminescence spectrum (λex = 520 nm) of rhodamine 6G, dissolved together with the neodymium salt NdCl3 in ethanol. The experiments were carried out with orientation of the direction of propagation of the exciting radiation at a right angle to the direction of detection. This variant of the experiment ensures the independence of re-absorption of the photoluminescence relative to the absorption coefficient of the exciting radiation, and allows us to make use of formulas (2) and (3). As we see from Fig. 5a, the absorption spectrum of the neodymium salt calculated from formula (3) agrees rather well with that measured by the usual procedure. Note that the error in measurement of the photoluminescence intensity Imeas(λm), as follows from Eq. (3), leads to errors of the same sign in determining the optical densities from the entire absorption contour. Therefore all the calculated values of the optical densities (Fig. 5a) are higher than those measured by the standard procedure. From Fig. 5b we see how the measurement error for the intensity Imeas(λm) affects the results of determining the absorption contour. The contours determined from formula (3) for λm = 660 nm and 620 nm (Fig. 5b, curves 1 and 2) are located respectively above and below the contour measured by the usual procedure. In order to improve the accuracy of determination of the contours and absorption coefficients by the luminescent probe method, we need to do calculations using the intensities Imeas(λm) measured at different wavelengths λm. The average value of D0 determined using formula (3) from measurement data for the photoluminescence intensities is equal to 0.25; the value obtained from the absorption spectrum is 0.265. Let us consider the possibilities for determining the absorption coefficients and the concentrations using a luminescent probe whose photoluminescence excitation spectrum overlaps the absorption spectrum of the analyte sub735

Fig. 6. Photoluminescence excitation (1) and absorption (2) spectra of the system probe + erbium salt + ethanol; absorption spectrum calculated from formula (9) for λm = 470 nm (°). stance. Figure 6 shows the photoluminescence excitation spectrum of rhodamine 6G, dissolved in ethanol together with the erbium salt Er(NO3)3. The wavelength for detection of the photoluminescence was 570 nm. At this wavelength, there is no absorption for either the salt or rhodamine. The photoluminescence excitation spectrum of rhodamine is distorted by absorption of the erbium compound. These distortions allow us to use formula (9) to determine the contour and absorption coefficients of the salt. The average value of the optical density D0 determined from measurements of the photoluminescence excitation spectrum (in the band with maximum at λ = 521 nm) was 0.31; the value determined by the conventional procedure was 0.31. The absorption bands of the erbium salt at λmax = 487 nm and 541 nm also are determined well from the photoluminescence excitation spectrum of rhodamine 6G. The data obtained allow us to conclude that the luminescent probe method, using measurements of the photoluminescence or photoluminescence excitation spectrum of the probe, can be successfully applied for determination of absorption band contours and absorption coefficients and consequently the concentrations of substances. Conclusion. We have developed methods for quantitative luminescent analysis using measurements of the photoluminescence intensities in relative units and not requiring use of reference samples with known content of the components to be measured. We have experimentally demonstrated the feasibility and good accuracy of these methods and the broad range of substances (including nonluminescent substances) which can be studied by them. Let us note the basic results and assumptions which made possible development and realization of the methods. First we should mention the analytical relations obtained in [5–7], connecting the photoluminescence intensities and the absorption coefficients of the analyte medium. Without these relations, it would have been impossible to develop the proposed methods. The second circumstance enabling our success was the suggestion to use the ratio of the photoluminescence intensities detected at two wavelengths, or for two wavelengths of the exciting radiation. This allowed us to eliminate from consideration some unknown constants characterizing the substance and the experimental geometry. The third factor involves drawing on information about the contours of the photoluminescence bands or absorption bands of luminescent probes in measurement of the photoluminescence excitation spectra. These contours play the role of an unusual kind of reference which can be compared with the measured spectra, and the deviation of the measured spectra from these contours provides information about the optical densities of the analyte substances. Finally, we should mention the suggestion to use a function describing the absorption contour for the analyte substance, which enabled proper solutions of the inverse problems in all the cases considered. The proposed methods can be used in analytical and research practice in cases when direct measurements of the absorption of the analyte media are not possible; the media can be in any phase state: solid, liquid, or gas. The results of determination of the absorption coefficients do not depend on attenuation of the signals to be measured as a result of reflection by various surfaces, since the photoluminescence intensities are measured in relative units. In this case, a necessary condition is that the reflection coefficients do not change within the working spectral interval.

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The methods we developed make it possible to carry out remote measurements, and also measurements in processing volumes that are difficult to access. The state of the art and the options for radiation sources, fiber optics and computer technology make it easy to realize such measurements using the proposed methods. We would like to thank G. E Malashkevich for providing the neodymium and erbium salts.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

V. L. Levshin, Photoluminescence of Liquids and Solids [in Russian], Gostekhizdat, Moscow (1951). C. A. Parker, Photoluminescence of Solutions [Russian translation], Mir, Moscow (1972). J. R. Lakowicz, Principles of Fluorescence Spectroscopy, 2nd Ed., Kluwer Academic/Plenum Publishers, New York (1999). C. Ronda, ed., Luminescence: From Theory to Applications, Wiley, Weinheim (2007). A. P. Voitovich, V. S. Kalinov, A. N. Gorbacheva, and A. P. Stupak, Zh. Prikl. Spektr., 75, No. 6, 788–795 (2008). A. P. Voitovich, V. S. Kalinov, and A. P. Stupak, Zh. Prikl. Spektr., 75, No. 3, 365–371 (2008). A. P. Voitovich, V. S. Kalinov, and A. P. Stupak, Opt. i Spektr., 106, No 2, 255-261 (2009). M. A. El’yashevich, Atomic and Molecular Spectroscopy, 2nd Ed., E′ ditorial URSS, Moscow (2001). H. Du, R. A. Fuh, J. Li, A. Corkan, and J. S. Lindsey, Photochem. Photobiol., 68, No. 2, 141–142 (1998).

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