Anal. Chem. 1992, 64, 2596-2603
2586
Regular Solution Theory in Model Interpretation of the Analyte Losses during Preatomization Sample Treatment in the Presence of Chemical Modifiers in Electrothermal Atomization Atomic Absorption Spectrometry Petko B. Mandjukov,' Emilia T. Vassileva, and Vasil D. Simeonov Chair of Analytical Chemistry, Faculty of Chemistry, University of Sofia, J. Bourchier Blvd. 1, 1126 Sofia, Bulgaria
The Influence of the modHler concentratlon on the thermal stablllzatlon effect, the analyte Ioos klnetlcs, and the shape of the absorbancesignal have been studled In the case of lead determlnatlonuslng a tungstentontalnlng chemlcal modlfler. The experlmental results obtained were found to be In acceptable agreement wlth the theory of regular solutlons. Speclal attentlon has been pald to the model Interpretlng the problem of analyte loss klnetlcs as presented In the Ilterature. Already publlshed general rules for selectlon of modlflersand oplnlons concerning the mechanism of thermal stablllzatlon of the analyte have been crltlcally discussed.
INTRODUCTION The chemical modification (former term: matrix modification') is a commonly used technique in electrothermal atomic absorption spectrometry (ETAAS), as reviewed recently.2 The interest in clarifying the chemical modification mechanism and, more generally, processes taking place in the graphite tube atomizer is ever increasing. A large number of modern analytical methods were employed for this purpose, namely scanning electron micromopy,*5 X-ray dBraction,"JO X-ray photoelectron spectroscopy,*JOmass spectrometry,"" Rutherford back-scattering spectrometry,12 thermogravimetry? etc. Another widely used approach to study the mechanism of these processes are kinetic studies. A variety of techniques for kinetic data treatment and kinetic models has been proposed in the literature on ETAAS.13-26 The main (1) Ediger, R. D. At. Absorpt. Newsl. 1975, 14, 127-130. (2) Tsalev, D. L.; Slaveykova, V. I.; Mandjukov, P. B. Spectochim. Acta Reu. 1990,13, 225-274. (3) Welz, B.; Curtius, A. J.; Sclhlemmer, G.; Ortner, H. M.; Birzer, W. Spectrochim. Acta 1986,41B, 1175-1201. (4) Welz, B.; Schlemmer, G.; Ortner, H. M.; Wegscheider, W. Prog. Anal. At. Spectrosc. 1989,12, 111-245. (5) Mandjukov, P.; Niinistd, L.; Nykiinen, E. Unpublished data. (6) Wendl, W.; Muller-Vogt, G. Spectrochim. Acta 1984, 39B, 237242. (7) Wendl, W.; Miiller-Vogt,G. J. Anal. At. Spectrom. 1988,3,63-66. (8)Xiao-quan, Shan; Dean-xun, Wang; Anal. Chim. Acta 1985,173, 315-319. (9) Styris, D. L. Fresenius' 2.Anal. Chem. 1986,323, 710-715. (10) Droesler, M. S.; Holcombe, J. A. Spectrochim. Acta 1987, 42B, 981-994. (11) Sturgeon, R. E.; Mithcell, D. F.; Berman, S. S. Anal. Chem. 1983, 55, 1059-1064. (12) Misaelides, P.; Tsalev, D. L.; Slaveykova, V. I.; Mandjukov,P. B. In Selected Papers from the X X V I t h CSI, July 2-7,1989, Sofia; Poster (2-52; Tsalev, D. L., Ed.; Sofia, 1989; Vol. 7, pp 245-251. (13) Fuller, C. W. Analyst 1974, 99, 739-744. (14) Paveri-Fontana,S. L.; Tessari, G.; Torsi, G. Anal. Chem. 1974,46, 1032-1038. (15) Sturgeon, R. E.; Chakrabarti, C. L.; Langford, C. H. Anal. Chem. 1976,48, 1792-1807. (16) van den Broek, W. M. G. T.; de Galan, L. Anal. Chem. 1977,49, 2176-2186.
part of the kinetic investigations have been carried out in order to clarify the mechanism of atomization processes and/ or to explain the atomic absorption peaks' shapes. Several kinetic studies20,22924,25are treating the problem of atomization mechanism in the presence of chemical modifiers. The commonly used approach for kinetic investigations is the calculation of the apparent activation energy of possible chemical reactions by means of the Arrhenius plot method. The main advantage of this method is its simplicity, however the results obtained by this method, which concern the mechanism of processes in ETAAS, were classified by Sturgeon26 as "fiction" due to the problems with correct interpretation of the activation energy values. The processes of analyte losses during the preatomization thermal treatment were scantily studied.24~25~27Recently, several works were reported on the problem of kinetics of analyte losses during the preatomization thermal treatment of the ~ample~~t25 in order to study the mechanism of thermal stabilization. The graphite furnace is expected to be a system very close to thermodynamic equilibrium before the atomization step. Thus, thermochemical calculations and kinetic studies are more suitable for modeling the processes in a graphite furnace before the atomization stage rather than during the atomization. On the other hand, the preatomization processes are obviously responsible for the thermal stabilization of volatile analytes. The concepts about the mechanism of thermal stabilization by chemical modifiers in ETAAS can be classified in two groups: (i)formation of individual chemical analyte-modifier compounds with defined structure and properties;6,7,9,24,26(ii) formation of analyte-modifier solid solutions and/or isomorphous substitution of atoms (ions) in the modifier's crystal lattice by the analyte atoms (ions).2,2&33 (17)Genc, 0.; Akman, S.; Ozdural, A. R.; Ates, S.; Balkis, T. Spectrochim. Acta 1981,36B, 163-168. (18) Frech, W.; Zhou, N. G.; Lundberg, E. Spectrochim. Acta 1982, 37B, 691-702. (19) Chan-Huan Chung Anal. Chem. 1984,56, 2714-2720. (20) Droessler, M. S.; Holcombe, J. A. J. Anal. A t . Spectrom. 1987,2, 78.5-792. . - - . - -. (21) DBdina, J.; Frech, W.; Lindberg, I.; Lundberg, E.; Cedergren, A. J.Anal. At. Spectrom. 1987, 2, 287-291. (22) DBdina, J.; Frech, W.; Cedergren, A.; Lindberg, I.; Lundberg, E. J. Anal. At. Spectrom. 1987,2,435-439. (23) Cathum, S. J.; Chakrabarti, C. L.; Hutton, J. C. Spectrochim. Acta 1991,46B, 35-44. (24) Slaveykova,V. I.;Tsalev,D.L. Spectrosc.Lett. 1991,24,139-159. (25) Slaveykova, V. I.;Tsalev, D. L. Graphite Atomizer Techniques in Analytical Spectroscopy. XXVIIth CSIPre-Symposium,June 6-8,1991, Lofthus, Norway; Poster P-22. J. Anal. At. Spectrom. 1992, 7,365-370. (26) Sturgeon, R. Fresenius' Z. Anal. Chem. 1986, 324, 807-818. (27) Fuller, C. W. Anal. Chim. Acta 1972, 62, 442-445. (28) Wendl, W. Fresenius' 2.Anal. Chem. 1986, 323, 726-329. (29) Mandjukov,P. B.;Tsalev, D. L.Proceedings of the XIth National Conference on Atomic Spectroscopy, Sept 24-27, 1986, Varna-Drujba, Bulgaria; pp 321-322. J.A.J. Anal.At.Spectrom. (30) Tsalev,D.L.;Mandjukov,P.B.;Stratis, 1987,2, 135-141.
0003-2700/92/0364-2596$03.00/0 0 1992 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
The analyte loss kinetics seem to be an important check point to distinguish between the two prevailing concepts about the mechanism of thermal stabilization. The first, “entirely chemical”, concept allows one to treat the process of analyte losses by means of conventional models of chemical reactions (e.g. Arrhenius method for first order chemical r e a c t i o n ~ ~ ~However l ~ ~ ) . is it not dangerous to make conclusionsbased solely on comparison of experiments carried out under completely different conditions and with different analyte/modifier molar ratios? The second concept requires application of a different viewpoint to the processes in the graphite furnace. The specific properties and behavior of the solid solutions have to be taken into account. The aim of the present work is to propose a model of the processes causing analyte losses during the preatomization thermal treatment based on the theories describing solid solutions. This approach is expected to explain some observed effects connected to application of chemicalmodifiers,to avoid some contradictions in previous studies, which will be discussed later, as well as to provide information on the possible mechanism of thermal stabilization of volatile and moderately volatile analytes.
THEORETICAL SECTION Critical Approach to Application of the Arrhenius Method To Study Analyte Loss Kinetics. The Arrhenius method for treatment of analyte evaporation during the atomization or thermal pretreatment stage is based on the following equations: In (AIA,) = k(T)t + constant
(1)
In k(T) = E,/(RT) + constant
(2)
where A and A, are respective absorbance values, t is time, k(T) is the rate constant of the vaporization process a t absolute temperature T, E, is the activation energy of the reaction accepted as rate-limiting, and R is the universal gas constant (R-8.314Jmol-1K-1). Thevaluesofk(T)andE,areobtained by means of a least squares method (linear regression) in coordinates In (AIA,) vs t and In k(T) vs UT, respectively. The basic assumptions behind this method are (i) firstorder chemical reaction kinetics, (ii) monolayer distribution of analyte atoms on the surface of the graphite tube, (iii) no redeposition or recombination of the released atoms, and (iv) constant temperature (or constant temperature gradientI4) in the whole furnance. All these assumptions are more or less appropriate for investigation on the atomization processes if carried out without a matrix or chemical modifier. Especiallygood results are to be expected when the rate-limiting process is a gasphase chemical reaction. An attempt to employ a kinetic model, based on the analyte loss study, for investigation of the mechanism of chemical modification has been recently made.24~25The processes of analyte loss were treated as controlled by a first-order chemical reaction. The Arrhenius plot method was used for the determination of experimental values for the activation energies of the vaporization processes, E.(loss). The E,(loss) values obtained were compared with thermodynamic data for the standard enthalpies of chemical reactions, AHo. Despite the impressive coincidence of &,(loss) and AHo, (31)Tsalev, D. L.; Dimitrov, T. A.; Mandjukov, P. B.; J. Anal. At. Spectrom. 1990,5,189-194. (32)Mandjukov, P.B.;Tsalev, D. L. Microchem. J. 1990,42,339-348. (33)Tsalev, D.L.;Slaveykova, V. I.; Mandjukov, P. B. Chem. Anal. (Warsaw) 1990,35,267-282.
Ar
>
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Flguro 1. Scheme of a graphite tube wRh the solid residue after the drylng of the sample. The dots lndlcate the consldered analyte distribution In the solid and gas phases. The arrows show the Internal purge gas flow.
demonstrated by the authors in some cases, a number of suggestions and conclusions are still doubtful: (i) The proposed model supposes a comparative independence of the rate of analyte losses on the modifier concentration. For the formation of a chemical compound (e.g. PbW04), the presence of a large excess of W species is not required. Thus, the thermal stabilization effect for an analytemodifier couple has to be identical at considerably lower concentrations of the modifier. (ii) It is not clear why the E,(loss) values are compared with AHo of the corresponding chemical reactions calculated at one fiied temperature. The AHo is generallya temperaturedependent thermodynamic function. At the same time, the Arrhenius-plot method for treatment of kinetic data requires the apparent activation energy to be constant at least in the temperature range studied (eq 2). (iii) There are no obvious reasons to accept as a presumption the monolayer analyte distribution. The kinetic investigations, in the works cited above,were carried out in the presence of lO3-lO5-fold excess of the modifier. In such cases, it is difficult to believe that the analyte atoms may form a monolayer in contact with the gas phase. Furthermore, there is experimental evidence about the formation of up to a 1012-pm-thick crust of chemical species onto a graphite furnace from modifiers similar to the studied one (e.g. V(V)5J2).There is also evidence about random distribution of the analyte within the solids formed by the chemical modifier.10 Thus, the model proposed in24925 seems to be contradictory and inconsistent. Model. Chemical modifiers are normally used in a large excess (x100-1OOO0) as compared to the analyte. In such diluted mixtures, the uniform distribution of the analyte in a bulk refractory matrix, originating from the modifier, is more likely than the formation of a stoichiometric compound with analyte:modifier ratio close to 1:l. Due to their properties, these systems are expected to be closer to solid solutions than to chemical compounds. If one suggests formation of an analyte-modifier solid solution, the analyte thermal stabilization could be explained by decreasing of the equilibrium partial vapor pressure of analyte in the presence of a modifier. The importance of the partial vapor pressure for the analyte evaporation has been noted in the literat~re.~~#a-36 Several basic assumptions are supporting the model presented in this work (Figure 1):(i) After the drying procedure, the modifier forms a thick (in comparison to the the crystal lattice parameter) layer of solid refractory oxides or metallic species on the graphite surface. (ii) The analyte species are randomly distributed into the volume of the solid modifier. (iii) In the nearest to the surface gas volume, the analyte partial vapor pressure is equal to the equilibrium pressure at the corresponding temperature. (iv) The main process controlling the analyte removal from the (34)L’vov, B.V.;Ryabchuk, G. N. Spectrochim. Acta 1982,37B,673684. (35)McNally, J.; Holcombe, J. A. Anal. Chem. 1987,59,1105-1112. (36)McNally, J.; Holcombe, J. A. Anal. Chem. 1991,63,1918-1926.
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ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
graphite atomizer is convective gas loss. (v) All processes causing the analyte loases are considered as quasi-static, taking place under isothermal conditions. Several models treating the problem of partial vapor pressure of components of solid solutions are widely used. Ideal Solution. A general assumption of this model is that there are no energy changes associated with the rearrangement of the atoms. According to this model, the partial vapor pressure of the analyte (PA)should be directly proportional to its molar part ( X A )in the mixture with the modifier (Raoult’s law):
PA = P A O X A (3) where P A O is the equilibrium vapor pressure over the pure analyte substance at the studied temperature. Regular Solution. Since 1929,37the regular solution model is one of the most popular models of solid or liquid solutions.3fi3 The basic assumptions of this model are3-0 (i) complete randomness of the atoms of the components in the common crystal lattice, (ii) entirely configurational mixing entropy, and (iii) pairwise interactions between the atoms. According to this model
where 12 is Boltzmann’s constant (k = 1.380 622 X lk23J K-l), T is absolute temperature, c is the parameter connected to the structure of the solution (coordination number), W is the energy parameter, and U u , U M Mand , UAM, are the energies of pairwise interactions between structural units A-A (analyte-analyte), M-M (modifiepmodifier), and A-M (analytemodifier), respectively. The physical significance of the parameter W needs an additional explanation. It is the difference between the energies of interaction of similar structuralunits (e.g. A-A, M-M) and the energy of interaction between different ones (e.g. A-M). It should be noted that the interaction energiesare negative quantities.39-41~52Figures 2 and 3 show two cases of deviation from Raoult’s law with a positive and negative sign of the parameter W (eqs 4 and 5). Although there are very few cases of strictly regular (37) Hildebrand, J. H. J. Am. Chem. SOC.1929,51,66-80. (38) Hildebrand, J. H.; Prauenitz, J. M.; Scott, R. L. Regular and Related Solutions. The Solubility of Gases, Liquids and Solids; Van Nostrand Reinhold Co.: New York, 1970. (39) Hill, Terrel, L. An Introduction to the Statistical Thermodynamics; Nauka i izkustvo: Sofia, 1972; Chapter 20. (40) Lupis, C. H. P. Chemical Thermodynamics of Materials; NorthHolland (Elsevier Science Publishing Co., Inc.): New York, 1983;Chapter 15. (41) Freeman, Mark P.; Halsey, G. D., Jr. J . Phys. Chem. 1956, 60, 1119-1125. (42) Walling, J. F.; Halsey, G. D., Jr. J.Phys. Chem. 1958,62,752-755. (43) Walling, J. F.; Halsey, G. D., Jr. J. Chem. Phys. 1959,30, 15141517. (44) Slaveykova, V. I.; Tsalev, D. L. Anal. Lett. 1990,23,1921-1937. (45) Arpadjan, 5.; Karadjova, I.; Tserovsky, E.; Aneva, Z.J. Anal. At. Spectrom. 1990,5, 195-198. (46)Miller, J. N. Spectrosc. Znt. 1991, 3, 41-43. (47) Welz, B.; Schlemmer, G.; Voellkpf, U. Spectrochim. Acta 1984, 39B, 601-510. (48) Sedykh, E. M.; Belyaev, Yu. I.; Ozhegov, P. I. Zh. Anal. Khim. 1979,34, 1984-1992. (49) Slaveykova, V. I.; Tsalev, D. L. In Selected Papers from the X X V I t h CSZ, July 2-7, 1989, Sofia; Paper INV-37; Tsalev, D. L., Ed.; Sofia, 1989; Vol7. pp 85-112. (50) Tsalev, D. L.; Slaveykova, V. I.; Mandjukov, P. B. Proceedings of the 5th Colloquium Atompectrometrische Spurenanalytik, April 7-9, 1989, Konstanz, Welz, B., Ed.; Bodenseewerk Perkin-Elmer GmbH: Ueberlingen, 1989; pp 177-205. (51) MacLaren, R. 0.; Gregory, N. W. J . Phys. Chem. 1955,59, 184186. Alcock, C. B. Metalurgical Thermochemistry; (52) Kubaschewski, 0.; Pergamon Press: New York, 1979; Chapter 3.
1.4 1.2
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a
0.6 0.4
0.2 0.0 0.0
0.2
0.4
0.6
0.8
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Flgure 2. Positive deviation from RaouR’s law. Dependence of the analyte’s relathre vapor pressure P/Po value on the molar fractlon of
the modifier.
XI4 Flgure 3. Negative deviation from RaouR’s law. Dependence of the analyte’s relative vapor pressure PIP, value on the molar fraction of the modifler.
solutions, this model may be applied as a first approximation
to a large number of real liquid3’* and solid3fi3 solutions. As noted by Hill,39 the regular solution model cannot be expected to provide exact quantitative description of the properties of the solutions, but it can be used for qualitative (or semiquantitative) explanation of these properties. In all cases of solid solution models, the partial vapor pressure of the analyte depends strongly on its molar concentration. Thus, strong influence of modifier concentration may be expected on both the rate of analyte losses and on the maximum loss-free pretreatment temperature. Of crucial importance is the examination of the relations between the analyte loss rate and concentration of analyte-modifier mixture, i.e. to check experimentally whether or not the behavior of the studied system is similar to that of a solid solution. The lead-tungsten analyte-modifier couple24,Mwas selected in the present work as being very near to the basic requirements for the components of a regular solution. Furthermore, just for this couple the best coincidence of E,(loss) value and the calculated AHo of the corresponding chemical reaction was demonstrated: which was assumed as responsible for the analyte losses.24
EXPERIMENTAL SECTION Apparatus. All experiments were performed using two atomic absorption spectrometers: (i) Perkin-Elmer Model 23800, equipped with an HGA-400graphite furnace atomizer and a
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
Table I. Temperature Program for the HGA-400 and HGA-600 A
~~
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a Varied; see Figures 4 through 10. * A ramp time of 10 s was used in studies of maximum pretreatmenttemperatures and 1s in studies of kinetic of losses. A hold time of 30 s was used for the determination of maximum pretreatment temperatures. A higher atomization temperature than usually was used in order to provide uniformly efficient atomization at largely different modifier concentrations.eA 1-s ramp time was selected in order to provide slower atomization at selected temperatures and thus better accuracy in peak area measurements.
deuterium background corrector; (ii) Perkin-Elmer Zeeman 3030, equipped with an HGASOO atomizer and an AS-60 furnace autosampler. Atomic absorption signals were recorded on an Anadex dot matrix printer. A hollow cathode lamp for lead, operating in the continuous mode (operating current 10 mA), was used as a primary source of radiation. A spectral band-pass of 0.7 nm was selected to isolate the 283.3-nm lead line. Pyrolitically coated graphite tubes were used in all experiments. The temperature program for HGA-400 and HGA-600 used is shown in Table I. In all experiments when the Perkin-Elmer Model 2380G spectrometer was used, the 10-20-fiL aliquots of the samples were injected into the graphite furnace by means of Eppendorf and Plastomed pipets with dispensablepolypropylene tips. Reagents. All solutions were prepared from analytical-grade reagents. The tungsten stock standard solution (lo00 mg L-l) was prepared from W powder (Fluka)dissolved in HzOz Perhydrol (E. Merck) in a ratio 1 mL of 30% HzOz for 0.25 g of W, as d e s ~ r i b e d . The ~ ~ *lead ~ ~ stock standard solution (1000 mg L-l) of Hopkin & Williams Ltd. was used in all experiments. The diluted standard solutions of tungsten and lead were prepared daily. Double-distilled water (from all-quartz still) was used throughout.
RESULTS AND DISCUSSION Influence of the Modifier Concentration. The effect of the chemical modifiers used at low concentrations, as compared to those of the analyte, have been scantily studied.& The curves of the absorbance-normalized value vs pretreatment temperature for 0.05 mg L-1 lead in the presence of 12 different concentrations of tungsten-containing modifier (from 0 to 5000 mg L-l W) are presented in Figure 4. The results show a big increase of the maximum pretreatment temperature with an increase of the modifier concentration (Figure 5). These results give experimental evidence that it is impossible to treat adequately the problem of analyte loss kinetics by means of a simple chemical reaction model, without taking into account the analyte:modifier ratio. Rate of Analyte Losses. In case of fixed thermal pretreatment time (10-5 ramp and 30-5hold time), losses of lead occur a t a temperature of about 770 K (Figure 4). The investigation of the kinetics of lead losses was carried out at temperatures higher than the maximum loss-free pretreatment temperature by means of plotting absorbance vs time. The experiment design was similar to that described recent1y.24925 The main differences were (i) experiments were carried out in the presence of different concentrations of chemical modifier and (ii) absorbance was normalized versus the value obtained after heating with a 1-s ramp and a 1-s hold time.
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ii 4
0 0.0
0
j
0.2
,
.
,
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The analyte losses observed after such short pretreatment times are negligible even at high (1470 K) temperature for all concentrations of modifier. This initial point provides the possibility of studying losses occurring after short (less than 5 s) heating times. The shape of the curves for a pure lead solution in the absence of (Figure 6) and in the presence (Figure 7) of a chemical modifier are quite similar and in good agreement with the previous data.% The existence of a large time interval (from about 40 to 100 s in Figure 6, curves a-c) without further significant lead losses may be interpreted as indication of analyte condensation on the cooler furnace surfaces and subsequent evaporation and atomization. This effect may be observed a t temperatures up to 1170 K. At higher temperatures, the whole furnace is obviously hot enough to minimize the condensation. In the presence of a modifier, the rate of analyte losses is different than that in the case of pure analyte. At low concentrations, comparable to those of the analyte, the observed rate is higher, while in the presence of a larger excess of modifier, it becomes considerably lower and the fraction of vaporized lead is also smaller. According to the model described above, the value of the partial vapor pressure of lead species can be experimentally
2600
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
Pb
without modifier
Figure 8. Normallzed absorbance (peak area) vs pretreatment time Indicating the kinetics of lead losses from a pyrolttlcally coated graphtte surface In the absence of chemlcal mcdlfler: (a) 800 "C; (b) 850 OC: (c) 900 "C; (d) 950 "C; (e) 1000 O C ; (f) 1050 "C.
11. As expected, the values obtained are of the same order as the energy of the particle in the crystal lattice:
E = 3kT (8) The differences between the values obtained for different temperatures and the generalized value are acceptable if one keeps in mind the indirect way for estimation of PA/PAO and the influence of unavoidable experimental errors. This holds true especially for a temperature of 1473 K. On the other hand, it must not be forgotten that the energy parameter W itself is a slowly varying function (decreasing) of the temperature as indicated in ref 43. The quality of fit can be examined by means of linear regression. In the case of good agreement between the experimental data and the regular solution model, a straight line dependence should be expected between experimentally obtained values of ( P ~ P A O )and the calculated ones using data from Table I1 and eq 4. The correlation between measured and calculated data was checked out by the Student's t criterion using equation
evaluated from absorbance data of analyte residue in graphite furnace:
where A, and A,, are normalized peak area abosrbances obtained after heating for a fixed time at a fixed temperature of the analyte-modifier mixture (with analyte molar fraction X) and the pure lead solution treated in the same manner, respectively. Thus, it is possible to evaluate whether the W-Pb system studied can be treated as solid (ideal or regular) solution or whether it has completely different properties (e.g. as individual chemical compound PbW04). Equation 4 can be transformed into
Obviously, the function In [PA/(PAoXA)]is linear versus (1
- X A ) ~Figure . 8 shows a trend to linearity in the region of modifier concentrations up to XM2: 0.9 and large deviations in the presence of higher tungsten concentrations. In this region whenX~+O,andP~-O, thefunctionln [Pp/(PA"XA)I becomes extremely sensitive to any fluctuations of the experimental results. In this region, poor accuracy of the experimentally estimated functions result. Figure 8 is selected as an example from a series of similar relationships In [PA/ (PA'XA)] vs XM*at other temperatures. The significant deviations from linearity observed at higher temperatures can be explained by more significant changes of analyte: modifier ratio during the thermal pretreatment. More precise results can be obtained by means of a least squares fit method of the function P~PAO versus XAor XM (eq 4) in the whole concentration interval studied. In this investigation, the value of PA/PAOwas plotted versus the modifier molar fraction XM. Let us note, however, that the modifier molar fraction (XM)continuously changes during the process of analyte vaporization. In order to obtain more precise results, an additional experiment with shorter heating times (down to 2 s) was carried out. The results of this experiment are presented in Figure 9. The values of XMare corrected to the respective mean of the initial and final values, and the curves of PdPAo vs XMfor four different temperatures are plotted in Figure 10. The curves are quite similar to the theoretical ones (Figure 2) in the case of regular solution with c W < 0. The most probable values of the parameter c W/2k, calculated by the least squares method are presented in Table
where K,is the coefficientof correlation between experimental and calculated values and n is the number of points. The texp must be compared to the critical t value with confidence probability (a)and n - 2 degrees of freedom.46 In the case of statistically significant correlation texp> t&,n - 2) (10) The comparison of taxpwith t,, a t a = 0.95 (Table 11) shows a satisfactory correlation between the examined data arrays. Inequality 10 is satisfied also in case of a = 0.99. This proves the possibility of using the regular solutions model to describe processes of chemical modification although the system studied cannot be assumed to be a strictly regular solution. Probably, in further investigations more sophisticated models could be applied. The negative sign of c W, indicates that
(11) ~ U A>MUAA+ UMM i.e. 2WAM is less negative than the sum of WAA+ WMM. Therefore the existence of an analyte-modifier mixture in the case of the Pb-W system is less advantageous (in terms of energy) than the existence of separate phases (Pb and W carbides9 In such a case, the solid solution can be stabilized by the positive entropy of mixing (Figure ll), being a configurational one, according to the presented model: = -R(X, In XA
+ XM In XM)
(12) where R is the universal gas constant and XAand X Mare the molar fractions of analyte and modifier in the mixture, respectively. This effect seems to be quite reasonable for the mixtures of metal carbides and lead, concerning the low affinity of Pb to carbon. Let us note also that always ASMIX > 0. It is a different case to that of energy changes: ASMIX
AUMIx = -RXAXM(c w)/(2k) (13) where the effect depends on the sign of c W. In this case, c W < 0 and AUMIX > 0 (Figure 11). Thus, the probable reason for lead thermal stabilization by tungsten-containing modifiers can be assumed as a formation of substitutional solid solution of lead in tungsten refractory compounds promoted by the configurational entropy of mixing. The positive AUprovides a possibility of separation of the solid solution in two phases (most probably P b and W carbides) when tungsten and lead concentrations are comparable. In the presence of
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
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2= e c
TIME
0
P. 4.0
-
40
2.0
-
0
/
From this point of view, an interesting object of further investigations is also the chemical modifiers existing in the graphite furnace in the form of metals, e.g. Pd, Pt, etc., where a different type of analyte-modifier interaction might be expected. Shape of the Absorbance Signal. There are literature data about the influence of the chemical modifiers on the peak shape. Usually, it is expressed as an increase of the delay time of peak appearance4' and decreases of the slope
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER 1, 1992
2602
:"i lloo'c
80
60 40 1
5
0
6
7
0
Fbwo 0. Normalized absorbance (peak area)vs pretreatment time indicating the kinetics of lead losses from a pyroliticaiiy coated graphite surface in the presence of different concentrations of chemical modifier tungsten: (a) without modifier (points are marked by *); (b) 0.05 mg L-l; (c)0.5 mg L-l; (d) 1 mg L-l; (e) 2 mg L-l; (f) 5 mg L-'; (9) 10 mg L-l; (h) 50 mg L-l; (I) 100 mg L-l; (i) 500 mg L-l; (k) 1000 mg L-l; (I) 5000 mg L-l.
A I
2.0 ./
1.5
0.5
0.0
4
"r/
I
I'
h
1
I-
0.0
,
0.2
1
, -
04
7-
0.6
0.8
1 .o
Flguro 10. Influence of the modifier concentration (molar fraction)on the experimentally estimated relative partial vapor pressure of the analyte at different temperatures: (a) 1173 K; (b) 1273 K; (c) 1373 K; (d) 1473 K.
and temperature for the leading part of the peak, which is, by the way, a substantial presumption of the Arrhenius-plot method. Lookingat Ways To Achieve More Efficient Thermal Stabilization. Several important general conclusions can be derived from current study. (i) Recently, a series of papers concerning guidelines for the selection of chemicalmodifiers have been p~blished.~,s,49@' The suggestions for the selection are based generally on comparison of the maximum loss-free pretreatment temperatures for various analyte-modifier couples. According to the works cited above, the substantial criteria for a possible modifier design are connected to chemical parameters like acid-base properties, electronegativity, ion potential, polarizability, etc. For instance,increasingthe efficiencyofthermal stabilization for the modifier group below49 Ce < La < Y < Sc (14) is the same as increasing the acidic character of the oxides. On the other hand it is the same as decreasing the modifier
atomic mass (i.e. decreasing the analyte molar fraction in the solid mixture). Therefore we are convinced that it is dangerousto arrive at conclusionsby comparing the maximum pretreatment temperatures of a selected analyte element with different chemical modifiers with the same weight concentrations in the liquid sample. Due to the differences in their atomic masses, the molar concentration of the modifier in the solid residue in the graphite furnace may be quite different. Of course, in some cases, this correlation can be disturbed by the significant energy of interaction between species in the mixture. Nevertheless, neglecting the effect of concentration (i.e. the entropy factor) is always dangerous. The same conclusion is also valid for the "synergetic effecta"49," of thermal stabilizationprovided by mixed modifiers and "trends in Periodic Table group^".^ It is important to note that in the presence of mixed modifiers the system becomes threecomponent and it willbe an object of our future investigations. (ii) The processes causing analyte thermal stabilization cannot be described adequately as a simple chemical interaction. Application of thermochemical calculations, based on the changes of standard thermodynamic potential or standard enthalpy of reaction, using data for pure analyte compounds seems to be wrong. This approach is applicable probably only to the reactionsattaching the chemicalmodifier. In the case of an analyte, the consideration of mixture properties must be taken into account. (iii) The investigation of analyte loss kinetics may provide useful information about the mechanism of processes in a graphite furnace. However, it should be noted that the rate of loss after the first 5-7 s is already completely different and so is the analyte concentration. Thus, the most important information may be obtained during the first few seconds. The Arrhenius-plot method, obviously, is not quite suitable for the study of complicated systems, especially for studying the kinetics of analyte losses in the presence of a modifier. The process of analyte losses may be treated as a pseudofirst-order reaction due to the temperature dependence of equilibrium vapor pressure ( P ) of solid compounds. It can be approximated by using an empirical equation much similar,
ANALYTICAL CHEMISTRY, VOL. 64, NO. 21, NOVEMBER I, 1992
Table 11. Statistical Parameters of Simulation of the PlP, Function* temp/K c W/2k/K n A B 1173 1273 1373 1473 general
10 12 14 14 50
-7651.64 -7688.41 -8620.06 -9310.17 -7970.31
0.238 0.007 -0.082 -0.159 0.001
260) ~
0.661 0.974 1.010 0.960 0.823
K*
EA(PIPo)?
0.9124 0.9750 0.9069 0.7670 0.8515
1.183 0.148 0.711 1.917 4.502
tcr
t,P
6.305 13.869 7.457 4.141 11.253
2.306 2.228 2.179 2.179 2.012
n = number of experimental points; A = intercept of y-axis;B = slope; EA(P/Po)iz= sum of the squared deviations between calculakd and experimental values.
a
- 10
1
0.0
7
0.2
---A 0.6 0.8 1 .o
7
0.4
x,
Fburr 11. Effect of the modifier concentratlon of the basic ; factor thermodynamicvalues: (a)energy of mlxlng ( A ~ I ~(b)) entropy (-TAhIX); (c) free energy of mixing. The functions were calculated using the values for the mixlng energy parameter (cw) obtained at 1273 K (Table 11).
I
0.0
-
/
0.1 t
90 \ \
\ \
60
0.1
h
0
E:
t
I
AA
2 30
e
I
L
v
w
-\
0.0 0
- 3( 0
D
0.992
0.994
0.996
0.998
1.C
I
Flgurr 12. Enlarged presentatlon of the region of X, Figure 11.
> 0.99 from
from a mathematical point of view, to eq 2:
In P = A / T + B
Al-lE2hL 0.01.0
X M
(15)
where A and B are empirical c0n~tant.s.~~ (iv) The furnace conditions may also affect strongly the kinetics of the processes taking place in an atomizer for ETAAS. During the experiments in the present study, a significant increasing of the rate of losses was observed due to corrosion of the graphite furnace causing an increase of the injection hole diameter. The probable reason for this corrosion is 0 2 emitted during the decomposition of the excess of HzOz.
TIM / s
3.0
Fburs 13. Absorbance signalsfor a 0.05 mg L-I lead solutioncontaining different concentratlons of tungsten modlfler: (a)A wtthout modifier; (b) 0.05 mg L-l; (c)0.5 mg L-l; (d) 5 mg L-l; (e) 50 mg L-l; (f) 500 mg L-I. The volumes of the allquots were varled from 15 to 8 pL In order to obtain an absorbance of about 0.1 in all cases.
analyte thermal stabilization effect caused by chemical modifiers. It offers a possibility to overcome some contradictions and limitations of the previous “entirely chemical” models treating the problem on the mechanism of chemical modification in ETAAS. It seems to be possible to employ this approach for semiquantitative description of a large number of processes in the graphite furnace connected with the interferences in condensed phase and chemical modification. This will be a subject of further investigations.
CONCLUSION The regular solid solution model was proposed as a comparativelypowerful theoretical approach to describe the
RECEIVED for review April 27, 1992. Accepted August 6, 1992.
