Simplex optimisation of inductively coupled plasmas

Analytica Chimica Acta, 115 (1980) 179-187 0 Elsevier Scientific Publishing Company, Amsterdam -

Printed in The Netherlands

SIMPLEX OPTIMISATION

COUPLED PLASMAS

L. EBDON*,

OF INDUCTIVELY

M. R. CAVE and D. J. MOWTHORPE

Department of Chemistry, (Gt. Britain)

Sheffield

City Polytechnic,

Pond Street,

Sheffield,

Sl

1 Wi3

(Received 4th October 1979)

SUMMARY Meaningful comparisons of the analytical performances of different inductively coupled plasmas necessitate preliminary optimisation. The variable step-size simplex procedure is applied to optimise signal-to-background ratios for the five continuously variable operating parameters of a plasma, i.e. the power in the plasma, the observation height, and the injector, plasma and coolant gas flow rates. A series of univariate searches confirmed the results and also illustrated the importance of the various parameters. Results are presented for the manganese 257.6-nm ion line in both argon- and nitrogencooled plasmas and for the arsenic 228.8-nm atom line with argon coolant. Optimal power levels in these three cases were identified as 0.59, >1.2 and 0.57 k-W, respectively.

The inductively coupled plasma (ICP) source offers a number of attractive advantages in analytical optical emission spectrometry, e.g. low detection limits, long linear calibration ranges, relative freedom from interference effects and multi-element capability. Two groups of workers are most closely identified with the development of the ICP as a practical analytical tool. These groups, one led by Greenfield [l] and the other by Fassel [ 21, at an early stage took divergent routes: the former used higher power with nitrogen as coolant and the latter used lower power with argon as coolant. More recently, there has been considerable discussion in the literature [3--51 of the effect of power on analytical sensitivity, and the advocates of high power and low power have tended to polarise. Similarly the use of argon or nitrogen as coolant gas has been the subject of controversy. It would at first appear to be a simple matter to resolve such arguments by experimentation, at least as regards the effect of power and coolant gas on obtainable limits of detection. This is, however, deceptive as the role of the spectrometer and measurement system must be considered and any true comparison must compare systems working at optimal conditions. Thus, for example, the results of Boumans and de Boer [5] showing the effect of power on the signal-to-background ratio cannot be taken as conclusive because, for example, a fixed observation height was used and the optimum viewing region may vary with the power in the plasma. Clearly, a rigorous optimisation technique is required which will enable a true optimum involving

180 aLI the plasma variables to be established, and an acceptable comparison of intrinsic merit independent of the associated spectrometric system to be achieved. In this paper, the use of the simplex technique [6-S] is described for optimisation of different plasmas based on signal-to-background ratio criteria. The simplex method allows numerous interrelated continuously variable parameters to be optimised with relative ease and speed. The intrinsic merit of two or more plasmas may be compared on a given spectrometer by using the net signal-to-background ratio criterion [9]. The order of merit of the plasmas should remain unchanged even though the spectrometer is altered. Thus it should be possible to make a true comparison of the relative advantages of high or low power generators, differing torch designs and plasma gases. A large number of parameters may affect the analytical performance of the plasma. These include the five parameters directly associated with the operation of the plasma (Le., the power, the height of observation, and the flow rates of the coolant, plasma and injector gases) and the parameters associated with the spectrometer system (e.g., monochromator slit width, photomultiplier voltage and amplifier gain). When the signal-to-background criterion is used, these latter parameters may be ignored in order to arrive at a comparison of the intrinsic merit of different plasmas. One parameter of importance in the operation of the plasma has, however, not always been defined unambiguously. Some workers report ‘the power’ as the forward power from the generator, while others report the difference between the forward and the reflected power. Greenfield and McGeachin [lo] have recently demonstrated that the power coupled into the plasma may be measured by a simple calorimetric method by using a dummy load consisting of a bundle of copper and iron rods. Since the power coupled into the plasma may vary with different gas flows, it seems sensible to use the term ‘power’ as meaning power coupled into the plasma. Accordingly, in the work reported here power measurements were made by the method of Greenfield and McGeachin, and throughout this paper the term ‘power’ refers to the power coupled into the plasma. Simplex

optimisation

The five continuously variable parameters mentioned above which affect the analytical performance of an ICP are clearly interrelated (e.g., the height of observation and the injector gas flow rate, and the power in the plasma and the plasma. and coolant gas flow rates). Thus a true optimum cannot be achieved by varying one factor while keeping the others constant. Traditionally, a factorial optimisation experiment is used to solve such a problem but these experiments may be very time-consuming and tedious, unless some factors are given priority, with attendant risks of not obtaining a true optimum. Greenfield and Bums [ll] have successfully used an alternating variable search method for optimising the plasma. An alternative approach is a modi-

181

fication of the simplex procedure of Nelder and Mead [7] which offers an elegant and speedy solution to the problem. The use of simplex optimisation in analytical chemistry has recently been reviewed by Deming and Parker [ 81. Nelder and Mead’s modification [7] of the original sequential simplex procedure of Spendley et al. [6] has been most widely applied. In the present case, a five-dimensional simplex was constructed, defined by six points in factor space, and each of these factors was varied according to the rules of the simplex algorithm [ 123. The variable step-size simplex [7] was chosen as this speeds the optimisation, prevents the attainment of a false optimum and permits closer definition of the optimum. The choice of the initial step size is a critical feature of this optimisation procedure. Yarbro and Deming [12] have demonstrated that it is desirable to begin with a large step size to ensure that most of the factor space is explored before the simplex collapses onto the optimum. These authors described a matrix and accompanying equations which can be used to design the initial simplex. The simplex was terminated when no significant difference was observed in the signal-tobackground ratio of successive new vertices. A univariate search 1131, in which four of the parameters were held constant and the fifth varied as the signal-to-background ratio was measured, was used to confirm the success of the simplex optimisation. This search also yielded valuable information on the influence of each parameter on the performance of the plasma. EXPERIMENTAL Instrumentation The instrumental system and the free-running r-f. generator as well as the versatile modified torch used in this comparison have already been described [ 141. The dummy load used for power measurements and the method of measurement were the same as described by Greenfield and McGeachin [ 101. Additional measurements were made with the brass support of the demountable torch [ 141 in position. Operation of the simplex An initial simplex was drawn up where the step size for each variable (S,) was calculated by subtracting the smallest value experimentally achievable from the largest possible value of that parameter. The experimental constraints were whether or not a stable plasma could be formed on the equipment used and the physical limits of this equipment. The p and q values described by Yarbro and Deming [12] were then evaluated and the initial vertices were calculated according to their method. The rules of the NelderMead algorithm [7] were used to move the simplex to search for the largest signal-to-background

ratio.

182

RESULTSAND DISCUSSION

The power dissipated in the dummy load was measured calorimetrically for various power settings on the generator; a series of graphs was drawn for different grid current vahcles. Above a grid current value of 7.5 mA, it wa possible to fit an empirical equation to the data by the least-squares technique.

At low grid currents, the power in the plasma decreased rapidly and the equation did not apply; in such cases the power in the plasma had to be interpolated from the experimental graphs. The empirical equation was: Power in the plasma (kW) = 0.351 plate power (kVA) + 0.047 grid current (mA) -

1.29

This enabled the power in the plasma to be calculated from the plate power

and grid current readings. Figure 1 shows the close agreement between this

empirical equation and the experimental values obtained with the dummy load, with and without the brass support of the demountable torch in position. This confirms that within experimental error there were no power losses to the brass support of the plasma torch. Progress towards the optimum by the simplex procedure was fairly rapid. Plasma parameters were optimised successfully by using both signal-to-noise ratio and signal-to-background ratio criteria. The latter criterion is more universally applicable and is easier to measure. Thus an optimum was normally achieved in approximately 25 steps. That an optimum had in fact been achieved was then confirmed by using univariate search. Figure 2 demonstrates the successful confirmation of the simplex optimisation for the five essential parameters; these results were obtained for the manganese 257.6-nm ion line with a I-pg Mn ml-’ solution and the modified torch (argon coolant) [14]. The shaded area on each graph corresponds to the region identified as optimal by the simplex procedure. Figure 2A shows the flow rate of injector gas to be a critical parameter and confirms the success of the optimisation experiment. The plasma gas flow rate was not very critical (Fig. 2B); above about 10 1 min-’ little change was observed in the signal-to-background ratio despite large variations in the plasma gas flow rate. Figure 2C ilhxstratesthe success of the simplex procedure in identifying the optimum coolant argon flow rate. Similarly, the optimum observation height was clearly identified by the simplex (Fig. 2D) as approximately 20 mm above the top-turn of the three-turn load coil. It is perhaps the identification of the optimum power to be used in plasma spectrometry which has generated the greatest controversy. Figure 2E illustrates how well the simplex procedure enables optimum power to be defined; in this case, with an argon-cooled plasma, a relatively low optimum power was indicated. This finding for an argon-cooled plasma is in agreement with the findings of Greenfield and Burns [ 111. Other lines for manganese, and for other elements, were also optimised by using the simplex procedure. The use of this procedure to evaluate the

183

i23456?8 Plate power

(kVAl

Fig. 1. Variation of power coupled into the plasma. (0) Measured with dummy load without brass support in position; (X ) measured with dummy load with brass support in position; (+ ) calculated from empirical equation.

analytical performance of plasma torches has been described elsewhere [14]. In all cases the only problems encountered in optimisation were when optimal settings beyond the physical limits of the equipment were indicated. An instructive illustration of the utility of the technique and of the univariate searches is given in Fig. 3. These show the optimal settings for a nitrogencooled and an argon-cooled plasma with manganese(I1) solution aspirated (1 pg ml-‘; measurements at 257.6 nm) and for an argon-cooled plasma with arsenic(II1) solution aspirated (100 pg ml-‘; measurements at 228.8 nm). While plasma spectrometry is traditionally regarded as being particularly suited to the determination of manganese, arsenic is often regarded as a difficult element. All results were obtained with the new modified torch 1141 and the argon- and nitrogen-cooled plasmas can be compared on the basis of their performance for manganese. The injector gas flow rate is a critical parameter with the new design of torch, as can be seen from the sharp peaks shown in Fig. 3A. In all cases the optimum is at about 0.4 1 min- ‘, which suggests that a universal setting for this parameter is possible. The plasma gas flow rate is less critical (Fig. 3B), and again a compromise plasma gas flow rate for these two elements can be used without much loss in sensitivity. The shallow nature of the manganese

tij. Ar El min-‘1 S/B

Coolant Af

It min+I

S/B

Power CkWl

Fig. 2. nonfiction of tfie simplex optimisation for the five variablesstudied. The shaded areas indicate the regions identified as optimal by the simplex method. Argonwaled plasma; mangauese 25’7.6-nm ion Iine. (A] Injector gas flow rate; (B) plasma gas Row rate; (C) coolant agon gas flow rate; (J3) observationheight (mm above the load coil);(E) power mupIed into the plasma-

186

Injjta

Ar [ 1

Plmma Ar [ 1 min“]

mh-‘I

[El

.20

1.6.

12

I.5

L2.

0.8

ID

0.8

9.4

0.5

0.4,

1.6

a

2

4

lb

6 8 Cmlant Cl mii’l

S/B wil3

-2D

D

12 Heiqht [mm]

i%: .2-o

1.5

LO

0.5

L

0

0.4

o.8 --&’

rates,observation height and power on signal-to-backgrcmnd ratios for manganese and arsenic lines in different &~~mas. Curves (1) nitrogen-cooled plasma, manganese 257.6-nm ion line; (2) argon-cooled plasma, manganese 257.6nm ion line; (3) argon-cooled plasma, arsenic 228.8-nm atom line. (A) Injector gas flow;(B) plasma gas ~IOW; (C) coolant gas flow; (D) observation height; (E) power coupled into the plasma.

Fig. 3. Effect5 of gas flow

curve when a nitrogen-cooled

plasma is used creates problems in identifying rapidly the optimum but such a situation is advantageous as regards day-today aalytical reproducibility-

186

In general, with nitrogen as the coolant the outer gas flow rate has little effect on the signal-to-background ratio but with argon as coolant this flow rate is more critical (Fig. 3C). This behaviour presumably derives from the fact that argon may play a role in the propagation of the plasma whereas nitrogen does not. The optimal viewing height in all three experiments was essentially similar (Fig. 3D) being approximately 20 mm above the load coil. This somewhat unexpected conclusion, and the similar optimal injector gas flow rates, could arise from the relatively large section of the plasma tail flame viewed (16 mm). Such a large section was used in order to minimise ionisation interferences in multi-element work, but it may disguise subtle differences in optimal viewing heights and injector gas flow rates. Accordingly, further experiments with a smaller monochromator entrance slit are required; With regard to the controversy referred to above, Fig. 3E may serve to justify claims that low power is optimal in an all-argon plasma whereas higher power is needed to optimise

a nitrogen-cooled

plasma. Apparently

the

nitrogen-cooled plasma required more power to reach an optimum for manganese than could be coupled into the plasma with the generator available here at the gas flow rates indicated by the simplex, i.e. ca. 1.2 kW. In an argon-cooled plasma, however, an optimum for this manganese 257.6-nm ion line was reached at 0.59 kW even though more power was available. The arsenic 228.8-nm atom line could be optimised at only 0.57 kW. Although there is quite a large difference in the energies required to excite these two lines, the difference in the optimum power in an argon-cooled plasma is small (0.02 kW). For the manganese ion line, the sum of the ionisation energy and the excitation energy is 12.2 eV, whereas for the arsenic atom line the excitation energy is 6.7 eV. Preliminary optimisation experiments on these and other lines in a nitrogen-cooled plasma tend to confirm the relationship between optimum power in this plasma and the difficulty of exciting a line, as reported by Greenfield and Burns [ 111. In practical terms it appears that compromise multi-element operating conditions will be less detrimental to individual element sensitivities with the argon-cooled plasma, or that the greatest improvements in analytical sensitivity for a given element may be achieved by judicious line and power selection with the nitrogencooled plasma. The authors thank the Science Research Council and the London Scandinavian Metallurgical Co., Rotherham, for help in purchasing the equipment, and the Science Research Council for financial support for one of us (M.R.C.). We are grateful to Dr. S_ Greenfield for helpful discussions and for the loan of the d ummy load used.

187 REFERENCES 1 S. Greenfield, I. Ll. Jones and C. T. Berry, Analyst, 89 (1964) 713. 2 R. H. Wendt and V. A. Fassel, Anal. Chem., 37 (1965) 920. 3 S. Greenfield, I. Ll. Jones, H. McD. McGeachin and P. B. Smith, Anal. Chim. Acta, 74 (1975) 225. 4 S. Greenfield, Proc. Anal. Div. Chem. Sot., 19 (1976) 279. 5 P. W. J. M. Boumans and F. J. de Boer, Spectrochim. Acta, Part B, 32 (1977) 365. 6 W. Spendley, G. R. Hext and F. R. Himsworth, Technometrics, 4 (1962) 441. 7 J. A. Nelder and R. Mead, Comput. J., 7 (1965) 308. 8 S. N. Deming and L. R. Parker, CRC Crit. Rev. Anal. Chem., (1978) 187. 9 S. Greenfield and D. Thorburn Burns, Spectrochim. Acta, Part B, in press. 10 S. Greenfield and H. McD. McGeachin, Anal. Chim. Acta, 100 (1978) 101. 11 S. Greenfield and D. Thorbum Burns, Anal. Chim. Acta, 113 (1980) 205. 12 L. A. Yarbro and S. N. Deming, Anal. Chim. Acta, 73 (1974) 391. 13 R. G. Michel, J. Coleman and J. D. Winefordner, Spectrochim. Acta, Part B, 33 (1978) 195. 14 L. Ebdon, D. J. Mowthorpe and M. R. Cave, Anal. Chim. Acta, 115 (1980) 171.