JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL. 7 135 Monte Carlo Study of Analyte Desorption Adsorption and Spatial Distribution in Electrothermal Atomizers* Invited Lecture Oscar A. Guell and James A. Holcombet Department of Chemistry and Biochemistry University of Texas at Austin Austin TX 78712 USA Monte Carlo simulations of electrothermal atomization are used to study the effects of surface re-adsorption and non-uniform spatial distribution as well as the interpretation of the activation energy of atomization and peak shapes. The work is based on an atomization model for Cu. The kinetic parameters are altered to follow their effect upon the measured activation energy of atomization and the spatial distribution inside the atomizer. For elements with similar desorption kinetics re-adsorption shifts the peak to higher temperatures (later times).The width of the peak increases with an accompanying decrease in peak height. Similar activation energies for atomization can be obtained from the linear region at the beginning ( i a early in time) of Smets and Arrhenius plots. These plots are methods that deal with the initial rates and neither linearity nor accuracy should necessarily be expected after the initial portion of the graphs. The activation energy for atomization gives an estimation of the energy barrier for desorption but the adsorption barrier is not available from these plots. Spatially resolved atomization profiles show defined trends during the rising portion as well as at the peak. Stronger interactions with the graphite surface produce a steeper gradient in the gas phase at the beginning of the atomization.The accuracy of the estimation of this energy barrier can be significantly affected by the viewing position of the spectrometer system. Keywords Monte Carlo simulation; atomization mechanism; electrothermal atomization; atomic absorption spectrometry The difficulties encountered in past efforts in developing an understanding of the kinetics and mechanisms for elec- trothermal atomization atomic absorption spectrometry (ETAAS) have slowed the development of models. They have been explained by the complexity of the geometry of the system and the chemical and physical processes occur- ring during atomization. An improved insight is provided by the use of Monte Carlo techniques to study the chemical and physical processes in ETAAS.lv2 Classical mechanistic studies generally start from the experimental determination of an activation energy of atomization (a,,,) for the analyte employed.However most theoretical approaches have neglected the presence of re-adsorption or the finite residence time required for diffusional loss in the absence of very fast removal (e.g. vacuum conditions) as well as the dependence of the absorbance signal on the radial position of observation and the existence of a non-isothermal environment inside the furnace (ie. temperature variations along the length of the atomizer are ignored). The role of re-adsorption has been proposed to be significant for analytes with fairly strong interactions with graphite.Several studies have been made suggesting that the broadening of the atomization peak3 as well as the existence of steeper gradients in the gas p h a ~ e ~ - ~ are a result of these interactions. Holcombe and c o - ~ o r k e r s ~ ~ ~ have shown that the distribution of the analyte in the gas phase is seldom uniform especially early in time. As discussed previously,1 the complex chemistry and geometry associated with the graphite furnace have made the theoretical approach to the application of conventional * Presented at the XXVII Colloquium Spectroscopicurn Interna- t To whom correspondence should be addressed. tionale (CSI) Bergen Norway June 9- 14 199 l . analytical solutions of equations nearly impossible for this system. Most approaches have included simplistic assump- tions and in some cases have ignored the chemical-physical basis for the system.This work presents a further extension to the ETAAS Monte Carlo algorithm and attempts to provide a better understanding of the effects of surface re-adsorption and non-uniform spatial distribution as well as the interpreta- tion of activation energies of atomization and peak shapes in ETAAS. Theory Determination of Activation Energies of Atomization The simplest atomization mechanism in ETAAS can be described by M(surface) = M(g in)-M(g out) (1) where M represents the analyte on the surface or in the gas phase inside or outside the furnace. The standard kinetic expression obtained for this case is where N represents the number of analyte atoms in the gas phase (proportional to the partial pressure of the analyte pM) t is time vd is a pre-exponential factor for desorption from the surface Ordm is the fractional surface coverage raised to an order of release a is the activation energy for desorption R is the gas constant T is the absolute temperature s* is the sticking coefficient for re-adsorption136 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL.7 upon collisions with the surface (O<s*< l) nads is an order of adsorption (unity in most cases) S,(@ represents the fraction of empty sites on the surface (close to unity at all times because of the small sample size used) a d s is an activation energy for re-adsorption and fdlr is a diffusional loss function dependent on the diffusion coefficient Do T and the gas phase concentration gradient Vws.This gradient is determined in part by the geometry of the furnace (e.g. tube length diameter and dosing hole size). The Ey,, values are obtained from absorbance and temperature data usually by Arrhenius-type plots. The basic assumption involved is that the absorbance at any given time is proportional to the rate of atomization:’ (3) at Then neglecting the re-adsorption and diffusion terms in eqn. (2) (i.e. early in time) (4) where r/ includes several constants. In keeping with a standard assumption made for vacuum thermal desorption studies (e.g. ref. 8) Smets9 suggested that for ETAAS it also holds that ( 5 ) and a plot of ___ ~ ~~ Table 1 Monte Carlo simulation conditions unless otherwise specified in the text Description of furnace- Furnace lengthkm Furnace diametedcm Dosing hole diametedcm Ramp rate/K s-’ Starting temperature/K Final temperature/K Sheath gas (argon)- Atomization step Heating program me (experim en tab- Description of analyte sample- Number of particles Distribution Spot diameterkm Offset from centrekm halyte kinetics and digusion- Desorption activation energy1k.I mol-I Pre-exponential factor Order of release Adsorption activation energy/U mol-’ Sticking coefficient Diffusion coefficient at 273 Wcm2 s-I Thermal order of diffusion .Description of simulation parameters- Simulation time incrementh Total time simulatedh 0.90 0.30 0.10 960 723 2373 stop flow 50000 Circular spot 0.10 0 126.0 1 .o 0 1 .o 0.070 1 S O 1 .3 ~ 105 LOX 1 0 - 4 3.0 (hereinafter referred to as a ‘Smelts plot’) should be a straight line with a slope of qlom (i.e.a,) for a first-order desorption. It is often assumed that 8 is constant early in time or that nd,=O and a plot of 1 Ln A versus - RT (hereinafter referred to as an ‘Arrhenius plot’) should yield a linear region with a slope of a,,,. Thus the value of a, gives an estimation of the desorption bamer qes. In reality the detected signal corresponds to the number of gas phase atoms AKNga (6) Hence the Arrhenius plot is a method of investigating initial rates and linearity should not necessarily be expected after the initial portion of the graph. However the cause of non-linearity on Arrhenius plots is still not very clear and has been attributed to multiple-generation functions,’*1° wall diffusi~n,~*l~ changes in particle size,12*13 changes in surface coverage“ and interferences with the supply func- tion by the removal function.1° Bass and H~lcornbe~~ studied the effects of diffusion errors in the assumed order of release and the presence of small systematic errors on Arrhenius plots.They found that these factors produced curvature in the plots similar to those commonly seen in the literature. However in all cases they showed a portion of the graph that was linear and produced the correct activation energy. Thus they did not invalidate the use of these plots. Nevertheless Rayson and Holcombe6 obtained absorbance data from isolated spatial regions within the furnace and found that the apparent a,,,,,. values increased in going from the bottom to the top of the furnace.Further considerations are discussed in this paper. Calculations ‘The program MCGFAA version 1.03.2 was used in the simulations presented here. Details of the algorithm em- ployed are given elsewhere.2 Table 1 describes the simula- tion parameters as well as other additional conditions employed in this study. The Varian CRA-90 furnace size was used for this study. It has a small 9 mm long tube that is heated at the sides with two graphite electrodes. The small volume makes it mostly isothermal [i.e. uniform qt)] and it has been chosen for several mechanistic The absorbance signal is assumed to be proportional to the number of particles in the gas phase throughout. All calculations were performed using a Cray X-MP/24 super- computer located at the University of Texas Center for High Performance Computing.,4tomization Parameters ‘This work is based on the atomization model for Cu (Table l ) which has been previously shown to give approximate experimental atomization profiles of this element.s-16 The kinetic parameters are altered in order to follow their effect upon the measured activation energy of atomization and the spatial distribution inside the atomizer. The value of a,=126 kJ mol-I for Cu is consistent with the work of Black et aL5 and Wang et u1.l’ for atmospheric pressure (ETAAS) and vacuum thermal desorption mass spectro- metry conditions. The pre-exponential factor n d a was determined with the new algorithm and the experimental appearance temperature of Cu. The Do value for Cu in Ar was calculated as described by Skelland’* with data from Hultgren et aI.l9 This value was reduced by 16% in order to obtain a closer fit to experimental profiles from integrated con tact cuvet t e furnaces.2oJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL. 7 137 12 000 cn ‘3 .- 10000 5 Q m r 8000 6000 m P c 2 4000 n z 0 5 2000 2 400 2 000 1600 2 .L.’ 1200 $ i? 800 400 n 0 0.5 1.0 1.5 2.0 2.5 3.01 Time/s Fig. 1 Atomization profiles for three similar elements that only differ in their activation barriers for adsorption (as) A 0; B 25.0; and C 126 kJ mol-l. The experimental temperature profile D is also shown. The relative areas under A-C are 265 1,3279 and 4023 respectively Results and Discussion Role of Re-adsorption Fig. 1 shows the atomization profiles from three similar elements that have the same desorption (i.e.a, vd, &.,) and diffusional (i.e. Do nd,f) properties but different activation barriers for adsorption. A low value of a d s is characteristic of a strong metal-graphite interaction. The intermediate value (2OOh of a,,) is typical of physisorption processes whereas a large ads indicates a large activation barrier that produces elastic collisions even at moderate temperatures. The presence of re-adsorption shifts the peak to higher temperatures (later times). Also the width of the peak increases with an accompanying decrease in peak height. These effects imply an increase in the average residence time of the analyte inside the furnace due to an increased time spent adsorbed on the surface. Fig.2 shows the distribution of the analyte particles during the atomization step. The initial sample is located on the furnace wall and after =0,7 s a significant transfer of material into the gas phase begins. The particles in the gas phase collide with the wall and re-adsorb or leave through the furnace openings (ie. the dosing hole or furnace ends). The relative rates of desorption collision and adsorption are also shown. The extreme cases of complete re-adsorp- tion upon collision (i.e. no adsorption barrier) and almost elastic collisions are compared. In the case of efficient re- adsorption ,[i.e. Fig. 2(a)] a gas phase concentration gradient along the tube length is noticed because of the earlier loss of particles through the dosing hole rather than through the furnace ends.The population on the surface remains constant for longer times with significant re- adsorption. It is also important to note the existence of a pseudo-equilibrium between the gas and the surface species because of the similarities in the desorption and re- adsorption rates i.e. E and G curves in Fig. 2(a). In contrast with no re-adsorption [Fig. 2(b)] the character- istics of the analyte are more similar to a diffusion- controlled process. The apparent atomization efficiencies (z.e. the maximum percentage of gas particles at the peak curve B) are 8 and 2 1% with the presence and absence of re- adsorption respectively . Understanding Peak Shape As discussed previously,*l the profile shape is determined by contributions from two Drocesses that split the peak into 50 000 40 000 30 000 20 000 fg 10000 5 - 0 .- a 0 50000 & n E c 40000 30 000 20 000 10 000 - 40000 ( a ) - 30000 - 20000 - 10000 100000 ‘i \ c a 80 000 60 000 40 000 20 000 0 0 0.5 1.0 1.5 2.0 2.5 3.0 Time/s Fig.2 Distribution of analyte particles during the atomization step for (a) total re-adsorption and (b) no re-adsorption. Particles A on the furnace wall B in the gas phase C total leaving the dosing hole and D total leaving the furnace ends. The relative rate of generation (E) wall collision (F) and re-adsorption (G) are also shown with the early profile shape being determined by the kinetics of desorption from the graphite; and a ‘loss’ region at the falling edge with the profile shape at later times governed by diffusional loss. These facts justify the use of a method of initial rates to determine at,,, but might disable further straightening of the Arrhenius-type plots because of the T3jZ dependence of the diffusional functionhif (Do T V,,).Arrhenius and Smets Plots and Eft,,, Values Fig. 3 compares Arrhenius and Smets plots for the situation with no re-adsorption barrier. The final temperature is 10 0 / Y -12 I 1 1 -4 1 ‘ 1 -14 0.050 0.070 0.090 0.110 0.130 (RT)-’/mol kJ-’ Fig. 3 Comparison between A Smets and B Arrhenius plots for the situation with no re-adsorption barrier. The data correspond to curve A in Fig. 1 two overlapping regions a ‘supply’ region at the rising edge I138 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL. 7 3 8.0 - Q) 0 - .- 6.0 - + L 2 4.0 - 5 - 5 2.0 - 0 - 0.040 0.070 0.100 0.130 0.160 (RT)-'/mol kJ-' Fig.4 Arrhenius plots obtained from the atomization profiles depicted in Fig. 1. A-C are the same as in Fig. 1. A straight line with a slope of 126 kJ mol-l is shown for reference obtained around 0.053 mol kJ-I producing an upward curvature of the Smets plot. Similar slopes (ato,,,= 126 kJ mol-I) are obtained from the linear region around 0.1 1 mol k J - I ( i e . at the beginning of the atomization). Both plots give a good estimation of the actual desorption energy a,. While the Smets plot is effective in extending the linear region to the left of the curve the extended linear region has a slightly smaller slope (1 14 kJ mol-I) because of the convolution of the loss function with the supply function near the atomization peak.Thus this part of the graph should not be used to obtain an a,,, value. A noticeably higher noise level is present at the useful portion to the right of the curves (around 0.12 mol H-l) resulting in uncertain- ties of 10-20 kJ mol-' in the &,, value. Arrhenius plots are used to obtain a value for a,,, in the remainder of this work but most of the conclusions apply to both methods. Fig. 4 depicts the Arrhenius plots obtained from the three profiles in Fig. 1. The value for a,,, is close to 126 kJ mol-1 at the beginning of all the curves. However by using most of the apparently linear portion values of 1 14 1 1 1 and 126 kJ mol-l are obtained for curves A B and C respectively. This shows that the Arrhenius method is valid only early in time [i.e.high values of (RT)-l] even though the later portion of the plot to the left might look straighter and less noisy. The surface interaction for the analyte in curve B is of intermediate strength and the analyte behaves as a weak interactor at low temperatures (k. as curve C) and like a strong interactor at higher temperatures (ie. as curve A). (a) Zone 10 Zone 7 Zone 4 Zone 1 Zone 10 Zone 1 Fig. 5 Spatially resolved observation zones in the CRA-90 furnace. (a) Magnified side view (0.090 mm2 cross-section each zone); and (b) lateral view the zone windows extend along the furnace length 6000 2400 /---I 0 0.5 1.0 1.5 2.0 2 5 3 Time/s 2000 1600 1200 800 400 * 0 s co 2400 & $ 2000 I- 1600 1200 800 400 0 .o Fig. 6 Spatially resolved atomization profiles using the observa- tion zones depicted in Fig.5; ( a ) and (b) correspond to the A and C analytes introduced in Fig. 1. The temperature profiles are also shown 10 "." 0.060 0.069 0.077 0.086 0.094 0.103 0.111 0.120 (RT) '/mol kJ ' Fig. 7 Spatially resolved Arrhenius plots from the atomization profiles shown in Fig. 6 (a) and (b) correspond to the A and C analytes presented in Fig. 1JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL. 7 139 Role of Spatial Distribution The furnace volume was sliced to obtain the ten 0.090 mm2 cross-sectional observation zones shown in Fig. 5. Zones 2-9 were selected for the study since zones 1 and 10 are too close to the furnace wall and would be difficult to observe experimentally. The spatially resolved atomization profiles obtained from analytes with different re-adsorption characteristics are illustrated in Fig.6. Defined trends during the rising portion of the curves as well as at the peak are observed. Similar tendencies have been observed in spatially resolved experimental measurements of several element^,^ although the effect of a single chemical interaction parameter of the analyte can only be studied through Monte Carlo tech- niques. Stronger interactions between the analyte and the graphite surface seem to increase the retention of the particles near the bottom of the furnace and to produce a steeper concentration gradient in the gas phase at the beginning. However the gradient at the signal peak is more prominent when the analyte interactions with the wall are weak. Subsequent to analyte diffusion from the bottom the strong interactors will fill up the volume of the furnace more uniformly since they have a longer residence time as a result of spending more time on the graphite surface.The presence of the dosing hole is partially responsible for the faster diffusional loss at the top of the furnace for the weak interactors. Actually if the dosing hole is removed as for B the gradient is only slightly affected on the rising edge but is 5 180 E c 140 .- Y Zones Fig. 8 Activation energies of atomization from spatially resolved Arrhenius plots corresponding to the three analytes presented in Fig. I . A B and C correspond to those in Fig. 1 respectively. The expected value of 126 kJ mol-l is depicted as a reference by the broken line (0% relative error is also shown as a broken line) .. . . * . . . . . . I ' . . . .. . . . . . * .- ,. . . . . . . .... . ' . .. ... . I .. . . . . . . . . .. -.. ... .;.. . . .. . . .' . . it;{. **.;:. . . . . . . - . noticeably reduced near the peak. Additional effects caused by the presence of the dosing hole have been discussed previously. I Fig. 7 shows the Arrhenius plots from the spatially resolved profiles in Fig. 6. The early gas-phase gradient clearly affects the accurate determination of the a,,, value (i.e. the estimation of aes) because of the increasing slope of the curves in going from the bottom to the top of the furnace. Thus the accuracy of the estimation of a can be drastically affected by the viewing position of the optical system. This is shown in detail in Fig.8. The analyte that is a weak interactor presents a more uniform distribution of E&,, values while the strong interactor presents a larger dependence on spatial viewing. The intermediate interactor behaves closer to the strong at the bottom and closer to the weak at the top of the furnace because of the temperature shift between the curves (cJ Fig. 6). Finally Fig. 9 shows the actual spatial distribution of the particles in the gas phase near the rising portion of the peak for the strong interactor.22 Most of the analyte is concen- trated at the centre of the furnace at this time. The gas concentration gradient from the bottom to the top is evident in this figure. Conclusions For elements with similar desorption kinetics the presence of re-adsorption shifts the peak to higher temperatures (later times) but does not alter the appearance temperature.The width of the peak increases with an accompanying decrease in peak height and apparent atomization effici- ency. These effects imply an increase in the average residence time of the analyte inside the furnace but during the increased time in the furnace the analyte is adsorbed onto the furnace wall. A strong graphite-analyte interaction might yield a pseudo-equilibrium between the species in the gas phase and those adsorbed on the graphite. Since the profile shape seems to be determined by contributions from two processes that split the peak into two overlapping regions*' (a 'supply' and a 'loss' region) the further straightening of the Arrhenius-type plots might be difficult. Similarly the q, value can be relatively ac- curately obtained from the linear region at the beginning (i.e.early in time) of the Smets and Arrhenius plots. The plots are methods of establishing initial rates and linearity should not necessarily be expected after the initial portion of the graphs. The Smets plot is effective in extending the linear region of the curve. However the extended linear region has a slightly smaller slope because of the convolu- tion of the loss function with the supply function near the atomization peak. The value of Es,, gives an estimation of the desorption barrier aes but a value for ads is not available from these plots. The spatially resolved atomization profiles show defined trends during the rising portion as well as at the peak.Stronger interactions with the graphite surface produce a steeper gradient in the gas phase at the beginning of the atomization. The gradient at the peak is more prominent for the weak interactors and is magnified by the presence of the dosing hole. Experimental values of & increase on going from the bottom to the top of the furnace. The accuracy of the estimation of aeS can be drastically affected by the viewing position of the spectrometer system. This work was partially supported by grants from the National Science Foundation (CHE 870424) and Cray Research. Fig. 9 Beginning of the atomization process for a strong interac- tor (a) absorbance-time profile; and (b) side view and; (c) lateral view of the furnace** References 1 Guell 0.A. and Holcombe J . A. Spectrochim. Ada Part B 1988 43 459.I40 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY MARCH 1992 VOL. 7 2 Giiell 0. A. and Holcombe J. A. Anal. Chem. 1990 62 529A. 3 McNally J. and Holcombe J. A. Anal. Chem. 1987 59 1105. 4 Holcombe J. A. Rayson G. D. and Akerlind N. Jr. Spectrochim. Acta Part B 1982 37 3 19. 5 Black S. S. Riddle M. R. and Holcombe J. A. Appl. Spectrosc. 1986 40 925. 6 Rayson G. D. and Holcombe J. A. Spectrochim. Acta Part B 1983 38 987. 7 Sturgeon R. E. Chakrabarti C. L. and Langford C. H. Anal. Chem. 1976,48 1792. 8 Redhead P. A. Vacuum 1962 12 203. 9 Smets B. Spectrochim. Acta Part B 1980 35 33. 10 van den Broek W. M. G. T. and de Galan L. Anal. Chem. 1977,49 2 176. 1 1 L'vov B. V. Bayunov P. A. and Ryabchuk G. N. Spectro- chim. Acfa Part B 1981 36 397. 12 Sturgeon R. E. and Arlow J. S. J. Anal. At. Spectrom. 1986 1 359. 13 L'vov B. V. and Bayunov P. A. Zh. Anal. Khim. 1985,4O,6 14. 14 Guerreri A. Lampugnani L. and Tessari G. Spectrochim. Acta Part B 1984 39 193. 15 Bass D. A. and Holcombe J. A. Spectrochim. Acta Part B 1988,43 1473. 16 Guell 0. A. Ph.D. Thesis University of Texas at Austin 1990. I7 Wang P. Majidi V. and Holcombe J. A. Anal. Chem. 1989 61 2652. 18 Skelland A. H. P. DifSusional Mass Transfer Wiley New York 1974 ch. 3. :I9 Hultgren R. Desay P. Hawkins D. Gleiser M. Kelley K. K. and Wagman D. D. Selected Values of the Thermo- dynamic Properties of the E/ements American Society for Metals Metals Park OH 1973. ;!O Giiell 0. A. and Holcombe J. A. paper presented at the XV Meeting of the Federation of Analytical Chemistry and Spectroscopy Societies (FACSS) Chicago USA October 1-6 1989 paper No. 34. 21 Guell 0. A. and Holcombe J. A. Spectrochim. Acfa Part B 1989,44 185. 22 Giiell 0. A. and Holcombe J. A. Monte Carlo Simulation of A tom iza t ion Processes in Elect rot hermal A tom izers U n i ve r si t y of Texas Austin videotape ed. 1989. Paper I /03000K Received June 19 1991 Accepted July 18 1991