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Influence of vapor redeposition and modifiers on the Arrhenius plots of copper in graphite furnace atomic absorption spectrometry
SPECTROCHIMICA ACTA PART B
ELSEVIER
Spectrochimica Acta Part B 52 (1997) 1269-1281
Influence of vapor redeposition and modifiers on the Arrhenius plots of 1 copper in graphite furnace atomic absorption spectrometry Dorys Rojas*, Maria A. Sfinchez, Wilmer Olivares Lab. Espectroscopia Analltica, Departamento de Qulmica, Facultad de Ciencias. Universidad de Los Andes, MOrida, Venezuela
Received 2 November 1996; accepted 3 February 1997
Abstract
A study is presented of the effects of the processes of redeposition of atomic vapor on the Arrhenius plots. For that purpose, a kinetic model that considers the redeposition of the initial atomic vapor, and the revaporization of the redeposited species, at a later time is proposed and tested for the electrothermal atomization of Cu. This model predicts Arrhenius plots which present negative deviations from the linear behavior expected for a single process of release and dissipation of the atomic vapor. The magnitude of the negative deviation increases as the readsorption rate and the temperature difference between the release and redeposition sites increase. This type of behavior is observed in the Arrhenius plots obtained when well used graphite tubes and ascorbic acid are employed for the atomization of Cu. However, when new pyrolytically coated graphite tubes, or tungstencoated tubes, are used, the Arrhenius plots show the expected linear behavior for the one-precursor model, with a first kinetic order of release. Additionally, when using Mo and Pd as modifiers, these plots shows two well defined slopes, which are characteristic of a two-precursor atomization mechanism. The experimental results indicate that the degree of vapor redeposition is determined not only by temperature gradients but also by the properties of the atomizer surface. © 1997 Elsevier Science B.V. Keywords: Arrhenius plot; Atomization; Copper; Electrothermal AAS; Modifier; Redeposition
1. I n t r o d u c t i o n
The kinetic parameters employed to explain the atomization mechanisms in electrothermal atomic absorption spectroscopy are obtained mainly from Arrhenius plots constructed from the absorbance profiles. Therefore the effects of processes of a n a l y t e surface interaction and those of formation and dissipation of the atomic vapor, which define the
* Corresponding author. Mailing address: Apartado Postal 478, Mdrida 5101A, Venezuela. E-mail: [email protected] Thie paper has been published in the special issue of the Second European Furnace Symposium, St. Petersburg, Russia, May 1996.
atomization profiles, are fundamental for the interpretation of the kinetic parameters and atomization mechanisms. The interaction of the atomic vapor with the surface of the atomizer and the spatial and temporal non-isothermality of the atomizer have been considered to cause the redeposition of the atomic vapor [1-3]. Holcombe et al. [1] interpreted the spatial atom distribution profiles within a graphite furnace atomizer as being due to the strong readsorption of the atomic vapor of certain metals on graphite. Gilmutdinov et al. [2,3] showed, by shadow spectral filming studies, that the cross-sectional distribution of an analyte within a graphite or a metal-lined furnace is non-uniform and that its characteristics depend on the
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D. Rojas et al./Spectrochhnica Acta Part B 52 (1997) 1269-1281
element. Accordingly, they proposed a cascade mechanism of analyte propagation in non-isothermal furnaces at low heating rates, which consists of a number of condensation-vaporization processes of the analyte as the temperature wave propagates along the length of the furnace during the heating cycle [3]. Signal tailing has been attributed in the literature to adsorption-condensation processes of the atomic vapor on the cool ends of the atomizer [4-8]. Holcombe and co-workers [4-7] have suggested that a series of adsorption-revaporization processes may occur along the length of the tube, so that the form of the absorbance profile is determined largely by the degree to which the analyte atoms adhere to the tube material. Additionally, Frech et al. [8] also proposed secondary adsorption-desorption processes to explain the signal tailing detected in the atomization of various elements in the presence of different metal modifiers. On the other hand, L'vov et al. [9] proposed the condensation of the atomic vapor at the cooler surfaces of the atomizer to explain the shape of the electrothermal absorbance profiles. Despite the amount of experimental data supporting the redeposition processes of the atomic vapor, few models have been reported to include the vaporsurface interactions after the initial release. G~ell and Holcombe [10] included readsorption of analyte on the furnace wall in a Monte Carlo simulation study on the dependence of the absorbance signal of Cu and Ag on furnace length. Signal tailing is predicted for the absorbance pulses of Cu, which is considered to exhibit marked interaction with graphite. Musil and Rubeska [11] proposed a mathematical model based on free atom redeposition and isothermal conditions to explain the atomization profiles of Mn, and observed that the model predicted the falling portion but not the rising portion of the absorbance pulse. Welz et al. [12] applied the same redeposition model to the atomization of several analyte elements using atomizers made of various materials. They concluded that one of the limitations of the model is the assumption of isothermality. This condition does not seem to be satisfied in commonly used atomizers, which, as shown in recent studies [13], display temporally and axially non-uniform temperature distribution. They therefore proposed an extended redeposition model that takes into account the
temporal and axial temperature non-uniformity in the tube during atomization. Their results showed that a better description of the rising and falling parts of the absorbance profiles is obtained by including the temperature dependence of the reaction rates. However, no work has been reported on the effects of redeposition processes on the Arrhenius plots commonly employed to determine the kinetic parameters of the atom release processes. To study these effects, in this work we propose a redeposition kinetic model that assumes that the initial atomic vapor could be readsorbed or condensed at surface sites having a lower temperature than the central part of the atomizer, and that its revaporization occurs when those sites reach the appropriate temperature. The effects of these type of processes on the Arrhenius plots are studied for different redeposition rate constants and for different temperature differences between the central part of the atomizer and the redeposition sites. The model also considers redeposited species with atomization energy lower or higher than or equal to that of the initial precursor of the atomic vapor. Finally, the theoretical predictions are compared with the experimental results obtained for the atomization of Cu alone by employi,g new pyrolytically coated graphite tubes, well used graphite tubes, and in the presence of chemical modifiers such as ascorbic acid, tungsten, molybdenum and palladium.
2. Experimental 2.1. I n s t r u m e n t a l
A graphite furnace (PE HGA-2100) equipped with standard pyrolytically coated, tungsten-coated or molybdenum-coated tubes was used as the atomizer. The absorbance signals of Cu were measured at 324 rim, using the stop flow mode, by cutting off the purge gas during the atomization cycle. Prepurified argon was used as the purge gas during the drying and ashing cycles. We used slow vaporization of the solvent and a pyrolysis stage of 20 s at 970 K, with a total time of 30 s. A peak atomization temperature of 2770 K was employed. To minimize temporal distortions of the registered profile, the absorbance signals were measured at the output of the photomultiplier
D. Rojas et al./Spectrochimica Acre Part B 52 (1997) 1269-1281
tube after demodulation and logarithmic conversion. The time dependent atomizer temperature was determined from measurements of the furnace emission focused onto a photodiode, as previously described [14]. Both the absorbance and the temperature data were digitized with a 12 bit resolution, 16 channel A/D card and were collected every 0.02 s with an Intel-286 microcomputer. The absorbance and temperature data were then fitted with a cubic spline algorithm to obtain the time derivative of the absorbance pulse, its characteristic parameters, and the atomization heating rate.
2.2. Reagents All the reagents employed to prepare the standard solutions were of analytical grade. The working solutions of Cu were prepared from a standard of 1000 ~g ml i, which was prepared by dissolving copper chloride in 0.01 M hydrochloric acid. The modifier solutions were prepared from standard solutions of 1% w/v ascorbic acid, 1% w/v tungsten (oxide) dissolved in 0.1 M sodium hydroxide, 100 txg ml -L of molybdenum (as phosphomolybdic acid), and 100/xg ml -~ palladium (as nitrate). To ensure temporal stability, all the working solutions were prepared daily in 0.01 M hydrochloric acid. Aliquots of 20/xl of the working solutions of Cu and the modifier were deposited on the wall of the graphite tube with an autosampler (Perkin-Elmer AS-l). The procedure reported by Iwamoto et al. [15] was employed to coat the graphite tubes with tungsten and molybdenum.
1271
kl(t)=ujexp[-E(al)/RT~(t)] and k3(t)= u3exp[-E~3)/RTr(t)] are the time dependent rate
where
constants of generation of the atomic vapor Y from the species X and V, respectively, kr(t)= urexp[-E~r)/RTr(t)] is the rate constant of redeposition of the atomic vapor, and kz(t ) = k 0 [T(t)/To]" is the rate constant of dissipation of the atomic vapor. Additionally, Z is the dissipated species, u is the pre-exponential factor, E~ is the corresponding atomization energy, R is the gas constant, and T and Tr are the time dependent temperatures at the center of the atomizer and at the redeposition sites, respectively; k ° is the rate constant of diffusion of the atomic vapor at a reference temperature T0 (273.15 K), and n is the diffusion factor. If a temperature gradient exists from the center to the ends of the graphite tube, the temperature at any position z is determined by the rate of propagation of the temperature wave along the tube. However, for simplicity, in this study we consider discrete redeposition sites with a temperature Tr, which is lower than the temperature T by an amount AT, namely T r = T AT. Therefore, in our model a time lag exists between the original process of generation of the atomic vapor and the revaporization of the redeposited species. This revaporization process will begin only at the time at which the temperature Tr reaches the appearance temperature of the redeposited species. From the kinetic equations of this atomization process, which are solved in Appendix A, one obtains the following expression for the rate constant k ](t) ~-+k2Y(t)
+ [krY(t ) - k 3 V ( t ) ]
kl(t)
(2)
3. Computational simulations Let us consider that a precursor X generates the atomic vapor Y, which could be dissipated or, by collision with the wall, could be re-adsorbed or condensed at the cooler ends of the atomizer [7,10,16,17] as a species V, which in turn vaporizes at a later time. This atomization process could be described schematically as
x~ K,
V
K2 j~
Y
> Z
(1)
Eq. (2) clearly shows how the redeposition and revaporization process affects the determination of the kinetic parameters of the initial release process. Thus, in order to quantify their effects, we construct the Arrhenius plots by using the method proposed by Rojas and Olivares [14]. Then, as shown by Eq. (A10) and Eq. (A13) of Appendix A, the Arrhenius plots are determined by E~~) lnW, (t) = In g(t) + In(u) - - -
RT(t)
(3)
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
1272
where g(t), as defined by Eq. (AI 1), takes into account the terms of the redeposition processes. Here we have assumed first order kinetics for all the processes of generation and dissipation of the atomic vapor. According to these equations, at the beginning of the atomization process, where there is no redeposition of the atomic vapor, the Arrhenius plots are determined by the kinetic parameters of k j(t) alone. However, as the redeposition of the atomic vapor becomes appreciable, the contribution of the term g(t) causes a diminution of the values of Wl(t), and therefore negative deviations are predicted from the linearity expected for a system without redeposition. Then, to study the effects predicted by the readsorption model, the theoretical atomization pro-
Table 1 Kinetic parameters employed in the computational simulations of absorbance profiles of Section 3 Parameter
Value
E~l)/(kJ tool -r)
150 104 75, 150, 300 l0 ~, 104, 108 0.0-1.0 0, 300, 600, 900 0.02 1.9
ul/s t E~3)/(kJ mol-;) t) 3/s -~
kfs -I ,aT~K) k0/s -' n
0.6
(A)
O o 0.4 rJQ 0¢) L
~
,.Q < 0.2
id c b a
1
2
3
4
5
Time, s
10.00 (B)
~
1.00
~ .
~
a
b '.
. -
",
0.10
0.01
6.8
6.2
5.6
5 -1
(1/T)x10 ,K 4
4.4
3.8
Fig. 1. Simulated absorbance profiles (A) and the Arrhenius plots for m = I (B), assuming a redeposition rate constant k r equal to (a) 0.0, (b) 0. I, (c) 0.5, and (d) 1.0 s -]. In this simulation, we assume a value o f ` a T = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E~~) is equal to E~,~).
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281 files Y(t) were computationally simulated by using the numerical solution of eqns ( A 1 - A 4 ) , and the values of the function Wl(t) are calculated by using Eq. (A9) with m = 1. For these calculations, the dissipation rate constant k2(t) is determined by using a diffusion type temperature dependence, with values of n and k ° equal to 1.9 and 0.020 s -~, as obtained experimentally by employing the RO-2 method proposed by Rojas and Olivares [18]. The atomization temperature T at the center of the tube was simulated by employing a six term polynomial, which was obtained by curve fitting the experimental temperature profile. In Sections 3.1, 3.2 and 3.3 we study the effect of the magnitudes of the redeposition rate constant, the redeposition temperature, and the revaporization rate constant on the Arrhenius plots. The general kinetic parameters employed for the computational simulations of the absorbance profiles are shown in Table 1. As can be seen from this table, we have chosen the precursor X to have the average activation energy and pre-exponential factor determined from the experimental atomization profiles of Cu when new pyrolytically coated graphite tubes were employed as the atomizer. For the process of redeposition we have assume an energy equal to zero, as has been considered earlier in the literature [10,11,16]. 3.1. Effect of the redeposition rate constant kr In general, the redeposition rate depends on the sticking probability [10,16] of the atomic vapor, and thus it depends on the number of active sites at the surface of the atomizer where redeposition can occur, and on the temperature of such sites. In this study we consider values of the redeposition rate constant kr between 0.01 and 1.0 s -~, which predict the form of the absorbance profiles obtained experimentally. In this section, we assume a value of AT = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E(a31is equal to Etll a
•
Fig. 1 shows the effects of the magnitude of the rate constant kr on the atomization profiles (A) and on the corresponding Arrhenius plots (B). From Fig. IA we can see that the time of maximum absorbance decreases, whereas the pulse tailing of the absorbance
1273
profile increases, as the redeposition rate constant increases from 0.0 to 1.0 s -l, as has previously been reported [8,11,12]. Similarly, from Fig. IB we can see that the initial slope of the Arrhenius plot, and therefore of the atomization energy and the pre-exponential factor determined therefrom, decreases as the value of kr increases. To quantify this effect, the atomization energy was determined for each case from the linear portion of the Arrhenius plots obtained for m = 1. Table 2 presents the effects of the magnitude of kr on the atomization energies so determined, and the percentage difference of that energy from that obtained for the system without redeposition, namely kr = 0. It was also observed that, when employing redeposition rates greater than 1.0 s -~, the tailing of the absorbance profile is so large that atomization times exceeding 12 s are required for the signal to return to the baseline. However, since this behavior is not common under our experimental conditions, such large redeposition rate constants are not included in this work. It should be mentioned that the Arrhenius plots for kinetic orders greater than one also show negative deviations from linear behavior. 3.2. Effect of the temperature of the redeposition sites According to Welz et al. [ 13] and Gilmutdinov et al. [2,3], the graphite tube exhibits a temperature gradient from its center to the ends, with temperature differences up to 1000 K. Therefore the temperature within the atomizer is a function of both the time and the spatial position of the redeposition site. However, this T(z,t) function is not well known and its description is not the aim of this work. Thus, for simplicity, Table 2 Effects of the redeposition rate constant on the kinetic parameters determined from the slope of the linear part of the Arrhenius plots for m = 1. E~ is the difference of the energies so obtained with and without redeposition of the atomic vapor. In this study, we assume a value of A T = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E~3) is equal to Etat)
k~/s-t
Ea/(kJ mol-I)
In (v)
AEal%
0.1 0.5 1.0
142.13 140.74 137.29
9.14 8.56 8.13
- 5.2 - 6. I - 8.3
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
1274
we shall not consider a continuous temperature propagation rate within the tube, but instead we shall assume that it is discretized. Then, from the center to the end, the tube is segmented in three zones, each with a temperature difference AT that increases as its distance from the tube center increases. Fig. 2 presents the effect of the temperature of the redeposition sites on the atomization profiles (A) and the corresponding Arrhenius plots (B) for values of T of 0, 300, 600 and 900 K. For this simulation we assumed a rate constant of redeposition k~ equal to 0.5 s -~, and that the species V has the same atomization energy as that of the original precursor X, that is, E(3) is equal to F(~) ~ .
0.6
(A)
0.4 (tl £ O .Q 0.2 <
As shown in Fig. 2A, an increase in the pulse tailing of the atomization profile is observed as the temperature difference z~T increases from 0 to 900 K, and therefore a greater time is required for complete atomization of the sample. Also, as displayed in Fig. 2B, the negative deviations from linearity shown by the Arrhenius plots remain essentially equal, but the curves fall faster as the temperature difference AT increases. Accordingly, when employing a graphite tube with a temperature gradient up to 900 K [2,3,13] from the tube center to its ends, the atomization profiles and the corresponding Arrhenius plots should behave as an average of those shown in Figs. 2A and 2B, respectively. In short, the absorbance signal will show peak tailing and the Arrhenius plots will present negative deviations from the linear behavior expected for a one-precursor mechanism without redeposition.
3.3. Effects of the kinetic parameters of atomization of the .wecies V
a~i
1
2
cI 3
4
d
5
6
Time, s
10.00 E
1.00
',
0.10
Id
0.01 r
s.s
s
s.s
s
4.5
4
( l / T ) x 10 4 , I~ 1 Fig. 2. Simulated absorbance profiles (A) and Arrhenius plots (B) for m = 1, assuming a temperature difference between the center part of the graphite tube and the redeposition site, AT, equal to (a) 0, (b) 300, (c) 600, and (d) 900 K. In this simulation, we assume a value of kr equal to 0.5 s J, and that the species V has the same atomization energy as that of the original precursor X, that is, E] ~ is equal to E/d1(
As the redeposited species could have the same or a different chemical nature compared with the original precursor X, in this section we study the effect of the kinetic parameters for the atomization of the species V, namely E(d~t and/)3, on the absorbance profiles and the Arrhenius plots. For this purpose we employ a redeposition rate constant kr equal to 0.5 s -~, AT = 600 K, and kinetic parameters for species V that, as shown in Table 1, are half, equal to and twice those used for the atomization of the species X. Accordingly, species V could be physically adsorbed (low energy), or it could be the same as the species X (equal energy), or it could be chemically adsorbed on the surface of the atomizer (high energy). Fig. 3 presents the atomization profiles (A) and the corresponding Arrhenius plots (B) obtained for values or~-~)t~ d a n d u 3 o f ( a ) 1 5 0 k J m o l l and104 s-], (b) 75kJ mo1-1 and 102 s -I, and (c) 300 kJ mol -I and 108 s -j. As can be seen from Fig. 3(A), the lowest kinetic parameters do not appreciably modify the absorbance profile (curve b), but the highest kinetic parameters (curve c) produce a greater elongation of the falling part of the absorbance pulse owing to the delayed atomization of species V. However, as could be seen from Fig. 3(B), the negative deviations exhibited by the Arrhenius plots are practically the same in all
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281 0.5
(A)
tin J~ 0.25 0 m .o
<
1
2
3
4
5
Time, s
10.00
o
(B)
E
~
Wo
1.00
0.10
0.01
7
6.5
6
5.5
5
4.5
4
( l r r ) x 10 4 , I~ 1 Fig. 3. Simulated absorbance profiles (A) and Arrhenius plots (B) for m = I assuming atomization energies of the redeposited species, V, equal to (a) 150, (b) 75, and (c) 300 kJ mol t. In this simulation, we assume a value of kr equal to 0.5 s -I , and ATequal to 600 K. The curve W~ corresponds to the system without redeposition of the atomic vapor, i.e. kr = 0.0 s -I.
cases, with a faster decay for the system with the highest kinetic parameters.
4. Experimental Arrhenius plots for the atomization of Cu Copper was chosen as the analyte to show the effects of the redeposition of the atomic vapor on the Arrhenius plots because of its high sticking adsorption coefficient on graphite [10,16,17]. Hence the atomization mechanism of Cu could be altered by employing chemical modifiers, such as ascorbic acid, tungsten, molybdenum and palladium, that modify the surface of the atomizer. In this section, we study the effects of these modifiers on Arrhenius plots
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corresponding to the experimental electrothermal atomization of Cu. To construct the Arrhenius plots, the values of the function Win(t) were calculated as a function of the kinetic order of generation of the atomic vapor m by using Eq. (A9) in Appendix A. It is important to point out that the experimental data for the entire absorbance profile are employed for the calculation of the integral function in the denominator of Win(t). However, the Arrhenius plots are constructed up to the time ty, where the time derivative of the absorbance signal reaches a minimum value [ 14,18], or up to the time at which the atomization temperature reaches its maximum value. The rate constant of dissipation of the atomic vapor, k2(t), as required by Eq. (A9), is determined by using the RO-2 method reported by Rojas and Olivares [18]. This method assumes that the dissipation of the atomic vapor is primarily a diffusion process, and it can be used for time-varying temperature conditions. Accordingly, from the absorbance and temperature profiles measured under the different experimental conditions specified in the following sections, values of n and k ° equal to 1.9 and 0.02 s -~ ( +_ 8%), respectively, were obtained for the atomization of Cu. These values of the parameters n and k~ are within the expected range for a gas diffusion process [19]. For comparison purposes, Figs 4 and 5 shows the absorbance profiles and the Arrhenius plots obtained 0.8
0.6
o 0.4
.~
e
c ; "l ...
..,
";I-X~
' UI I
0.2
;:1
",
a
d',.-:X2", ..,.
0 0
2
4
6
8
Time, s Fig. 4. Absorbance profiles obtained for the atomization of 1.2 ng of Cu, employing pyrolytic graphite tubes (a), and in the presence of 0.01% w/v of ascorbic acid (b), W (c), Mo (d), and 1 tzg of Pd (e).
1276
D. Rojas et a/./Spectrochimica Acta Part B 52 (1997) 1269-1281
100.00
(A)
~
10.00
E
1.00
f
f
/t
/
/ m=2
10
m=l
E
(B)
.~ .-
1
~ m=2
i / ~ i I/'r" /" / / / / 1~/f/
0.1
0.10
J
~i
m=l m=0
~. m=O /
0.01
0.01 7
6.5
6
5.5
5
4.5
7.5
7
6.5
6
( l / T ) 104 , K I
5.5 4
5
(l/T) x 10 , !~
4.5
1
100
(C) /
100
/J . , . ~
E
I
/
/" m=2
(D)
I
m=2
m=l
s
.
~
~
m=l
m=O
m=O
0.01
0.01 9
8
7
6 4
(1/Tlxl0,
100
7.8
-1
6.8
K
5.8
4
-1
4.8
3.8
(1/1") x 10 , K
(E) /
10
/
!
I
m=2
/
I / t
j
F: 1 m=O 0.1
0.01 8.2
7.2
6.2
5.2
4.2
3.2
(1/3") X 104 , K" 1 Fig. 5. Experimental Arrhenius plots obtained for the atomization of 1.2 ng of Cu, employing pyrolytic graphite tubes (A), and in the presence of 0.01% w/v of ascorbic acid (B), W (C), Mo (D), and 1 p.g of Pd (E).
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
Table 3 Effects of chemical modifiers on the atomization energies of Cu. The symbols E]u and E]2! are the atomization energies calculated from the slopes of the Arrbenius plots in the low and the high temperature regions, respectively Modifier
E]I)/(kJmol-I)
E~2)/(kJmol-i)
None Ascorbic acid W Mo Pd
145 147 155 203 192
145 Negative deviations 155 143 133
for the atomization of Cu alone and in the presence of the modifiers employed in this study. Also, Table 3 shows the atomization energies obtained in the absence and in the presence of the modifiers. As a reference, Fig. 5A shows the Arrhenius plots obtained by employing new pyrolytically coated graphite tubes for the atomization of 1.2 ng of Cu. This plots indicates a first kinetic order of release, with an average atomization energy of 145 kJ mol -] ( _+ 10%), and apparently no redeposition of the atomic vapor. 4.1. Effect o f ascorbic acid
It has been reported that the pyrolysis of ascorbic acid produces active carbon species and an alteration of the surface of the graphite tube [20-22] when ascorbic acid is employed as a chemical modifier. Thus, the use of this acid as chemical modifier could induce redeposition of the original atomic vapor. The effects of variable concentrations of ascorbic acid on the electrothermal atomization of Cu are therefore studied in this section. An increase in the peak absorbance and the area of the absorbance signals of Cu is detected when the concentration of ascorbic acid added is varied from 0.005 to 0.1% w/v, indicating an increase in the atomization efficiency of the analyte. This behavior is shown in Fig. 4 for the atomization of 1.2 ng of Cu in the presence of 0.01% w/v of ascorbic acid (curve b). Similarly, Fig. 5B shows the Arrhenius plots obtained for the electrothermal atomization of 1.2 ng of Cu in the presence of 0.01% w/v of ascorbic acid. As can be seen from Fig. 5A and 5B, the Arrhenius plots obtained for the atomization of Cu in the presence of ascorbic acid, for physically
1277
meaningful kinetic orders of release, display negative deviations from the linear behavior obtained in Fig. 5A for m = 1. A comparison of these plots with those predicted in Fig. 1A by our model of redeposition of the atomic vapor indicates a good qualitative correlation, and suggests the redeposition of the atomic vapor of Cu in the presence of ascorbic acid. It is also observed that the negative deviations from linearity of the Arrhenius plots increase as the concentration of ascorbic acid increases, which would be the expected behavior if the pyrolysis of ascorbic acid increases the number of active sites and thus the redeposition sites on the surface of the atomizer. Table 3 gives the atomization energy obtained from the linear part of the Arrhenius plot for m = 1 for the atomization of 1.2 ng of Cu with 0.01% w/v of ascorbic acid added. Similarly, when employing well used graphite tubes, meaning those with more than 80 firings, the Arrhenius plots obtained for the atomization of Cu show negative deviations, such as those in Fig. 5B. The likelihood of redeposition of the atomic vapor on the well used tube is expected because of its greater number of active sites compared with those in a new pyrolytically coated tube. As shown in Table 2, if the redeposition of the atomic vapor becomes appreciable, the deviation from linearity in the Arrhenius plots leads to kinetic parameters that are appreciably lower than those expected without redeposition of the atomic vapor. Since the magnitude of the redeposition depends on the analyte-surface interaction, the kinetic parameters determined will depend on the type and the number of active sites and on the temperature propagation along the atomizer. All these effects could explain the variety of atomization energies that have previously been reported in the literature, in the range 125-195 kJ mol -~, for the atomization of Cu [14,23,24]. 4.2. Effects o f tungsten-coated tubes
In this study, the graphite tubes are coated with tungsten to produce a saturation of the active sites on the surface of the atomizer and therefore to reduce the number of redeposition sites. As shown in Fig. 4 (curve c), it is found that, when W-coated tubes are used for the atomization of Cu, the absorbance pulse is sharper, with a higher rate of release and less tailing of the falling part than those obtained with new
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D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
pyrolytically coated graphite tubes (curve a). This kind of behavior has been reported when employing a Ya atomizer [5]. Fig. 5C shows the Arrhenius plots obtained for the atomization of 1.2 ng of Cu by employing W-coated graphite tubes. From this figure, we can see that the plots exhibits the linear behavior expected for a system without redeposition of atomic vapor. From these plots, a first kinetic order of release and an atomization energy of 155 kJ mol -I are obtained. This atomization energy indicates desorption of the analyte from the surface of the atomizer without redeposition of the atomic vapor. Accordingly, the saturation of the active sites of the atomizer with tungsten seems to minimize the processes of redeposition of the atomic vapor of Cu. Thus, if the temperature gradient within the graphite tube is not appreciably changed by coating the tubes with W, the experimental results seem to indicate that the redeposition of the atomic vapor depends on the properties of the surface of the atomizer. 4.3. Effect o f Mo-coated tubes
As Mo forms stable carbides [25], it is expected that it would also saturate the active sites and therefore would decrease the number of possible sites for redeposition of the atomic vapor of Cu. As shown in Fig. 4 (curve d), only small variations are detected in the sensitivity and the appearance temperature when Mo-coated tubes are employed for the atomization of Cu. Furthermore, as presented in Fig. 5D, the Arrhenius plots obtained for the atomization of 1.2 ng of Cu employing Mo-coated tubes display two slopes. This behavior has been reported as characteristic of a two-precursor atomization mechanism [18]. From Fig. 5D, it is observed that the kinetic order of release is not well defined in the low temperature region, but a first kinetic order of release is defined in the high temperature region. Thus, from the plot with m -- 1, average atomization energies of 203 and 143 kJ tool ~are obtained in the low and the high temperature regions, respectively. The energy obtained in the low temperature region correlates well with the dissociation energy of the copper dimer, which has a dissociation energy of 196 kJ tool -~ [26], and indicates an increase in the analyte-
analyte interactions. In addition, the energies obtained in the high temperature region seem to correspond to a desorption process of the analyte from the surface of the atomizer. Accordingly, the use of Mo also seems to minimize the redeposition process of the atomic vapor of Cu. 4.4. Effect o f Pd
Palladium is one of the most widely used chemical modifiers in graphite furnace atomic absorption spectrometry. Different mechanisms have been proposed to explain the stabilizing effect of Pd on the atomization of volatile elements. A physical mechanism was proposed by Qiao and Jackson [27], whereas Yang and Ni [28] and Styris and Redfield [29] proposed the formation of a stable intermetallic solid solution. Furthermore, Volynsky et al. [30] proposed a catalytic process of reduction of metal oxides by Pd. Additionally, Frech et al. [8] found signifcant trapping of the analytes at the ends of the tube, and thus signal tailing, when Pd was employed as a modifier. Accordingly, they postulated changes in the adsorption properties of the tube and secondary adsorption-desorption processes. When Pd is employed as a modifier for the atomization of Cu, it is observed that the peak absorbance, the area and the appearance temperature increase as the initial mass of Pd increases from 0.1 to 2.0/~g. The increase in the appearance temperature reaches a maximum value of 200 K for 1 and 2 #g of Pd. This behavior is presented in Fig. 4 (curve e) for the atomization of 1.2 ng of Cu in the presence of 1 #g of Pd. It is also observed that, in the presence of Pd, the temperature of maximum absorbance of Cu remains unchanged as the initial amount of Cu increases, which has been taken in the literature as indicative of a first kinetic order of release with one precursor of the atomic vapor and a constant atomization energy [5,10,17,23]. However, the corresponding Arrhenius plots show two slopes, which is characteristics of a two-precursor mechanism of generation of the atomic vapor [18]. This behavior clearly invalidates the assumption of a precursor with first order kinetics, as suggested by the method of alignment of the time of maximum absorbance with the initial mass of the analyte.
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
Fig. 5E shows the experimental Arrhenius plots obtained for the atomization of 1.2 ng of Cu in the presence of 1/xg of Pd. From these plots it is observed that the kinetic order is equal to one in the high temperature region but is not well defined in the low temperature region. Then, from the plot for m = 1, atomization energies of 192 and 133 ( -+ 10%) kJ mo1-1 are obtained in the low and the high temperature region, respectively. This result seems to indicate that at temperatures lower than 1700 K the effect of Pd prevails at the surface of the atomizer, but at temperatures higher than 2100 K, where Pd has been vaporized from the surface [7], the analyte is freely desorbed from the graphite surface without redeposition. The energy obtained in the low temperature region correlates well with the dissociation energy of copper dimer [26], and accordingly it seems that the presence of Pd, at temperatures lower than 2000 K, favors the analyte-analyte interaction. This effect could be explained by a mechanism of trapping of the analyte by Pd, as has been reported previously [27,29]. Thus, the generation of the atomic vapor of Cu would be kinetically controlled by the release of the modifier, and so, at temperatures above 2000 K, the analyte would be freely released from the graphite surface. Hence this experimental result also points out the surface dependence of the redeposition process of the atomic vapor of Cu. Furthermore, the behavior of the Arrhenius plots shown in Fig. 5E indicates no redeposition of the atomic vapor. Accordingly, the result indicates that in our experimental conditions no analyte appears to be trapped at the ends of the tube, which is contrary to the behavior proposed by Frech et al. [8] for high initial masses of modifier. Instead, it seems that the analyte is concentrated at the hotter central region of the tube, as proposed by Frech et al. [31] since, as indicated by the energy obtained in the high temperature region of the Arrhenius plots, as Pd is released, the analyte desorbs freely from the graphite tube.
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atomization of Cu in the presence of surface modifiers. The theoretical redeposition model predicts an elongation of the falling part of the absorbance profile and negative deviations of the Arrhenius plots from the linear behavior expected for a single-precursor kinetic mechanism. It is shown that the magnitude of the negative deviations is proportional to the magnitude of the redeposition rate constant and to the temperature difference between the center of the atomizer and that of the redeposition sites. By analyzing the theoretically predicted Arrhenius plots, we have shown that the RO-I method can be safely applied to determine the kinetic parameters of the initial atomization process from the linear part in the low temperature region, since the redeposition process becomes appreciable at later times after the initial vapor has been propagated along the tube. It is observed that, under conditions where a high number of active sites prevails on the surface of the atomizer, such as those in well used tubes and when ascorbic acid is used for the atomization of Cu, the Arrhenius plots show the negative deviations predicted by our theoretical model of redeposition of atomic vapor. However, the Arrhenius plots obtained for the atomization of Cu in the presence of metal modifiers with a high degree of interaction with the graphite surface, such as tungsten, molybdenum, and palladium, indicate the absence of redeposition of the atomic vapor. It seems that these metal modifiers saturate the active sites on the graphite surface and therefore the redeposition process is suppressed. The experimental results indicate that the degree of vapor redeposition is determined not only by temperature gradients but also by the properties of the atomizer surface. Furthermore, the behavior of the Arrhenius plots obtained for the atomization of Cu in the presence of Mo and Pd indicates a two-precursor atomization mechanism. In the low temperature region, the presence of Mo and Pd seems to increase the analyteanalyte interaction, whereas in the high temperature region the desorption of Cu from the surface of the atomizer prevails.
5. Conclusions A kinetic model that takes into account the redeposition of the atomic vapor is proposed to explain the behavior of the Arrhenius plots for the electrothermal
Acknowledgements This work was supported by the Consejo de
D. Rojas et al./Spectrochbnica Acta Part B 52 (1997) 1269-1281
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Desarrollo Cientffico y Humanfstico of the University of the Andes (grants C-712 and C-714), M6rida, Venezuela.
This equation, together with Eq. (A1) and Eq. (A2), gives dY Ir~_~t+ k: Y(t)]
+[krY(t)-k3v(t)]
AppendixA If in the model of redeposition of the atomic vapor we assume a first kinetic order for the release and dissipation processes, and also assume that the rate of change of the atomic population, dY/dt, is determined by the rates of atom generation dX/dt and dV/dt, and by the rates of dissipation of the atomic vapor, the kinetic process is then described by
According to this expression, the redeposition of the atomic vapor affects the determination of the kinetic parameters of the initial process of generation of the atomic vapor. Now, since only Y(t) is experimentally measured by the absorbance signal, we proceed as in the RO-1 method of Rojas and Olivares [14] and define the function Wm(t) by
dX dt
Win(t) =
kl(t)X
(A1)
:~
D(t) + k2(t)A(t)
m
(A9)
[], k2(r)A(r)dr-A(t)] dV
~ f =kr(t)Y-k3(t)V
(A2)
dY ~ - = k,(t)X + k3(t)V -
Substituting
[k2(t) + kr(t)]Y
(A3)
Eq. (A1) and Eq. (A2) into Eq. (A3), one
obtains
W~(t) = g(t)k I(t)
dY 4-k2Y=- {dX+ d V ) d--7 k.d7 ~ Then, if X ° is the species, and there vapor at the initial atoms vaporized at Eq. (A4) Y(t) +
i
(A4)
initial amount of the is no redeposition of time (i.e V ° = 0), the a time t is obtained by
generating the atomic number of integrating
I
k2(r)Y(r)dz = X ° -
X(t) - V(t)
(A5)
0
Now, since Y vanishes at the time boundaries, from Eq. (A4) we have
J~ kz(t)Y(t)dt
= X°
(A6)
0
I/
k2(r)Y(r)dr = X(t) + V(t)
(A 10)
where W~(t) is the lunction Win(t) for a first kinetic order (i.e., m = 1), and g(t) is a factor that takes into account the terms of the redeposition process. This factor g(t) is defined by [(dV/dt)]
l+ g(t)=
k~/d~-J
l+(v'/x')
I+(V/X)
I+(V/X)
lnWl (t) = lng(t) + lnk l (t)
(A12)
and by substitution of the expression for the rate constant k Lit) we have
RT(t)
(A7)
(All)
where V' = dV/dt and X' = dX/dt. Then, the Arrhenius plots in terms of W, and following the RO-1 method, are given by
E~~) lnW 1(t)-- lng(t) + In(v)- - -
and therefore Eq. (A5) becomes: - Y(t) +
where A(t) and D(t) are the absorbance profile and its time derivative (dA/dt), respectively, and m is the kinetic order of release of the atomic vapor. Then, rearranging the terms in Eq. (A8) and by using Eq. (A1) and Eq. (A2), one obtains
(A 13)
Thus, from Eq. (A 11) one can see that, for the case of no redeposition of the atomic vapor, the amounts V and V' are zero and therefore g(t) is equal to unity.
D. Rojas et al./Spectrochimica Acre Part B 52 (1997) 1269 1281
Consequently, from eqns (A12) and (A13) we deduce that in this situation the Arrhenius plots are determined by the kinetic parameters of k l(t) alone. However, as the redeposition of the atomic vapor becomes appreciable, the quantity V/X, which is the ratio of the amount of redeposited vapor to the amount of the initial precursor at a given time, increases faster than V'/X', the ratio of the rate of revaporization to the rate of vaporization from the original precursor, and therefore g(t) decreases from unity. Then, according to eqns (A12) and (A13), the Arrhenius plots should give the kinetic parameters of the rate constant k l(t) at the earlier stage of generation of the atomic vapor, and will present negative deviations from linear behavior as the rate of redeposition of the atomic vapor, k,(t), increases.
References [I] J.A. Holcombe, G.D. Rayson, N. Akerlind, Jr., Spectrochim. Acta Part B, 37 (1982) 319-330. [2] A.Kh. Gilmutdinov, Yu.A. Zakharov, V.P. Ivanov, A.V. Voloshin, J. Anal. At. Spectrom., 6 (1991) 505-519. [3] A.Kh. Gilmutdinov, Yu.A. Zakharov, V.P. Ivanov, A.V. Voloshin, J. Anal. At. Spectrom., 8 (1993) 387-395. [4] J.A. Holcombe, G.D. Rayson, Prog. Anal. At. Spectrosc., 6 (1983) 225-251. [5] R.W. Fonseca, O. Giiell, J.A. Holcombe, Spectrochim. Acta Part B, 45 (1990) 1257-1264. 16] O. Gfiell. J.A. Holcombe, Spectrochim. Acta Part B, 47 (1992) 1535-1544. [7] J. McNally, J.A. Holcombe, Anal. Chem., 63 (1991) 19181926. [8] W. Frech, K.M. Berglund, D. Baxter, J. Anal. At. Spectrom., 7 (1992) 141-145. [9] B.V. L'vov, A.V. Novichikhin, L.K. Polzik, Spectrochim. Acta Part B, 47 (1992) 289-296.
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[ 10] O. GiJelk J.A. Holcombe, Spectrochim. Acta Part B, 44 (1989) 185-196. [11] J. Musil, I. Rubeska, Analyst, 107 (1982) 588-590. [12] B. Welz, B. Radziuk, G. Schlemmer, Spectrochim. Acta Part B, 43 (1988) 749-762. [13] B. Welz, M. Sperling, G. Schlemmer, N. Wenzel, G. Marowsky, Spectrochim. Acta Part B, 43 (1988) 1187. [14] D. Rojas, W. Olivares, Spectrochim. Acta Part B, 47 (1992) 387-397. [15] E. lwamoto, H. Shimazu, K. Yokota, T. Kumamaru, J. Anal. At. Spectrom., 7 (1992) 421-424. [16] J.R. Arthur, A.Y. Cho, Surf. Sci., 36 (1973) 641-66(I. [ 17] S.S. Black, M.R. Riddle, J.A. Holcombe, Appl. Spectrosc., 40 (1986) 925. [18] D. Rojas, W. Olivares, Spectrochim. Acta Part B, 50 (1995) 1011-1030. [19] B.V. L'vov, Atomic Absorption Spectrochemical Analysis, Adam Hilger, London, 1970. [20] S. Imai. K. Okuhara, Y. Nishiyama, T. Tanaka, Y. Hayashi, J. Anal. At. Spectrom., 10 (1995) 439-442. [21] N. Tomaidis, E. Piperaki, C. Efstathiou. J. Anal. At. Spectrom., 10 (1995) 221-226. 122] J. Byrne, C. Chakrabarti, G. Gilchrist, M. Lamourex, P. Bertles, Anal. Chem., 65 (1993) 1267-1272. [23] P. Wang, V. Majidi, J.A. Holcombe, Anal. Chem., 61 (1989) 2652-2658. [24] S. Lynch, R.E. Sturgeon, V. Loung, J. Anal. At. Spectrom., 5 (1990) 311-319. [25] H. Fritzsche, W. Wegscheider. G. Knapp, H. Ormer, Talanta, 26 (1979) 219-226. [26] Studies in Surface Science and Catalyis: Metal Clusters in Catalysis, Vol. 29, Elsevier, New York, 1986, p. 34. [27] H. Qiao, K.W. Jackson, Spectrochim. Acta Part B, 47 (1992) 1267-1276. [28] Y.P. Yam Z. Ni, Spectrochim. Acta Part B, 48 (1993) t3151323. [29] D.L. Styris, D.A. Redfield, Spectrochim. Acta Rev., 48 (1993) 71-123. [30] A. Volynsky, S. Tikhomirov, A. Elagin, Analyst, 116 (1991) 145. [31] W. Frech, M. Arshadi, D.C. Baxter, B. Hutsch, J. Anal. At. Spectrom., 4 (1989) 625-629.
ELSEVIER
Spectrochimica Acta Part B 52 (1997) 1269-1281
Influence of vapor redeposition and modifiers on the Arrhenius plots of 1 copper in graphite furnace atomic absorption spectrometry Dorys Rojas*, Maria A. Sfinchez, Wilmer Olivares Lab. Espectroscopia Analltica, Departamento de Qulmica, Facultad de Ciencias. Universidad de Los Andes, MOrida, Venezuela
Received 2 November 1996; accepted 3 February 1997
Abstract
A study is presented of the effects of the processes of redeposition of atomic vapor on the Arrhenius plots. For that purpose, a kinetic model that considers the redeposition of the initial atomic vapor, and the revaporization of the redeposited species, at a later time is proposed and tested for the electrothermal atomization of Cu. This model predicts Arrhenius plots which present negative deviations from the linear behavior expected for a single process of release and dissipation of the atomic vapor. The magnitude of the negative deviation increases as the readsorption rate and the temperature difference between the release and redeposition sites increase. This type of behavior is observed in the Arrhenius plots obtained when well used graphite tubes and ascorbic acid are employed for the atomization of Cu. However, when new pyrolytically coated graphite tubes, or tungstencoated tubes, are used, the Arrhenius plots show the expected linear behavior for the one-precursor model, with a first kinetic order of release. Additionally, when using Mo and Pd as modifiers, these plots shows two well defined slopes, which are characteristic of a two-precursor atomization mechanism. The experimental results indicate that the degree of vapor redeposition is determined not only by temperature gradients but also by the properties of the atomizer surface. © 1997 Elsevier Science B.V. Keywords: Arrhenius plot; Atomization; Copper; Electrothermal AAS; Modifier; Redeposition
1. I n t r o d u c t i o n
The kinetic parameters employed to explain the atomization mechanisms in electrothermal atomic absorption spectroscopy are obtained mainly from Arrhenius plots constructed from the absorbance profiles. Therefore the effects of processes of a n a l y t e surface interaction and those of formation and dissipation of the atomic vapor, which define the
* Corresponding author. Mailing address: Apartado Postal 478, Mdrida 5101A, Venezuela. E-mail: [email protected] Thie paper has been published in the special issue of the Second European Furnace Symposium, St. Petersburg, Russia, May 1996.
atomization profiles, are fundamental for the interpretation of the kinetic parameters and atomization mechanisms. The interaction of the atomic vapor with the surface of the atomizer and the spatial and temporal non-isothermality of the atomizer have been considered to cause the redeposition of the atomic vapor [1-3]. Holcombe et al. [1] interpreted the spatial atom distribution profiles within a graphite furnace atomizer as being due to the strong readsorption of the atomic vapor of certain metals on graphite. Gilmutdinov et al. [2,3] showed, by shadow spectral filming studies, that the cross-sectional distribution of an analyte within a graphite or a metal-lined furnace is non-uniform and that its characteristics depend on the
0584-8547/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PH S05 84-8547(97)00021-9
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D. Rojas et al./Spectrochhnica Acta Part B 52 (1997) 1269-1281
element. Accordingly, they proposed a cascade mechanism of analyte propagation in non-isothermal furnaces at low heating rates, which consists of a number of condensation-vaporization processes of the analyte as the temperature wave propagates along the length of the furnace during the heating cycle [3]. Signal tailing has been attributed in the literature to adsorption-condensation processes of the atomic vapor on the cool ends of the atomizer [4-8]. Holcombe and co-workers [4-7] have suggested that a series of adsorption-revaporization processes may occur along the length of the tube, so that the form of the absorbance profile is determined largely by the degree to which the analyte atoms adhere to the tube material. Additionally, Frech et al. [8] also proposed secondary adsorption-desorption processes to explain the signal tailing detected in the atomization of various elements in the presence of different metal modifiers. On the other hand, L'vov et al. [9] proposed the condensation of the atomic vapor at the cooler surfaces of the atomizer to explain the shape of the electrothermal absorbance profiles. Despite the amount of experimental data supporting the redeposition processes of the atomic vapor, few models have been reported to include the vaporsurface interactions after the initial release. G~ell and Holcombe [10] included readsorption of analyte on the furnace wall in a Monte Carlo simulation study on the dependence of the absorbance signal of Cu and Ag on furnace length. Signal tailing is predicted for the absorbance pulses of Cu, which is considered to exhibit marked interaction with graphite. Musil and Rubeska [11] proposed a mathematical model based on free atom redeposition and isothermal conditions to explain the atomization profiles of Mn, and observed that the model predicted the falling portion but not the rising portion of the absorbance pulse. Welz et al. [12] applied the same redeposition model to the atomization of several analyte elements using atomizers made of various materials. They concluded that one of the limitations of the model is the assumption of isothermality. This condition does not seem to be satisfied in commonly used atomizers, which, as shown in recent studies [13], display temporally and axially non-uniform temperature distribution. They therefore proposed an extended redeposition model that takes into account the
temporal and axial temperature non-uniformity in the tube during atomization. Their results showed that a better description of the rising and falling parts of the absorbance profiles is obtained by including the temperature dependence of the reaction rates. However, no work has been reported on the effects of redeposition processes on the Arrhenius plots commonly employed to determine the kinetic parameters of the atom release processes. To study these effects, in this work we propose a redeposition kinetic model that assumes that the initial atomic vapor could be readsorbed or condensed at surface sites having a lower temperature than the central part of the atomizer, and that its revaporization occurs when those sites reach the appropriate temperature. The effects of these type of processes on the Arrhenius plots are studied for different redeposition rate constants and for different temperature differences between the central part of the atomizer and the redeposition sites. The model also considers redeposited species with atomization energy lower or higher than or equal to that of the initial precursor of the atomic vapor. Finally, the theoretical predictions are compared with the experimental results obtained for the atomization of Cu alone by employi,g new pyrolytically coated graphite tubes, well used graphite tubes, and in the presence of chemical modifiers such as ascorbic acid, tungsten, molybdenum and palladium.
2. Experimental 2.1. I n s t r u m e n t a l
A graphite furnace (PE HGA-2100) equipped with standard pyrolytically coated, tungsten-coated or molybdenum-coated tubes was used as the atomizer. The absorbance signals of Cu were measured at 324 rim, using the stop flow mode, by cutting off the purge gas during the atomization cycle. Prepurified argon was used as the purge gas during the drying and ashing cycles. We used slow vaporization of the solvent and a pyrolysis stage of 20 s at 970 K, with a total time of 30 s. A peak atomization temperature of 2770 K was employed. To minimize temporal distortions of the registered profile, the absorbance signals were measured at the output of the photomultiplier
D. Rojas et al./Spectrochimica Acre Part B 52 (1997) 1269-1281
tube after demodulation and logarithmic conversion. The time dependent atomizer temperature was determined from measurements of the furnace emission focused onto a photodiode, as previously described [14]. Both the absorbance and the temperature data were digitized with a 12 bit resolution, 16 channel A/D card and were collected every 0.02 s with an Intel-286 microcomputer. The absorbance and temperature data were then fitted with a cubic spline algorithm to obtain the time derivative of the absorbance pulse, its characteristic parameters, and the atomization heating rate.
2.2. Reagents All the reagents employed to prepare the standard solutions were of analytical grade. The working solutions of Cu were prepared from a standard of 1000 ~g ml i, which was prepared by dissolving copper chloride in 0.01 M hydrochloric acid. The modifier solutions were prepared from standard solutions of 1% w/v ascorbic acid, 1% w/v tungsten (oxide) dissolved in 0.1 M sodium hydroxide, 100 txg ml -L of molybdenum (as phosphomolybdic acid), and 100/xg ml -~ palladium (as nitrate). To ensure temporal stability, all the working solutions were prepared daily in 0.01 M hydrochloric acid. Aliquots of 20/xl of the working solutions of Cu and the modifier were deposited on the wall of the graphite tube with an autosampler (Perkin-Elmer AS-l). The procedure reported by Iwamoto et al. [15] was employed to coat the graphite tubes with tungsten and molybdenum.
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kl(t)=ujexp[-E(al)/RT~(t)] and k3(t)= u3exp[-E~3)/RTr(t)] are the time dependent rate
where
constants of generation of the atomic vapor Y from the species X and V, respectively, kr(t)= urexp[-E~r)/RTr(t)] is the rate constant of redeposition of the atomic vapor, and kz(t ) = k 0 [T(t)/To]" is the rate constant of dissipation of the atomic vapor. Additionally, Z is the dissipated species, u is the pre-exponential factor, E~ is the corresponding atomization energy, R is the gas constant, and T and Tr are the time dependent temperatures at the center of the atomizer and at the redeposition sites, respectively; k ° is the rate constant of diffusion of the atomic vapor at a reference temperature T0 (273.15 K), and n is the diffusion factor. If a temperature gradient exists from the center to the ends of the graphite tube, the temperature at any position z is determined by the rate of propagation of the temperature wave along the tube. However, for simplicity, in this study we consider discrete redeposition sites with a temperature Tr, which is lower than the temperature T by an amount AT, namely T r = T AT. Therefore, in our model a time lag exists between the original process of generation of the atomic vapor and the revaporization of the redeposited species. This revaporization process will begin only at the time at which the temperature Tr reaches the appearance temperature of the redeposited species. From the kinetic equations of this atomization process, which are solved in Appendix A, one obtains the following expression for the rate constant k ](t) ~-+k2Y(t)
+ [krY(t ) - k 3 V ( t ) ]
kl(t)
(2)
3. Computational simulations Let us consider that a precursor X generates the atomic vapor Y, which could be dissipated or, by collision with the wall, could be re-adsorbed or condensed at the cooler ends of the atomizer [7,10,16,17] as a species V, which in turn vaporizes at a later time. This atomization process could be described schematically as
x~ K,
V
K2 j~
Y
> Z
(1)
Eq. (2) clearly shows how the redeposition and revaporization process affects the determination of the kinetic parameters of the initial release process. Thus, in order to quantify their effects, we construct the Arrhenius plots by using the method proposed by Rojas and Olivares [14]. Then, as shown by Eq. (A10) and Eq. (A13) of Appendix A, the Arrhenius plots are determined by E~~) lnW, (t) = In g(t) + In(u) - - -
RT(t)
(3)
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
1272
where g(t), as defined by Eq. (AI 1), takes into account the terms of the redeposition processes. Here we have assumed first order kinetics for all the processes of generation and dissipation of the atomic vapor. According to these equations, at the beginning of the atomization process, where there is no redeposition of the atomic vapor, the Arrhenius plots are determined by the kinetic parameters of k j(t) alone. However, as the redeposition of the atomic vapor becomes appreciable, the contribution of the term g(t) causes a diminution of the values of Wl(t), and therefore negative deviations are predicted from the linearity expected for a system without redeposition. Then, to study the effects predicted by the readsorption model, the theoretical atomization pro-
Table 1 Kinetic parameters employed in the computational simulations of absorbance profiles of Section 3 Parameter
Value
E~l)/(kJ tool -r)
150 104 75, 150, 300 l0 ~, 104, 108 0.0-1.0 0, 300, 600, 900 0.02 1.9
ul/s t E~3)/(kJ mol-;) t) 3/s -~
kfs -I ,aT~K) k0/s -' n
0.6
(A)
O o 0.4 rJQ 0¢) L
~
,.Q < 0.2
id c b a
1
2
3
4
5
Time, s
10.00 (B)
~
1.00
~ .
~
a
b '.
. -
",
0.10
0.01
6.8
6.2
5.6
5 -1
(1/T)x10 ,K 4
4.4
3.8
Fig. 1. Simulated absorbance profiles (A) and the Arrhenius plots for m = I (B), assuming a redeposition rate constant k r equal to (a) 0.0, (b) 0. I, (c) 0.5, and (d) 1.0 s -]. In this simulation, we assume a value o f ` a T = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E~~) is equal to E~,~).
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281 files Y(t) were computationally simulated by using the numerical solution of eqns ( A 1 - A 4 ) , and the values of the function Wl(t) are calculated by using Eq. (A9) with m = 1. For these calculations, the dissipation rate constant k2(t) is determined by using a diffusion type temperature dependence, with values of n and k ° equal to 1.9 and 0.020 s -~, as obtained experimentally by employing the RO-2 method proposed by Rojas and Olivares [18]. The atomization temperature T at the center of the tube was simulated by employing a six term polynomial, which was obtained by curve fitting the experimental temperature profile. In Sections 3.1, 3.2 and 3.3 we study the effect of the magnitudes of the redeposition rate constant, the redeposition temperature, and the revaporization rate constant on the Arrhenius plots. The general kinetic parameters employed for the computational simulations of the absorbance profiles are shown in Table 1. As can be seen from this table, we have chosen the precursor X to have the average activation energy and pre-exponential factor determined from the experimental atomization profiles of Cu when new pyrolytically coated graphite tubes were employed as the atomizer. For the process of redeposition we have assume an energy equal to zero, as has been considered earlier in the literature [10,11,16]. 3.1. Effect of the redeposition rate constant kr In general, the redeposition rate depends on the sticking probability [10,16] of the atomic vapor, and thus it depends on the number of active sites at the surface of the atomizer where redeposition can occur, and on the temperature of such sites. In this study we consider values of the redeposition rate constant kr between 0.01 and 1.0 s -~, which predict the form of the absorbance profiles obtained experimentally. In this section, we assume a value of AT = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E(a31is equal to Etll a
•
Fig. 1 shows the effects of the magnitude of the rate constant kr on the atomization profiles (A) and on the corresponding Arrhenius plots (B). From Fig. IA we can see that the time of maximum absorbance decreases, whereas the pulse tailing of the absorbance
1273
profile increases, as the redeposition rate constant increases from 0.0 to 1.0 s -l, as has previously been reported [8,11,12]. Similarly, from Fig. IB we can see that the initial slope of the Arrhenius plot, and therefore of the atomization energy and the pre-exponential factor determined therefrom, decreases as the value of kr increases. To quantify this effect, the atomization energy was determined for each case from the linear portion of the Arrhenius plots obtained for m = 1. Table 2 presents the effects of the magnitude of kr on the atomization energies so determined, and the percentage difference of that energy from that obtained for the system without redeposition, namely kr = 0. It was also observed that, when employing redeposition rates greater than 1.0 s -~, the tailing of the absorbance profile is so large that atomization times exceeding 12 s are required for the signal to return to the baseline. However, since this behavior is not common under our experimental conditions, such large redeposition rate constants are not included in this work. It should be mentioned that the Arrhenius plots for kinetic orders greater than one also show negative deviations from linear behavior. 3.2. Effect of the temperature of the redeposition sites According to Welz et al. [ 13] and Gilmutdinov et al. [2,3], the graphite tube exhibits a temperature gradient from its center to the ends, with temperature differences up to 1000 K. Therefore the temperature within the atomizer is a function of both the time and the spatial position of the redeposition site. However, this T(z,t) function is not well known and its description is not the aim of this work. Thus, for simplicity, Table 2 Effects of the redeposition rate constant on the kinetic parameters determined from the slope of the linear part of the Arrhenius plots for m = 1. E~ is the difference of the energies so obtained with and without redeposition of the atomic vapor. In this study, we assume a value of A T = 600 K, and that the species V has the same atomization energy as that of the original precursor X, that is, E~3) is equal to Etat)
k~/s-t
Ea/(kJ mol-I)
In (v)
AEal%
0.1 0.5 1.0
142.13 140.74 137.29
9.14 8.56 8.13
- 5.2 - 6. I - 8.3
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
1274
we shall not consider a continuous temperature propagation rate within the tube, but instead we shall assume that it is discretized. Then, from the center to the end, the tube is segmented in three zones, each with a temperature difference AT that increases as its distance from the tube center increases. Fig. 2 presents the effect of the temperature of the redeposition sites on the atomization profiles (A) and the corresponding Arrhenius plots (B) for values of T of 0, 300, 600 and 900 K. For this simulation we assumed a rate constant of redeposition k~ equal to 0.5 s -~, and that the species V has the same atomization energy as that of the original precursor X, that is, E(3) is equal to F(~) ~ .
0.6
(A)
0.4 (tl £ O .Q 0.2 <
As shown in Fig. 2A, an increase in the pulse tailing of the atomization profile is observed as the temperature difference z~T increases from 0 to 900 K, and therefore a greater time is required for complete atomization of the sample. Also, as displayed in Fig. 2B, the negative deviations from linearity shown by the Arrhenius plots remain essentially equal, but the curves fall faster as the temperature difference AT increases. Accordingly, when employing a graphite tube with a temperature gradient up to 900 K [2,3,13] from the tube center to its ends, the atomization profiles and the corresponding Arrhenius plots should behave as an average of those shown in Figs. 2A and 2B, respectively. In short, the absorbance signal will show peak tailing and the Arrhenius plots will present negative deviations from the linear behavior expected for a one-precursor mechanism without redeposition.
3.3. Effects of the kinetic parameters of atomization of the .wecies V
a~i
1
2
cI 3
4
d
5
6
Time, s
10.00 E
1.00
',
0.10
Id
0.01 r
s.s
s
s.s
s
4.5
4
( l / T ) x 10 4 , I~ 1 Fig. 2. Simulated absorbance profiles (A) and Arrhenius plots (B) for m = 1, assuming a temperature difference between the center part of the graphite tube and the redeposition site, AT, equal to (a) 0, (b) 300, (c) 600, and (d) 900 K. In this simulation, we assume a value of kr equal to 0.5 s J, and that the species V has the same atomization energy as that of the original precursor X, that is, E] ~ is equal to E/d1(
As the redeposited species could have the same or a different chemical nature compared with the original precursor X, in this section we study the effect of the kinetic parameters for the atomization of the species V, namely E(d~t and/)3, on the absorbance profiles and the Arrhenius plots. For this purpose we employ a redeposition rate constant kr equal to 0.5 s -~, AT = 600 K, and kinetic parameters for species V that, as shown in Table 1, are half, equal to and twice those used for the atomization of the species X. Accordingly, species V could be physically adsorbed (low energy), or it could be the same as the species X (equal energy), or it could be chemically adsorbed on the surface of the atomizer (high energy). Fig. 3 presents the atomization profiles (A) and the corresponding Arrhenius plots (B) obtained for values or~-~)t~ d a n d u 3 o f ( a ) 1 5 0 k J m o l l and104 s-], (b) 75kJ mo1-1 and 102 s -I, and (c) 300 kJ mol -I and 108 s -j. As can be seen from Fig. 3(A), the lowest kinetic parameters do not appreciably modify the absorbance profile (curve b), but the highest kinetic parameters (curve c) produce a greater elongation of the falling part of the absorbance pulse owing to the delayed atomization of species V. However, as could be seen from Fig. 3(B), the negative deviations exhibited by the Arrhenius plots are practically the same in all
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281 0.5
(A)
tin J~ 0.25 0 m .o
<
1
2
3
4
5
Time, s
10.00
o
(B)
E
~
Wo
1.00
0.10
0.01
7
6.5
6
5.5
5
4.5
4
( l r r ) x 10 4 , I~ 1 Fig. 3. Simulated absorbance profiles (A) and Arrhenius plots (B) for m = I assuming atomization energies of the redeposited species, V, equal to (a) 150, (b) 75, and (c) 300 kJ mol t. In this simulation, we assume a value of kr equal to 0.5 s -I , and ATequal to 600 K. The curve W~ corresponds to the system without redeposition of the atomic vapor, i.e. kr = 0.0 s -I.
cases, with a faster decay for the system with the highest kinetic parameters.
4. Experimental Arrhenius plots for the atomization of Cu Copper was chosen as the analyte to show the effects of the redeposition of the atomic vapor on the Arrhenius plots because of its high sticking adsorption coefficient on graphite [10,16,17]. Hence the atomization mechanism of Cu could be altered by employing chemical modifiers, such as ascorbic acid, tungsten, molybdenum and palladium, that modify the surface of the atomizer. In this section, we study the effects of these modifiers on Arrhenius plots
1275
corresponding to the experimental electrothermal atomization of Cu. To construct the Arrhenius plots, the values of the function Win(t) were calculated as a function of the kinetic order of generation of the atomic vapor m by using Eq. (A9) in Appendix A. It is important to point out that the experimental data for the entire absorbance profile are employed for the calculation of the integral function in the denominator of Win(t). However, the Arrhenius plots are constructed up to the time ty, where the time derivative of the absorbance signal reaches a minimum value [ 14,18], or up to the time at which the atomization temperature reaches its maximum value. The rate constant of dissipation of the atomic vapor, k2(t), as required by Eq. (A9), is determined by using the RO-2 method reported by Rojas and Olivares [18]. This method assumes that the dissipation of the atomic vapor is primarily a diffusion process, and it can be used for time-varying temperature conditions. Accordingly, from the absorbance and temperature profiles measured under the different experimental conditions specified in the following sections, values of n and k ° equal to 1.9 and 0.02 s -~ ( +_ 8%), respectively, were obtained for the atomization of Cu. These values of the parameters n and k~ are within the expected range for a gas diffusion process [19]. For comparison purposes, Figs 4 and 5 shows the absorbance profiles and the Arrhenius plots obtained 0.8
0.6
o 0.4
.~
e
c ; "l ...
..,
";I-X~
' UI I
0.2
;:1
",
a
d',.-:X2", ..,.
0 0
2
4
6
8
Time, s Fig. 4. Absorbance profiles obtained for the atomization of 1.2 ng of Cu, employing pyrolytic graphite tubes (a), and in the presence of 0.01% w/v of ascorbic acid (b), W (c), Mo (d), and 1 tzg of Pd (e).
1276
D. Rojas et a/./Spectrochimica Acta Part B 52 (1997) 1269-1281
100.00
(A)
~
10.00
E
1.00
f
f
/t
/
/ m=2
10
m=l
E
(B)
.~ .-
1
~ m=2
i / ~ i I/'r" /" / / / / 1~/f/
0.1
0.10
J
~i
m=l m=0
~. m=O /
0.01
0.01 7
6.5
6
5.5
5
4.5
7.5
7
6.5
6
( l / T ) 104 , K I
5.5 4
5
(l/T) x 10 , !~
4.5
1
100
(C) /
100
/J . , . ~
E
I
/
/" m=2
(D)
I
m=2
m=l
s
.
~
~
m=l
m=O
m=O
0.01
0.01 9
8
7
6 4
(1/Tlxl0,
100
7.8
-1
6.8
K
5.8
4
-1
4.8
3.8
(1/1") x 10 , K
(E) /
10
/
!
I
m=2
/
I / t
j
F: 1 m=O 0.1
0.01 8.2
7.2
6.2
5.2
4.2
3.2
(1/3") X 104 , K" 1 Fig. 5. Experimental Arrhenius plots obtained for the atomization of 1.2 ng of Cu, employing pyrolytic graphite tubes (A), and in the presence of 0.01% w/v of ascorbic acid (B), W (C), Mo (D), and 1 p.g of Pd (E).
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
Table 3 Effects of chemical modifiers on the atomization energies of Cu. The symbols E]u and E]2! are the atomization energies calculated from the slopes of the Arrbenius plots in the low and the high temperature regions, respectively Modifier
E]I)/(kJmol-I)
E~2)/(kJmol-i)
None Ascorbic acid W Mo Pd
145 147 155 203 192
145 Negative deviations 155 143 133
for the atomization of Cu alone and in the presence of the modifiers employed in this study. Also, Table 3 shows the atomization energies obtained in the absence and in the presence of the modifiers. As a reference, Fig. 5A shows the Arrhenius plots obtained by employing new pyrolytically coated graphite tubes for the atomization of 1.2 ng of Cu. This plots indicates a first kinetic order of release, with an average atomization energy of 145 kJ mol -] ( _+ 10%), and apparently no redeposition of the atomic vapor. 4.1. Effect o f ascorbic acid
It has been reported that the pyrolysis of ascorbic acid produces active carbon species and an alteration of the surface of the graphite tube [20-22] when ascorbic acid is employed as a chemical modifier. Thus, the use of this acid as chemical modifier could induce redeposition of the original atomic vapor. The effects of variable concentrations of ascorbic acid on the electrothermal atomization of Cu are therefore studied in this section. An increase in the peak absorbance and the area of the absorbance signals of Cu is detected when the concentration of ascorbic acid added is varied from 0.005 to 0.1% w/v, indicating an increase in the atomization efficiency of the analyte. This behavior is shown in Fig. 4 for the atomization of 1.2 ng of Cu in the presence of 0.01% w/v of ascorbic acid (curve b). Similarly, Fig. 5B shows the Arrhenius plots obtained for the electrothermal atomization of 1.2 ng of Cu in the presence of 0.01% w/v of ascorbic acid. As can be seen from Fig. 5A and 5B, the Arrhenius plots obtained for the atomization of Cu in the presence of ascorbic acid, for physically
1277
meaningful kinetic orders of release, display negative deviations from the linear behavior obtained in Fig. 5A for m = 1. A comparison of these plots with those predicted in Fig. 1A by our model of redeposition of the atomic vapor indicates a good qualitative correlation, and suggests the redeposition of the atomic vapor of Cu in the presence of ascorbic acid. It is also observed that the negative deviations from linearity of the Arrhenius plots increase as the concentration of ascorbic acid increases, which would be the expected behavior if the pyrolysis of ascorbic acid increases the number of active sites and thus the redeposition sites on the surface of the atomizer. Table 3 gives the atomization energy obtained from the linear part of the Arrhenius plot for m = 1 for the atomization of 1.2 ng of Cu with 0.01% w/v of ascorbic acid added. Similarly, when employing well used graphite tubes, meaning those with more than 80 firings, the Arrhenius plots obtained for the atomization of Cu show negative deviations, such as those in Fig. 5B. The likelihood of redeposition of the atomic vapor on the well used tube is expected because of its greater number of active sites compared with those in a new pyrolytically coated tube. As shown in Table 2, if the redeposition of the atomic vapor becomes appreciable, the deviation from linearity in the Arrhenius plots leads to kinetic parameters that are appreciably lower than those expected without redeposition of the atomic vapor. Since the magnitude of the redeposition depends on the analyte-surface interaction, the kinetic parameters determined will depend on the type and the number of active sites and on the temperature propagation along the atomizer. All these effects could explain the variety of atomization energies that have previously been reported in the literature, in the range 125-195 kJ mol -~, for the atomization of Cu [14,23,24]. 4.2. Effects o f tungsten-coated tubes
In this study, the graphite tubes are coated with tungsten to produce a saturation of the active sites on the surface of the atomizer and therefore to reduce the number of redeposition sites. As shown in Fig. 4 (curve c), it is found that, when W-coated tubes are used for the atomization of Cu, the absorbance pulse is sharper, with a higher rate of release and less tailing of the falling part than those obtained with new
1278
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
pyrolytically coated graphite tubes (curve a). This kind of behavior has been reported when employing a Ya atomizer [5]. Fig. 5C shows the Arrhenius plots obtained for the atomization of 1.2 ng of Cu by employing W-coated graphite tubes. From this figure, we can see that the plots exhibits the linear behavior expected for a system without redeposition of atomic vapor. From these plots, a first kinetic order of release and an atomization energy of 155 kJ mol -I are obtained. This atomization energy indicates desorption of the analyte from the surface of the atomizer without redeposition of the atomic vapor. Accordingly, the saturation of the active sites of the atomizer with tungsten seems to minimize the processes of redeposition of the atomic vapor of Cu. Thus, if the temperature gradient within the graphite tube is not appreciably changed by coating the tubes with W, the experimental results seem to indicate that the redeposition of the atomic vapor depends on the properties of the surface of the atomizer. 4.3. Effect o f Mo-coated tubes
As Mo forms stable carbides [25], it is expected that it would also saturate the active sites and therefore would decrease the number of possible sites for redeposition of the atomic vapor of Cu. As shown in Fig. 4 (curve d), only small variations are detected in the sensitivity and the appearance temperature when Mo-coated tubes are employed for the atomization of Cu. Furthermore, as presented in Fig. 5D, the Arrhenius plots obtained for the atomization of 1.2 ng of Cu employing Mo-coated tubes display two slopes. This behavior has been reported as characteristic of a two-precursor atomization mechanism [18]. From Fig. 5D, it is observed that the kinetic order of release is not well defined in the low temperature region, but a first kinetic order of release is defined in the high temperature region. Thus, from the plot with m -- 1, average atomization energies of 203 and 143 kJ tool ~are obtained in the low and the high temperature regions, respectively. The energy obtained in the low temperature region correlates well with the dissociation energy of the copper dimer, which has a dissociation energy of 196 kJ tool -~ [26], and indicates an increase in the analyte-
analyte interactions. In addition, the energies obtained in the high temperature region seem to correspond to a desorption process of the analyte from the surface of the atomizer. Accordingly, the use of Mo also seems to minimize the redeposition process of the atomic vapor of Cu. 4.4. Effect o f Pd
Palladium is one of the most widely used chemical modifiers in graphite furnace atomic absorption spectrometry. Different mechanisms have been proposed to explain the stabilizing effect of Pd on the atomization of volatile elements. A physical mechanism was proposed by Qiao and Jackson [27], whereas Yang and Ni [28] and Styris and Redfield [29] proposed the formation of a stable intermetallic solid solution. Furthermore, Volynsky et al. [30] proposed a catalytic process of reduction of metal oxides by Pd. Additionally, Frech et al. [8] found signifcant trapping of the analytes at the ends of the tube, and thus signal tailing, when Pd was employed as a modifier. Accordingly, they postulated changes in the adsorption properties of the tube and secondary adsorption-desorption processes. When Pd is employed as a modifier for the atomization of Cu, it is observed that the peak absorbance, the area and the appearance temperature increase as the initial mass of Pd increases from 0.1 to 2.0/~g. The increase in the appearance temperature reaches a maximum value of 200 K for 1 and 2 #g of Pd. This behavior is presented in Fig. 4 (curve e) for the atomization of 1.2 ng of Cu in the presence of 1 #g of Pd. It is also observed that, in the presence of Pd, the temperature of maximum absorbance of Cu remains unchanged as the initial amount of Cu increases, which has been taken in the literature as indicative of a first kinetic order of release with one precursor of the atomic vapor and a constant atomization energy [5,10,17,23]. However, the corresponding Arrhenius plots show two slopes, which is characteristics of a two-precursor mechanism of generation of the atomic vapor [18]. This behavior clearly invalidates the assumption of a precursor with first order kinetics, as suggested by the method of alignment of the time of maximum absorbance with the initial mass of the analyte.
D. Rojas et al./Spectrochimica Acta Part B 52 (1997) 1269-1281
Fig. 5E shows the experimental Arrhenius plots obtained for the atomization of 1.2 ng of Cu in the presence of 1/xg of Pd. From these plots it is observed that the kinetic order is equal to one in the high temperature region but is not well defined in the low temperature region. Then, from the plot for m = 1, atomization energies of 192 and 133 ( -+ 10%) kJ mo1-1 are obtained in the low and the high temperature region, respectively. This result seems to indicate that at temperatures lower than 1700 K the effect of Pd prevails at the surface of the atomizer, but at temperatures higher than 2100 K, where Pd has been vaporized from the surface [7], the analyte is freely desorbed from the graphite surface without redeposition. The energy obtained in the low temperature region correlates well with the dissociation energy of copper dimer [26], and accordingly it seems that the presence of Pd, at temperatures lower than 2000 K, favors the analyte-analyte interaction. This effect could be explained by a mechanism of trapping of the analyte by Pd, as has been reported previously [27,29]. Thus, the generation of the atomic vapor of Cu would be kinetically controlled by the release of the modifier, and so, at temperatures above 2000 K, the analyte would be freely released from the graphite surface. Hence this experimental result also points out the surface dependence of the redeposition process of the atomic vapor of Cu. Furthermore, the behavior of the Arrhenius plots shown in Fig. 5E indicates no redeposition of the atomic vapor. Accordingly, the result indicates that in our experimental conditions no analyte appears to be trapped at the ends of the tube, which is contrary to the behavior proposed by Frech et al. [8] for high initial masses of modifier. Instead, it seems that the analyte is concentrated at the hotter central region of the tube, as proposed by Frech et al. [31] since, as indicated by the energy obtained in the high temperature region of the Arrhenius plots, as Pd is released, the analyte desorbs freely from the graphite tube.
1279
atomization of Cu in the presence of surface modifiers. The theoretical redeposition model predicts an elongation of the falling part of the absorbance profile and negative deviations of the Arrhenius plots from the linear behavior expected for a single-precursor kinetic mechanism. It is shown that the magnitude of the negative deviations is proportional to the magnitude of the redeposition rate constant and to the temperature difference between the center of the atomizer and that of the redeposition sites. By analyzing the theoretically predicted Arrhenius plots, we have shown that the RO-I method can be safely applied to determine the kinetic parameters of the initial atomization process from the linear part in the low temperature region, since the redeposition process becomes appreciable at later times after the initial vapor has been propagated along the tube. It is observed that, under conditions where a high number of active sites prevails on the surface of the atomizer, such as those in well used tubes and when ascorbic acid is used for the atomization of Cu, the Arrhenius plots show the negative deviations predicted by our theoretical model of redeposition of atomic vapor. However, the Arrhenius plots obtained for the atomization of Cu in the presence of metal modifiers with a high degree of interaction with the graphite surface, such as tungsten, molybdenum, and palladium, indicate the absence of redeposition of the atomic vapor. It seems that these metal modifiers saturate the active sites on the graphite surface and therefore the redeposition process is suppressed. The experimental results indicate that the degree of vapor redeposition is determined not only by temperature gradients but also by the properties of the atomizer surface. Furthermore, the behavior of the Arrhenius plots obtained for the atomization of Cu in the presence of Mo and Pd indicates a two-precursor atomization mechanism. In the low temperature region, the presence of Mo and Pd seems to increase the analyteanalyte interaction, whereas in the high temperature region the desorption of Cu from the surface of the atomizer prevails.
5. Conclusions A kinetic model that takes into account the redeposition of the atomic vapor is proposed to explain the behavior of the Arrhenius plots for the electrothermal
Acknowledgements This work was supported by the Consejo de
D. Rojas et al./Spectrochbnica Acta Part B 52 (1997) 1269-1281
1280
Desarrollo Cientffico y Humanfstico of the University of the Andes (grants C-712 and C-714), M6rida, Venezuela.
This equation, together with Eq. (A1) and Eq. (A2), gives dY Ir~_~t+ k: Y(t)]
+[krY(t)-k3v(t)]
AppendixA If in the model of redeposition of the atomic vapor we assume a first kinetic order for the release and dissipation processes, and also assume that the rate of change of the atomic population, dY/dt, is determined by the rates of atom generation dX/dt and dV/dt, and by the rates of dissipation of the atomic vapor, the kinetic process is then described by
According to this expression, the redeposition of the atomic vapor affects the determination of the kinetic parameters of the initial process of generation of the atomic vapor. Now, since only Y(t) is experimentally measured by the absorbance signal, we proceed as in the RO-1 method of Rojas and Olivares [14] and define the function Wm(t) by
dX dt
Win(t) =
kl(t)X
(A1)
:~
D(t) + k2(t)A(t)
m
(A9)
[], k2(r)A(r)dr-A(t)] dV
~ f =kr(t)Y-k3(t)V
(A2)
dY ~ - = k,(t)X + k3(t)V -
Substituting
[k2(t) + kr(t)]Y
(A3)
Eq. (A1) and Eq. (A2) into Eq. (A3), one
obtains
W~(t) = g(t)k I(t)
dY 4-k2Y=- {dX+ d V ) d--7 k.d7 ~ Then, if X ° is the species, and there vapor at the initial atoms vaporized at Eq. (A4) Y(t) +
i
(A4)
initial amount of the is no redeposition of time (i.e V ° = 0), the a time t is obtained by
generating the atomic number of integrating
I
k2(r)Y(r)dz = X ° -
X(t) - V(t)
(A5)
0
Now, since Y vanishes at the time boundaries, from Eq. (A4) we have
J~ kz(t)Y(t)dt
= X°
(A6)
0
I/
k2(r)Y(r)dr = X(t) + V(t)
(A 10)
where W~(t) is the lunction Win(t) for a first kinetic order (i.e., m = 1), and g(t) is a factor that takes into account the terms of the redeposition process. This factor g(t) is defined by [(dV/dt)]
l+ g(t)=
k~/d~-J
l+(v'/x')
I+(V/X)
I+(V/X)
lnWl (t) = lng(t) + lnk l (t)
(A12)
and by substitution of the expression for the rate constant k Lit) we have
RT(t)
(A7)
(All)
where V' = dV/dt and X' = dX/dt. Then, the Arrhenius plots in terms of W, and following the RO-1 method, are given by
E~~) lnW 1(t)-- lng(t) + In(v)- - -
and therefore Eq. (A5) becomes: - Y(t) +
where A(t) and D(t) are the absorbance profile and its time derivative (dA/dt), respectively, and m is the kinetic order of release of the atomic vapor. Then, rearranging the terms in Eq. (A8) and by using Eq. (A1) and Eq. (A2), one obtains
(A 13)
Thus, from Eq. (A 11) one can see that, for the case of no redeposition of the atomic vapor, the amounts V and V' are zero and therefore g(t) is equal to unity.
D. Rojas et al./Spectrochimica Acre Part B 52 (1997) 1269 1281
Consequently, from eqns (A12) and (A13) we deduce that in this situation the Arrhenius plots are determined by the kinetic parameters of k l(t) alone. However, as the redeposition of the atomic vapor becomes appreciable, the quantity V/X, which is the ratio of the amount of redeposited vapor to the amount of the initial precursor at a given time, increases faster than V'/X', the ratio of the rate of revaporization to the rate of vaporization from the original precursor, and therefore g(t) decreases from unity. Then, according to eqns (A12) and (A13), the Arrhenius plots should give the kinetic parameters of the rate constant k l(t) at the earlier stage of generation of the atomic vapor, and will present negative deviations from linear behavior as the rate of redeposition of the atomic vapor, k,(t), increases.
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