JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY APRIL 1991 VOL. 6 239 Optimization of Cold Vapour Atomic Absorption Spectrometric Determination of Mercury With and Without Amalgamation by Subsequent Use of Complete and Fractional Factorial Designs With Univariate and Modified Simplex Methods George A. Zachariadis and John A. Stratis* Laboratory of Analytical Chemistry Department of Chemistry Aristotelian University Thessaloniki 54006 Greece Experimental conditions for the determination of Hg with commercially available purpose-built apparatus were opti- mized by sequential use of two multiple parameter methods based on a factorial design and a modified simplex procedure. The responses that were evaluated to determine the optimum conditions were the peak height and peak area of the Hg signal.The significance of the effects was tested using the analysis of variance (ANOVA) at a 99% level of significance. Interactions observed between the parameters were quantitatively evaluated and dis- cussed. The flow-rate of air volume of sample solution use of a desiccant and the interactions between these pa- rameters in the determination of Hg by cold vapour atomic absorption spectrometry (CVAAS) without amalgamation were optimized according to a complete 23 factorial design and a univariate method. The experi- mental design was also considered for the determination of Hg after amalgamation on an Au-Pt gauze. The flow- rate of nitrogen mass of the amalgamator trapping time releasing time and interactions between them were sta- tistically evaluated according to a fractional factorial design (half-replicate of a complete 24 factorial design) and subsequent use of the modified simplex method.This approach for partial optimization of a commercial system is rapid and has many advantages over simple univariate methods. An absolute detection limit of 0.33 ng of Hg was achieved using the amalgamation technique for a total solution volume of 50 ml. This is comparable to the limits obtained by univariate methods of optimization. An approximately 1 0-fold improvement in the detection limit was observed with this technique in comparison with the direct method. Keywords Cold vapour atomic absorption spectrometry; mercury determination; gold-platinum amalgamator; fac- torial designs; modified simplex The application of modem statistical methods of experimental optimization such as factorial designs or simplex methods in analytical procedures is rare although factorials have been in use since about 1960 and simplex methods since 1969.Massart et al.‘ have produced a comprehensive account which covers more than 30 references on applications of complete and fractional factorials in various analytical procedures in ad- dition to some for simplex methods. The original simplex method was modified in order to reach the optimum conditions sooner giving the so called ‘modified simplex’ method. Long2 has provided detailed information on the application of the simplex method in analytical chemistry while Deming and Morgan3 have reviewed the application of the method up until 1973. Factorial designs have an advantage over simplex methods in that in the region preceeding the optimum a large amount of quantitative information can be obtained about the significance of the various effects and interactions However both strategies may fail if there is more than one optimum.Also factorial methods can deal with non-quantitative para- meters (e.g. experimental circumstances or attributes) while a simplex lacks this possibility. One obvious disadvantage is the large number of experiments required when several factors are examined but this can be minimized by the use of fractional factorials. For the simplex this is not a serious limitation because incorporation of many factors does not increase the number of experiments to a large extent but the difficulty of si- multaneously changing all the factors remains.Another serious disadvantage compared with simplex methods which has been discussed previously,J is that factorial experiments cover a pre-defined region so there is a real possibility of mis- interpreting the position of the optimum. This problem appears * To whom correspondence should be addressed. in situations where the initial values of the effects are too close together to give a significant difference or are too far apart giving a large but useless significant difference. The purpose of this work was the application of the above methods to an experimental procedure and their sequential use in order to extract more information about the optimum conditions of an analytical determination. This combination was suggested by Morgan and Deming4 and was employed to avoid the disad- vantages of each method.It can be applied to other dynamic systems in addition to the cold vapour atomic absorption spec- trometric (CVAAS) determination of Hg. The analytical procedure selected for investigation was the determination of Hg by CVAAS using a commercially avail- able instrument (Perkin-Elmer Model MAS-SOA). The purpose was to investigate the combination of multiple para- meter methods in a real dynamic situation. This system proved to be ideal for such an investigation because a number of factors with obvious interactions between them affect the de- termination. In addition the method is not time consuming hence allowing easy duplication or triplication of the experi- mental results.Although the cold vapour technique in the atomic absorp- tion spectrometric determination of Hg is the most widely used method and has been optimized by many workersS-X using uni- variate methods use of the factorial design or modified simplex method has not been reported. On the other hand it is known that many factors affect the determination and interac- tions between some of these factors have been recognized. So the classical optimization strategy using a univariate method is insufficient alone to estimate and evaluate these interactions. Mercury can be determined by CVAAS without a pre- concentration step or after pre-concentration by amalgamation on a suitable noble or alloy such as Au-Pt. The Au- Pt alloy has been reported in the as being one of the best and is used in commercial instrumentation.240 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY APRIL 199 1 VOL.6 In this work a study of the MAS-5OA system without amal- gamation as it is intended to be used was carried out in addi- tion to investigations with a pre-concentration step on an amalgamator utilizing the statistical optimization methods dis- cussed above. The absolute amounts of Hg determined were in the range 10-100 ng in the former instance and 1-100 ng in the latter. Experimental Reagents All the reagents were of analytical-reagent grade (Merck pro analysi). The acids used were HNO (maximum Hg content O.OOO0005%) and HCI (Suprapur). The SnCI solution was prepared by dissolving 10 g of SnCI,.2H20 (maximum Hg content O.OOOOOl%) in 10 ml of 50% HCI and diluting to 100 ml with doubly de-ionized water.This solution was aerated for 15 min with nitrogen in order to minimize the Hg content. The desiccant used was Mg(CIO,),. A stock standard solu- tion of lo00 mg I-' of Hg" was prepared by dissolving 1.7081 g of Hg(N01)2.H20 in 5 ml of HNO and diluting to 1000 ml with doubly de-ionized water. Working solutions were prepared daily by appropriate dilutions of the stock solu- tion in 0.5% v/v HNO,. The amalgamator material was a gauze (0.25 mm mesh size with the diameter of the wire being 0.025 mm) made from an Au-Pt alloy (90% Au-10% Pt). G - J G- 1 r U U E Fig. 1 Mercury vapour trap with amalgamator. A Electrical supply ( I 10 V); B polytetrafluoroethylene (PTFE) caps PTFE fixation; C quartz tube (12 cm long 0.5 cm i.d); D thick glass wool; E Au-Pt gauze ( 1 cm long) F Ni-Cr wire spiral resistance (17 R) and G flow of nitrogen The purge and carrier gas for the determination without pre- concentration was air pre-purified to remove trace amounts of Hg by passing over a similar Au-Pt gauze.High-purity (99.99%) nitrogen purified in the same manner was used as the carrier gas in the procedure with the pre-concentration step. Instrumentation The determination of Hg was carried out using a Perkin-Elmer mercury analyser system MAS-SOA equipped with the origi- nal pump cylindrical plastic cell and mercury vapour lamp as illustrated in the manufacturer's These parameters were unmodified. The amalgamator accessory was connected to the MAS-5OA in the same manner as it can be connected to an MHS-20 system." The tube with the amalgamator is illustrated in Fig.1 and was constructed from a quartz tube ( 1 2 cm length and 0.5 cm i.d.) which was connected to the circuit liu PTFE screw caps at both sides. The Au-Pt gauze was placed in the centre of the tube with glass wool on both sides. The gauze evenly filled the interior of the tube to ensure quantitative amalgamation of the Hg vapour on the gauze. A Ni-Cr wire spiral (electrical resistance 17 R) was placed around the middle of the quartz tube and was connected to a I10 V d.c. electrical supply. After heating the resistance for 17-18 s a suitable temperature (>600 "C) was reached and the Hg vapour released from the amalgam. It was necessary to test the efficiency and repeatability of the whole trap.The temperature measurements were carried out with a Rh-Pt thermocouple (calibrated in the range 1W 1100 "C) by placing the thermocouple in the Au-Pt gauze. The capacity for Hg trapping was tested by placing a second amalgamator just after the first. The second amalgamator did not trap Hg in detectable amounts even after four subsequent cycles of measurements. The stability and repeatability of the resistance was tested because the surface of the Ni-Cr wire was gradually oxidized by atmospheric oxygen although the electrical resistance was not changed. The whole amalgamator was cooled after the determination by use of a continuous flow of nitrogen for 10 min. This time is the same as recommended by Bricker,Is although after 4 min the temperature of the alloy fell to below 250 "C.Below this temperature Welz and Schubert-JacobsI2 found that trapping of Hg was not achieved and water vapour did not condense; this observation is limited to matrix-free solutions. An altema- tive proposed by these workers was the use of fritted glass to trap the water droplets prior to the tube Hence two thick sec- tions of glass wool were placed inside the connecting tubing. The purpose of the first experiment was to test the thermal efficiency of the amalgamator in relation to the releasing time. The results are given in Fig. 2. The two graphs show the be- haviour of the amalgamator with two different nitrogen flow- rates and it is clear that at low flow-rates the required temper- ature is achieved faster. The next test was to establish the time needed to reach a temperature of 600 OC over the whole range of the flow-rates.As illustrated in Fig. 3 for a range of flow- rates of between 0.2 and 0.6 I min-' the required temperature is achieved in 17 s. 800 I 1 0 4 8 12 16 20 24 28 32 Ti me/s Fig. 2 Effect of firing time of the resistance (Ni-Cr wire) on the temper- ature of the Au-Pt gauze for two different flow-rates of nitrogen A 0.8 and B 2.0 1 min-I I" 0.2 0.6 1 .o 1.4 1.8 2.2 Flow-rate/l min-' Fig. 3 perature of 600 "C in the amalgamator Effect of nitrogen Row-rate on the time needed to achieve a tem- Good repeatability is attained after 4-5 firings and it is maintained for at least 30 firings. In practice it was found that even after 80 firings (18 s each) both the amalgamator and the resistance remained stable and did not need to be changed.All that was required was the careful cleaning of the Au-Pt gauze with hot dilute HNO and a blank firing before trapping of the Hg.JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY. APRIL 199 1. VOL. 6 24 1 Procedure I Each sample contained 100 ng of Hg". The water-vapour trap was filled with 4 g of fresh Mg(C104)? and was used for eight determinations before replacement. GardneP reported some problems with this desiccant because when it becomes damp some losses of Hg occur but it is better than CaCl," and it is the desiccant usually employed for this purpose. The Hg vapour generation was performedI7 by reduction of Hg2+ with 1 ml of 10% SnClz solution. Air was used as the carrier gas in this procedure and a stable base line was achieved when air was passed through an amalgamator before entering the Dres- chel bottle.The factors affecting the direct determination of Hg can be classified into four groups chemical physico-chemical geo- metrical and mechanical. For the partial optimization in this work the factors of the first three groups were not optimized but the optimum values were taken from the available litera- ture. The main factors in the fourth group that were optimized were the flow-rate of air (A) the volume of the sample ( B ) and the presence or absence of the desiccant (C) before the Hg vapour entered the cell. Hence a complete factorial design of three factors at two levels (27 was selected" (Table l) to evaluate the significance of the above factors and possible in- teractions between them at a 99% probability level.Table 1 Table of signs in a complete 23 factorial design Effect Treatment Sum (1) a h ah c' a(* hc ahc x A - + - + - + - + I l + + - - + + .v2 + + + + .v3 AB + - - + + - - + .Y4 AC + - + - - + - + .vs ABC - + + - + - - + s7 Result v ?'2 Y3 r4 Y Y s Y7 Y s - - B C - - - - + + + + - - - - BC The experimental results were obtained in triplicate so as to allow for the possibility of estimating the interaction ABC and the residual error. Every factor is investigated at two levels so each factor loses 2-1=1 degrees of freedom. Consequently all the effects have 7 degrees in total. If there is no replication 8-1=7 degrees of freedom are available so no degrees of freedom are available for the estimation of the residual error.Replication of experimental results is then necessary in order to obtain extra degrees of freedom. If the experiments are re- peated in triplicate 24-1=23 degrees of freedom are available while the sum of the degrees for the particular effect remains as 7. So there are 23-7=16 degrees available for estimating the re- sidual error. Another approximate solution to the problem would be the incorporation of the third-order interaction into the residual error or expression of the residual error by means of this interaction based on the fact that the high-order interac- tions are usually negligible as described below. Analysis of variance (ANOVA) is a suitable test of significance for the statistical interpretation of the results. As described in the experimental section the univariate method was used to complete the optimization.In this instance the re- sponse was measured as either peak height or peak area of the Hg signal (in arbitrary units). The statistical interpretation was the same for the results obtained for peak height and peak area. Procedure I1 The Hg vapour generation was performed as in Procedure I. However in this part of the study an Au-Pt gauze was used as the amalgamator for the pre-concentration of the Hg vapour. Mertens and Althaus" stated that both nitrogen and argon were suitable as carrier gases although helium was found" to contribute less noise than other inert gases. In this procedure nitrogen after being purified through an amalgamator was used which eliminated the noise sufficiently.The flow-rate of nitrogen was kept constant during the trapping and was reduced to 0.1 1 min-' during the releasing period. This proce- dure was applied for two ranges of concentration 20-200 and 200-2000 ng 1-I. Four 'mechanical' factors were tested in this type of determination the flow-rate of nitrogen (A) mass of the gauze (B) trapping time (C) and releasing time (D). Hence a 24 factorial design should be used or a half-replicate (24- '=29. The volume of sample was not optimized and a 50 ml volume was employed throughout so that the simplex was not moved to a higher level (see below). This limitation exists because absorbance is the response used for the optimi~ation.'~ For a complete 24 design 24=16 experimental results are re- quired.The complete factorial with interactions was designed according to reference 4. The half-replicate was designed as detailed in Table 2. This is produced by incorporation of factor D to a complete 23 factorial by replacing one effect (e.g. ABC) with D . In this instance the third-order interac- tion ABC is considered to be negligible so the replacement is D=ABC. Also taken into account in this replacement is the fact that interactions of D are negligible as is seen from the procedure became the releasing time is obviously indepen- dent of the other factors. Because of the null interactions of D (releasing time) 'the aliases are confounded just theoretically ,4 and from the pairs of aliases of Table 2 only the first repre- sent the real effect. The experimental results were duplicated so as to obtain the degrees of freedom available for the esti- mation of the residual error.~~ ~ ~ ~ ~~~~ Table 2 Table of signs in a half-replicate of a complete 24 factorial ex- periment (fractional factorial) Effect Alias Treatment Sum A B C AB AC BC D Result BCD ACD ABD CD BD AD ABC Because some interactions between quantitative parameters proved to be significant the modified simplex method4 was used to complete the optimization for the two ranges of con- centrations being considered. In this instance the peak height of the Hg signal (instrument units) was the response used because this gave better reproducibility compared with the peak area. The variances were compared by use of the F-test. Results and Discussion Optimization of Procedure I The experimental conditions and results are presented in Table 3. The sequence in which the results were taken was random as shown in the second row of the table.The two levels for each factor are also described. The significance of the effects was tested with ANOVA and the results are shown in Tables 4 and 5 . In Table 4 the peak height results are presented and in Table 5 the peak area results. The mean sums of the squares are approximated in some instances. When the factor has a high value (high level +) the peak is increasing. This is expressed in the sign (+) of242 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY APRIL 1991 VOL. 6 Table 3 Experimental results of the complete two level-three factor fac- torial design in the determination of Hg without amalgamation (respons- es peak height and peak area) Parameter Treatment ( I ) a h ah ( 9 a(.hc uhc Sequence (random) 1 8 2 7 4 5 3 6 Air flow-rate A - + - + - + - + Volume B - - + + - - + + Desiccant C + + + + - - - - Peak height- I 127 125 98 96 130 126 101 100 I1 126 126 98 95 131 127 100 99 111 128 127 96 96 131 129 100 98 I 663 313 692 301 901 309 953 305 11 687 277 683 294 758 278 903 301 I11 674 240 628 274 852 297 860 296 Peak area- The low (-) and high (+) levels of the factors are the following Factor Unit Symbol (-) Value (+) Value Air flow-rate 1 min-’ A 0.6 2.0 Sample volume ml B 50 100 Desiccant - C No Yes Table 4 tion of Hg without pre-concentration Analysis of variance for peak height signals in the determina- Sum s s 2 .v3 x4 s g .v() s7 -22 -356 +34 +4 -6 4 8 (X,)* 484 126736 1156 16 36 16 64 ANOVA- Source of Degrees of Sum of Mean sum F, variation freedom squares of squares F 8.53 A 1 B 1 C 1 AB 1 AC 1 BC 1 ABC 1 Residual error 16 20.2 5280.7 48.2 0.7 1.5 0.7 2.7 15.3 Total 23 5370.0 * S significant.t NS not significant. 20.2 21.0 s* 5280.7 5500.7 S 48.2 50.2 S 0.7 0.7 NSt 1.5 1.6 NS 0.7 0.7 NS 2.7 2.8 NS 0.96 the sum. If the high value (+) of the factor causes a decrease in the peak this is expressed in the sign (-) of the sum. The value of the ratio F is also an indication of the power of the effect (e.g. 5500.7 describes a strong effect by factor B and 50.2 a serious effect by factor C). According to the ANOVA table of peak heights the follow- ing conclusions can be made at the 99% probability level.(i) The flow-rate of air ( A ) seriously affects the peak height ‘low flow-rate causes on increase in peak height’. This is owing to the low dispersion of the Hg vapour in the air stream when the flow-rate is low. (ii) The volume of the sample ( B ) strongly affects the peak height ‘small volume causes an increase in peak height’. As the volume of the sample decreases the aera- tion of the Hg vapour becomes spontaneous and a more con- centrated air-Hg stream is delivered to the cell. (iii) The desiccant (C) seriously affects the peak height ‘presence of the desiccant causes an increase in peak height’. It is obvious that the circulation of the dried air stream is advantageous under these conditions although the desiccant provides a me- chanical stop. (iv) There are no significant interactions Table 5 Analysis of variance for peak area signals in the determination of Hg without pre-concentration s 5 .x-s s -5766 -240 +I284 -126 -1 104 +204 -328 (.v,)’ 33246756 57600 1648656 15876 1218816 41616 107584 Sum S’ ,v* x3 X4 ANOVA- Source of Degrees of variation freedom A 1 B 1 C 1 AB 1 AC 1 BC 1 ABC 1 Residual error 16 Sum of squares 1385282 2400 68624 662 50784 1734 4483 21941 Total 23 1535910 *S significant.tNS not significant. Mean sum of squares 1385282 2400 68624 662 50784 1734 4483 1371 Fw F 8.53 1010.0 s* 1.7 NSt 50. I S 0.5 NS 37.1 S 1.3 NS 3.2 NS between the above parameters however incorporation of them in the residual error was investigated. 2 15.3+0.7+1.5+0.7+2.7 00 = = 1.05 ( 1 1 16+ 1 + 1 + ! + 1 According to equation (l) the evaluation of the effects is not affected (1.05 compared with 0.96).From the ANOVA table of the peak areas it is concluded that at the 99% probability level (a) the flow-rate of air (A) strongly affects the peak area according to the relationship ‘low flow-rate causes an increase in peak area’; (h) the volume of the sample ( B ) has no significant effect on the peak area; (c) the desiccant (C) seriously affects the peak area according to the relationship ‘existence of desiccant causes an increase in peak area’ which is related to a similar increase in peak height; and (6) the interaction between factors A and C is significant according to the relationship ‘presence of desiccant x lowering of the flow-rate causes an increase in peak area’. When a water vapour trap is used the flow-rate must be lowered in order to trap the vapours efficiently.From the analysis of variance of the peak heights it was concluded that no interactions were significant and hence the univariate method can be applied to give a better approxima- tion of the optimum region. On the other hand analysis of var- iance of the peak areas has revealed a significant interaction between the flow-rate (parametric factor) and the presence of the desiccant (a non-parametric factor). Because a non- parametric factor cannot be quantified the univariate method must be applied in a separate experiment. The experimental results of this approach are plotted in Figs. 4-7. The response (peak) was plotted on the y-axis and the factor being varied on the x-axis.In Fig. 4 the negative effect of flow-rate and the positive effect of the desiccant on peak height are shown. The optimum region is compressed at flow-rates ~ 0 . 8 1 min-’ because the peak area shows no changes in this region. The curve obtained in the presence of the desiccant is almost parallel to that with no desiccant because there are no interactions between the flow-rate and desiccant. Also the former curve is above the latter indicating the positive effect of the desiccant on the peak height. Fig. 5 il- lustrates the strong negative effect of sample volume on peak height which is demonstrated by the sudden change in direc- tion of the graphs with a negative slope. The parallel graphs again confirm the absence of interactions between flow-rateJOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY APRIL 1991.VOL. 6 243 I 1 I 1 1 0 0.4 0.8 1.2 1.6 2.0 2.4 Flow-rate/l mi n-l Fig. 4 Effect of air flow-rate on peak height of 100 ng of Hg for a sample volume of 50 ml. A With desiccant; and B without desiccant w 0 25 50 75 100 125 150 Volume of sample/ml Fig. 5 Effect of volume of liquid sample on peak height of 100 ng of Hg for an air flow-rate 0.4 1 m i d . A. With desiccant; and B without desiccant 600 '""I f A loo' 1 I 1 J 0.2 0.6 1 .o 1.4 1.8 2.2 Flow-ratefl min-' Fig. 6 volume of 50 ml. A With desiccant and B without desiccant Effect of air flow-rate on peak area of 100 ng of Hg for a sample 5001 1 200 I 1 1 0 25 50 75 100 125 150 Volume of sample/rnl Fig. 7 Effect of volume of liquid sample on peak area of 100 ng of Hg for an air flow-rate 0.4 1 min-'.A With desiccant; and B without desiccant and desiccant. In Fig. 6 the strong effect of flow-rate on peak area is evident together with the interaction between the flow- rate and the presence of the desiccant. This interaction is dem- onstrated by the irregularities along the graphs. In Fig. 7 it can be seen that the effect of sample volume on the peak area of the Hg signal (arbitrary units) is not significant because the graphs show no evident gradient and must be regarded as being parallel to the x-axis. Calibration study in procedure I The base line of the spectra was more stable in the presence of the desiccant. This advantage together with an increase of peak heights and areas should be balanced against the disad- vantages of dampening the desiccant and the possibility of trapping the Hg.However it was decided that a desiccant would be used for the calibration study. The peak height appears to be free from interactions. The optimum conditions determined from the univariate experiment were flow-rate of air 0.4 1 min-I; volume of sample 25 ml; presence of a desic- cant; and signal measured using peak height. The peak height is expressed in absorbance units (AHg) and increases linearly with the absolute amount of Hg (in ng) present (XHg). The calibration graph is given by the equation The slope (sensitivity) is in good agreement with the experi- mental value of 6 ng of Hg which gave an absorbance of 1%. The detection limit is derived according to IUPAC Definitive Rules2" using the sum of the mean of eight blank measure- ments plus three times the standard deviation of these meas- urements.The absolute detection limit is 3.3 ng of Hg. The repeatability expressed as relative standard deviation from ten repeat determinations of 40 ng of Hg was 6.9%. AHg= 1 . 5 1 6 ~ 1 0 ~ + 5.886~10~X (2) Optimization in Procedure I1 The experimental conditions and the results obtained are pre- sented in Table 6. The results of the ANOVA experiments ex- pressed as peak height are shown in Table 7. The following conclusions can be made at the 99% probability level. (i) The flow-rate of nitrogen (A) strongly affects the peak height 'low flow-rate-increase in peak height'. The low flow-rate leads to a more efficient trapping of Hg vapours on the amalgamator gauze.(ii) The mass of the Au-Pt gauze (B) seriously affects the peak height 'small mass of gauze causes an increase in peak height'. A small mass of amalgamator causes a spontaneous release of Hg from the amalgam and produces a more concen- trated stream. However this behaviour depends on the actual value of flow-rate (see interactions below). (iii) The trapping time (C) seriously affects the peak height 'long trapping time causes an increase in peak height'. (iv) The interaction between the flow-rate and the mass of the gauze is significant 'low flow- rate x small mass causes an increase in peak height'. Hence with high flow-rates it is necessary to use a greater mass of amalgamator. (v) The interaction between the flow-rate and the trapping time is significant 'low flow-rate x long trapping time causes an increase in peak height'.(vi) The effect of the releas- ing time (D) above 18 s is not significant. Table 6 Experimental results of the fractional factorial (half-replicate of a two level-four factor design) in the determination of Hg after amalgama- tion on an Au-Pt gauze (response peak height) Parameter Treatment ( 1 ) ad hd ah cd ac hc abcd Sequence (random) 7 5 2 3 8 6 1 4 Nitrogen flow-rate A - + - + - + - + Mass of Trapping time C amalgamator B - - + + - - + + Releasing time D - + + - + - - + + + + + - - - - Peak height I 48 12 25 10 72 18 46 10 I1 45 15 27 8 80 14 42 15 The low (-) and high (+) levels of the factors are the following Factor Unit Symbol (-) Value (+) Value Nitrogen flow-rate 1 min-' A 0.6 2.0 Trapping time S C 60 I80 Releasing time S D 18 28 Mass of amalgamator g B 0.2 0.4244 JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY.APRIL 1991. VOL. 6 270 240 v) 210 .- E 180 p 150 a Q 120 E \ c .- 90- 60- 30 I- Table 7 on an Au-Pt gauze Analysis of variance for peak height signals after amalgamation - - - - - - i- Sum .II X' .v3 .v4 .vs .Yo .v7 -283 -121 +lo7 +89 -83 -21 +25 (x,)' 80089 14641 11449 7921 6889 441 625 ANOVA- Source of Degrees of Sum of Mean sum F99 variation freedom squares of squares F 11.3 A I B 1 C 1 AB 1 A C 1 BC 1 D 1 Residual error 8 5005 915 716 495 43 1 27 39 73 Total 15 7702 *S significant. tNS not significant. 5005 550 S* 915 101 S 716 79 S 495 54 S 43 1 53 S 27 2.9 NSt 39 4.3 NS 9.1 From the analysis of variance of the peak heights it was concluded that the interactions between flow-rate and mass of Au-Pt gauze and between flow-rate and trapping time are significant hence an approximation of these parametric factors should be obtained by the modified simplex method.An approximation of the optimum conditions for flow-rate and trapping time was performed separately for 10 and 100 ng of Hg. The simplex procedures,"." with variable step sizes are shown in Figs. 8 and 9. In some instances the allo- cation of the vertices is limited by the actual readings on the flow-meter (to one decimal point). For this reason (a) flow- rates ~ 0 . 1 1 min-I were not tested; (h) some simplexes are not precisely isosceles triangles; and ( c ) the expansion or contraction factors (usually 2 or 0.5 respectively)" are vari- able.The position of the initial simplex was chosen accord- ing to the normal conditions used for the determination of Hg. However the size of this simplex was the minimum that could be considered reliable according to the significant figures of the flow-meter readings. From the optimum response surfaces given in the striped area of Figs. 8 and 9 the conditions selected to be most appro- priate are 120 s trapping time and 0.3 1 min-' flow-rate for 10 ng of Hg and 180 s and 0.2 1 min-' for 100 ng of Hg. 300 I \ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Flow-rate/l min-' Fig. 8 Progress of simplexes to the optimum surface for nitrogen flow- rate and trapping time for 10 ng of Hg. The striped area is the maximum response surface. The vertex No. 16 is chosen as optimum.See text .- 150 120 90 60 30 0 0.1 0.2 0.3 0.4 Flow-rate/l min-' 1 0.5 Fig. 9 Progress of simplexes to the optimum surface for nitrogen flow- rate and trapping time for 100 ng of Hg. The striped area is the maximum response surface. The vertex No. 15 is chosen as optimum. See text The values for the trapping time are in good agreement with those found by Welz,'? and were selected as the minimum values on the optimum response surface on which the sim- plexes were recycled. Calibration study in procedure I1 Although the analysis of variance has shown that the factors A B and C should be optimized the mass of the amalgamator was not tested because 0.24.25 g of the gauze is the minimum amount required to fill the tube adequately and homogeneously." It should be re-stated that these small amounts apply only to the low flow-rates because for higher flow-rates of nitrogen a larger amount of amalgamator is required.I7 The releasing time chosen as the best was 18 s because a lower value is not recommended for increasing the temperature of the amalgamator as has been discussed under Instrumentation.The volume of the sample in Table 10 Optimum conditions according to the simplex procedure Parameter 1-10 ng of Hg 10-100 ng of Hg Flow-rate of N 0.3 1 min-' 0.2 1 min-' Mass of gauze 0.2 g 0.2 g Trapping time 120 s 180 s Releasing time 18 s 18 s this study was 50 ml. Finally the optimum conditions according to simplex procedure are applied as given in Table 10. Two calibration studies were required and the ranges chosen were 20-200 ng 1-I (1-10 ng of Hg absolute) and 200-2000 ng I-' (10-100 ng of Hg absolute).If the calibration for the second range is performed using the optimum conditions of the first range the graph is still linear but the sensitivity is poorer. The peak heights used to prepare the calibration graph are expressed in absorbance units. The equations of the calibration graph can be expressed as follows (3) (4) The slope (sensitivity) of equation (3) is in agreement with the experimental value of 0.8 ng of Hg which gave an absorbance of 1%. The calculation of the detection limit based on three times the standard deviation of the blank (eight repeat blank measurements) alniost corresponds to the values obtained at the 90% confidence level.'" The absolute detection limit for the concentration level 20-200 ng I-' is 0.33 ng of Hg. The rela- AHg= 1.036 x104 + 3.7 18 x10-3x~g A Hg = 1.333 x 1 0-3 + 4.062 x I O-jX,,JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY APRIL 199 I VOL.6 245 tive standard deviation was 5.5% for 6 ng of Hg absolute and 8.8% at the 10 ng level (ten repeat determinations). Conclusions The CVAAS determination of Hg is an excellent system in which to study optimization by experimental design. There are advantages of optimization procedures while using a commer- cial portable instrument for Hg determination to establish the detection limits after a pre-concentration step. One of the pur- poses of this work was to develop a sequential technique for ex- perimental designs that can be applied as rapid and efficient optimization schemes for various samples under different con- ditions when data given in the literature cannot be applied di- rectly.The sequential optimization strategy in the direct determina- tion of Hg with an MAS-5OA (procedure I) gave a detection limit of 3.3 ng of Hg. This limit was further improved by em- ploying amalgamation on an Au-Pt gauze (procedure 11) when the detection limit was 0.3 ng of Hg. To improve the de- tection limit further for the general cold vapour technique op- timization of more parameters is required e.g. the type of gauze and modification of the shape of the cell or improve- ment in the relative detection limits by increasing the sample volumes. It is recommended that modem statistical methods of exper- imental design are used in order to extract as much quantita- tive and qualitative information as possible from the procedure.Factorial designs are the first tool in this strategy in order to eliminate areas where subsequent research would not be useful and to evaluate the significance of various effects quantitatively. Care should be given to the selection of a suitable design and the number of replicate measurements required. The presence of significant interactions between the parame- ters in a dynamic method is also demonstrated for the determi- nation of Hg with and without amalgamation. Hence a simplex method is the second tool in an optimization process to reduce further the number of experiments needed. The authors express their gratitude to Bernhard Welz and Marrianne Schubert-Jacobs Perkin-Elmer Bodenseewerk Uberlingen Germany and V.Simeonov Faculty of Chemistry University Sofia Bulgaria for useful discussions and supply- ing the amalgamation material. 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 References Evaluation and 0ptimi:ation of Laboratory Methods and Analytical Procedures. eds. Massart D. Dijkstra A. and Kaufman L. Elsevier Amsterdam 4th edn. 1986 p. 23 1. Long D. Anal. Chim. Acta 1969,46 193. Deming S. and Morgan S. Anal. Chem. l973,45,278A. Morgan S . and Deming S. Anal. Chem. 1974,46 1 170. Wittmann 2.. Talanta 1981,28,271. Bouzanne M. Sire J. and Voinovitch I. 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IUPAC Compendium of Analytical Nomenclature eds. Irving. H . Freiser H. and West. T. Pergamon Press Oxford 1978 p. 1 17. Paper 9104392F Received October I I th I989 Accepted November 28th I990