3. In the absence of interferents, the precision and detection limits of SWS and DWS are normally comparable. DWS may, however, be more precise than SWS where the latter measurement has substantial associated sample presentation error. 4. In the presence of interferents, DWS precision is markedly reduced because of increase of independent and square root errors. In particular, dark current noise may become significant under these conditions. 5 . T h e use of very small wavelength differences, as in differential spectroscopy, results in poor measurement precision. While the above conclusions are generally valid, it must be stressed t h a t the different functional dependences of errors of different types on A I and D lead to a complex overall dependence which will vary with individual instruments and measurements. T o some extent, therefore, it is appropriate to consider each instrument and each type of measurement as a special case.
LITERATURE CITED (1) (2) (3) (4)
B. Chance, Rev. Sci. Instrum., 22, 634 (1951). B. Chance, Methods Enrymol., 24, 322 (1972). T. J. Porro, Anal. Chem., 44 (4), 93A (1974). S . Shibata, M. Furukawa, and K. Goto, Anal. Chim. Acta, 46, 271 1969). (5) S Shibata, M. Furukawa, and K. Goto, AnalChim. Acta, 53, 369 1971). ( 6 ) S.Shibata, K. Goto, and Y. Ishiguro, Anal. Chim. Acta, 62. 305 1972).
(7) R . L. Sellers, G. W. Lowry, and R. W. Kane, Am. Leb, March (1973). (, 8,) S. M. Gerchakov. Saecfrosc. Lett.. 4. 403 (19711. (9) J. D.Ingle, Jr., and's. R . Crouch, Anal Chem., 44, 1375 (1972). (10) J. D. Ingle, Jr., and S. R . Crouch, Anal Chem., 44, 785 (1972). (11) J. D. Ingle, Jr., Anal. Chem., 45, 861 (1973). (12) C. D. Rothman, S . 3. Crouch, and J. D. Ingle, Jr.. Anal. Chem., 47, 1226 (1975). (13) H. L. Pardue, T. E . Hewitt, and M. J. Milano, Clin. Chem. ( Winston-Salem, N . C . ) . 24, 1023 (1974). (14) P. C. Kelly and G. Horlick, Anal Chem., 45, 518 (1973). (15) K . Steiglitz, "An Introduction to Discrete Systems", Wiley, New York, N.Y., 1974. (16) K . L. Ratzlaff. K . R. O'Keefe, and E. F . S . Natusch, manuscript in preparation. (17) V i . J . McCarthy, in "Spectrochemical Methods of Analysis", J. D. Winefordner, Ed., Wiley, New York, N.Y., 1971, pp 493-518. (18) RCA Photomuttiplier Manual, RCA E!ectronic Components, Harrison, N.J., 1970. (19) H. V. Malmstadt, M. L. Franklin, and G. Horlick, Anal. Chem.. 44 (8), 63A (1972). (20) M. L. Franklin, G. Horlick, and i-l.V. Malmstadt, Anal. Chem., 41, 2 (1969). (21) H. V. Malmstadt, C. G. Enke, S. R. Crouch, and G. Horlick, "Optimization of Electronic Measurements", W. A. Benjamin, Menlo Park, Calif., 1973. (22) W . Heller, H. L. Bhatnager, and M. Nakagaki, J Chem. Phys., 36, 1163 (1962). (23) K. L. Ratzlaff 2nd D.F.S. Natusch, submitted to Anal. Chem. (24) J. D.Defreese. Ph.D. Thesis, University of Illinois, Urbana, IN, 1975.
RECEIVED for review January 19, 1976. Resubmitted December 20,1976. Accepted August 22,1977. This work was supported by the National Institute of Environmental Health Sciences, NIH, under Grant No. 7-R01 ES 01472- 01.
Supply and Removal of Sample Vapor in Graphite Thermal Atomizers Wim M.
G. T.
van den Broek and Leo de Galan"
Laboratorium voor Analytische Scheikunde, Technische Hogeschool, P. 0. BOX 5029, Delft, The Netherlands
The timedependent supply and removal of sample atoms have been measured separately for two commercial graphite thermal atomizers. I n either type the release of the atoms from the graphlte wall Is determlned by the wall temperature and descrlbed by an Arrhenlus-type rate constant. With common heatlng rates, the equivalent tlme constant Is about 1 8. The removal of the atoms from the cell depends on the type of atomizer used. I n the Varian Techtron mlnlfurnace, dlffuslon Is the domlnatlng process and the equlvalent time constant is less than 70 ms. I n the larger Perkln-EIPner furnace operated under flow conditions, convection leads to equally small time constants. I f , however, the argon flow is slopped completely, dlffudon and, to some extent, expansion raise the time constant to about 1 s. Theoretical analysis and experimental measurement show that only In the latter case some 25% of the sample can be contained in the cell. Under common operating conditions, this efficlency is less than 10%.
T h e great sensitivity and the correspondingly low limits of detection of the thermal atomizers in atomic absorption spectrometry stem from the ability to contain a substantial amount of the analyte in the observation zone for a finite period of time. The basic condition towards the realization of this goal has first been formulated by L'vov ( 1 ) : the rate of supply of the analyte into the observation region must a t least be equal to its rate of removal from this zone. There is no doubt that constricted, furnace-type atomizers fulfil this 2176
ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
condition better than open filament-type atomizers. This advantage partly explains the waning interest in the latter type atomizers in favor of the enclosed cylindrical graphite cuvettes. Of the different designs described in the literature or commercially available, two extremes have beccme popular and typical: a Varian Techtron minifurnace with a lengthldiameter ratio of 3 and a Perkin-Elmer furnace with a length/diameter ratio of 6. However, a t present very little is known about t h e timedependence of the analyte supply into and its removal from either type of furnace. Henceforth, their efficiency in containing the analyte inside the graphite enclosure i s equally unknown. I t is true t h a t t h e mechanism of sample release from the graphite wall has received increased attention in the past few years (2-4), but the time-dependence and the shape of the transient signal has been considered in only a few papers. Fuller ( 5 ) assumes a very simple model consisting of two exponentials to describe the release and removal of copper in a Perkin-Elmer HGA-70 graphite furnace. He concludes from curve fitting his transient absorbance signal that the rate of removal exceeds the supply rate 3-20 times, depending on the atomization temperature. A much more thorough study has been described by Tessari, Torsi, and Paveri-Fontana (6-8), who describe the supply of the analyte by an Arrhenius-type rate constant and relate the removal of the analyte to diffusion and convection. Unfortunately, these investigations refer t o a home-made open graphite rod atomizer and their data cannot be used for t h e enclosed commercial furnaces. Recently, Sturgeon and Chakrabarti
(9) studied the removal of analyte vapor from an enclosed furnace, but it will be shown that their data on removal rates may be subject to a serious systematic error. The major object of the present study is the accurate and independent measurement of the supply and the removal of analyte vapor under typical analytical conditions in two commercial atomizers. The actual mechanisms of sample supply and removal need not be known to obtain quantitative data from which conclusions can be drawn about the efficiency of sample containment of either furnace. However, it appears that the results can be interpreted in terms of relatively simple expressions and vapor loss mechanisms.
THEORY Relation between Absorbance a n d N u m b e r of Atoms i n s i d e t h e F u r n a c e . Experimental information about the number of analyte atoms inside the cylindrical furnace is obtained by measuring the absorbance of a characteristic spectral line. At any moment, t , the relation between these two quantities can be expressed through Beer’s law as
A(t)=
0.4 3 2 & x 2 e’ h2fgo L H(t , x ) d N (t,x,Ay ,A z )
mc2 Z
1
o
Ah,(t,x)AyAz
where e and m are the charge and the mass of the electron, c is the velocity of light, X and f a r e the wavelength and the oscillator strength of the resonance line considered and go and 2 are the statistical weight of the ground state and the partition function of the element in concern. All these factors are independent of the time, t , and the position, x , along the line of observation, but the same is not necessarily true of the terms under the integral sign. Here AXD is the Doppler width of the atomic absorption line inside the furnace and H allows for the shift and collision width of this absorption line in relation to the width of the hollow-cathode primary source line ( I O , 11). Finally dN(t,x,Ay,Az) is the number of analyte atoms inside a small volume dxAyAz and the integration extends over the length, L , of the furnace. The awkward integral in Equation 1 is easily solved by introducing the following approximations. (i) The Doppler width, AXD, and the line shape factor, H, both increase with the gas temperature, T ( t , x ) ,inside the furnace and, hence, depend upon the time, t , and the position, x , of observation. Fortunately, the ratio is much less temperature-dependent than either factor and its variation over the tube length is less than 10% a t any time. This will allow us to place this ratio before the integral sign. In a second approximation we shall also ignore the time-dependence of this ratio, so that we can equate the variation of the atom number with that of the absorbance. This is not entirely valid during the initial rapid heating of the furnace, as will be discussed below. (ii) Narrow beam observations across the furnace revealed that the variation of the absorbance over the diameter of the furnace is less than 10% for the minifurnace and less than 25% for the larger furnace. This allows us to assume a homogeneous distribution of the atoms over the cross section of the furnace, s. The ensuing uncertainty in the proportionality between absorbance, A , and atom number, N , is less than 10% in all cases. I t should be noted that the atoms need not be distributed homogeneously over the tube length, because the measured absorbance always reflects the integral of the number density along the line of observation. Insofar, however, as the atoms persist in front of the furnace, the effective tube length may be larger than the geometrical length, L. This will also be discussed below. With these approximations, Equation 1 becomes
0.4 3 2 4 w e 2 h*gof H
A ( t )=
N(t)
mc2AhDZs
where N ( t ) is the time-dependent total number of analyte atoms in the furnace. The uncertainty in the proportionality factor between absorbance and atom number arises mainly from the oscillator strength, f , and the line shape factor, H . The latter was estimated from the studies by Wagenaar and de Galan in flames (12). Note, however, that this uncertainty only impairs the absolute application of Equation 2 in estimating the furnace efficiencies. I t is unimportant for the analysis of the time-dependence of the transient signal, which is the major object of the present investigation. Time-Dependence of t h e Atom Number. Two approaches have been proposed in the literature to describe the variation of the number of analyte atoms in the furnace. The first originates from L’vov (1)and has also been utilized by Fuller ( 5 )
“““‘=(““j -(g) dt
dt
in
out
(3)
where the two terms on the righthandside express the rate of supply and the rate of removal of the atoms. In the maximum of the transient absorbance signal, the rates are equal. I t is tempting to assume t h a t the rising slope of the transient signal is equal to the rate of supply ( 4 ) and that the falling portion of this signal is determined entirely by the rate of removal (9). However, Equation 3 shows that this is true only if the smaller term in the difference is negligible in comparison with the larger one. If this condition is not fullfilled, a systematic error is made. Although Equation 3 is quite general, it can only be solved for special cases. Indeed, it is generally assumed that (dN/dt)o,,tis proportional to N ( t ) . This is equivalent to an exponentially decaying removal of the atoms. However, this is not always observed in practice. Also, the formulation of N ( t ) in terms of a differential equation does not lend itself easily for experimental analysis. To this end, a second approach formulated by Tessari et al. (6) is more useful. Here, the rate of supply is retained, but the timedependent variation of N ( t ) is expressed as a convolution
‘ N ( t )= I f S ( t ‘ ) R (-t t ’ ) d t ’ 0
(4)
where S ( t ) = (dN/dt)i, is the supply rate of the atoms and R ( t ) is the normalized response of the system (Rmu= 1)upon the supply of an infinitely rapid pulse of atoms. This formulation is equally general as Equation 3 but it is much more amenable to experimental verification. T o this end we shall review a few properties of the convolution integral. (i) If the removal function R ( t )is very rapid in comparison to the supply function, then
where TR is defined as the equivalent time constant of the removal function. Thus the shape of N ( t )or A ( t )in this case reflects the time-dependence of the supply function. Conversely, if the supply of the analyte vapor is very rapid in comparison with the removal function, then
N ( t ) = R ( t)FS(t ) d t = R ( t).N, 0
(6)
where N o is the total number of analyte atoms introduced into the graphite furnace. Hence, the shape of the experimental A ( t ) curve is now equivalent to the shape of R ( t ) . The convolution integral thus expresses much more clearly than ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
2177
the differential Equation 3 the conditions that must be fulfilled in order to measure the supply and removal function independently. Experimental realization of both alternatives will be described in t h e next section. (ii) T h e integral of the time-dependent number of atoms is given by
7N ( t ) d t = [TS(t ) d t ][7R(t ) d t ]= NO.rR 0
0
0
(7)
so that in combination with Equation 2 the total area of the measured absorbance curve is also proportional to NOrR provided that all analyte elements are completely atomized, i.e. no molecules or ions are formed in the vapor phase. (iii) Just as was done for the removal function in Equation 5 , i t is possible to define an equivalent time constant for the supply function as
Now, the efficiency of the graphite furnace in containing the analyte atoms is directly related to the ratio T R / T S (1). If this ratio is very small, it means that the atoms are slowly released and rapidly removed, so that Equation 5 applies and the maximum number of atoms in the furnace is given with Equation 8 as
N,,
=
SmrR
NOrR
=-
7s If, on the other hand, T R / T S becomes very large, the atoms are rapidly supplied and slowly removed, so that Equation 6 applies and the maximum of analyte atoms is given by This means that with increasing value of T R / T S the efficiency 7 = Nm,/No is first equal to q / T S and ultimately approaches unity. The exact correlation between N,,,jNo and T ~ / T S depends, of course, upon the relative shapes of the supply function, S ( t ) ,and the removal function, R ( t ) . P h y s i c a l Description of the S u p p l y Function. One of t h e objects of the present investigation is to relate the measured transient signals to physical parameters of the analyte and the atomizer. For the supply of the sample we can use the extensive studies that have been published in the past few years. It is generally assumed that after evaporation of the solvent (during drying) and the matrix (during ashing), the analyte is retained as a mono-atomic layer on the graphite surface. Indeed, 1 ng of analyte atoms then covers a n area of about 1 mm2, which is much less than the cross section of t h e droplet introduced on the furnace wall. For the release of the analyte atoms, L'vov first assumed t h a t t h e rate of evaporation is constant ( I ) and in a later publication took it to increase linearly with time (13). Fuller ( 5 ) assumed that the rate of supply is proportional to the number of analyte atoms still retained a t the graphite wall. This assumption greatly facilitated the solution of the differential Equation 3. Tessari et al. (6) utilized the same model, b u t also accounted for a variation of the rate constant during atomization. This is necessary, because in most atomizers the release of the analyte takes place during and as a consequence of the warming u p of the graphite wall. In other words, the heating of the tube is the rate-determining step and Tessari et al. showed that their data could be well described by an Arrhenius-type expression for the rate constant
where Tuis the temperature and N , is the number of analyte atoms at the graphite wall. Realizing that JS(t)dt = N o = Nu ( t = 0), we obtain for the rate of supply of the analyte atoms
During the first moments of analyte release, the integral in Equation 11 is practically zero and a semilogarithmic plot of S ( t ) vs. l/T,(t) will yield the values for the activation energy, E , and the frequency factor, B. Provided S ( t ) is slow in comparison with R ( t ) (Equation 5), the initial portion of the normal absorbance signal measured in commercial atomizers yields the same information. This procedure has been successfully utilized by Sturgeon e t al. ( 4 ) in order to clarify the processes and reactions responsible for analyte release. The present derivation demonstrates the validity of this approach more clearly than their analysis, where a t one point of the derivation it was necessary to assume steady-state conditions ( d N / d t = 0). Obviously, this is only valid in the maximum of the absorbance curve, whereas in fact the initial part of this curve must be used, as has been done by Sturgeon e t al. ( 4 ) . They were able to assign the experimentally observed activation energies to those of distinct chemical and physical processes, such as vaporization, dissociation, carbide formation. The exponential term in the Arrhenius expression thus appears to be well validated. Much less is known about the frequency factor, B. The experimental determination as described above is very imprecise. Indeed from curve-fitted supply functions, Tessari et al. derived values of B between 10" s-' and 10" s-l (8, 14) in agreement with estimates calculated by Cordes (15). In summary it appears t h a t at present Equation 11 offers the best description of the analyte introduction process. Of the two parameters, the activation energy is readily measured and well correlated with actual processes at the graphite surface, but the frequency factor is only roughly known and still impredictable. P h y s i c a l Description of the Removal F u n c t i o n , In comparison to the supply of the analyte atoms into the graphite cell, the removal of the vapor from the furnace has received much less attention. After L'vov (1) most authors ( 5 , 9, 16) simply state that the rate of analyte loss is proportional to the number of analyte atoms present in the furnace. This is equivalent to a n exponentially decaying removal function. This behavior would be expected from a purely diffusion controlled transport process and the rate constant would then be proportional to D / L 2 ,where D is the mass diffusivity. Indeed, Fuller observed a slight increase of his rate constant for sample removal with temperature. In real furnaces, several factors disturb this simple picture. (i) In the first place the sample is introduced onto and released from the center of the furnace wall only. Consequently, even for a pure diffusion process, the analyte vapor requires some time to reach the open furnace ends and disappear gradually into the ambient space. This means that the response function will be constant for a n initial period of time and then decrease exponentially. T h e mathematical description of this process is presented in the appendix and yields that R ( t ) is stationary for a period of time equal to 0.024 L 2 / D and decays exponentially with a time constant equal to 0.101 L 2 / D . Hence the total equivalent time constant due to diffusion is equal to 7-d
=
0.125L2 D
which agrees with the expression of L'vov ( I ) . 2178
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CHEMISTRY,
VOL. 49, NO. 14, DECEMBER 1977
T h e diffusivity depends, of course, upon the vapor temperature inside the furnace. For tube lengths of about 1 cm and a diffusivity of 3 cm2/s, this time constant is of the order of 40 ms. (ii) As remarked earlier, the analyte is supplied into and removed from the furnace during a period of time, when the wall temperature and hence the gas temperature is still increasing. consequently, the vapor inside the furnace is expanding and this will expel the analyte from the furnace. The equivalent time constant for this process is approximately given by
where T(to)and (dT/dt)toare the temperature and the heating rate of the vapor at the moment, to, of introduction of a particular analyte atom. For ordinary heating rates, this time constant generally exceeds the diffusive time constant by far, except in rare cases of long tubes and small diffusivities. (iii) In the larger commercial graphite furnaces, a constant flow of protecting gas is employed that partly enters the furnace through holes drilled in the wall. This induces a convective transport of the vapor from the furnace. The time constant of this process will be related to the ratio of the cell volume, V, and the cold gas flow rate through the furnace, F. In addition the cold gas is heated after its introduction into the furnace and this enhances the effective flow rate through expansion, i.e.
However, the proportionality factor, K , is difficult to predict, because it depends upon the flow pattern through the furnace. Still, it is obvious that for a typical cell volume of a few cm3, a flow rate of 1 L/min a t 300 K and a furnace temperature, T, of 1000 K, the time constant can easily become as small as 50-100 ms, which is much smaller than either expansive or diffusive time constants in large furnaces. (iv) So far we have only considered transport processes in the gas phase that can be described in general terms. In real furnaces, element-specific removal processes may also occur. For example, element recombination in the gas phase ( Z ) , diffusion through the porous graphite wall ( 4 , 16), condensation a t and possibly redesorption from the cooler furnace ends (9, 14) have all been suggested as possible sample loss processes. These will not be considered, because they can, in principle, be prevented by appropriate furnace design. In t h e present study, the elements were selected in such a way t h a t these disturbing effects are minimal, but the reader is warned t h a t our results need not necessarily apply to the conditions prevailing in a particular analysis. I n general then, the removal function of a graphite furnace is t h e complex result of a t least three different transport processes: diffusion, expansion, and convection. The integration into one analytical expression is a formidable problem t h a t surpasses the object of this investigation. If, however, all three processes can he approximated by an exponential decay, then the overall response function will also be a decreasing exponential. This is true because a n exponentially decaying response function is equivalent to a rate of analyte loss proportional to the number of atoms in the furnace, hence (~)o,=-[;+;++.-
1 i Ti
with t h e solution
L
Therefore the time constant of the overall removal function is equal to
1
-=rR
1 Td
+ -1+ re
1 7,
(15)
This wili at least be approximately true for the systems presently investigated. Equality of Wall Temperature and Vapor Temperature. Whereas the surface temperature, T,, of the graphite wall, which is responsible for the release of the analyte (Equation ll),is readily measured, this is not true for the vapor temperature, T , which appears in all removal time constants (Equations 12, 13, 14). T h e equality of these two temperatures has lcng been taken for granted, b u t has been shown to be incorrect for larger furnaces in two recent publications (17 , 18). With some simplifying but realistic assumptions, this problem is readily treated in terms of heat transfer coefficients. The full results will be presented elsewhere (19),but the conclusions of these calculations can be stated as follows. (i) In static systems, without convection, the time lag between wall temperature and gas kinetic temperature is no more than 5 ms and the difference between those two temperatures depends upon the heating rate and the furnace diameter, but a t any cross section never exceeds 5 K in the system presently investigated. Naturally, there will be a gradient of both the wall temperature and the vapor temperature along the furnace, but this does not impair the conclusion for each infinitesmal cross section. (ii) With forced convection this situation is markedly different, because at any moment during the atomization the cold inert gas needs time to reach the wall temperature. This time can be converted into an equivalent distance travelled by the inert gas. Obviously, the distance needed for the inert gas to reach the wall temperature depends upon the furnace diameter, the wall temperature, and the flow rate of the inert gas. For the larger furnace considered in this study it may take 1.5 cm before the centrally introduced argon has been heated to 90% of the wall temperature. Consequently, towards the end of the atomization step the wall temperature of the graphite can exceed the average gas temperature inside the furnace by several hundred degrees. This agrees with the experimental evidence (17 , 18).
EXPERIMENTAL Two different atomizers have been investigated. One a Varian Techtron Carbon Rod Atomizer model 63 and the other a home-made copy of the Perking-Elmer HGA-72. In the latter case the commercial model could not be used as such, because it did not permit the measurement of the temperature distribution along the furnace wall. To this end a narrow slit was engraved in the housing, allowing a variable observation position through a sliding window. The wall temperatures were measured with a pyrometer utilizing a silicon photo element (Siemens BPY 11.) with a response time less than 1 ms. The voltage across a 100 k n output impedance was recorded on an ordinary strip-chart recorder (0.6 s full scale deflection). Control measurements on a rapid UV-recorder showed this observation system to be ten times more rapid than the fastest temperature variation recorded. The pyrometer was calibrated against a commercial optical pyrometer and against the melting points of small metallic particles introduced in the furnace, The pyrometer selects an area of about 4 mm2 from the outer furnace wall, but the calibration procedure ensures that the reading reflects the inner wall temperature. The furnaces are heated with a constant voltage derived from a 5-kW variable transformer. Maximum temperatures up to 3COO ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
2179
fl
a
j2
b
w graphite furnace
Injection piece for t h e rapid introduction of mercury vapor into the heated graphite furnace
Figure 1.
K are possible with either furnace. The absorbance is measured in the usual way. Primary radiation from commercial hollow-cathode lamps is mechanically chopped at 400 Hz, dispersed by a 0.25-m monochromator and phase-sensitively detected by a photomultiplier and a lock-in amplifier. Because the absorbance varies much more rapidly than the furnace temperature, this cannot be recorded accurately on an ordinary recorder. Instead, a rapid two-pen recorder is used to record the atomizing voltage of the furnace on one channel and the transmittance on the other channel. The frequency bandwidth of 125 Hz was verified to be sufficient to record the fastest signals undistorted. As stated in the preceding section,the absorbance signal reflects either the supply function or the removal function of the graphite furnace if the alternative process is made very rapid. A comparatively rapid removal function was realized by forcing a high flow of inert gas through the furnace. With increasing flow rate the peak absorbance continuously decreases, but the signal shape ultimately becomes unvariable. At this point the supply function is obtained. A rapid, pulse-like introduction of metal was realized in the following manner. An injection syringe is filled with 10 pL (for the smaller furnace) or 50 pL (for the larger furnace) of air saturated with mercury vapor. The syringe is placed in an injection piece provided with a ceramic guiding tube, as illustrated in Figure 1. The distance between the end of the tube and the introduction orifice of the furnace is about 2 mm, whereas the distance between the orifice and the end of the injection needle is about 12 mm. In this way the injection needle is protected against the furnace heat. At any moment during the atomization cycle, the mercury vapor could be manually injected into the furnace, so that the variation of the removal function with the furnace temperature could be studied. Using a suitable injection syringe, the mercury vapor could be introduced in less than 10 ms, which is three times more rapid than the fastest removal function recorded. All chemicals were reagent grade or better.
RESULTS AND DISCUSSION The S u p p l y Function. Figure 2a presents the absorbance signals obtained for a constant amount of silver and a particular atomizing voltage applied to the larger furnace with increasing argon flow through the furnace. As expected, the signal first becomes narrower with increased forced convection, b u t a t a n argon flow rate of 0.8 L/min a constant shape is reached which describes the supply function at this particular heating program. Simultaneously, the maximum absorbance continues to decrease (Figure 2b), but the equivalent time 2180
ANALYTICAL CHEMISTRY, VOL. 49, NO. 14, DECEMBER 1977
04
1
1 0
05
10
15 FArgo"
20
t/mln
Flgure 2. Experimental measurement of the supply function. (a) Transient signals measured for silver in the HGA-72 furnace for a constant heating program (extreme right drawing) and increasing forced-convection flow rates. (b) Peak absorbance (0)and normalized as a function of convective argon flow rate. With peak area 7 (*) increasing flow rate, the latter parameter approaches the time constant, T ~ of, the supply function
constant obtained from the normalized signal is constant within the experimental error of about 10%. I t was verified that these results are independent of the amount of silver introduced as long as we stay within the linear portion of the analytical curve (
