Microwave digestion: an analysis of procedures

267

Analytzca ChwntcaActa, 259 (1992) 267-219 Elsevler Saence Publishers B V , Amsterdam

Microwave digestion: an analysis of procedures S Kokot * School ofChenustry, Queen&d

Unrversuyof Technology,Bnrbnne (Australw)

G Kmg Government Chemtcal Laboratones, Kessels Rd, Cooperk Hams, Bnsbane (Austraha)

H R Keller and D L Massart Farmaceutxh Instttuut, VnJeUnwersrtertBrussel, Laarbeeklaan 103, Brussels (Belgrum) (Received 24th October 1991)

AbStlYlCt

Prmclpal component analysts @‘CA) and the multlcntena declslon makmg methods, PROMBTHEE and GAIA, were used to select a suitable nucrowave digestion method for metal analysls of sol1 samples When the residuals matnx derived from the Cu, Pb, Co, Mn and Zn analyses of 18 different digests of the NBS 2704 SRM, was subjected to PCA and PROMETHEE rankmg, two prefered methods were isolated This PROMETHEE rankmg together wth the mxrowave oven settmgs and the digest and cornposItion were then used as vanables The corresponding data matrm was subJected to PROMETHEE analysis coupled with the vlsuahsatron technique, GAIA. This lllustrated the relationship between the different practical variables and method performance leading to the selection of the most suitable digestion method Keywords Prmclpal component analysis, Metals, MIcrowave dlgestlon

The use of microwave ovens for acid dlgestlon of many types of solid samples IS well documented, (e g , Refs l-11) and 1s commonly regarded as a possible alternative for the classical open air hot plate digestion procedures Many kmds of methods have been tried usmg various acid and additive (e g , hydogen peroxide) comblnations m open and pressure vessels m domestic and sclentlfic microwave ovens In general the results of such studies have mdlcated that rmcrowave methods are comparable m performance wth the classical procedures as well as being comparatively rapid and offering a reduced risk of contammatlon when PTFE pressure vessels are used Notwlthstandmg this apparent acceptance of the microwave oven acid digestion approach, there appear to be only a few studies

(e g , Refs 11-13) which have attempted to provlde any guldehnes for choosing the most suitable combmatlon of acids and nucrowave oven setting condltlons for a particular sample type m which several analytes have to be determined In this paper we present a systematic approach for the selectlon of a suitable microwave dlgestlon method for a solid sample which has been analysed for several metals The problem described here 1s typical for many atuatlons where different alternative methods have to be compared and where there are many cntena for such assessments Thus m the present work, the quality of the result for Cu can be considered as one criterion and that for Co as another and so on If among the alternative methods there exsts one which satlsfles all the criteria then there should

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S KOKOT ET AL

268

selection of a suitable method for microwave dlgestlon The emphasis 1s on the apphcatlon of the decision makmg approach for the mterpretatron of multlvarlate analytlcal data The results which relate to specific settings and conditions for microwave dlgestlon of sol1 samples may be useful in practice The solid material used m this work was the NBS 2704 Buffalo river sediment, samples of which were dissolved by eighteen different dlgestlon procedures and the analyses of Cu, Pb, Co, Mn and Zn were used to illustrate the method selection procedure

be no dlfflculty m makmg the selectlon However, this 1s often not the case and a method with the best overall performance 1s sought Such a method should also provide a good startmg pomt for new apphcatlons Because of the multlvarlate nature of the problem, chemometncs can be used to assist with the selectlon The approach m our work 1s based on two such methods (1) prmclpal component analysis (PCA), and (2) two multlcrlterla declslon makmg routines, PROMETHEE (Preference Rankmg Orgamsatlon METHod for Enrichment Evaluation) and GAIA (Geometrical Analysis for Interactive Ad) PCA 1s a well known statlstlcal procedure that has been described m the chemical lrterature (e g , Refs 14, 15), and 1s also quite accessible through software It was applied to study user preferences for method attributes m microwave digestion [131 PROMETHEE and GAIA are multicriterIa declsron makmg routmes that have been described only recently [16-181 This commumcat~on provides a summary of the basis of the chemometrlcs mvolved and mdlcates how the three procedures may assist m the TABLE

EXPERIMENTAL

Mmowave oven procedure A CEM MDS-81D microwave oven operating at a frequency of 2450 f 13 MHz with an energy output of O-630 f 70 W adjustable in 1% mcrements from O-100% was used to perform the acid digestions The oven was equipped vvlth a PTFE osallatmg turntable designed to hold 12 low pressure (830 f 70 kPa) screw top PTFE dIgestion vessels each of which was normally connected by

1

Acid digest composltlons and nucrowave oven settmgs Method

Acids

Mixture

Step 2

Step 1 Power (%I

t (mm)

Power (%I

Step 3 t

Power

(mm)

(o/o)

Total f (mm)

“)

H,BO,

Vent

2A 2B

HF-HNO,-HCl mo3

5 2 2 522

100 loo

8 8

50 50

15 15

0 0

0 0

23 23

yes _

-

4A 4B 4c 6A 7A

HF-HNO,-HCl HF-HNO, HNO,-HCI HF-HNO,-HCl HNO,-HCl

2 5 5 25 13 111 13

loo loo loo loo loo

10 10 10 10 10

75 75 75 65 70

20 20 20 20 20

25 2.5 25 30 25

5 5 5 5 5

35 35 35 35 35

yes yes yes _

_

8A 8B

HF-HNO,-HCl HF-HNO,-HCl

5 2 2 5 17 17

loo loo

15 15

0 0

0 0

0 0

0 0

15 15

-

8C 9A 9B 9C 11A 11B 12 13

HF-HNO,-HCl HNO,-HCl Hl-HNO,-HCl HF-HNO,-HCI HNO,-H,O, HNO,-H,O,-HF HNO,-H,O,-HF Ace&

5 9 27 13 113 126 5 1 5 1+ 4ml 5 1 + 4ml 10 ml

100 70 70 70 loo 100 100 100

15 7 7 7 10 10 10 10

0 100 100 100 70 70 70 70

0 5 5 5 20 20 20 20

0 0 0 0 25 25 25 25

0 0 0 0 5 5 5 5

15 12 12 12 35 35 35 35

yes _

yes yes yes

yes _

MICROWAVE

DIGESTION

a venting tube to a central waste container The usual pressure controller setting was 700 f 7 kPa The digestion vessels were sealed at a capping statlon to a torque of 16 3 Nm The rmcrowave oven was calibrated at 712 W as described elsewhere [19] and from these results 120 ml mmlmum total acid volume was selected for the full carousel, I e , 10 ml acid per vessel The expenments were always carried out with a full complement of containers

Mzcrowave dzgestzon For each dlgestlon, 1 g of the NBS 2704 sample was accurately weighed mto a PTFE dlgestlon vessel, the acid mixture was added, the vessels were capped, placed m the turntable and the mlcrowave program was run On completion of the dlgestlon, the vessels were cooled to room temperature, uncapped and the digests were dlluted to 100 ml with delorused water The details for the 17 nucrowave procedures used m this work are summarlsed m Table 1 In general, 10 ml of an acid mixture was added to a sample, however, for vented samples more aad was included to prevent evaporation to dryness, 1 e , samples 8A, 8B, 8C (20 ml) and sample 9C (22 5 ml)

Ventzng procedure The ventmg tubes were unscrewed from the dlgestlon vessels and the pressure allowed to build up beyond the 830 kPa, thus causing the pressure relief valve to open

Addztzon of H3BO, Boric acid was added after a sample was submltted to a particular mlcrowave digestion procedure and the vessel cooled 40 ml 4% H,BO, solution was added to the digest vessel which was then recapped and further heated m the mlcrowave oven with the followmg settmgs step 1 power = lOO%, time = 3 mm Step 2 power = 50%, time 10 mm The digest contamers were then cooled and digests made up to 100 ml with delomsed water

Hot plate dzgestzon The hot plate dlssolutlon procedure was carried out by accurately weighing 1 g sample mto a comcal flask, adding 10 ml of aqua regla and digesting for at least 1 h untd complete dlssolutlon, extra acid was added as required to prevent the digest going to dryness The drgests were made up to 100 ml with delomsed water Chemzcals The acids used were HNO, and HCl (both BDH, AnalaR), HF and glacial CH,COOH (both AR, AJAX),the additives were H,BO, and H,O, (both AnalaR, BDH) The mtrlc acid was further purlfled by sub-bolmg 1000 mg 1-l stock solutions were made up by dlssolvmg m HCI or HNO,, Suprapur (Merck) or Specpure (Johnson Matthey) metals or salts as appropriate Delomsed water was obtamed by reverse osmosis followed by purification through an lon-exchange cartrldge Instrz4mentatwn A Varlan SpectrAA 300 and a VarlanAA 400 Zeeman graphite tube atomizer were avallable for atormc absorption flame analysis (FAAS) and graphite furnace analysrs (GFAAS) respectively Standards and sample anulyszs Mured metal standards were prepared from the spectroscopically pure 1000 mg 1-l stock solutions These were diluted to encompass a callbratlon range of 0 5-20 ppm for each element as required Cu, Pb, Mn and Zn were determined using FAAS with instrumental parameters being adjusted as suggested by the mstrument manufacturer 1201 Where HF was present m the acid digest, a mixed metal standard contammg Zn, Pb, Cu, Nl, Cd, Cr and Co was used The standards were matrm matched usmg a 10% solution of each HF-HNO,-HCl murture Where H,BO, addltlons were Involved, the standards m addrtlon to the acid mixture, contamed 40% of a 4% H,BO, solution Two sets of standards were avallable for all other FAAS work (I) Cu, Zn and Pb were anal-

--

914 159 160 569 433

99 5

166 15 0 550 432

4B

103

4A

155 126 483 441

2B

CU Pb co Mn Zn

.

--.

0480 0 824 6667 0 158 0833

2A

0880 0 353 2333 3789 0250

2B

- -

.

1440 0 118 3333 0737 0417

0180 0294

1667 0263 0500

4B

4A

-

0667 0368 1083

1480 0059

4C

-.

103 145 13 7 570 432

106 162 13 6 548 425

0880 0941 0500 0789 0500

6A

6A

4C

297 271

538 421

159 13 0

98

8B

.-

13917

6676 5000 13579

1720

8A

475 110

90

8A

._.-

2000 1895 1083

0360 0353

7A

968 155 128 519 425

7A

506 445

540 435

0080 0176 1667 0789 0250

0120 0118 1667 0895 1417

8C

156 140

117

9A

164 13 0

99

8C

8B

m NBS 2704 as determined from various acid digests

Residuals N18S 2704 Buffalo River sediment

TABLE 3

96 2

147 180 552 448

Cu

Pb Co Mn Zn

2A

Metal content (pg g-‘)

TABLE 2

1053 loo0

2579 0583

..--

OOOO 1412 5167

3680 0294 0000

9B

551 444

535 426

9A

150 16 1

102

9C

137 17 1

98 6

9B

-

3474 1333

0211 0500

._

0400 0118 3333

0680 0647 3500

11A

549 422

489 422

9C

88 150 15 0

11B

966 159 120

11A

.I -

1579 4333

0316 1333

-

0400 2059 0000

12

49 3 976 40 286 258

13

2120 0647 1667

11B

525 386

96 6 126 140

12

.

0020 0706 16667 2 895 2083

9860 3 729 16667

_.. -

14 158 15ooO

HP

986k 50 161$-17 14Ok 06 555 f 19 438+12

NBS 2704

13

985 149 40 500 413

HP

MICROWAVE

ysed usmg a mixed metal standard contammg Cu, Pb, Zn, Cd and NI dissolved in 5% HCl and (u) all Mn analyses were carried out usmg a 5% HCI mixed metal standard contammg Fe, Mn, Co and Cr Co was determined using a Lvov platform and the instrumental parameters were consistent with common practice as described elsewhere [21,221 A 4% HNO, mured metal standard contammg Cu, Pb, Cd, Nl, Cr and Co m the 50-200 kg I-’ range was used to prepare a suitable set of cahbratlon standards Data processwag All data was processed usmg an IBM PS/2 Model 55 computer The analytical data matrx (Table 2) was manipulated using Excel 3 0 spreadsheet from whnzh appropriately formated data was exported to SIRIUS (PCA) [231 or PROMCALC (PROMETHEE and GAIA) [24] for analysis

RESULTS AND DISCUSSION

The analytical data mattlx (Table 2) consists of five rows of determmatlons for the elements Cu, Pb, Co, Mn and Zn respectively and of 19 columns, eighteen of which correspond to the different dlgestlon methods defined m Table 1, the last column m Table 2 (NBS 2704) contains the certrfied values of the analytes [251 together with their associated uncertainties This data was transformed into a table of residual values (Table 3) according to the following equation R=

271

DIGESTION

I(A-C)/U)

(1) where A = the analytical result of a selected metal from a particular digest, C = the corresponding certified value of the selected metal, U = the uncertainty for the selected metal as given m the last column of Table 2 and R = residuals Data m this form facilitated a comparison between the variables, 1 e , methods of digestion, thus for example for any analytical result shown m Table 2, a value of R = 1 would indicate that the bias of that determmatlon was equivalent to

one uncertamty unit This residuals data matrix was subjected firstly to exploratory analysis by PCA and then to the multrcrltena decision makmg procedures Exploratory anaiysu by PCA PCA IS a multivariate data reduction method which 1s particularly effective for two dlmenslonal visual display of the reduced data without serious loss of mformatlon In PCA, data 1s transformed mto uncorrelated components (or factors) which are hnear combmatlons of the orlgmal variables pcJk

=

ajlXkl

+

aj2xk2

+

+a,n%-l

(2)

where PC,, = the score (or value) for ObJect k on component J, a,, = the loading (or welghtmg) of a variable 1 on component J, xkr = the measured value of a variable 1 on object k and n = total number of original variables Scores determine the location of an ObJeCt on a PC while loadmgs reflect the contnbutlon of each variable to a PC PCs are computed m such a way that the first PC accounts for the largest amount of variation m the data set while subsequent components describe progressively decreasmg amounts of data variance Graphical displays of scores or loadings plotted m a PC plane (usually PC1 vs PC2), can provide useful mformatlon about any underlymg trends or features m the data structure such as clustermg of obJects or vanables and charactensation of outhers Au economical method for dlsplaymg such mformation 1s by means of a blplot, 1 e , an appropriately scaled PC diagram of scores and loadings together [26] Thrs graphical method of PC analysis has been adopted m this work Data pretreatment Sn-ms PCA software provides for the typical data pretreatment procedures [27] The generally recommended variance scalmg procedure 1s of particular interest to this study PCA 1s a least squares procedure which nnphes that variables with large vanance will have large loadings and will bias the outcome Consequently each cohunn variable 1s standardlsed to unit vanance However, m the present case the size of the variance

S KOKOTETAL

272

for a given column wJ1 m fact reflect the analytlcal performance of a dlgestlon procedure m comparison to that of the other digests and to the Ideal case of 0 variance, I e , where results are identical to the certified values If the variance size aspect 1s neglected then the resulting PC blplot will reflect only some general patterns of the data structure This important point IS illustrated m Figs 1 and 2 which show the PC1 versus PC2 blplots from standardlsed and unstandardlsed data sets respectively Method 13 (acetic acid) 1s normally regarded as an extractwe rather than a digestive system and should therefore perform poorly This expectation was readily confirmed by the results m Tables 2 and 3 Thus m any visual representation of results, Method 13 should emerge as a definite outher However, m Fig 1 it was not dlstmgulshed on that basis at all On the other hand, m Fig 2, which was based on unstandardlsed data, Method 13 was readily drscrlmmated as an outher Similarly the three other methods subsequently chosen as outhers (methods 8A, 12 and HP) were also unremarkable from the general pattern m Fig 1 Thus It was mapproprrate to use the normal variance standardlsatlon approach for

N ;ooo.

13dgC PB -

@I 6

06*

9R

A9A *CO

E -120. o

AIL

0

OllB -240.

l CU -180

180 000 Component

360

540

I

Rg 1 PC1 versus PC2 blplot derived from the standardlsed residuals data obtamed from analysis of differently digested NBS 2704 SRM samples, 0, objects, methods of digestion (variables) 0, with HF and A, wlthout HF m a mutture, 0, acetlc acid (method 13) and hot plate dlgestlon (method HP) Method labels refer to Table 1

oeo-

Zn*

M::

q l3

040. N

z

120

z $000.

:

,A*

‘3 p

:: -040.

(4%

q HP l CO

l Pb l CU -5 30

5 30 -000 Component 1

IO 60

1590

Fig 2 PC1 versus PC2 blplot derived from the unstandardlsed residuals data obtained from analysis of differently dlgested NBS 2704 SRM samples The V-shaped cluster of 14 methods IS m the centre of the diagram and the outher methods are labelled 0, objects, methods of digestion (vanables) 0, with HF and P , without HF m a nuxture, 0, acetx acid (method 13) and hot plate digestion (method HP) Method labels refer to Table 1

this work and the results were obtained using the unstandardlsed data set Interpretatzon of the PCA results The blplot m Fig 2 shows that 14 of the 18 methods form a V-shaped cluster, which IS approximately blsected by the PC1 axis Three methods @A, 13 and HP) he well outside this fairly compact group A perusal of the residual values m Table 3 shows that these methods recorded some exceedmgly high R values, e g , R > 10, and were therefore classified as outhers Method 12 was also outslde the cluster performmg comparatively poorly on 3 of the 5 analyses and was also excluded as an outher The new data set of the 14 methods was resubmitted to PCA and the resultmg blplot IS presented m Fig 3 This shows that the loadings (the method vanables) still form a V-shaped structure that 1s less compact than m Fig 2 The methods group roughly mto two classes (1) HF present m and (11)HF absent from, the acid digest mixture V-shaped data structures often occur m PCl/PC2 plots, the arms of the V being due to some

MICROWAVE

___-

273

DIGESTION

-2‘30

2 30 0'00 Component 1

160

690

Fig 3 PC1 versus PC2 blplot derived from the unstandardlsed residuals data obtained from analysis of 14 dtierently digested NBS 2704 SRM samples The outbr methods have been removed The dIgestIon methods usmg HF (0) cluster to the right of the dlvldmg hne (---_) and the methods w&out HF (A) are on the left, 0, objects, method labels refer to Table 1

dlscrlmmatmg effect In ths case, some digestion methods performed very poorly for Co and others for Mn analyses The ObJects, Cu, Pb, Co, Mn and Zn form three classes Co wth a high posItwe score on PCl, Mn with a high posltlve score on PC2 and the Cu, Pb and Zn group with comparatively low, negative scores on PC1 and PC2 The first two PCs account for 87% of the variance and therefore Mn and Co analyses must account for most of the varlatlon m the data Further, variables (methods of dlgestlon) with high absolute values of the loadings on a particular PC will make large contnbutlons to the vanance accounted for by that PC Thus methods 2B, 11A and possibly 9A and 7A should perform poorly on Mn analysis, while methods 2A, 9B and 9C should have high R values for Co This conclusion was readily supported by reference to Table 3 which showed that m the cases of the relevant Co and Mn analyses for these seven methods, the R values fell m the range of ca 2 5 to 7 Thus from the nature of the clustering of the loadings, it would appear that digest mtiures contammg HF gave comparatrvely

poor Co analyses, while the nuxtures without HF, performed poorly on Mn determmatlons The remammg 7 methods (4A, 4B, 4C, 6A, 8B, 8C and 11B) have firly low loadmg values on the first two PCs, consequently, their contribution to the total variance of the data set would be relatively small Since the seven methods cluster comparatively closely to the orrgm, then analytical performance across the suite of the five elements analysed, must be reasonable Thus they should rank well on any other performance analysis on this data set Six of these remaining seven methods contam HF m the digest nuxture, hence it would appear that lower residuals are likely to result m sod sample analysis for the suite of the five elements investigated if HF was added to the HNO,-HCI mixture

Multtcntena decrston makmg usrng PROMETHEE and GAL4 PROMETHEE 1s a procedure which facdltates the rankmg or ordering of a number of actions (m this work, the methods of digestion) according to preference and welghtmg conditions which are selected or provided by the user and which are applied to the crltena (the five metals analysed) Thrs user supplied mformatlon leads to one of three possible results for any pauwrse comparison of actions (A> one action 1s prefered to the other, (B) there 1s no difference between the two actions, (C) the two actions cannot be compared The first requirement 1s to provide a mathematical method for selecting one result m preference to another, 1 e a preference fwctzon must be chosen PROMETHEE provides a choice of SK such functions Irrespective of the selected preference function, for each criterion all the entries m the data matrix are compared panwlse m all possible combmatlons by subtraction, resultmg m a difference, d, for each comparrson It 1s also necessary to mdlcate rf higher or lower cntenon values are prefered by nommatmg to “maxlmuse” or to “mtnim~esel’ a given criterion For example, m this work all crlterla (the five metals) were required to mmnmse since lower values of

S KOKOT

274

the resrduals would mdlcate a better performing method of analysis Sunple preference, P, rules [18] now have to be used to generate a preference table Such rules are Illustrated m Eqns 4-8 below Using the entfles 111the preference table, W-W dtces are computed by summmg the weighted preferences across all of the crlterla for each of the actions 7r-Indices mdlcate the global preference of one action (a dlgestlon method) over another To refine the preference selection process, the out rankmg flows, 4’ and +- are computed by summmg the r-mdlces 4+, the posltlve out rankmg flow, expresses how each action (a method of digestion) outranks or outperforms all others, while 4-, the negative out rankmg flow, mdlcates how an action 1s outranked by all others Comparisons of the 4’ and b- values by another set of simple rules produces a part& rank order accordmg to the three possible categories A, B and C referred to earlier Thus procedure IS called PROMETHEE I and produces a flow chart as well as a table of the out rankmg flow values The PROMETHEE results m this work are presented usmg the convenient dlagramatlc display of the PROMCALC software 1241 The software also provides for the computation of a net out rankmg flow value, 4, for each actlon 4 1s defined by the equation ##=4+-4-

(3)

Thus creates a complete ranking of the actlons and attempts to ehmmate the mcomparabrhty option (result C> Thus procedure 1s termed PROMETHEE II, and although it IS apparently more efflaent, can produce results which are less rehable than those from PROMETHEE I GAIA is a procedure for the display and evaluatlon of PROMETHEE results Usmg graphical presentation, It faclhtates the Interpretation of the relative locations of the actions, of the slgmflcance and the interdependence of the cnterta, and of the declslon axis, ?r Such a display results from a mathematical decomposltlon of the net out rankmg flows, 4, such that the actlons may be regarded as ObJects and the criteria may be considered as variables gwmg a data table m the

ET AL.

form smtable for PCA 1181 The results of this analysis are presented on a blplot with properties sundar to those already dlscussed A declslon vector, W, 1s included m the GAIA blplot and may be consldered as the weighted mean of the different crltena vectors The projectlons on that vector follow the rankmg of PROMETHEE II [18] If ths axis IS long the best actions (methods of dlgestlon) wtil be located along Its dlrectron and as far removed from the orlgm as possible A short axis indicates opposmg criteria, low level of declaon power and that a reasonably performmg action should be located near the orlgm It should be noted that such interpretations would be slgmflcant only if the amount of variance accounted for by the first two components m the PCA was high, ca > 85% The value of a two dunenslonal GAIA plot would dlmmlsh with decrease m the variance accounted Interpretatwn of the mzcrowaue dzgestzon method procedures The set of methods of dlgestlons excludmg the four outhers was submitted to PROMETHEE analysis The five metal cntena were equally welghted and set to rnmlmue The preference function selected 1s described by Eqns 4-6 Thus function has one threshold value set to zero A second threshold value (2) was set to - 1, 1 e equal to one uncertamty unit for the residuals wth the negative sign mdlcatmg that smaller d values were prefered as required by the “mmlmuse” condltlon P-l

for d sz

(4)

P=d/z

for O
(5)

P=O

for d 2 0

(6)

The results are shown m a preference flow chart (Fig 4) which was computed from the out rankmg preference flows, 4’ and 4 The general rules for the interpretation of the flow chart are (1) actions that are comparable are Joined by arrows, (2) any action to the left of another IS prefered, (3) any actlons that are mcomparable remam unconnected and appear roughly vertically ahgned m parallel horizontal rows

275

MICROWAVE DIGESTION MOST PREFERED

LEAST

PREFERED

Fig 4 PROMETHEE I partlal preference flow chart obtamed from the residuals data derived from the analysis of the 5 metals for the 14 methods of dIgestIon

Accordmgly Fig 4 may be interpreted as follows all 14 methods appear on the flow chart, thus there are no cases which fall mto the “result B” category mentioned previously On the left hand side of the chart, methods 8C and 4A are prefered to the other 12 methods However, these two methods cannot be compared, I e, the performance of one method on the 5 crltena 1s different from that of the other Thus with reference to Table 3, it can be seen that the residuals are higher for method 4A m the cases of Cu, Pb and Zn, the opposite 1s true for Mn and the performance 1s equal for Co However, the mcomparability aspect of the two methods is not self evident from such a cursory exammatlon of the data and arises from the step by step apphcatlon of the preference rules for the out ranlung flows m PROMETHEE I Such calculations are described m detail elsewhere [18] The mterpretatlon of the left half of the chart proceeds m a similar manner, applymg rules 1 and 3 above, until method 4B, e g ,8C 1s prefered to 4C which is prefered to 6A, 8C is also prefered to 8B which however 1s incomparable to 4C and

6A, 9A 1s mcomparable to all methods between 9C and 11B The right hand side of the chart shows that 4B 1s prefered to all of the methods to the right but that 2B 1s incomparable to 7A and 2A The two poorest performing methods are 9B and 11A but they too cannot be compared Thus PROMETHEE I provides a partial rankmg of the methods of dlgestlon and suggests that there are two methods, 8C and 4A, which are better than the rest PROMETHEE II full rankmg (Table 4) offers little extra information It shows that methods 8C and 4A are prefered over the others but as the net out rankmg flow values, 4 are so close together, the differentiation 1s strictly numerical and is unhkely to be of practical slgnlficance It should be noted that the PROMETHEE rankings are m agreement with the exploratory PCA SIX of the seven well performing methods identified by the PCA appear m the first seven PROMETHEE selections, with five of the methods occupying the top rankmgs Thus the results of the two approaches reinforce each other Sgmjicance

of dlgestwn method condltlons

A further refinement of method selectlon may result from an mvestlgatlon of the relationship between the PROMETHEE rankmgs and some of the ObJectives for methods of digestion m general and microwave dlgestlons m particular Thus m prmclple, it 1s desirable to achieve sample dlssolutlon with the simplest acid murture possrble In the context of this work, cone HCl was considered to be the simplest solvent and the other acids were generally regarded as additives Further it 1s preferable to operate with mmlmum rmcrowave power and time settmgs so as to achieve the desired dlssolutlon m the sunplest manner

TABLE 4 PROMETHEE II full rankmg of the 14 methods of dlgestlon

&Value Rank

8C

4A

4C

6A

8B

9C

4B

7A

9A

2B

2A

11B

11A

9B

035 1

0345 2

0149 3

0124 4

0099 5

0035 6

-0034 7

-0066 8

-0069 9

-0095 10

-011.5 11

-017 12

-0267 13

-0285 14

S KOKOT

276

When HF IS used m dlgestlon mixtures, the addltlon of boric acid IS commonly recommended to reduce the effect of excess HF m subsequent analysis Consequently such an addltlon was considered “desirable” PROMETHEE analysis was performed on the data for the 12 methods of dlgestlon shown m Table 5 (methods 11A and 11B were excluded because the ratlo of HF added to the nuxture was unknown) This table shows that PROMETHEE rankmgs were included as a vanable, thus provldmg a method to mvestlgate the slgnlficance of the settings and the acid rmxtures It also shows that the presence or absence of the “Vent” procedure or the “H3B03” additive was Indicated either by “1” or “0” respectively The simplest type of preference function was used for all cases either, for the maxlmlse case, P=Ofor

d10,

otherwise P= 1

(7)

or, for the munmlse case, P=lford
(8) For reasons noted above the total power, total time, HF and HNO, criteria were set to mmnmse and H,BO, was set to maxltnlse Ventmg can occur during mrcrowave digestion However, m general ventmg would seem to be an undesirable process m mcrowave digestion because one of the consrdered advantages of the technique IS its ability to perform dlgestlons un-

MOST

PREFERED RANKING

LEAST

PREFERED RANKING

-m

-

Fig 5 PROMETHEE I partial preference flow chart showmg the rank order of the 12 digestion methods The cntena used the PROMETHEE I rankmgs obtained from residuals data, microwave oven settings and acid composltlon The venting procedure and the bone acid addition vanables were excluded

der high pressure condltlons Hence the Vent variable was set to mmunrse The remammg crltenon, HCl, was maxmnsed because the addltlve acids were generally preferred to be present m the smallest possible quantities The PROMETHEE analysis was carried out m three parts (1) all crlterla included except Vent and H,BO,, (2) exploratory analysis was performed m the presence or absence of either the Vent or the H,BO, criteria, (3) all crlterla meluded

TABLE 5 Settmgs and condmons data for the PROMETHEE

ET AL

and GAIA analysis

Method

PROM rank

Total power (%o)

Total time (mm)

HF

HNO,

HCl

Vent

H,BG,

SC 4A 4c 6A 8B 9c 4B 7A 9A 2B 2A 9B

1 1 3 5 3 6 8 9 6 9 11 13

100 200 200 195 100 170 200 195 170 150 150 170

15 35 35 35 15 12 35 35 12 23 23 12

0 122 0 166 0000 0 333 0 128 0 111 0286 0000 0000 0 555 0 555 0 200

0 220 0 416 0250 0 333 0 436 0 222 0 714 0250 0250 0 222 0 222 0200

0 658 0 416 0 750 0 333 0 436 0 666 0000 0 750 0 750 0 222 0 222 0600

1 0 0 0 1 1 0 0 0 0 0 0

0 1 0 1 0 0 1 0 0 0 1 0

MICROWAVE

DIGESTION

271

tfx,

40

1

I

0 77

00

L

AC

-0 77

r9A 7A x

Q,

SCALE

HF

l3g 6 PROMETHEE II complete rankmgs for the 12 nucrowave chgestlon methods The net out rankmg flow q%scale IS used to show the spread of the actIons (methods of dlgestion) The further apart any two actIons are the larger 1s the preference of the a&on on the left over the one on the r&t

This approach facrhtated the mvestlgatlon of the slgmflcance of the digest acids m relation to the PROMETHEE rankmg, total power and tnne crlterla The PROMETHEE I rankmgs flow chart 1s shown m Fig 5 The mterpretatlon of this dlagram can proceed m a manner similar to that described for Fig 4 It shows that method 8C is prefered to all the other 11 methods, while method 4A IS prefered to only two other methods on the right hand side of the diagram Clearly the practlcablhty criteria such as time, have been taken mto account method 8C 1s one of the shortest and method 4A one of the longest A plot of PROMETHEE II complete rankmgs (Fig 6) which can be obtained usmg the PROMCALC program, indicates that method 8C 1s well separated from the rest, supportmg the results m Fig 5

I%g 7 PROMETHEE I partial preference flow chart showmg the rank order of the 12 digestion methods The cnterla used the PROMETHEE I rankmgs obtamed from residuals data, nucrowave oven settmgs and acid composltlon The ventmg procedure and the Borg acid ad&Ion vanahles were meluded

128 x2A

Fig 8 GAIA PC1 versus PC2 plot for the SIX criteria PROMETHEE I rankmg of the methods accordmg to residuals (PJ, microwave oven settmgs- total time (ft) and total rmcrowave power Ct,>, and the chgestlon acids (HF, HCI and HNO,) The declslon axts (rr) points m the dlrectlon of the prefered methods Object (methods of digestIon) labels refer to Table 5

If the H,BO, vanable 1s included m the PROMETHEE analysis, the results are not altered significantly, 1 e , method 8C remains the prefered optlon followed by methods 9A and 9C with method 4B remammg on the last rank Inclusion of this vanable effectively introduces more mcomparablhty mto the nuddle order of the ranked methods When all eight criteria are submltted for analysis, the flow chart shown m Fig 7 is produced The most slgmficant change from Fig 5 1s that methods SC and 9A are prefered to the rest and are mcomparable Thus the mcluslon of the Vent variable resulted m further mcomparablhty m rank order However, method 4A 1s still prefered only to three other methods and method 4B remains the least prefered one According to the GAIA PCA for the case excluding the Vent and the H,BO, cntena, only three PCs are needed to account for about 90% of the variance The correspondmg PC1 versus PC2 blplot (Fig 8) mdlcates that the criteria cluster m two fairly Independent groups, one consisting of total tune, power and HNO,, and the other of HF and HCl The PROMETHEE I ranking crltenon (P,) hes closer to this group and

S KOKOTJSTAL.

278

X9A X.4B

x6A

v B

x2A

2xB

..9c

PC1

“8C

x98

l3g 9 GAIA PC1 versus PC2 plot for the eight cntena PROMETHEE I rankmg of the methods accordmg to reslduals (P,), microwave oven settings- total time (rr) and total mtcrowave power (t,), the dIgestIon acids (HF, HCl and HNO,), venting procedure (V) and ad&on of H,BO, (B) The decision axis (+~r)IS short and has a low level of signtficance Object (methods of chgestlon) labels refer to Table 5

IS almost m opposltlon to the fu-st cluster This suggests that the sign&ant vanables are HF and HCI However, this conclusion 1s rather tentative because the first two PCs account for only 74% of the variance Interestmgly the total time and power appear to be less important than the acid composltlon The r-axis 1s long, mdlcatmg a high degree of slgmficance It pomts m the general dlrectlon of the thre.e top methods chosen by the PROMETHEE rankmg procedures The mcluslon of the Vent and the H,BO, varrables (Fig 9) indicates that these two vanables are independent from the PROMETHEE rankmgs and are m opposltlon to the other cntena, the other features of the blplot remam essentlally unchanged m comparison to those m Fig 8 The final method selectton The systematic approach to the selection of the most sultable dlgestlon method for sol1 samples by exploratory PCA followed by progressrve PROMETHEE and GAL4 analyses of the readuals and the dIgestIon procedure condltlons, yielded the followmg group of prefered methods to be considered for the final selection methods

8C and 4A from the analysis of the residuals and methods 9A and possibly 9C m addition to SC from the analysis of the settmgs and condltlons Methods 9A and 9C did not rank well on the PROMET’HEE analysis of the residuals and therefore despite their high rankmg with respect to settings and condltlons, they should be avoided Thus suggests that the PROMETHEE rankmg crlterron should have had a weighting greater than 1 Provision for such weighting adjustments 1s available m the program, however, since there was no systematic method for choosing a value for the weighting, this software feature was not utlhsed Method 4A could not be compared with method 8C on the PROMETHEE I rankmg of residuals, however, the results of the analysis of the method settings and condltlons mdlcated that method 8C was consistently prefered Consequently this method of dlgestlon appears to be the best choice Its condltlons and settings could be modified by excludmg the ventmg procedure as It was shown that the PROMETHEE rankmgs of the residuals were independent of this vanable c0nc1uswns

Apphcatlon of exploratory PCA and the multlcriteria declslon makmg methods, PROMETHEE and GAIA, has successfully demonstrated how one may select a suitable method of nucrowave acid dlgestlon for the preparation of sol1 samples for metal analysis The unstandardlsed residuals data matrvr obtamed from the metal analysis of the various digests of the NBS 2704 SRM, was submitted to PCA followed by the PROMETHEE rankmg procedure This approach progressively unravelled and ordered the data structure until two methods, both usmg HF, HNO, and HCl, were found to be prefered Further mformatlon about method performance was then obtamed by mvestlgatmg the relatlonshlp between the PROMETHEE method rankmg based on residuals and the method vanables concerned with the microwave oven settmgs and the composltlon of the digest murture In this case the PROMETHEE results produced rankings for the methods of dlgestlon accordmg to the

MICROWAVE

DIGESTION

user-selected condlhons, e g , maxmuse/ mmlrmse, that were apphed to the crltena The GAIA plots provided a visual display of the relatlonshlp and slgmficance of the vanous method variables From this addltlonal chemometncs analysxs, it was possible to decide that on balance Just one method should be prefered D L Massart and S Kokot thank FGWO and NFWO respectively, for financial assistance REFERENCES A Abu-Samra, J S Morris and S R Koutyohann, Anal Chem , 47 (1975) 1475 P Barrett and L J Davldowsh, Jr, Anal Chem ,50 (1978) 1021 R Blust, A Van der Lmden, E Verheyen and W Declelr, J Anal At Spectrom, 3 (1988) 387 S A. Borman, Anal Chem ,58 (1986) 1424A L B Gdman and W G Engelhardt, Spectroscopy, 4 (1988) 14 G M timber and S Kokot, Trends Anal Chem ,9 (1990) 203 H M Kmgston and LB Jassle (Eds ), Introduction to Mrcrowave Sample Preparation Theory and Practice, ACS, Washington, DC, 1988 8 H Matuslewlcz and R E Sturgeon, Prog Anal Spectrosc , 12 (1989) 21 9 R A Nadkami, Anal Chem , 56 (1984) 2233 10 R T White, Jr and GE Douhlt, J Assoc Off Anal Chem , 68 (1985) 766

279

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