JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY JUNE 1994 VOL. 9 669 General Computer Program (AAS-TOOLS) for Theoretical Studies in Electrothermal Atomic Absorption Spectrometry Liang Yan Zhong and Ni Zhe-ming* Research Centre for Eco-environmental Sciences Academia Sinica P. 0. Box 2877 Beijing China 700085 A general computer program (AAS-TOOLS) is described which can act as a tool-box for theoretical studies in electrothermal atomic absorption spectrometry. This tool-box consists of general data processing tools an on-line data collection system and attendant database. Application of the tool-box is demonstrated by several practical and theoretical examples ( i ) fitting and filtering of analytical data; (ii) on-line data collection for the atomization of Be; (iii) use of Smets' method to determine the kinetic parameters of Mn; and (iv) theoretical simulation of an atomic absorbance signal based on an exponentially modified Gaussian function.Pull-down menus are adopted in the program with on-line help information. The results of data acquisition or processing and graphs (lines or curves) are saved on a diskette as files which can be retrieved directly by Lotus-123 and Wordperfect (V 5.1 or 5.0). Some algorithms for data processing are given in the Appendix. Keywords Computer program; electrothermal atomic absorption spectrometry; data processing The widespread availability of the microcomputer has greatly enhanced its application in analytical chemistry.'-' At present in atomic absorption spectrometry (AAS) the personal com- puter is principally utilized in the following three areas firstly controlling the instrument for data collection;&' secondly for computer ~imulation;~*'*~ and thirdly for signal (or data) proces~ing.'*~*~ With the advance in theoretical studies in electrothermal atomic absorption spectrometry (ETAAS) a large amount of data needs to be processed in order to obtain kinetic parameters such as atomization energy and order of release in atom desorption.However different research have generally employed their own programs and algorithms (e.g. differentiation integration fitting smoothing and regression) for final calculations which is not only time consuming but also makes resultant data difficult to compare with one another due to the variations in the data processing techniques used.In order to attenuate these drawbacks it would be useful if algorithms and a general data processing program could be recommended for theoretical studies in ETAAS. Despite the fact that some efforts have been made to achieve ~niformity,j-~ an integrated software for on-line data collection and data processing is not yet available. The aims of this paper are (i) to present an integrated software (AAS-TOOLS) that has been developed to permit researchers to expedite on-line data collection and data- processing in an integrated environment; and (ii) to provide algorithms for data-processing that are as concise and valid as possible. Experimental Apparatus A Perkin-Elmer 4000 atomic absorption spectrometer with deuterium-lamp background correction and an HGA 400 electrothermal atomizer were used throughout this work.Manganese Zn and Be hollow cathode lamps were utilized with wavelengths of 279.5 307.6 and 234.9 nm respectively. The spectral bandpass was 0.7 nm and the lamp currents were set according to the recommendation of the manufacturer (Beijing Vaccum Instrument Factory China). High-purity argon was employed as the internal gas. Experiments were performed with Perkin-Elmer standard graphite tubes in the mode of inner gas flow on for Mn and Zn and off for Be. The Ge photo-transistor (B 1918-01 Hamamatsu) utilized to obtain the graphite tube wall temperature was calibrated by focusing * Author to whom correspondence should be addressed. an optical pyrometer (Ircon UX-10 USA) through the sample injection hole in the graphite tube. Temperature and atomic absorbance signals were recorded simultaneously by a personal microcomputer (AP-A2OT) during each atomization cycle at 20 ms intervals via a fast 12-bit analogue-to-digital conversion circuit.All programs were tested on an IBM compatible 80386 personal computer. Reagents Analytical-reagent grade Mn( NO3) ZnNO and Be (Specpure Beijing China) were used to prepare stock solutions that contained lOOOpgml-' of Mn Zn and Be respectively. The working solutions were prepared daily by serial dilution of the stock solutions containing lo00 pg ml-' of the analytes as their nitrates with 0.01 mol 1-' nitric acid. Manganese (0.3 ng) Zn (0.5 pg) and Be (0.016 pg) were used for data collection experiments. A solid pyrolytic L'vov platform was employed when studying the atomization of Be.Program Description The software for AAS-TOOLS is written in C using Borland International's Turbo C (version 2.0) compiler and can be run under DOS operating systems. Hardware requirements include a monochrome or colour display monitor CGA EGA VGA or Hercules graphics cards and an IBM XT/AT or compatible 80286 80386 or 80486 personal computer. The output of general data-processing by AAS-TOOLS is stored on a diskette as an ACSIJ file in the format of a Lotus file. The graphics file is stored in the format of a Wordperfect (5.0-5.1) file. Lay-out The program is driven by pull-down menus with on-line help information which reduces the need for the user to interpret input and output filenames or variables.The main menu of AAS-TOOLS is composed of eight sub-menus. Each sub-menu contains about five subroutines which can be run indepen- dently. The initial layout is shown in Fig. 1. The footnote gives explanatory information about each function. All operation orders are displayed in a pop-up window. Functions General services such as file operation OS-shell print clock exit etc. are given in the first sub-menu.670 File Fic/l.'iller Sma*ing JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY JUNE 1994 VOL. 9 Integration Tapflma~ Differentation k2 Sturgeon mclhod Fuller - Kabkov method I 1 FOOTNOTE k=(I/b)NjP Ad1 Fl=Help ESUCUI-X = h i 1 Fig. 1 Initial lay-out map of AAS-TOOLS The second sub-menu consists of three parts smoothing fitting and filtering. Five point cubic smoothing and seven point four order smoothing can be used to slide data points.An improved Gaussian function and a general order (2-20) orthogonal polynomial can be chosen for fitting equally spaced data points. The rx-,4-y filter can be employed to eliminate white noise. Examples of fitting and filter are given in the next section. Differentiation and integration at each of the uniform data points are achieved by the use of the functions listed in the third sub-menu. For differentiation both polynomial and spline methods" are offered. With the integration subroutine one can calculate the integration value at any interval based on a numerical method." The functions for finding the appearance temperature or appearance time peak temperature or peak time ending temperature or time and rate constant of atom removal k based on the method proposed in ref.11 are presented in the fourth sub-menu. The rate constant k can be calculated at any interval using the decay portion of the absorbance pulse. Six models for calculating the activation energy of atom formation are given in the fifth sub-menu namely Smets model,' the improved Smets' method proposed by Yan et ul.,13 Chung's model,14 Akman method,15 Fuller16 and Kaskov" methods for constant temperature atomization and the method of Yan et ~ 1 . ~ Except for Yan et a!. the resultant data for the Arrhenius plot of the corresponding model is stored on a diskette in Lotus file format. This program also gives the slope (activation energy) and intercept (the logorithm of the fre- quency factor) of the Arrhenius plot in a window.One can draw an Arrhenius plot via Lotus 123 by retrieving the data file stored or by calling the graphics functions offered in sub- menu 6 which comprises drawing lines or curves and a dual y-axis plot. The maximum number of lines or curves can be up to 15 which is very convenient for concentration study in AAS,9 as exemplified in the next section. The AAS-TOOLS program contains four kinds of random data generators (in sub-menu 7). The principle of the generator is derived from the multiplicative congruence meth~d.'~*''*'~ These generators can yield infinite random data with uniform or Gaussian distribution between 0 and 1 or at any interval of data without repetition of the cycle. The eighth sub-menu contains several practical programs.The first one is developed for constant temperature atomiz- ation such as probe atomization based on the method cited in ref. 20. A large number of the functions introduced above are involved in this program. The second is the signal simu- lation program based on an exponentially modified Gaussian function ( EMG),21*22 which can yield an absorbance peak with any given height and width. The synthetic signal is a combi- nation of theoretically computed data and random white noise generated by AAS-TOOLS. The simulated absorbance data and corresponding temperature ("C) data are stored together in the file. The linear temperature data are generated by inputing the beginning temperature and heating rate. The third program is a data collection system.With the appropriate hardware interface this program can be used to collect on-line a transient absorbance signal and temperature synchronously. After the acquisition cycle any functions cited above can be called to process the data by returning to the main menu. An IBM/AT and compatible 80286 or more advanced personal computer can finish all the data processing tasks including smoothing fitting filtering regression and plotting within 2 min. Therefore during pre-atomization data processing can be finished without waiting for the next data collection cycle. This sub-menu also contains a database which stores references on the atomization mechanism of a range of elements. Results and Discussion Use of AAS-TOOLS is best illustrated by several practical examples to show how the tool-box can be employed in theoretical studies and how the data collection system should be utilized.General Data Processing Fitting of unalytical duta The fitting of the absorbance signal is an important procedure in the theoretical study of ETAAS7-9*'3 The results of the fitting of a sixth order polynomial to experimental data is shown in Fig. 2 and the corresponding fitting deviation which is the sum of the squares of the deviations between the fitting value and the experimental value is 0.00529. In the fitting pro- cess the coefficients of the polynomial and the fitting deviation are listed in a pop-up window the fitting curve and the experimental curve are also drawn together in a graphical window. Orthogonal polynomial algorithms are given in the Appendix.Filtering of analyticul dutu The absorbance-time curve of Zn and the corresponding filtering curve are shown in Fig. 3. As can be seen the white noise of the experimental data has essentially been filtered. Details of the filter principle are presented in the Appendix. p21 - $ 0.1 f $ 0 1 2 3 4 t m Time/s < Fig. 2 Manganese absorbance profile and corresponding fitting curve of sixth order orthogonal polynomial A experimental; B fitted Y 0.20 r 1 2000 - .- C 3 2 0.15 h 4- .- f - 0.10 Q) C 4 0.05 4 1500 y E . 1000 E al P E 500 P) I- L I I 1 1 I 10 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time/s 2 Fig. 3 Filtering of Zn absorbance signal A original; and B filtered. C Temperature uersus time curveJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY JUNE 1994 VOL.9 67 File On-line Data Collection The following is an example of an application of the data collection system on the Perkin-Elmer 4000 atomic absorption spectrometer. The transient absorbance signal of Be the back- ground absorbance and the temperature data (“C) collected synchronously are demonstrated in Fig. 4 and Fig. 3 presents an example of data-collection for Zn absorbance without background absorbance. This performance can be achieved by highlighting the data-collection item in the eighth sub-menu. The data collection system can also be employed for other atomic absorption spectrometers as long as there is a proper interface between the spectrometer and the computer. In brief this data collection system is independent of the hardware such as the computer and the model of atomic absorption spectrometer used.FiVFilter Integration Tapp/Tmaa Graph Randomdata practical generators programs Smoothing Differentation k2 Determination of Activation Energy and Release Order of Mn via AAS-TOOLS Experimental data for the atomization of Mn are obtained by the data collection system introduced above. As an example of the operation of AAS-TOOLS the determination of the activation energy of Mn using Smets’ method12 and deduction of the release order based on a concentration study,’ are given below. Fig. 5 demonstrates procedures for the calculation of acti- vation energy and sequential outputs in a window with high- lighting of Smets’ item from sub-menu 5 where under-lined inputs are filled in by the operator. To deduce the release order the graphical functions listed in sub-menu 6 can be conveniently called to draw concentration curves as shown in Fig.6 which indicate that the release order of Mn is unity. The Arrhenius plot shown in Fig. 7 is drawn uia Lotus 123 by retrieving the data file stored in the process of computing the activation energy. Simulation of Absorbance Signal Based on the Exponentially Modified Gaussian Function (EMG)” Theoretical absorbance signals with and without the addition of random white noise as shown in Fig. 8(a) and (b) can be produced by calIing the EMG applied program in sub-menu 8 where the values of parameters rs z S and t are 0.5 0.5 0.7 and 2.7 respectively where CT is the standard deviation of the Gaussian constituent z is the time constant of the exponential modifier S is the peak area and tg is the difference between peak time and appearance time.Simulated absorbance signals with different shape height and width are shown in Fig. 9 where the values of parameters (r z S and t are 0.5 0.5 I 1 2700 C .z 0.4 2270 3 0 1 2 3 4 5 Time/s Fig. 4 Beryllium absorbance profile as a function of atomization temperature A absorbance profile of 0.016ng of Be; and B background absorbance of 1.4 pg of CaC1,. C Temperature versus time curve I Input dam filename I C:\AGS\1 coeff. oTpolynomid a0:0.175al:-0.299 a0.716 a3:2.251 a40.7982 a5:-4.498 Deviation of Fimng D1:0.005 D20.423 d3:O.m Ln&=16.2 FI=He$ ESC/Ctrl-X =Exit QOTNOTE k=(I/p)A/j,“ Adt Fig.5 Flow-chart of the determination of activation energy of Mn using Smets’ method 10 I 0 1 2 3 4 Time/s 3 Fig.6 Absorbance versus time profiles for various initial masses of Mn.Initial masses are A 0.05; B 0.10; C 0.20; D 0.30; E 0.40; F 0.50 G 0.80; and H 1.00 ng 1.5 I I 1.0 0.5 c 5 0 -I - 0.5 1 .o I I I 60 62 64 66 68 ’/ T x 1 0 - 5 o c Fig. 7 Arrhenius plot of Mn based on Smets’ model 0.7,0.5 and 2.0 respectively. The principle of the EMG function and the definitions of the terms used are given in the Appendix. Conclusion This program is specially developed for the theoretical research of fundamental processes in ETAAS. It integrates on-line data672 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY JUNE 1994 VOL. 9 0.7 0.6 0.5 0.4 0.3 v) 0.2 3 0.1 *.’ .- C L- 2 0 c z -0.1 1 I I I I I s o 1 2 3 4 5 a C m e 2 a 0.8 0.6 0.4 0.2 0 1 2 3 4 5 6 Time/s Fig.8 Simulation of absorbance signals (a) with and (b) without white noise respectively; u = 0.5 7 = 0.5 S =0.7 and t = 2.7 0.6 0.5 - 0.4 0.3 0.2 0.1 0 a 5 0.6 0.5 0.4 0.3 0.2 0.1 1 0 1 2 3 4 5 Time/s Fig.9 white noise respectively; u = 0.5 t =0.7 S = 0.5 and t = 2.0 Simulation of absorbance signals (a) with and (b) without collection data processing and a database with user-friendly and software-friendly interfaces. All subroutines can be called from an integrated menu and used independently. The program developed can be run on IBM-AT or compatible personal computers. This work was supported by the Chinese Academy of Sciences under contract No. KM 85-47.Appendix Fitting The algorithm based on the orthogonal p o l y n ~ m i a l ’ ~ * ~ ~ .~ ~ is given below. Assuming there are n evenly spaced data points (xi yi,) (i = 1,2 . . . n) based on the properties of orthogonal poly- nomials10.22 a general order fitting polynomial (Pm) can be expressed as follows Pm(x)=a +a,x+u,x2+ ... +amxn-’ where m < n m < 20. The fitting polynomial may be defined as Pm(x)= CI QI(x) + C2Q2(x) + * a * + CmQm(X) where C,(j= 1,2 ... rn) are coefficients be constructed from the following sequences Qj(x)(j= 1,2 ... m) are orthogonal polynomials which can Qi(x)= 1 Q2(x) = (X - 4 Qj+l(X)=(X-j+,)Qj(X)-jQj-l(X) (j=2 3 m-1) postulating n dj= C Q?(X~) (j=1,2 ... m) i = l aj + 1 = Pj=dj/dj- xi Q:(xi )/dj ( j = 1,2 ... m- 1) Application of the least-squares criterion gives i = 1 n C,= y,Qj(xi)/dj (j= 1 2 ... m) i = 1 finally the fitting polymial is Pm(x) = a + u2x + a3x2 + .. . + umxm-’ where ai (i= 1,2 ... m) are the coefficients of the polynomial. a-py Filter This filter can eliminate the white noise of evenly spaced data points.” The principle of the filter can be expressed as x*(t)=x(t)+q(t) x*(t) is the measured data x(t) is the accurate value of a useful signal and h ( t ) are white noises the mean of which equals 0 namely E Cm3 = 0 Prediction of the one step value of the next time is based on the formulae given below Xn + l / n = Xn + X’n T + XI’ ( T2/2) X‘ + l/n = X’ + X”,T X ” + 11 = X ” The following equations are used to assess the filter value at this time Xn+ 1 =Xn+ l / n + a(X*n + 1 - x n + l / n ) X’n+l=X’n+l/n+P/T(X*n+l-Xn+1/n) Xt’n+l =X”n+,/n+2y/T2(X*n+ -Xn+l/n) where X*n+l is the measured value at this time and Xn+l,n is the one step prediction assessment of the location at this time compared with the previous time. X’n+l/n is the one step prediction assessment of the rate at this time as compared with the previous time.X ” + l/n is the one step prediction assessment of acceleration at this time as compared with the previous time.JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY JUNE 1994 VOL. 9 673 Xn+l is the filtering assessment of the location at this time; X’ + is the filtering assessment of the rate at this time; X” + is the filtering assessment of acceleration at this time; T is the interval of data collection; and a p and y are the structural parameters of the filter. Differentiation via the Spline Function In some kinetic m o d e l ~ ~ ’ ~ ~ the differentiation term dA/dt is calculated.There is an apparent variation in values obtained from different algorithms. In this program two algorithms are offered one is based on the derivation of a fitting polynomial the other is via the spline function. Here only the latter is given.” First assuming that function y=f(x) has n evenly spaced data points (nodes) xl x2 ... x and yl y2 ... y are the corresponding functional values and setting y’(xl) and y‘(x,) to be derivatives of boundary nodes then the values of the other n-2 nodes can be calculated from the following sequences a1=0 b1= Y’(X1) h j = x j + l - ~ j aj=hj_,/(hj-,+hj) forj=2 3 ... n-1 for j = 1,2 ... n - 1 P j = 3 C( 1 - aj>( yj - y j - 1 ) / h j - 1 + aj( ~j + 1 - yj)/hj 1 forj=2 3 ...n-1 aj= -~!~/[2+(1-a~)a~-~] forj=2 3 ... n-1 bj= [ P j - ( 1 - M j ) b j - I]/[ 2 + ( 1 - aj)aj- 11 forj=2 3 ... n-1 y ’ ( x j ) = u j y ’ ( x j + ) + b j j=n-1 n-2 ... 2 where a b CI P and h are all intermediate parameters. Simulation of Absorbance Signal The EMG function h( t ) is a regular Gaussian function G( t S G(t)= ___ e ~ p [ - o& convoluted by an exponential decay term H ( t ) of unit area H(t)=-exp - - tdO ( 3 H(t)=O t<O The expression of the EMG function h ( t ) is or deviation of the Gaussian constituent t the difference between peak time and appearance time and t’ a dummy variable of integration. The above equation contains an integral form that is difficult to estimate numerically the error function erf(t) which has the form j exp [t2] dt’ erf(t)= J;r 0 has often been used to calculate h(t) by using the relation- ship22,24 with but inputing different z S t and CT values one can obtain different absorbance profiles with various peak heights widths and positions.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 References Pawson J. B. Duffield R. J. King P. R. Hajizadeh-Saffar M. and Fisher G. W. Spectrochim. Acta Part B 43 1133. Voigtmall E. Anal. Chim. Acta 1991 246 9. 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Chem. 1990 62 529A. Box G. E. P. and Muller M. E. Ann. Math. Stat. 1958 29 610. Yan X.-p. and Lin T.-z. Acta. Chim. Sin. 1989 47 1139. Berthod A. Anal. Chem. 1991 63 1879. Hanggl D. and Carr P. W. Anal. Chem. 1985 57 2394. Peter A. G. Anal. Chem. 1991 63 534. Gladney H. M. Dowden B. F. and Swalen J. D. Anal. Chem. 1969 41 883. Paper 3/06450F Received October 28 1993 Accepted February 7 1994 where h ( t ) is the EMG peak height at time t S the peak area z the time constant of the exponential modifier Q the standard