Effect of Heating Rates in Graphite Furnace Atomic Absorption Spectrometry D. C. Gregoire, C. L. Chakrabarti,” and P. C. Bertels Metal
Ions Group, Department of Chemistry, Carleton University, Ottawa, Ontario, Canada K1S 566
and ~ 2 are / atomization time and residence time, respectively. L‘vov’s (16) model for electrothermal atomization in an isothermal graphite cuvette also predicts that provided the sample is completely atomized during the time of measurement, the integrated absorbance, QN’, is proportional to the residence time, T;, of atoms in the analysis volume, and the total number of analyte atoms in the sample, N;.
The peak and integrated absorbances of Mo, V, AI, Ni, Cu, Zn, and Cd as a function of the rate of heating of the graphite tube In a modlfled HGA 2100 atomizer are reported. The increase In peak absorbance with heating rate is correlated with the activation energy of the rate-determining step in the atomizatlon process. Integrated absorbances of relatively volatile elements decreased exponentially with increasing heating rates, whereas those of relatively involatile elements, such as Mo and V, Increased exponentially with increasing heating rates. Characterization times ( T,, 72, 71/72) of the absorption pulse are discussed and their applicability to analysis of real samples Is assessed.
QN’
In recent years, models for temporal signal profiles obtained using various types of electrothermal atomizers have been proposed (1-15). The instrumental parameters that affect the absorption signals obtained with various atomizers have been studied also ( e l l ) .Among these are the drying, ashing, and atomization temperatures, atomizer design, the influence of different sheath gases on absorption signals, the rate of heating of the atomizer, and the response time of the measurement system. Assuming, for the sake of simplicity, that analyte atoms are introduced into the analysis volume simply by the vaporization of analyte from the graphite surface (Le., ignoring all other intermediate steps that may be involved in the atom formation), the rate of evaporation R ( t ) of an analyte element as a function of the absolute temperature is given by
R ( t ) = Ae-Ey/RT
(1)
where A is a pre-exponential factor and E , is the heat of vaporization for the analyte element. Since the temperature of the graphite furnace increases rapidly during the atomization step, Equation 1 is modified as shown in Equation 2:
where t is time in ms and cy is the rate of heating of the graphite tube in K ms-l. This exponential dependence of the rate of vaporization of the analyte atoms from a graphite surface can be used to account for exponential rise in the peak absorbance with increasing heating rates. L’vov’s model (16) for electrothermal atomization in an isothermal graphite cuvette describes the temporal variation of a n absorption signal profile. L’vov ( 2 7) and Katskov and L’vov (18) have shown that, for accelerated atomization, the variation of the atomic population within the analysis volume with time may be described by:
where Nt is the analyte atomic population a t any instant of time t, N o is the number of analyte atoms in the sample, T ~
’
0003-2700/78/0350-1730$01 .OO/O
=
L V ~ T ~ ‘
(4)
The primes on T ~ ’ , r2‘,and Q N ’ will be used for designating these parameters as they appear in L’vov’s model ( 1 4 ) , and they will be differentiated from their experimentally observed counterparts (Le., the values obtained using commercial , and QN. atomizers), which will be designated simply as T ~ T?, Atomization time, T ~ ’ ,is defined as the time elapsed from the appearance time to the peak of the absorption pulse ( 1 0 , l l ) . Residence time, T ~ ’ , is defined as the time taken for any absorbance value in the decay part of the absorption pulse to decay to l / e of its value provided that complete atomization has occurred before the initial point in the measurement (10, 11). However, with commercial graphite tube atomizers, the latter proviso is sometimes not fulfilled and the experimental T < and 721 values are sometimes different from the theoretical T~ and T~ values, respectively (10, 2 1 ) . Equation 3 shows that the measured absorbance ( A a N,) should increase as the T I / T ~ decreases. For constant T ? , the absorbance should increase exponentially as T * decreases. Since the peak of the absorbance-time profile (Le., a t t = T ~ ) is taken as the measure of the absorbance signal, the peak height should increase exponentially with a, the rate of heating of the atomizer, because T~ decreases exponentially with ck (Table I). Equation 4 shows that the integrated absorbance is entirely independent of the atomization time, T ~ ’ ,i.e., independent of the kinetics of atomization, and hence, is independent of the heating rate. Here the only requirements are complete atomization and maintenance of experimental conditions so that the length of time spent by the atoms in the analysis volume (Le., residence time, T ~ ’ )remains constant. I t has been reported (10, 2 2 ) that the above mentioned conditions are not fulfilled by commercial graphite tube atomizers; hence, Qr;(experimental integrated absorbance) may not be independent of the kinetics of atomization and the heating rate. Based upon the L’vov’s model (26),Sturgeon et al. proposed mechanisms of atom formation ( 2 4 ) and atom loss (15) in a commercial graphite tube atomizer. This paper is based upon the above model ( 2 4 , 15) and reports the results of studies made on the effect of the heating rate on the peak and the integrated absorbances in a graphite tube atomizer. Torsi, Tessari, et al. (5-9) developed a theoretical model and reported experimental results for the release of gaseous atoms at the electrothermal rod atomizer. The most important features of the model were the following: (i) the overall atomization process was assumed to be kinetically controlled by the atom transfer at the solid/gas interphase, the possibility of redeposition of atoms being ignored; (ii) in a preliminary C 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
simplified model ( 5 ) , only the convective mechanism of transport was considered; whereas in a following more sophisticated treatment (6) the diffusive and convective mechanisms were both included in order to calculate the time-dependent number of atoms present in the volume of optical observation; (iii) reliance on thermodynamic data from the literature was a priori avoided and an effort was made (7) to obtain directly from the experimental data some information about the binding energy between the solid substrate and the atom to be released. The reported experimental result-nickel (8) and lead (9), both in hydrogen atmosphere-confirmed the validity of this model. In the above model (5-9), the authors assumed that the analyte atoms are bound to the graphite surface with a monolayer distribution, and the gaseous phase behaves as an infinite sink for the evaporating atoms. It was further assumed that the linear velocity of the evaporating atoms was constant, and also t h a t the diffusion coefficient of the released atoms was constant in time and position. Taking into account the depletion of the surface layer of atoms with time in the atomization step, a linear increase in the analytical sensitivity was predicted with increasing heating rates. Experimentally, these results were verified for 4.0 X lo-'* kg of chromium atomized at heating rates of up to 4.0 K ms-'. Above this heating rate, the absorbance began to show progressively smaller increases with increasing heating rates. The model developed by Torsi, Tessari, and co-workers (5-9) for the electrothermal rod atomizer is not applicable to the electrothermal graphite tube atomizer for a t least four reasons. First, in the graphite tube atomizer, since the partial pressure of the analyte atomic vapor is not zero, the gaseous phase above the atomizer surface does not behave as an infinite sink for the evaporating atoms; also, the evaporation of atoms may not be an irreversible process because of the possibility of condensation of the analyte atoms in cooler parts of the graphite tube and their subsequent re-evaporation (15). Secondly, it will be shown in this paper that the residence time of the atoms in the graphite tube atomizer is not a constant and therefore the velocity of the atoms must be changing with time. Thirdly, in the graphite tube atomizer, diffusional mechanism of transport is predominant (15),whereas in the electrothermal rod atomizer (5-9), both the convective and the diffusional mechanism of transport play an important role. Fourthly, in the model developed for the electrothermal rod atomizer (5-9), the prompt establishment of equilibrium conditions at the interphase between solid and gas phase plays a central role in the overall atomization process, whereas in the model for the graphite tube atomizer (14, 15) quasiequilibrium conditions are assumed for the release process. The effect of heating rates of an electrothermal atomizer on the absorbance of elements has been reported in the literature (4, 5 , 10, 11, 13, 19-22). The heating rate of a graphite tube or filament atomizer has been found to have a large effect on the absorbance of elements. Using a graphite tube atomizer, Johnson et al. (19) found that the shape of the germanium absorbance signal varied with the voltage applied to the atomizer unit. Above a certain minimum voltage, the absorption pulse increased in height and decreased in width as the input power was increased. A heating rate of 1.6 K ms-' was observed a t the maximum applied voltage, 11 V. These authors postulated that the germanium atomic vapor was formed by the gas phase dissociation of the volatile GeO species, and that high atomizer heating rates were necessary in order to reach rapidly a temperature at which the thermal decomposition of GeO(g) was thermodynamically favorable; the time to reach the above temperature must be much shorter than the time required for the GeO(g) to diffuse out of the graphite tube. This conclusion was supported by the fact that
1731
an open filament-type atomizer gave extremely low sensitivities for Ge since in these atomizers, the residence time of gas-phase species in the analysis volume was far less than in the enclosed, tube-type atomizer. A similar effect was observed by Donega and Burgess (20), who determined Si in an enclosed Ta boat atomizer. These authors also concluded that the rapid loss of gaseous Si0 (which was supposed to be the precursor of the gas-phase Si atoms) below a minimum input power level accounted for the low sensitivity obtained at low atomizer heating rates. Montasser and Crouch (23)pointed out that for those cases where the atomization process goes through an oxide formation step and voltilization of the oxide occurs a t a temperature much lower than the atomization temperature, it is essential (in order to prevent sample loss) that the atomizer achieve the desired final temperature instantaneously. Cresser and Mullins (24) have also stated that the rate a t which any given molecular species leaves the atomizer (graphite filament) and the degree of atomization depend on the rate of increase of temperature ai, temperatures a t which the analyte molecular species exhibits a significant vapor pressure. Torsi and Tessari ( 5 ) have published a mathematical treatment of heating rates and its effect on the peak absorbance for Cr. Their model predicts (and they have experimentally verified the prediction using a carbon filament atomizer), that a linear relationship exists between the peak absorbance and the input power. These authors (51,however, have not observed this linear relationship above the heating rate of 4 K ms-l. Maessen and Posma (21) have reported the effect of the heating rate of the graphite tube for a Carbon Rod Atomizer-63 (CRA 63) on the peak separation between the analyte peak and the matrix peak. The present authors have plotted these results-absorbance vs. the squme of the input voltage, V-for gold and cobalt in blood plasma and have found that the curves show an initial, approximately linear increase in the peak absorbance with increasing V z (Le., the heating rate), followed by a slower increase in the absorbance with higher V2 values. Work done with a carbon filament atomizer by Johnson et al. (4) indicates that the peak height absorbance is a linear function of and, hence, is also a linear function of the filament heating rate. These authors (4) have observed a correlation between the temperature at which the atomic vapor becomes just detectable (Le., the appearance temperature) and the heat of vaporization of the metal or the bond dissociation energy of the metal oxide, whichever is larger. Posma et al. (13) have reported variation of peak height absorbance for copper with the heating rate of a CRA 63 for various time constants. These authors (13)have found that when recording undistorted signals, peak height absorbance increases up to a heating rate of about 0.850 K ms-', but when recording signals under optimum signal-to-noise ratio conditions, (e.g., a time constant of 0.3 s), the measurement system can follow the signal increase up to about 0.400 K ms-', whereafter the peak height absorbance remains constant. Using a very slow response system, Le., a time constant of 3.0 s, these authors (13)have observed that peak height absorbance increases slowly up to 0.450 K ms-l, after which it decreases slowly. They have obtained similar results with silver and cobalt. The use of extremely high heating rates, up to 40 K ms-', with a capacitive discharge system, as a means of improving analytical sensitivity has been suggested by L'vov (25), and the present authors (26). Sturgeon and Chakrabarti (22) have reported that increased heating rates of the HGA 2100 graphite tube generally increase peak height absorbance;
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
however, few conclusions of general applicability to high heating rates can be drawn from the results presented. In most of the studies discussed above, the power supply was so designed that any change in the rate of heating of the atomizer also resulted in a change in the maximum temperature of the atomizer. Since the maximum temperature of the atomizer affects the characteristics of the absorption pulse of elements (10, 11), the effect of the heating rate cannot be separated from the effect of the temperature attained. In order to achieve a complete separation of these two effects, the power supply needs to be so designed that the heating rate and the maximum temperature attainable must be independently controllable. Such independent control was provided by the power supply used in this study. EXPERIMENTAL Apparatus. The atomic absorption spectrophotometer used for this study has been described in earlier publications (10, 1 1 , 22, 27) from this laboratory. The design of the graphite tube atomizer built in this laboratory, is similar to that of the Perkin-Elmer HGA 2100 (and, hence, the apparatus will be called a modified HGA 2100). It is fitted with large water-cooled chambers to prevent over-heating of the metal from the atomizer during long or high-temperature atomization cycles. Single-piece unit construction of the atomizer allows its use at power input levels of 15 V at 1000 A. The graphite cones and graphite tubes were those commerically available from the Perkin-Elmer Corporation for HGA 210+the graphite tubes were pre-coated with pyrolytic graphite in the authors’ laboratories. A novel power supply used for this study was designed and fabricated in this laboratory so as to separate the maximum temperature attainable by the atomizer from its rate of heating (22). Unlike conventional graphite furnace power supplies, this has, in addition to the usual dry and ash stages, two hightemperature atomization stages. In addition, its power capabilities are much greater than the commercial units. A custom-wound transformer (Electrodesign Ltd.. Ville Lasalle, Quebec, Canada) operating at 208 V provides 1000 A at 15 V to the atomizer. It has been demonstrated by numerous authors ( 4 , ,5, 20, 1 1 , 13, 19-22) that the rate of rise of temperature of the atomizer is an important parameter in determining peak absorbance. With conventional atomization units, the highest rate of rise of temperature requires the maximum atomization setting, resulting in the maximum temperature of the atomizer being attained. The power supply described above allows maximum rate of heating of the atomizer for a short period of time with the first atomization stage while maintaining a controllable upper limit on the temperature with the second atomization stage. This flexibility allows use of a wider variety of heating regimes which may be used to achieve very rapid heating to a present temperature followed by isothermal conditions. This allows one to separate the effects of the heating rate from the effects of the temperature on the analytical parameters of an absorption pulse. There are two significant differences between this power supply and conventional graphite furnace power supplies: (1) The same (maximum) temperature can be attained with this power supply using different heating rates, whereas this can be achieved with conventional graphite furnace power supplies using only one particular heating rate; (2) temperatures > 3000 K can be attained with this power supply, whereas such temperatures cannot be attained with conventional graphite furnace power supplies using low heating rates ( 2 7 ) . All temperatures were measured with an automatic pyrometer, series 1100 (Ircon Inc., Niles, Ill.), which had been calibrated by the manufacturer, and the calibration checked in this laboratory by measurement with thermocouples and by the melting points of selected pure metals covering the entire range of temperatures studied. Perkin-Elmer and Varian Techtron single-elementhollow cathode lamps were used as narrowline sources. Aliquots of 5 pL of sample solution were delivered to the graphite tube by means of an Eppendorf pipet fitted with disposable plastic tips. Reagents. AU reagents used were of ACS reagent-grade purity. Stock solutions of 1000 pg/mL of each metal studied were prepared from pure metals dissolved in appropriate acids or bases with the exception of vanadium, which was prepared from va-
3000i
2800
w 2400
f 2000
1600
1200
TIME
/
ms
Figure 1. Temperature-time curves of the graphite tube heated at different heating rates. 0 4.33 K ms-‘, 0 4.17 K ms‘’, 0 3.68 K ms-’, W 3.40 K ms-’, A 2.60 K ms-’, A 2.17 K ms-’
nadium pentoxide, and molybdenum, which was prepared from molybdenum trioxide. Immediately prior to use, each standard solution was diluted to the desired concentration with ultrapure water obtained directly from a Milli-Q water system (Millipore Corporation). Argon gas used to sheath and to purge internally the atomizer was of 99.95% purity and was supplied by Roncar Oxygen Company.
RESULTS AND DISCUSSION Temperature-Time Characteristics of the Atomizer. The surface temperatures of the graphite tube as a function of time a t different heating rates are presented in Figure 1. The curves in Figure 1 show an initial linear part during which the atomizer is heated to some temperature, followed by a short nonlinear part, the end of which marks the end of the first atomization stage and the beginning of the second atomization stage; and finally, a nearly horizontal part where the atomizer asymptotically approaches the preset maximum temperature. The maximum temperature marks the balance between the input power and the heat losses. The power supplied to the atomizer is partly dissipated by radiation, conduction, and convection, and is partly used in raising the temperature of the graphite tube atomizer. A t low temperatures, and at the center of the inner surface of the graphite tube (where experimental surface temperatures are measured), heat losses arising from radiation, conduction, and convection should be small; hence, at low temperatures, the rate of heating ( a ) of the atomizer can be related to the input power by Equation 5 :
dT _ - a = - -P dt
mc
(5)
where d T / d t is the rate of heating of the atomizer (K ms-‘), P is the power consumption of the atomizer (,J.s-’), m is the mass of the carbon tube (kg), and c is its specific heat capacity (J kg-’ K-’). According to Equation 5 , at low temperatures, a linear relationship exists between the input power and the initial rate of heating of the atomizer. This linear relationship has been experimentally confirmed by the present authors for the atomizer unit described above for the range of input power reported in this study. Each curve in Figure 1 represents a different heating rate of the graphite tube surface. This heating rate is determined by the input power set on the first atomization stage and, therefore, one could reach any preset maximum temperature of the graphite tube surface a t a rapid or slow heating rate. With the power supply described in this paper, heating rates of up to 4.33 K ms-’ were achieved. The fact that the rate of heating is variable and that the maximum temperature a t each new rate of heating is the same, allowed the authors to study changes in the analytical parameters as a function of the heating rate a t a nearly constant maximum temperature.
ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
0.2oL
14
004
I
4
Figure 2. Peak absorbance as a function of graphite tube heating rates. A Zn, A Cd, Cu, 0 Mo, 0 V, 0 41, 0 Ni
Unless stated otherwise, a drying temperature of 370 K maintained for 30 s and an ashing temperature of 570 K maintained for 20 s were used. Maximum temperatures above 3200 K were impractical since at higher temperatures excessive scattering of the incident radiation occurs by the carbon ejected from the graphite tube surface, and the useful life of the graphite tube is greatly shortened. Although the highest absorption signals were not obtained for some of the elements studied a t this high maximum temperature, a constant maximum temperature was used to provide a basis for comparison of the elements studied. A high maximum temperature was necessary in order to ensure that low-volatility elements, such as Mo and V, were atomized. Sturgeon e t al. ( 1 1 ) presented a good discussion of the peak and the integrated absorbances for a series of elements in a HGA 2100 as a function of the maximum temperature employed. It is interesting to compare the performance of this modified HGA 2100 with the unmodified HGA 2100. The input power of the unmodified HGA 2100 determines the maximum temperature of the atomizer surface. Its power supply can give a maximum temperature of -3000 K; its rate of heating, at the temperature setting of 2700 C is 1.23 K ms-'. However, with the unmodified HGA 2100, when the power input (and, hence, the rate of heating) is altered, the maximum temperature is also altered. For example, power inputs giving maximum temperatures of 2370,2770, and 2970 K give heating rates of 0.73, 1.06, and 1.23 K ms-', respectively. These heating rates agree with those reported by Sturgeon and Chakrabarti ( 2 7 ) . This coupling of the maximum temperature attained and the heating rate in the case of the commercial atomizer makes it difficult to study the changes in the analytical parameters of an absorption signal caused solely by changes in the heating rate of the graphite tube. The modified HGA 2100 provides linear heating curves over the entire absorption pulse of the elements studied with the exception of the less volatile metals, Mo and V. In the case of Mo and V, only a part of the decay region of the absorption pulse occurs during the final, nonlinear part of the heating curves. Effect of H e a t i n g Rate on Peak Absorbance. Figure 2 presents peak absorbance as a function of the graphite tube heating rate from 0.33 to 4.33 K ms-' for a number of elements atomized. The elements studied were chosen from each of the three groups referred to in this paper as the relatively volatile elements (Cd, Zn), medium-volatility elements (Cu, Al, Nil, and low-volatility elements (Mo, V). The relationship seen in Figure 2 between the peak absorbance and the rate of heating appears to be complex. Close examination, however, reveals that the curves are approximately sigmoid in shape.
1733
For relatively volatile elements (Cd and Zn) and for a medium-volatility element (Cu), the curves can be divided into three distinct regions. At low rat,es of heating, a rather slow increase in the peak absorbance occurs with increasing rates of heating. This is followed by a second region in which a n exponential increase occurs in the peak absorbance wibh increasing heating rates. Finally, there is a third region where further increase in the heating rate produces little change in the peak absorbance. These results agree with those obtained by other workers (13,21). For the elements of medium and low volatility, only certain parts of the curves obtained for the relatively volatile elements are seen in Figure 2. For example, A1 and Ni show an increase in the peak absorbance with the increasing heating rate, and then the peak absorbance of both show signs of levelling off at the highest rates of heating studied. Molybdenum and vanadium, however, still show an exponential increase in the peak absorbance a t a heating rate of 4.17 K ms-'. At still higher heating rates (Le., >4.33 K ms-' which are not attainable with the present equipmentj, it is expected that the peak absorbance of Mo and V would follow the trend observed with the other elements, i.e., with Further increase in the heating rate, the increase in the peak absorbance would be progressively smaller and finally, the peak absorbance would level off. Figure 2 also shows that in a series of elements, with decreasing volatility, the point of vertical inflection in the sigmoid-shaped curve is shifted to higher rates of heating. For example, Zn and Cd both have their inflection points a t a heating rate of about 0.50 K ms-', whereas that of Al is shifted to 2.75 K ms-'. The inflection points of Mo and V are not reached even at the highest rate of heating available with the present equipment. Mathematically, a point of vertical inflection is defined as the turning point in a curve the slope of which increases (or decreases). becomes infinity a t the inflection point, and thereafter decreases (or increases). In Figure 2, as any point of vertical inflection is approached from the side of low heating rates, the slope of the curve increases, becomes infinity a t the inflect,ion palint, and thereafter decreases. It would be instructive to find out why the peak absorbance initially increases with increasing heating rates up t o the point of inflection and thereafter decreases with further increase in heating rates. The above phenomenon is interpreted as follows. It has been shown by Sturgeon et al. ( 1 4 , 1 5 ) that both the magnitude and the position of the peak of an absorption pulse are determined by the rates of formation and loss of atoms, the absorption maximum marking the point o f balance between these rates (Le., a t the pulse maximum, the net rate of increase in the number of atoms is zero), and that an increase in the rate of loss both decreaises the peak height and shifts the pulse maximum to an earlier point in time. Sturgeon e t al. (15) demonstrated the above fact by means of a n oscilloscopic trace showing the effect of an internal purge gas (i.e., forced convection) on the peak of absorption pulses from kg Cu atomized in a HGA 2100; in the presence of 4X the internal purge gas (Le., forced coavection) the peak decreased in magnitude and shifted to an earlier point in time. Since the peak of an absorption pulse marks the point of balance between the rates of formation and loss of atoms, an increase in the rate of loss decreases the peak height and shifts the peak to an earlier point in time. Like the convection in the above case, any increase in any other loss processes, viz., diffusion, forced expulsion due to expansion of the purge gas, formation of refractory compounds, may affect the peak of an absorption pulse both in magnitude and position in time. An increase in the pulse height and position can result from either an increase in the rate of atom formatitsn and/or a
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
Table 11. Effect of Heating Rates on Experimental Residence Times, T *
Table I. Effect of Heating Rates on Experimental Atomization Time, T~ dT1 dtl K m s - ’ Mo 4.33 450 4.17 500 3.68 650 3.40 750 2.60 1000 2.17 1400 1.47 2500 1.23 0.79
7,
V A1 180 140 200 160 210 200 230 250 245 350 300 410 - 560
-
-
-
Ims Ni
320 340 400 490 600
780 1160
-
-
Cu 180 195 212 230 250 275
-
-
-
Cd 120 120 130 140 150 160 200 270 360
Zn 90 90 95 100
115 125 160 220 290
decrease in the rate of atom loss. For relatively volatile metals (Zn and Cd), at the heating rates used in this study the entire absorption pulse occurs in the period of time during which the temperature of both the atomic vapor and the diffusion medium is rapidly increasing; hence, the diffusion coefficient of the analyte species increases with time (Le,, with increasing temperature) causing an increased diffusional loss of the analyte atomic vapor (15,22). This is because the rate of diffusional loss increases according t o T’ (28), where T is the temperature of the gas phase in degrees Kelvin. The greater the heating rate, the greater is this diffusional loss, and the earlier the pulse peak occurs. With increasing heating rate, besides increased diffusional loss, there are also losses due to expulsion of the analyte species from the analysis volume by rapid expansion of the purge gas inside the graphite tube, and also due to convection-all of these factors contribute to the atom loss. Given a constant rate of atom loss, the peak absorbance should increase with increasing heating rate (Le., decreasing il’values), and as r I 1 becomes much smaller than ~ 2 / the , peak absorbance reaches a limiting (maximum) value. However, for relatively volatile elements, increased atom loss with increasing heating rates makes TZ/ progressively smaller, decreases the peak height, and shifts the peak position to an earlier point in time. This is reflected in the inflection points occurring a t lower heating rates for the relatively volatile elements than for the relatively involatile elements. For relatively involatile elements, increasing heating rates decreases T’’ without a proportionate decrease in T ; with the result that the peak absorbance continues to increase with increasing heating rates and the inflection points are not reached even with the highest heating rate available with the power supply. T h e practical significance of the above observations is that with the commercial, semi-enclosed graphite tube atomizers, high heating rates increase the peak height sensitivity of elements; the more involatile the element the greater, generally, is the increase in the peak height sensitivity-the greatest increase in the peak height sensitivity with increasing heating rates (up to a heating rate of at least 4.33 K ms-’ and probably, much higher heating rates) is found with relatively involatile elements. Heating rates higher than about 5 K ms-I are best accomplished by capacitive discharge heating (25,261. T h e above discussion based solely on the relative volatility of elements is valid only in the simple case in which the atom formation and loss reactions for an analyte element are not complicated by the formation of its intermediates of significantly different volatilities in the temperature range studied, and is generally valid for the above elements. T h e experimental atomization time, T ~ measured , for the elements over the range of heating rates studied is presented in Table I. For each element studied, the experimental atomization time, T ’ , a t first decreases rapidly with increasing heating rates and then decreases slowly at higher heating rates. The latter effect may be the results of the atom loss increasing
’
Kms-l 4.33 4.17 3.68 3.40 2.60 2.17 1.47 1.23 0.79
V 360 390 430 440 475 500
Mo 900 950 1200 1250 1500 1750
-
-
A1
Ni
125 130
460 470
130
480
150 210 245
480 560
-
-
Cu 135 150 155 170 205 270
600
-
-
-
-
Cd 80 80
Zn 70
110
70 75
140 150 165 230 260 430
145 160 175 180 250
YO
Table 111. Effect of Heating Rate on the Ratio of Experimental Atomization Time/Experimental Residence Time dT/ dtl
Kms-I 4.33 4.17 3.68 3.40 2.60 2.17 1.47 1.23 0.79
ratio
T , / T ~
V 0.50 0.50 0.53 0.51 0.54 0.49 0.60 0.52 0.67 0.52 0.80 0.60 Mo
-
-
A1
Ni
1.12 1.23 1.54 1.67 1.67 1.67
0.69 0.72 0.83 1.02 1.07 1.30
-
-
-
-
Cd 1.33 1.50 1.30 1.50 1.37 1.18 1.35 1.00 1.22 1.00 1.02 0.97 0.87 1.04 0.84 Cu
Zn
1.29 1.29 1.27 1.11 0.79 0.78 0.91 1.22 1.16
a t a faster rate (relative to the atom formation) as the rate of heating approaches the highest rate of heating available; the consequence of this being that the time to reach the peak absorbance ( T ~ does ) not decrease as rapidly as a t lower rates of heating. At high rates of heating, thermal gradient across the length of the graphite tube increases sharply and atom loss due to diffusion and convection across this thermal gradient toward the cold end-cap windows also increases. Furthermore, because of the rapid expansion of the purge gas inside the graphite tube, there is an increase in the loss due to mechanical expulsion of atoms through the sample injection port. At high rates of heating, there is probably also an increase in the loss by diffusion through the pyrolytic graphite tube walls although such loss is probably negligible a t lower rates of heating (15). The experimental residence time, r2, is presented in Table 11. L‘vov‘s model (16)predicts that a maximum in the pulse peak height orcurs when the ratio T’’/Tp’ 2237 N o mechanism has been established Ni 1 5 9 0 - 1 6 8 8 Ni(,) -* Ni(,) >1688 Ni, (g) 2Nl(g) V 2200-2360 VO(,) --* V(g) + O(,) > 2360 V(1) -* VW Mo > 2 1 0 0 M o w MO(,) Taken from reference 1 4 . CU
1270-1326 >1326 >720 >1140 2080-2237
-+
-t
+
-
320
180 210 200
980 480 4 10 2 10 640 490 690
energy, E,, for the rate-determining step, is governed by the Boltzmann factor, e-Ea/RT(this factor determines the number of activated complex, N).This number, N. can be written in terms of the Boltzmann distribution as
N
=
~~t~-E./fi'T
(6)
where E, is the activation energy of the rate-determining step in the atom-releasing process; N is the number of analyte species having energy equal to or greater than E,; No' is the number of analyte atoms in the sample, R is the universal gas constant, and T i s the temperature in degrees Kelvin. The exponential term in Equation 6 indicates that the effect of a given change in the temperature, T, on the number of activated complex, N, will be greater, the larger the value of the activation energy, E,. Since temperature is a linear function of the heating rate, a t least. during the initial part of the temperature-time curve (Figure l),the latter can be substituted for the temperature in the above discussion. Thus, the greater the heating rate, the greater is the number of analyte species having energy equal to or greater than E,. Also, for those elements which are relatively difficult to atomize, Le., which have larger values for the activation energy, E,, a given change in the heating rate will produce a greater change in the number of activated complex species, N , and hence in the analytical sensitivity than for those elements which are relatively easy to atomize, Le., which have smaller values for the activation energy, E,. This was experimentally observed, as is seen from Figure 4. Figure 4 is a correlation plot of the activation energy, E,, and the PEAK HEIGHT RATIO which is the ratio of the peak absorbance at the heating rate of 4.0 K ms-' to that a t
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 13, NOVEMBER 1978
9
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Flgure 5. Integrated absorbance as a function of graphite tube heating rates 0 Mo, 0 V, 0 Ni, H Cu, A Cd, A Zn, 0 AI
the heating rate of 2.0 K ms-’. The activation energy values taken from the paper by Sturgeon et al. (14) who used the same experimental setup are presented in Table V. Figure 4 shows that the higher the E’, value of the rate-detmiiiniag step in the atom-releasing process, the greater the increase in the peak absorbance due to a given increase in the heating rate. Effect of Heating Rates on Integrated Absorbance. Integrated absorbances of a number of metals as a function of the heating rate are presented in Figure 5 . Three general trends emerge from examination of these curves. Copper, Al, Cd, and Zn show an exponential decrease in the integrated absorbance with increasing heating rates; Mo and V show an exponential increase in the integrated absorbance with increasing heating rates; the integrated absorbance of Ni is virtually independent of the heating rate over the range of the heating rates studied. According to Equation 4, the integrated absorbance is directly proportional to the residence time, T;, of the atoms in the analysis volume; this equation t o be valid, however, requires fulfillment of two conditions, viz., complete atomization of the analyte and a constant residence time. These conditions, however, are not always fulfilled in the case of commercial atomizers. For example, even for relatively volatile elements such as Zn and Cd where complete atomization is expected, the atomizer surface temperature is changing rapidly throughout the duration of the absorption pulse (27). A continuously changing thermal gradient across the longitudinal axis of the graphite tube surface greatly affects the residence time, 721, of the analyte atomic vapor in the analysis volume. Also, except for a 200-300 ms period from the beginning of the absorption pulse, the temperature of the vapor phase in a HGA 2100 graphite tube lags behind the graphite tube surface temperature; the magnitude of the lag continues to increase throughout most of the duration of the pulse and becomes constant only for a short period a t the end of the absorption pulse ( 2 7 ) . ‘rhus, as the heating proceeds, the rapidly changing temperature and the large thermal gradient across the longitudinal axis of the graphite tube yield an analyte atom population, No,which is less than N:, which is the number of analyte atoms present in the sample. Thus, the experimental values of the integrated absorbance, Q N , are not constant and are less than the theoretical value, QN‘. Furthermore, complete atomization of the analyte element sometimes did not occur, as was evidenced by Mo (2.5 ng) which even after prolonged atomization periods (8 s at 3000 K)still yielded a “memory effect” in subsequent blank firings of the graphite tube. Although Equation 4 cannot be strictly applied to this case, the “memory” signal resulting from a typical quantity of Mo (1.0 ng), atomized under the experimental conditions used in
this study, did not account for more than a few percent of the total signal, and, hence, such residual Mo does not alter the interpretation of the experimental results for Mo presented here. For commercial graphite furnaces, Equation 4 should be modified as shown in Equation 7: where QN = experimental integrated absorbance, No = number of atoms in the analysis volume, and T~ = experimental residence time. QN will be a constant if both No and r2or their product remains constant. Using Equation 7 , the curves in Figure 5 for Cu, Al, Cd, and Zn can be rationalized in terms of the number of analyte atoms N o in the analysis volume and experimental residence time, 72. In Figure 2, if it is realized that the number of analyte atoms at the peak of the absorption pulse is given by No rather than the number of analyte atoms in the sample, N,’, as would be when r1/
