ANALYTICAL CHEMISTRY, VOL. 50, NO. 8, JULY 1978
(4) H. Koizumi, T. Hadeishi, and R. D. McLaughlin, Submitted to Anal. Chem., 1977.
1105
(19) W. P. Kelly and C. 6. Moore, Anal. Chem., 45, 1274 (1973). (20) A. C. G. Mitchell and M. W. Zemansky, "Resonance Radiationand Excited Atoms", 2nd ed., Cambridge University Press, New York, N.Y., 1961. (21) H. Kuhn, Proc. R . SOC. London, Ser. A , , 158, 212 (1937). (22) R. A. Mostyn and A. F. Cunningham. Anal. Chem., 39, 433 (1967). (23) S. Yasuda and H. Kakiyama, Jpn. Anal., 23, 620 (1974). (24) Y. Endo and Y. Nakahara, J . Iron SteelInst. Jpn., 59 (6), 800 (1973). (25) "Experimental Transition Probabilities for Spectral Lines of Seventy Elements", Natl Bur. Stand. (U.S.), Monogr., 53 (1962). Clrc., 467 (1958). (26) "Atomic Energy Levels", Natl. Bur. Stand. (U.S.), (27) "MIT Wavelength Table," John Wiley and Sons, New York, N.Y., 1939. (28) "Coincidence Tables for Atomic Spectroscopy", Elsevier Publishing Co. Amsterdam, 1965. (29) D. C. Manning, Private Communication (1977). (30) S. Slavin, Private Communication (1977). (31) J. A. Galeb and C. R. Midkiff, Jr., Appl. Spectrosc., 29, 44 (1975).
(5) W. Slavin, At. Absorp. Newsl., 24, 15 (1964). (6) S. R. Koirtyohann and E E. Pickett, Anal. Chem., 37, 601 (1965). (7) J. Kuhl, G. Marowsky, and R. Torge, Anal. Chem., 44, 375 (1972). (8) T. Hadeishi, D. A. Church, R . D. McLaughlin, 6. D. Zak, M. Nakamura, and 6. Chang, Science, 187, 348 (1975). (9) H. Koizumi and K. Yasuda, Spectrochim. Acta, Part.6, 31, 237 (1976). (IO) R. J. Lovett, D. L. Welch, and M. L. Parsons, Appl. Spectrosc., 29, 470
(1975). (11) A. T. Zander and T. C. O'Haver, Anal. Chem., 49, 838 (1977). (12) "Contemporary Topics in Analytical and Clinical Chemistry", Volume 2, D. Hercules, Ed., Plenum Press, New York, N.Y., 1978. (13) V. A. Fassel, J. 0. Rasmuson, and T. 0. Cowley, Spectrochlm Acta, Part 6,23, 579 (1968). (14) J. D. Winefordner, W. W. McGee, J. M. Mansfield, M. L. Parsons, and K. E. Zucha, Anal. Chlm. Acta; 36, 25 (1966). (15) 6. V. L'vov, Zh. Anal. Chem., 26, 510 (1971). (16) S. Slavin and T. W. Sattur, At. Absorp. Newsl., 7, 99 (1968). (17) J. E. Allan, Spectrochlm. Acta, Part B , 24, 13 (1969). (18) D. C. Manning and F. Fernandez, At. Absorp. Newsl., 7, 24 (1968).
RECEIVED for review February 13, 1978. Accepted April 7, 1978.
Shape and Position of the Analytical Response in Flameless Atomic Absorption Spectrometry Jdnos Zsak6' Department of Chemistry, University of Constantine, Constantine, Algeria
An equation is proposed for the description of slgnals in flameless atomic absorption spectrometry, by presuming a simplified model and the validity of the Arrhenius equation. Theoretical signals have been constructed and the influence of heating rate and of kinetic parameters Is discussed. The possibility of deriving kinetic parameters from the shape and position of the signals is shown. The physical significance of kinetic parameters is dlscussed.
T = To
+ art (with
QI
d T / d t = const.)
=
(3)
as well as the validity of the following Arrhenius type law:
K = Z exp(-EIRT)
(4)
From Equations 2, 3, and 4, Torsi and Tessari (1) obtain
9 nt = Z q -U exp(-EIRT)
(5)
and Flameless atomic absorption spectrometry (FAAS) is based upon a heterogeneous process occurring in dynamic temperature conditions, viz. the evaporation of atoms during thermal flash. A theoretical model of the process has been proposed by Torsi and Tessari (1). According to these authors, by presuming a monoatomic layer distribution, the rate of evaporation of the sample to be analyzed can be written as
d6
82
dt
a
- - - --
exp(-EIR T )
THEORETICAL SHAPE OF THE SIGNALS The solution of Equation 6 is not discussed by Torsi and Tessari. The variables are separable, but the integration is not possible in finite form. By introducing the variable u = E / R T and the notation
e-" -Jz7 du
p ( ~= ) where q is the surface concentration at d = 1 , d is the fraction of surface coverage, t is the time, and K is the apparent rate constant for the evaporation. The concentration nt of atoms in the gas phase is obtained by dividing Equation 1 by the linear velocity v of the evaporating atoms,
U
one has ( 2 )
E R
J(: e x p ( - E / R T ) d T = - p ( x )
(7)
and the solution of Equation 6 can be given as This magnitude is presumed to be prpportional to the instantaneous absorbance. Thus, the equation of nt gives a theoretical description of the signal obtained in FAAS. Further, a linear temperature variation program is presumed Permanent address, Faculty of Chemistry, Babes-Bolyai University, Cluj-Napoca, Rumania.
0003-2700/78/0350-1105$01 .OO/O
since for T = 0, one has d = 1. Equations 5 and 8 give
1
nt = - e x p --x zq u
+p
( x )
R zEa
0 1978 American Chemical Society
I
(9)
1106
ANALYTICAL CHEMISTRY, VOL. 50, NO. 8,JULY 1978
i
1
6 60F-
- 1000 I
0
5 Heatfng rate (X)’K sx 7
I
10
I
Figure 2. Influence of heating rate upon the peak characteristics. E = 10 kcal mol-‘, Z = lo2 s-‘, q / v = l o i 3 atoms s
Tme (seci
Figure 1. Influence of heating rate upon the FAAS signals. E = kcal mol-’; Z = 102s-’;q / v = atoms ~ m s.- Heating ~ rate:
loi3
103,(2) 2 x 103,(3) 3 x 103,(4) 4
x
103, (5)5
x 103 K
10 (1)
s-1
Since the numerical values of the exponential integral p ( x ) are tabulated ( 3 ) , and to a first approximation the linear velocity of the evaporating atoms can be presumed to be constant, Equation 9 allows us to construct theoretical signals and to study the influence of the heating rate a and of the parameters E and 2 upon the theoretical shape of the signals. The main characteristics of the signal are the peak temperature T, and the concentration maximum ( n J , corresponding to this temperature. Concerning these magnitudes, Torsi and Tessari ( I ) give the following relations:
R In T , - l n a =
E RTm
ZR E
-- In -
T h e last one can be written as
T, =
E R(ln Z R T m 2- In E
-
In a)
(11)
Torsi and Tessari ( I ) presume 29, and T, to be independent of the heating rate a and therefore, according to Equation 10, they expect a linear increase of the analytical sensitivity by increasing a. Since Equation 11 suggests T , to increase by increasing a , in reality one cannot expect ( n J , to be a linear function of a.
INFLUENCE OF HEATING RATE AND OF KINETIC PARAMETERS E AND 2 I n order to test the influence of the heating rate, several theoretical signals have been calculated by using Equation 9. In these calculations, tabulated p ( x ) values and the following parameter values have been used: E = lo4 cal mol-I, 2 = lo’s-*. Some of the resultant curves are given in Figure 1. Numerical values of the concentration nt correspond to the arbitrarily chosen ratio q / u = atoms cm-3 s and they are represented both vs. temperature ( a ) and vs. time ( b ) . As seen from Figure 1, the peak temperature T , is not constant; it increases by increasing heating rate. On the other hand, the concentration maximum, i.e. the analytical sensitivity, increases by increasing a , as expected on the basis of Equation 10. Figure 2 shows the peak characteristics for the same E and 2 parameters as a function of the heating rate. It is obvious,
that the peak coverage 6, is practically constant, as presumed by Torsi and Tessari ( I ) , but the peak temperature varies importantly with the heating rate. This is why the variation of (at),,,is not linear. It is worth mentioning, that the shape of the last curve is the same as found experimentally by Torsi and Tessari ( I ) in the case of chromium. These authors presume the nonlinear character of the curve to be due to the imperfection of their model, but our results show this curve to be in good agreement with this model. According to Equation 9, the shape and position of the signal depends also upon the kinetic parameters E and 2. These are introduced by presuming the validity of an Arrhenius type law for the apparent rate constant of the evaporation. The validity of the Arrhenius equation is proved only for homogeneous systems and its application in heterogeneous kinetics is not an entirely correct approach ( 4 ) and the parameters E and 2 cannot have the same physical significance as in homogeneous kinetics. It is not justified a t all to consider E as being an “activation energy”, or 2 a “frequency factor”. The physical significance of E and 2 is completely obscure; their part is to allow Equation 9 to describe a great variety of signals. In order to clear up the influence of the kinetic parameters upon the shape of the signals, a great number of curves have been calculated by using Equation 9 and different E and 2 values. Some of them are presented in Figure 3. Figure 3a shows the influence of E. It is obvious that increasing E increases the peak temperature, but the heights of the signals decrease. Figure 3b shows a similar influence of decreasing 2 values. Since both E and 2 influence the peak temperature and the signal intensity, there must be an infinite number of E and 2 pairs ensuring the same peak temperature, and also an infinite number of such pairs ensuring the same peak height. Figure 4 shows some “isotherms” of this kind, and also several curves corresponding to the same peak height value. In Figure 5 , several theoretical FAAS signals are given, corresponding all to the same peak temperature T, = 1500 K, but their shapes are different. The peak area usually corresponds to the total amount of the analyte, Le., to a first approximation the product of the peak height and of the peak width is constant. This is why in Figures l b , 3, and 5 , the peak area is the same for all curves. Consequently, all conclusions referring to the peak height can be properly extended to the peak width, the latter being inversely proportional to the former.
DISCUSSION On the basis of the above given examples, it is obvious that Equation 9, developed in this paper, is able to describe a great variety of FAAS signals. Parameters E and 2 determine together the peak temperature and the peak height and so
ANALYTICAL CHEMISTRY, VOL, 50, NO. 8, JULY 1978
1107
Flgure 5. FAAS signals with the same temperature. T, = 1500 K. CY = 2500 K s-’, q / v = 1013 atoms ~ m s.- (1) ~ E = 85.4kcal mol-’, Z = 1014s-; (2)E = 58.7 kcal mol-’, Z = 10‘’ si; (3)E = 33.2kcal mol-’, Z = l o 6 s-l; (4) E = 20.6 kcal mol-’, Z = l o 4 s-’
Temperature 1K)
Figure 3. Influence of €and Zupon FAAS signals. (a) Influence of E. CY = 2500 K s-l, Z = l o 4 s-’, q / v = loi3 atoms ~ m s - (1) ~E= 5, (2)E = 10, (3) E = 20,(4)E = 40 kcal mol-’. (b) Influence of Z. cy = 2500 K s-’, E = 20 kcal mol-’, q / v = atoms ~ m s- (1) ~ z = ioio, (2) = 108, (3) = 106, (4) z = 104 s-1
z
2
loi3
z
4
8
6 log z
10
12
14
’
Figure 4. Dependence of peak temperature and of signal height from the parameters € a n d Z. cy = 2500 K s-‘, q / v = loi3 atoms S
there is a possibility to derive an E and 2 value, taking in account the position and the shape of the signals. We must emphasize once again, that we can tell nothing about the physical significance of these “activation energy” and “frequency factor” terms; however, it is clear that an E-2 pair can characterize a FAAS signal, but we cannot state that these kinetic parameters do characterize the substance to be analyzed, irrespective of working conditions. Taking in account Torsi and Tessari’s remark, that “the temperature of
the peak of chromium vaporization remains practically unchanged despite the large variation in heating rate” ( I ) , one can presume that in FAAS appears a similar phenomenon as with the thermal decomposition of solids in the conditions of thermogravimetric (TG) analysis. Kinetic analysis of T G curves has shown the possibility to characterize T G curves by means of the same kinetic parameters E and 2 as the above discussed FAAS signals. These parameters do not characterize a chemical reaction, but only a single T G curve. The variation of working conditions implies a systematic variation of both E and 2 values. In many cases a linear variation of E with log 2 has been observed (e.g., 5-7) and it has been called the “kinetic compensation effect”. Torsi and Tessari’s experimental results concerning the increasing signal intesity with increasing heating rate, at practically the same temperature, suggests the idea that with increasing heating rate, both E and 2 values must increase (cf. Figure 5 ) . In order to clear up the physical significance of the “kinetic parameters” E and 2,it is necessary to derive these parameters from a great number of experimental FAAS signals and t o study the influence of working conditions upon them.
ACKNOWLEDGMENT Thanks are due to A. Rehioui, director of the Department of Chemistry, University of Constantine, for helpful discussions and for encouragement during the course of this work. LITERATURE CITED (1) G. Torsi and G. Tessari, Anal. Chem., 45, 1812 (1973). (2) J. Zsakb, J . Therm. Anal., 8 , 593 (1975). (3) “Handbook of Mathematical Functions”, M. Obranowitz and 1. A. Stegun, Ed., Dover Publ. Inc., New York, N.Y., 1965,p 238. (4)J. Zsakb, J. Therm. Anal., 5 , 239 (1973). (5) J. Zsakb and M. Lungu, J. Therm. Anal., 5 , 77 (1973). (6) J. Zsak6 and H. E. Arz, J . Therm. Anal., 6, 651 (1974). (7) J. Zsakb, Cs.VBrhelyi, G. Llptay, and K. SzilBgyi, J. Therm. Anal., 7 ,
41 (1975).
RECEIVED for review November 3,1977. Accepted March 20, 1978.
