Comments on: A Compact Facility for Trace Analysis of Solutions Sir: In developing their discussion of plasma operating parameters in an inductively heated discharge, Scott et al. computed the relationship between frequency and plasma discharge radius based upon the assumption that the plasma behaved similar to a metallic cylinder of uniform temperature and electrical conductivity ( I ) . We wish to comment on the limitations of this approach. A number of models for the radio frequency induction plasma which date to work begun 25 years ago have been developed. One of the simplest approaches is the “metallic cylinder” model in which a cylinder of gas of constant temperature and electrical conductivity corresponding to that temperature is substituted for a true solid metal cylinder in a radio frequency induction coil. The basic principles used in calculations based on the metallic cylinder model were developed in 1947 by Brown et al. in a mathematical analysis of the radio frequency heating of metals (2). In this simple form of the metallic cylinder model, the plasma discharge temperature and the discharge radius are independent variables. In practice, however, temperature and radius are dependent variables, and generator parameters, coil geometry, tube geometry, and gas flow rates are the independent variables. The application of the metallic cylinder model is limited but is useful in estimating the power input to the discharge and the coupling efficiency between the generator and a plasma of known radius and temperature in a static gas atmosphere. In more advanced calculations based on the metallic cylinder model which consider heat transfer to the confining tube walls, the plasma radius is established a t a radial position which ensures that the energy input to the discharge is exactly balanced by heat conduction to the tube walls (3, 4).
trochemical source (5, 6). A mathematical model of the induction coupled plasma discharge, if it is to be of any use to the spectroscopists, must predict temperature profiles and gas velocities from experimental operating parameters and fundamental properties of the support gas. Based upon these predicted temperature profiles and gas velocities, the spatial distribution of the analyte particles, the degrees of dissociation and ionization, and the atomic radiation within the plasma discharge may be computed. In order to calculate the temperature distributions in an induction plasma, the model must consider the heat conduction equations as well as the electrodynamic equations. Models of this type have been developed in the past few years which enable the calculation of temperature distributions for which no previous assumption of a plasma radius or constant electrical conductivity need be made (7, 8). Miller developed a comprehensive model of the induction plasma to predict axial and radial temperature distributions and the effects of gas velocity profiles on plasma stability and temperature distributions (8). We have reported preliminary results of the influence of various gas flow patterns, such as those used in references ( 5 ) and (6), on gas velocity and plasma temperature distributions with an extended version of Miller’s model (9). This type of analysis can provide information of direct interest to the spectroscopist, while the metallic cylinder model requires that important properties of the discharge must be either neglected or guessed. Therefore, we recommend that the metallic cylinder model be used only within the clearly defined limitations imposed upon it by its basic premises. R. M. Barnes R. G . Schleicher
From the spectrochemical viewpoint, the properties of an excitation source of primary interest are the effective temperature and sample interaction time. The radio frequency induction coupled plasma discharge in atmospheric pressure argon provides both favorably high dissociation temperatures and relatively long particle-plasma interaction times, and, as a result, has proved to be an excellent spec-
Received for review January 9, 1974. Accepted April 25, 1974.
(1) R. H. Scott, V. A. Fassel, R. N. Kniseley, and D. E. Nixon. Anal. Chem., 46, 75 (1974). (2) G. H. Brown, C. N. Hoyler, and R. A. Bierwirth, “Theory and Application of Radio-Frequency Heating,” Van Nostrand, New York, N.Y.. 1947. (3) M. P. Freeman and J. D. Chase, J. Appl. Phys., 39, 180 (1968). (4) R. E. Rovinskii, L. E. Belousova, and V. A. Gruzdev, High Temp., 4, 322 (1966).
(5) G. W.Dickinson, and V. A. Fassel, Anal. Chem.. 41, 1021 (1969). (6) P. W.J . M. Bournans and F. J . deBoer, Spectrochim. Acta. 278, 391 (1972). (7) D. C. Pridmore-Brown, J. Appl. Phys., 41, 3621 (1970). (8) R. C. Miller and R. J . Ayen, J. Appi. Phys., 40, 5260 (1969). (9) R . M. Barnes and R. G. Schleicher, Spectrochim. Acta, 298, in press, (1974).
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Department of Chemistry University of Massachusetts Amherst, Mass. 01002
ANALYTICAL CHEMISTRY, VOL. 46, NO. 9, AUGUST 1974
