8
Anal. Chem. 1981, 53, 1279-1286 1279 Combining eq A8, All, and A12 Ti = L2/(pi4p) establishes a relation between the characteristic decay time and the ionic mobility in terms of the distance between the probes and the applied potential. Using eq A10 and A13 which agrees with the solution found for the so-called plas- ma-capacitor in the limit of low charge density (23). Due to the absence of the diffusion term in eq A5, the charge density does not obey the boundary conditions Ni(*L) = 0. LITERATURE CITED Ni = n exp(-x/L) -L < x < L (~14) (1) Lucatorto, T. B.; McIlrath, T. J. fhys. Rev. Left. 1978, 37, 428. (2) Colllns, C. B.; Curry, S. M.; Johnson, 6. W.; Mlrza, M. Y.; Chellehmal- zadeh, M. A.; Anderson, J. A.; Popescu, D.; Popescu, I. fhys. Rev. A. 1978, 14, 1662. (3) Bridges, W. B. J. Opt. SOC.Am. 1977, 68, 352. (4) Keller, R. A.; Engleman, R.; Zalewski, E. F. J. Opt. SOC. Am. 1978, 69. 738. (5) Travis. J. C.: Schenck. P. K.: Turk. G. C.: Mallard. W. G. Anal. Chem. (10) Alkemade, C. Th. J., Plenary lecture, V I Annual FACSS Meeting, Phila- delphia, PA, Sept 17, 1979. (11) Bellum, J. C.; George, T. F. J. Chem. Phys. 1978, 68, 134. 112) Hansch. T. W. ADD/.Oot. 1972. 11. 895. (A13 i13j Omeneito, N.; Bower, J:; Bradshaw, J.; van Dijk, C. A.; Winefordner, J. D. J. Quant. Spectrosc. Radiat. Transfer 1980, 24, 147. (14) Helifeld, A. V.; Caddlck, J.; Welner, J. fhys. Rev. Lett. 1978, 40, 1369. (15) Bearman, G. H.; Leventhal, J. J. fhys. Rev. Lett. 1978, 47, 1227. (16) Turk, G. C.; Travis, J. C.; DeVoe, J. R.; O’Haver, T. C. Anal. Chem. 1979, 51, 1890. (17) Behmenburg, W. J. Quant. Spectrosc. Radiat. Transfer 1984, 4, 177. (18) Muller C. H., 111; Steinberg, M.; Schofleld, K. ACS Symp. Ser. 1980, No. 134, 192. (19) van Calcar, R. A.; van de Ven, M. J. M.; van Uitert, B. K.; Blewenga, K. J.; Hollander, Tj.; Alkemade, C. Th. J. J. Quant. Spectrosc. Radlet. Transfer 1979, 21, 11. (20) Ashton, A. F.; Hayhurst, A. N. Trans. Faraday SOC. 1970, 66, 833. (21) Wilson, H. A. Rev. Mod. Phys. 1931, 3, 156. (22) McDanlel, E. W.; Mason, E. “The Mobility and Diffusion of Ions in Gases”; Wiley: New York, 1973; p 17. (23) Turk, 0. C.; Mallard, W. G.; Schenck, P. K.; Smyth, K. C. Anal. Chem. . . 1979, 51, 2408. McGraw-Hill: New York, 1973; p 71. (24) Krall, N. A,; Trlvelpiece. A. W. “Prlnclples of Plasma Physics“; , I 1979, 51, 1516. (6) Vidal, C. R. Opt. Lett. 1980, 5, 158. (7) van Dijk, C. A.; Alkemade, C. Th. J. Combust. Flame 1980, 38, 37. (8) Panock, R.; Freeman, R. R.; White, J. C.; Stwz, R. H. Opt. Left. 1980, 5, 160. (9) Hurst, G. s.; Payne, M. G.; Kramer, s. D.; Young, J. p. Rev. ~od. fhys. 1979, 51, 767. RECEIVED for review December 29, 1980. Accepted April 6, 1981. Parrtial support was provided for this work by the Michigan State University Foundation through on All Univ- ersity Research Initiation Grant. Trace Analysis by Metastable Energy Transfer for Atomic Luminescence William B. Dodge I11 and Ralph 0. Allen” Department of Chemistty, University of Virginia, Charlottesville, Virginia 2290 1 An atomic emlsslon source based upon the energy transfer from metastable nitrogen molecules to metal atoms has been Investlgated. A dlelectric discharge through flowing nitrogen Is used to generate a large population of metastable NZ- (A3&+) molecules whlch are then mixed with atomlc species In a reactlon cell to produce a chemllumlnescent reaction. This method of generating active nitrogen molecules appears to produce several orders of magnitude higher concentrations of active nitrogen than can be achieved wlth a microwave dlscharge. In thls paper, electrothermal atomlzatlon of Zn- contalnlng solutlons and direct atmospheric sampling of Hg are described. The low-cost emission source exhibits ex- cellent sensltlvlty with detection llmits as low as lo7 atoms ~rn-~ and a dynamic range of at least 8 orders of magnitude. At pressures on the order of 1 torr an electrical or microwave discharge in flowing nitrogen has been found to produce an “activity” which manifests itself most strikingly in a luminosity which can persist for as much as several hours (I). The ni- trogen afterflow in ita various forms is a complex system, and despite intense study the mechanisms for its formation are not completely understood (2). Since the properties of the active nitrogen afterglow depend upon energy exchange pro- cesses in the gas, the emission is sensitive to subtle changes in experimental conditions including the presence of trace impurities. For instance, a 253.7 nmHg emission has been shown to be selectively excited by the Nz(A38,+) metastable state of the nitrogen molecule even when the mercury was present in concentrations as low as lo9 atoms cm-3 (3). Al- though the atomic emission from impurities was usually secondary to the study of the active nitrogen, it is clear from the bibliography by Wright and Winkler (4) that atomic emission excited in a nitrogen afterglow could be the basis for a very sensitive detection technique (5). Sutton and his co-workers (6-8) have shown a number of applications of metastable transfer emission spectrometry (MTES) using active nitrogen produced in a microwave discharge. The principle energy carriers in the nitrogen (Lewis-Ray- leigh) afterglow that are responsible for atomic excitation are either the metastable triplet state molecules Nz(A) or the vibrationally excited ground-state molecules NJX). This uncertainty is due in part to the inability to selectively remove one or the other species after they are formed in the afterglow (9-11). Yamashita’s observation (12) that the triplet state [N2(A3Z,+)] was responsible for exciting atomic lines requiring greater than 4.5 eV while the vibrationally excited ground state [N2(X*Z,)] was responsible for emission lines requiring less than 4.5 eV may help explain the conflictingclaims of different investigators (e.g., 10, 11,13,14). It does appear that when the metastable triplet Nz(A) is available in sufficient quantity, the dominant atomic excitation mechanism is due to energy exchange during a spin conserving collision between the electronicallyexcited molecule (donor) and the atom (acceptor) (14). While the loss of energy from the donor Nz(A) is 0 1981 American Chemical Society 0003-270018 110353-1279$0 1.2510

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Page 1: Trace analysis by metastable energy transfer for atomic luminescence

Anal. Chem. 1981, 53, 1279-1286 1279

Combining eq A8, A l l , and A12 Ti = L2/(pi4p)

establishes a relation between the characteristic decay time and the ionic mobility in terms of the distance between the probes and the applied potential. Using eq A10 and A13

which agrees with the solution found for the so-called plas- ma-capacitor in the limit of low charge density (23). Due to the absence of the diffusion term in eq A5, the charge density does not obey the boundary conditions Ni(*L) = 0.

LITERATURE CITED

Ni = n exp(-x/L) -L < x < L ( ~ 1 4 )

(1) Lucatorto, T. B.; McIlrath, T. J. fhys. Rev. Left. 1978, 37, 428. (2) Colllns, C. B.; Curry, S. M.; Johnson, 6. W.; Mlrza, M. Y.; Chellehmal-

zadeh, M. A.; Anderson, J. A.; Popescu, D.; Popescu, I. fhys. Rev. A . 1978, 14, 1662.

(3) Bridges, W. B. J. Opt. SOC. Am. 1977, 68, 352. (4) Keller, R. A.; Engleman, R.; Zalewski, E. F. J. Opt. SOC. Am. 1978,

69. 738. (5) Travis. J. C.: Schenck. P. K.: Turk. G. C.: Mallard. W. G. Anal. Chem.

(10) Alkemade, C. Th. J., Plenary lecture, V I Annual FACSS Meeting, Phila- delphia, PA, Sept 17, 1979.

(11) Bellum, J. C.; George, T. F. J. Chem. Phys. 1978, 68, 134. 112) Hansch. T. W. ADD/. Oot. 1972. 1 1 . 895.

( A 1 3 i13j Omeneito, N.; Bower, J:; Bradshaw, J.; van Dijk, C. A.; Winefordner, J.

D. J. Quant. Spectrosc. Radiat. Transfer 1980, 24, 147. (14) Helifeld, A. V.; Caddlck, J.; Welner, J. fhys. Rev. Lett. 1978, 40,

1369. (15) Bearman, G. H.; Leventhal, J. J. fhys. Rev. Lett. 1978, 47, 1227. (16) Turk, G. C.; Travis, J. C.; DeVoe, J. R.; O’Haver, T. C. Anal. Chem.

1979, 51, 1890. (17) Behmenburg, W. J. Quant. Spectrosc. Radiat. Transfer 1984, 4 ,

177. (18) Muller C. H., 111; Steinberg, M.; Schofleld, K. ACS Symp. Ser. 1980,

No. 134, 192. (19) van Calcar, R. A.; van de Ven, M. J. M.; van Uitert, B. K.; Blewenga,

K. J.; Hollander, Tj.; Alkemade, C. Th. J. J . Quant. Spectrosc. Radlet. Transfer 1979, 21, 11.

(20) Ashton, A. F.; Hayhurst, A. N. Trans. Faraday SOC. 1970, 66, 833. (21) Wilson, H. A. Rev. M o d . Phys. 1931, 3 , 156. (22) McDanlel, E. W.; Mason, E. “The Mobility and Diffusion of Ions in

Gases”; Wiley: New York, 1973; p 17. (23) Turk, 0. C.; Mallard, W. G.; Schenck, P. K.; Smyth, K. C. Anal. Chem. . .

1979, 51, 2408.

McGraw-Hill: New York, 1973; p 71. (24) Krall, N. A,; Trlvelpiece. A. W. “Prlnclples of Plasma Physics“;

, I

1979, 51, 1516. (6) Vidal, C. R. Opt. Lett. 1980, 5 , 158. (7) van Dijk, C. A.; Alkemade, C. Th. J. Combust. Flame 1980, 38, 37. (8) Panock, R.; Freeman, R. R.; White, J. C.; Stwz, R. H. Opt. Left. 1980,

5, 160. (9) Hurst, G. s.; Payne, M. G.; Kramer, s. D.; Young, J. p. Rev. ~ o d .

fhys. 1979, 51, 767.

RECEIVED for review December 29, 1980. Accepted April 6, 1981. Parrtial support was provided for this work by the Michigan State University Foundation through on All Univ- ersity Research Initiation Grant.

Trace Analysis by Metastable Energy Transfer for Atomic Luminescence

William B. Dodge I11 and Ralph 0. Allen”

Department of Chemistty, University of Virginia, Charlottesville, Virginia 2290 1

An atomic emlsslon source based upon the energy transfer from metastable nitrogen molecules to metal atoms has been Investlgated. A dlelectric discharge through flowing nitrogen Is used to generate a large population of metastable NZ- (A3&+) molecules whlch are then mixed with atomlc species In a reactlon cell to produce a chemllumlnescent reaction. This method of generating active nitrogen molecules appears to produce several orders of magnitude higher concentrations of active nitrogen than can be achieved wlth a microwave dlscharge. In thls paper, electrothermal atomlzatlon of Zn- contalnlng solutlons and direct atmospheric sampling of Hg are described. The low-cost emission source exhibits ex- cellent sensltlvlty with detection llmits as low as lo7 atoms ~ r n - ~ and a dynamic range of at least 8 orders of magnitude.

At pressures on the order of 1 torr an electrical or microwave discharge in flowing nitrogen has been found to produce an “activity” which manifests itself most strikingly in a luminosity which can persist for as much as several hours ( I ) . The ni- trogen afterflow in ita various forms is a complex system, and despite intense study the mechanisms for its formation are not completely understood (2). Since the properties of the active nitrogen afterglow depend upon energy exchange pro- cesses in the gas, the emission is sensitive to subtle changes in experimental conditions including the presence of trace impurities. For instance, a 253.7 nmHg emission has been

shown to be selectively excited by the Nz(A38,+) metastable state of the nitrogen molecule even when the mercury was present in concentrations as low as lo9 atoms cm-3 (3). Al- though the atomic emission from impurities was usually secondary to the study of the active nitrogen, it is clear from the bibliography by Wright and Winkler (4 ) that atomic emission excited in a nitrogen afterglow could be the basis for a very sensitive detection technique (5). Sutton and his co-workers (6-8) have shown a number of applications of metastable transfer emission spectrometry (MTES) using active nitrogen produced in a microwave discharge.

The principle energy carriers in the nitrogen (Lewis-Ray- leigh) afterglow that are responsible for atomic excitation are either the metastable triplet state molecules Nz(A) or the vibrationally excited ground-state molecules NJX). This uncertainty is due in part to the inability to selectively remove one or the other species after they are formed in the afterglow (9-11). Yamashita’s observation (12) that the triplet state [N2(A3Z,+)] was responsible for exciting atomic lines requiring greater than 4.5 eV while the vibrationally excited ground state [N2(X*Z,)] was responsible for emission lines requiring less than 4.5 eV may help explain the conflicting claims of different investigators (e.g., 10, 11,13,14). I t does appear that when the metastable triplet Nz(A) is available in sufficient quantity, the dominant atomic excitation mechanism is due to energy exchange during a spin conserving collision between the electronically excited molecule (donor) and the atom (acceptor) (14). While the loss of energy from the donor Nz(A) is

0 1981 American Chemical Society 0003-270018 110353-1279$0 1.2510

Page 2: Trace analysis by metastable energy transfer for atomic luminescence

1280 ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981

R

Flgure 1. Blow up diagram of basic components in METAL analysis system. Nitrogen flows through the top of dielectric discharge source (a) where metastable nitrogen species are produced. After flowing through a light trap (b) the metastable enters the reaction cell (c) where it is mixed with atomic species carrled in by a nitrogen or argon flow from the atomization chamber (f). Either an eiectrathermal atomizer (9) or a capillary leak c a n be used as the source of atoms. The atomization chamber can be isolated with a Teflon and Piexigiass shutter valve (e). Monochromator and detector are placed before the quartz viewing window (d) in order to observe atomic emissions.

quantized, even nonresonant (nonquantized) energy transfer to the acceptor atom seems to be an efficient process (14,151. If the concentration of N2(A) molecules is much greater than the concentration of the atomic species being excited, then the emission should follow pseudo-first-order kinetics so that the intensity of atomic emission depends directly upon the concentration of the acceptor atoms. However, the analytical application of this energy transfer process is limited by the concentration of the metastable N2(A) molecules. In micro- wave and condensed flow discharge systems the N2(A) con- centration depends directly on the concentration of nitrogen atoms and the total pressure. In these discharge systems the metastable N,(A) state is populated through nitrogen atom recombinations while at the same time the N2(A) is rapidly quenched to the singlet ground state N2(X) by collisions with nitrogen atoms (16-18). This means that the N2(A) concen- tration has an upper limit which is dependent upon the rates for the competing process of formation and quenching. The steady-state concentration of N,(A) in the microwave discharge afterglow appears to be on the order of 5 X lo9 molecules (16) and very dependent upon total pressure. This in turn limits the maximum concentration of atomic species that will still give an atomic emission intensity which is a linear function of the atomic concentration. The work on the MTES system by Sutton et al. (6-8) confirms the inherent limitation in linear

Flgure 2, Gas flow system for nitrogen flow through discharge gen- erator and atomization chamber. The liquid nitrogen trap need not be used unless one wishes to eliminate NO emission. Lettered compo- nents are referred to in text under Experimental Section.

dynamic concentration range that results from the nitrogen atom quenching process in microwave discharges. The effi- cient formation of much higher concentrations of the meta- stable Nz(A) in the low power dielectric discharge described in this paper is the basis for an analytical emission source of extreme sensitivity with wide dynamic range which we have called METAL (for metastable energy transfer for atomic luminescence).

EXPERIMENTAL SECTION The analytical system (Figure 1) provides for the transfer of

excitation energy from active nitrogen generated by a dielectric discharge (of the type used for Berthelot ozonizer) in a reactiod chamber where the active nitrogen is mixed with the atomic species generated by various means in the atomizer. The design of each of the individual components will be discussed below. Atomic emissions from the reaction chamber were monitored by using a small 0.25 m monochromator (Jarrell-Ash 82-410) and photomultiplier (RCAlP28). For this work the entrance and exit slits of the monochromator were set at 50 pm. The output from the photomultiplier, which was operated at 950 V, was measured by using a picoammeter (Pacific Photometric Model 15). The photocurrent was recorded with either a strip chart recorder or a multichannel ahalyzer (Nuclear Data, Model ND60) operated in the multichannel scaling mode (19).

A. Active Nitrogen Generator. Active nitrogen was gen- erated as the gas flowed through the low power discharge chamber (a) in Figure 1. Nitrogen flows between two concentric glass tubes which are separated by a 3 mm anndar space. The two glass tubes which act as electrodes for a high-voltage ac discharge, are held in place by Macor ceramic spacers epoxied at each end. In order to spread the discharge as evenly as possible along the length of the tube, we filled the center tube, which is closed at the lower end, with saturated NaCl solution. A copper wire makes electrical contact with the electrolyte in the center tube. The outer tube is wrapped with an electrically conducting tape (3M No. Y9183-41315-L92-6). The high voltage for the discharge is sup- plied by a 10-kV oil burner ignition transformer which is controlled through a Variac. To eliminate the possibility of electrical shocks the outer electrode was grounded and the center electrode was attached to the transformer HV terminal. The glass and plastic construction eliminates the metal lines associated with metal electrode discharges and avoids the quenching of the active ni- trogen due to collisional deactivation on metal surfaces. When the center electrode was replaced by a metal rod, no metastable nitrogen was observed even a centimeter beyond the end of the metal rod. In the discharge between two glass dielectric electrodes, the acceleration of electrons depends upon the total dielectric strength of the medium. It is therefore not unexpected to ex- perimentally find that the amount of metastable nitrogen pro- duced depends upon the dielectric constant of the glass, the gas pressure, and the applied voltage.

The nitrogen flow system is shown in Figure 2. Reagent grade nitrogen (a) passes through a liquid nitrogen cold trap (b) before passing through (later experiments showed that the cold trap was not necessary and that air could be used rather than tank nitrogen) a flow regulator and a precision metering valve (c). A calibrated gas flow meter (d) is used to measure the flow rate of the nitrogen

Page 3: Trace analysis by metastable energy transfer for atomic luminescence

ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 1281

through the discharge (e). The actual pressure in the active nitrogen generator and the reaction cell is measured with a Consolidated Vacuum Corp. mechanical pressure gauge (f) con- nected to the reaction cell (g). The pressure is controlled by varying the flow rate of the nitrogen into the generator and the rate at which it is pumped out of the reaction cell. The pump (h) used (Precision Scientific Model 25) is of a larger capacity than is needed for the volume, so a ballast volume (1 ft3) was included along with a throttle valve (i) for controlling the pumping speed. Under normal operating conditions the flow rate was kept at 5 cm3 min-l (STP), and the pressure in the reaction chamber was on the order of 1-5 torr. The voltage necessary to maintain a certain discharge current varied inversely with the nitrogen pressure.

An important part of the generator is the light trap between the active nitrogen generator and the reaction chamber. The trap is made of glass and has two right angle bends so that light emission from the active nitrogen generator will not contribute to the background radiation in the reaction cell. The outside walls of the trap were painted black (to avoid reflections) and then wrapped with the same type of electrically conducting tape as the outer tube of the generator. The outer surface of the light trap was grounded because it decreased the sparking due to ionization of the nitrogen as will be discussed below. B. Atomization Source. Two types of samples have been

analyzed. In the first instance analyte atoms or molecules are already present in a gaseous form and are carried into the reaction cell either by using a flowing stream of nitrogen or by directly leaking atmospheric samples through a capillary into the cell. In the former case the flow rate of the nitrogen is controlled by a flow restrictor and precision metering valve and the flow rate monitored with the same type of orifice-differential pressure gauge as used for the nitrogen flow into the generator (Figure 2). In the direct atmospheric samples the size of the capillary and pressure differential determine the amount of sample introduced into the reaction chamber per unit time. Sampling rates can be varied while maintaining the ratio of active nitrogen to sample by changing the flow rates through the active nitrogen generator.

For aqueous solutions a tungsten filament was used for atom- ization. While several types of filaments were used during the course of these studies, a no. 47 light bulb filament proved to be a uniform, rugged, low-cost filament atomizer. The filament was extracted from the light bulb by crushing the bulb and cutting the wires between the glass support head and the bulb base. The atomizer chamber is separated from the reaction cell by a shutter valve made of Teflon and Plexiglass. This allowed the loading of the filament or boat at atmospheric pressure without turning off the active nitrogen generator. Liquid samples of up to 10 pL were places on the filament and dried by passing a low current through the filament. After the drying cycle the sample cell is evacuated and the nitrogen is allowed to flow through the shutter valve. Sample atomization was initiated by an electronically switched current pulse of 0.15 A at 6.3 V passing through the electrode assembly and filament.

C. Reaction Cell. For versatility all connections to the reaction cell are made with 14/20 ground glass connections. The active nitrogen from the generator passes into the reaction cell opposite the 2.5 cm diameter quartz viewing window. Whenever it is necessary to put samples on the filament atomizer, the active nitrogen generator can be kept at a low pressure by using the shutter valve. The outlet to the pumping system is positioned so that the active nitrogen travels the length of the cell and is removed just in front of the viewing window. The optical system is aligned to look down the length of the reaction cell where the large population of long-lived metastable species can produce multiple excitation-emission cycles of the same atom which results in improved sensitivity. In some experiments the shutter valve-atomizer assembly was replaced by a filament placed di- rectly in the cell through the same hole 2 cm from the quartz window.

RESULTS AND DISCUSSION A. Characteristics of the Active Nitrogen Generator.

To determine the relative concentrations of the various metastable nitrogen species, it is necessary to characterize the emission in the afterglow. In most discharges, the charac-

Wavelength nm

Figure 3. Emission observed in afterglow of nbogen at 1 ton pressure produced by a dielectric discharge in the generator shown in Figure 1 operated at 8.5 kV. Point of observation was about 0.1 s after gas left discharge region. This is the so-called second positive emission.

teristics of the nitrogen afterglow are strongly dependent upon the mode of excitation, total pressure, and distance (time) from the discharge to the point of observation. The emission from the nitrogen afterglow was scanned between spectral limits of 200 and 800 nm under various experimental conditions (including direct observation of the discharge region), and the only strong emission was from the so-called nitrogen second positive (2P) band system. This system results from the radiative decay of triplet state nitrogen molecules: Nz(C311u) - Nz(B311g). The prominence of this system is consistmt with the predominantly blue afterglow observed visually in all afterglows at pressures greater than 0.5 torr. Only a few very weak transitions from low vibrational levels of the first positive (1P) system (N2(B3Q - Nz(A3Zu+) could be identified in the red and near-infrared regions of the spectrum. The intensity distribution of the 2P emission bands is considerably different from that observed in other nitrogen afterglows (20, 21). Figure 3 is a representative spectrometer scan of the emission produced by this dielectric discharge. This particular emission was observed in the reaction cell after the excited species have moved a t least 100 ms beyond the discharge region operated under conditions of 1 torr and 8.5 kV applied voltage.

The detection of the well-developed second positive system in the afterglow is rather interesting since the excitation energy for N2(C311u)u = 0 is 11.1 eV, and its radiative lifetime is 50 ns. In order to observe the second positive emission in the reaction cell, the Nz(C) state must be populated by production from some other metastable species. The collision of two A-state metastables (6.2 eV of energy) has been shown to populate the C state (11.1 eV excitation energy) via an efficient energy pooling reaction (22, 23)

Only in the afterglow from systems in which a large population exists does this blue afterglow dominate. In our system this energy pooling process is not the only one in view of the marked difference in the relative intensity distributions be- tween the 2P system observed by Stedman and Setser (22) and the afterglow generated in this study. Since the energy pooling process populates three excited states of nitrogen, Le., Nz(C), Nz(C'), and Nz(B), the virtual absence of the Gold- stein-Kaplan (GK) system, Le., N2(C3IIU) - N2(B3n,), and the very low intensity of emissions from the first positive system, i.e., Nz(B3n,) - Nz(A3Z,+), would seem to indicate that energy pooling by N2(A) is not the most important process in the present afterglow. From kinetic considerations, the more probable process for the formation of N2(C3IIU) in the afterglow produced by the dielectric discharge is that suggested by Ung (24) who studied a similar discharge system

where Nz(XIZE+)u represents vibrationally excited ground-

Page 4: Trace analysis by metastable energy transfer for atomic luminescence

1282 ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981

state nitrogen (u > 20) with an excitation energy of greater then 5 eV. This process assumes that all the Nz(A) molecules have relaxed to their lowest vibrational level 0.2 s following the discharge.

When air is used for the gas in the discharge region, a small amount of emission from the NO, system is observed. The source of the small amount of NO is not known, but very little atomization of nitrogen can occur in the discharge as in the presence of so much oxygen a considerable amount of NO would be produced. The observation of the NO, system with no observable NO, emission is also evidence that a consid- erable amount of Nz(A) is present in the afterglow. The reaction of NO with N,(A) gives almost exclusively NO, emission (25, 26).

It is important to remember that the afterglow of this generator shows little or no evidence of the straw yellow color of the first positive band emission (sometimes called Lewis- Rayleigh afterglow).

N2(B311g) - N2(A38,+) This means that the N&) - Nz(B) transition observed must populate only the low vibrational levels in the B state (v < 6) from which no visible emission in the N,(B) - N,(A) transition is observed (27).

The blue afterglow is strong evidence of a large metastable population. In most discharge systems (e.g., microwave dis- charge) the population of the N,(A) state is considered to be the result of the recombination of two nitrogen atoms which means that the maximum population of the metastable state is limited since a single nitrogen atom can quench numerous metastable N,(A) molecules (28). In this metastable nitrogen generator it would appear that another mechanism must be responsible for the Nz(A) state since the population appears to be much greater. The absence of significant production of NO even when air is used in the discharge and the lack of nitrogen atomic emission at 347 nm suggest that little atom- ization of nitrogen occurs. The most reasonable explanation for the production of the afterglow is a direct excitation by electron impact (29). Studies by Bont and Chang (32) indicate that the maximum cross section for the 0,O vibrational ex- citation of Nz(C311,) by electron impact peaks sharply around 15 eV while that to populate the N2(B311g) state peaks around 10 eV. When the emission from the discharge region is ob- served directly (rather than 100 ms downstream in the reaction chamber), the blue second positive (N2(C) - N,(B)) system lines are the only strong ones observed. This indicates a large population of nitrogen in the N,(C) state which must be formed directly from the ground state by electron impact since the cascade contributions to the N,(C) state from higher lying electronic states are small (31, 32). Since the first positive emission from the N,(B) - N,(A) is very weak even in the discharge region, only the low-lying N,(B) vibrational levels must be populated. In addition there must be little population of the higher (u > 6) vibrational levels directly by electron impact. If the average energy of the electrons in the discharge were in the range of 9-11 eV, one would expect high vibra- tional levels of N,(B), so we conclude that the average impact energy must be greater than 11 eV when the applied voltage for this generator is between 8 and 8.5 kV. Since the intensity of the afterglow increases as a function of applied voltage until there was a saturation of the HV power transformer at 8.5 kV, one must assume that the average energy of the electrons under these conditions are still less than the 15 eV for which the cross section for excitation of the Nz (C) state is maximum.

B. Discharge Mechanism. Electron flow through the dielectric discharge is current-limited by the breakdown mechanisms of both the glass electrode material and the ni- trogen fill gas. Electrons that pass through the nitrogen must first escape the metal foil contact with the outer electrode and

8

4 e Y 4 - z - 2 - b

0 -

A l2iC. B

I

Page 5: Trace analysis by metastable energy transfer for atomic luminescence

ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 1283

Flgure 5. Relevant energy levels for N2 molecules, Hg and Zn atoms after Duthler and Brolda ( 77). Emissions observed by this technique were the 253.7-nm line of Hg and the 307.6-nm and 468.0-nm lines of Zn.

tending through the bottom spacer in the discharge tube to permit cooling of the electrolyte in a passive flow system through a second condenser. This configuration also required that the outer electrode be attached to the HV supply posing a significant shock hazard to the operator. Fortunately, the gas flow serves the remove most of the energy passing through the discharge so that external cooling was eliminated in the discharge generator shown in Figure 1.

Interestingly, the discharge generator having the metal center electrode produced no observable afterglow. The glow within the discharge tube was bright blue but was confined to only the surface of the metal electrode. Apparently the large metal surface-to-volume ratio within the discharge tube serves to quench the metastable N2(A) species that is re- sponsible for both the afterglow and metal excitation. The dielectric (glass) electrode material eliminates the catalytic surface deactivation by the metal of N2(A) and since it limits the electron current within the discharge, there is no nitrogen dissociation and little ionization.

C. Metastable Energy Transfer to Hg Atoms. In order to study the transfer of energy from the metastable nitrogen to atoms in a flowing system as it passes through the reaction cell, we designed a continuous source of Hg atoms. A glass capillary leak was employed to meter Hg vapor directly from the atmosphere. The concentration of the Hg atoms was determined by the vapor pressure (which could be varied by controlling the temperature) and the flow rate through the micropipet capillary (several different sizes were used). A unique aspect of the metastable generator used in this work is that the introduction of oxygen into the reaction cell during direct atmospheric sampling does not do much quenching of the active nitrogen (N2(A)). In systems where nitrogen atoms are present it will react with oxygen to form NO and N20 which are very effective in quenching the N2(A) to the N2(X) ground state (16).

When Hg vapor is introduced into the afterglow produced by the dielectric discharge, an intense atomic emission at 253.7 nm is observed. This corresponds to an excitation of the 63P level which is shown in Figure 5 along with the relevant energy levels for nitrogen and zinc (33). No emission could be de- tected from the higher lying states of Hg (404.6 nm and 365.0 nm) which have been excited by the metastable species in the afterglow of a microwave discharge (33). This is a further indication that the N2(A) population is greater than any other metastable species produced in this dielectric discharge sys- tem. The efficiency of the energy transfer is very high as even with a relatively inefficient optical system, atomic emission was observed when the concentration of Hg in the reaction cell was calculated to be less than lo' atoms ~ m - ~ .

The atomic emission from this continuous source of Hg atoms was used to study the effects of various parameters on

I 2 3 4 5 Time (See.)

Figure 8. Intensity at 468 nm (Zn emission) during atomization of Zn(NO,), deposited on tungsten filament. Current is applied for 1 s and is initiated 1 s after scan of multichannel analyzer begins.

the atomic excitation. For instance it was observed that a t pressures less than 0.1 torr +N2 ions were formed and sparking to ground occurred. The result was a 30% fluctuation in the discharge current; however, the fluctuation in the intensity of the second positive system (which depends upon the vi- brationally excited ground state and the metastable molecules) was only on the order of 2%. Under these conditions the variation in the emission from atomic Hg was even smaller (<0.1%) which indicates that even with fluctuations in the populations of the N2(A) state molecules, the concentration remains much larger than the concentration of the Hg atoms.

D. Analysis with METAL. No complete systematic survey has been made to determine all the atomic and mo- lecular species that will react with metastable nitrogen. Wright and Winkler (4) compiled an extensive list of investigations where active nitrogen reactions induced light emission, and this included 38 metallic elements and 7 nonmetallic elements. Since the various systems were so different from the system used for this investigation, it is not clear that all of these elements can be excited by using the dielectric discharge afterglow.

Studies of the lines excited for Hg, Zn, and several other elements suggest that the energy available from the metastable nitrogen is primarily below about 8 eV. The zero vibrational level of the N,(A) is 6.17 eV above the ground state. While even nonresonant energy transfers to metal atoms appear to be efficient, there is a marked preference for the conservation of spin during the collision (14). Thus any element with an energy level below the 6-8 eV range should be excited espe- cially if a triplet state of the atomic species can be excited.

In order for energy transfer to occur, an element must be atomized and mixed with the metastable nitrogen. A wide variety of approaches to the atomization problem are appli- cable to this excitation system, but in this paper we will report only on the use of electrothermal filament atomizers which allow the analysis of aqueous solutions. While a number of elements have been electrothermally atomized and excited by the active nitrogen (34), only the results for Zn are included in this report. Figure 6 shows the intensity of light a t 468.0 nm as a function of time when 1 FL of 0.001 M Zn(NO& is atomized from the tungsten filament. The emission is re- corded automatically with a multichannel analyzer started 1.0 s before current is applied to the filament.

When Zn atoms are mixed with metastable nitrogen from the dielectric generator intense emissions at 307.6 nm and 468.0 nm are observed. As with Hg, the triplet levels of Zn are apparently populated preferentially (Figure 5) . No emission could be detected at 213.8 nm (from singlet state). The intensity of the 468.0-nm emission was measured as a function of Zn concentrations as shown in Figure 7. Various concentrations of Z ~ ( N O B ) ~ in deionized water were deposited (5 ILL) onto the filament, dried by passing low current through the filament, and then atomized with higher currents. The

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1284 ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981

8r

b 61

0 3

/

8 10 12 14 I6 Log Atom Density

Flgure 7. Intensity of Zn emission as a function of the amount of Zn atomized into the reaction chamber using filament atomizer. reproducibility of this process was f10% due primarily to variations in deposition, drying, and atomization from a light bulb filament. The METAL emission for Zn shows a large dynamic range extending from lo8 atoms cm-3 to 10l6 atoms cmS. These gas-phase concentrations are upper limits based upon atomizations of 5-jcL aliquots of solutions with con- centrations ranging from 2 x IOw3 to 2 x IO-" g of Zn/mL. While the calibration curve in Figure 7 is straight, it does not show a one to one relationship between Zn concentration and intensity. A nonunity slope has been observed by others using electrothermal atomizers (35). While the explanation of this behavior may involve several factors, the form in which the solute is volatilized can play an important role. Analyte re- actions with oxygen are important in decreasing the absorption signals when electrothermal atomizers are used, and the nitrate salts are an important source of oxygen (36). In this system the nonunity slope does not appear to be due to the excitation process but either to the electrothermal atomization process or to the transport of the atomized sample into and through the reaction cell. If the light bulb filament used to generate the data shown in Figure 7 is replaced by a simple V-shaped wire placed directly into the reaction cell a similar curve results, but the slope is much nearer unity (0.95 f 0.03). When the light bulb filament atomizer is placed in the reaction cell the slope is again low (0.72) suggesting that the analyte vapor released within the coil has more of an opportunity to react with oxygen before mixing with the active nitrogen.

Transport phenomena are clearly important in this system as they effect residence time in the reaction cell. Since the vaporized analyte diffuses in the carrier gas as it travels to the reaction cell, the atomic emission profile is spread over a longer time as compared to placing the filament directly into the reaction cell. The atomic emission intensity shown in Figure 7 was obtained by integrating over the relatively broad emission profile (about 0.5 9). The filament was refired in order to determine the system noise (from black body emission and photometric noise) and this was subtracted from the emission signal. The uncertainty in the background was of significance at the lowest concentrations. The amount of background subtracted may not have been large enough which could account for the apparent slope change a t the lower concentrations. Another explanation is contamination of the sample or some molecular emission especially since such a low-resolution monochromator was used. The background in this spectral region was very low so the dark current noise of the photomultiplier was significant.

The decrease in the slope of the curve a t higher concen- trations (10" Zn atoms ~ r n - ~ ) is most likely a result of quenching which results in a decrease in the metastable Nz(A) population. Linear atomic excitation assumes of large and constant excess of Nz(A). In cases where we tried a microwave discharge, a much lower concentration of metastable N,(A)

was produced and the linear range was limited to about lo9 Zn atoms (34). Evidence of quenching of the metastable at high atomic concentrations is the decrease in the intensity of the second positive band emission which also depends upon the high concentration of the Nz(A) metastable. For example, the atomization of 5 jcL of a 0.2 M ZII(NO,)~ solution halves the intensity of the principle second positive band emission at 334 nm. It should be kept in mind that some molecular species (such as NO) can also quench the metastable nitrogen so the matrix could affect the maximum concentration which would fall on the straight line portion of the calibration curve. The rate at which the active nitrogen in the reaction chamber is replaced affects the degree of quenching. In these studies the active nitrogen flows a t a rate which should replace the nitrogen in the reaction cell every 0.2-0.5 s. When the larger Zn samples are atomized the emission is observed upstream in the flowing active nitrogen which indicates that diffusion is more rapid than the rate at which the sample is being pumped out of the reaction cell.

D. Interferences. The utilization of metastable energy transfer for atomic luminescence in complex materials requires a proper understanding of the nature of the spectra and chemical interferences to be expected in the excitation- emission process. The source of the spectral interferences may be the metastable nitrogen generator itself or the other ele- ments in the sample matrix.

The dielectric discharge generator can interfere with the atomic analysis if there is spectral overlap of the atomic emission sought and the second positive band system present in the afterglow. This interference is inherent with this atomic excitation process; however, it is only a problem in a limited region of the visible spectrum. Unlike the afterglow produced by a microwave discharge which includes weak emission from 300 to 400 nm and intense emission extending from 450 to 700 nm, the dielectric discharge afterglow emission is confined to a few bands in one spectral region from 300 to 400 nm (Figure 4). Spectral interferences from the sample matrix are less of a problem with this chemiluminescent emission source than with other atomic emission sources because fewer atomic lines are excited due to the low energy and selectivity inherent in the metastable energy transfer process.

The sample matrix is a potential source for interference to the quantitative measurement of the atomic emission. The matrix interferences may be manifest through quenching in- teractions with the metastable species in the reaction cell or through chemical interactions with the analyte during the sample atomization from the metal surface of the atomizer heater. In the latter case, since similar atomization methods are used in this atomic emission source as in flameless atomic absorption analysis the same phenomena observed for sample atomization are also operative (35,36). Any number of sample atomizers might be used (e.g., microarc, boats, hydride gen- erators) with the exception of graphite furnaces which may cause excessive quenching and production of cyanogen bands.

With this system there is the added complication of the possible preferential quenching of the exciting species by components in the sample matrix. I t is assumed that the chemiluminescent reaction is pseudo first order in the con- centration of the atoms (M): I = k[M]. The reaction constant k does include the concentration of the metastable nitrogen, assumed to be Nz(A): k = kTNz(A)]. As long as the con- centration of the metastable species is not diminished ap- preciably (for instance by more than 1%) by matrix species acting as quenchers, the assumption of pseudo-first-order kinetics should hold, The dielectric discharge generates a large metastable population and although its actual concentration can not be measured it has been estimated in two ways. One approach has been to use curves such as Figure 7 in order to

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ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 1285

the results for high Zn concentrations shown in Figure 7 in- dicate that the metastable concentration in the afterglow is large enough to cope with the relatively high populations of metastable quenchers that might be introduced along with the sample.

There have been no extensive attempts to carry out mul- tielement analysis using this technique, but such an analysis should be possible with an appropriate optical detection system. In one experiment with the Z ~ I ( N O ~ ) ~ solutions, it was found that there was emission at 253.7 nm. This was found to be from Hg and the impurity in the original Zn(NO& solid was calculated to be 90 ppmHg.

determine the concentiration above which the slope decreases since this change is interpreted as being caused by a significant depletion in the metastable population. In these approxi- mations it has been aeisumed that all the metal is atomized and that only metal atoms cause quenching of the active nitrogen. It is recognized that neither assumption is correct, but the errors do tend to cancel. If some of the metal is released from the filament in the molecular form, it can still quench the metastable nitrogen. The estimate that a 10% deviation in the slope of the calibration curve is due to a metal atom concentration that is 10% of the population of the active nitrogen is a conservative approximation. It is assumed that the metal released from the filament fills the entire reaction cell uniformly. There is most likely a localized depletion of active nitrogen near the filament and, especially in cases where the filament is in front of the spectrometer slits, this may cause deviation from the slope at even lower metal concentrations. It is interesting that using a variety of solutions (different metal cations and different anions) and several filament configurations, the estimate of metastable nitrogen concen- tration always falls within the range of 5 X 10l6 to 9 X 10l6 metastables cm-3 at a pressure of 7 torr. The other approach, noted earlier, was the atomization of large concentrations of metal atoms while monitoring the second positive band emission. Since the population of the NZ(C) state depends upon the concentration of the N2(A) (or if the energy pooling process is important the C state concentration depends upon the A state concentration squared) a decrease in the 2P emission is attributed to a decrease in the Nz(A) molecules. Several types of samples have been used and all give about the same results. For example the 5 p L of 0.2 M ZII(NO~)~ solution dried and atomized should have given about 6 X 10'' Zn atoms (or some ma:y have been in a molecular form that would still cause quenching) in the 10 cm3 reaction cell. The 2P emission decreased by half suggesting that there were at least lo1' metastable niolecules cm-3 at a pressure of 7 torr. While neither approach is absolutely correct it does appear that a substantial fraction of the nitrogen (>1%) is in an excited state. The dielectric discharge generates a sufficiently large metastable population (estimated to be at least 10'' molecules ~ m - ~ ) so that the effect of matrix quenching is greatly reduced. Interference with the metastable formation process by matrix components (e.g., H20, COz) does not occur since the exciting species are formed in the discharge tube and travel to the reaction cell where the atomic excitation occurs. In contrast, the metastable species in the microwave discharge afterglow region are being formed through nitrogen atom recombinations with subsequent radiative decay from high vibration levels of N,(B). The presence of a third body, e.g., atomic species from tho sample matrix, during the recombi- nation of nitrogen atomls to form N,(A), dramatically affects the metastable nitrogen concentration in the microwave discharge afterglow.

The excitation process in the reaction cell depends upon the collisionally induced exchange of electronic energy between the metastable nitrogein and the atomic species. Each ex- change of energy and subsequent emission of light occurs independently of the nature of the other species in the aft- erglow. The only potential problem would be production of so many atoms or queniching molecules that the metastable N&A) became the limiting reagent. The atomic species from the sample matrix most likely to cause quenching of the metastable nitrogen are! nitrogen atoms, oxygen atoms, and fragments with a nonbonded electron pair or a low-lying triplet state (e.g., ammonia) since these species have been shown to be exceptionally efficient metastable quenchers (e.g., 16,37, 38). The observation of the same emission intensity for Zn solutions made up in urine, KCl solution, and water along with

CONCLUSION It is common for the description of a new analytical tech-

nique to include the suggestion that the new method is the solution to all analytical problems. In this case, it should be remembered that this chemiluminescent detector is designed to compliment the existing techniques for trace metal analysis. The principal advantages of this detector are its extreme sensitivity and low spectral background. Since this is an emission process, it is more suited to trace analysis than ab- sorption spectroscopy in that a small positive signal is being measured against a relatively low background in contrast to the much more difficult measurement of a small difference between two very intense signals. However, the luminescent detector lacks some of the selectivity inherent in atomic ab- sorption or resonance fluorescence although in most cases simultaneous multielement analysis should be possible. The diffuse emission associated with chemiluminescence occurs in a large active volume from which photons may be collected; and when the exciting species is maintained in sufficient excess, multiple excitation-emission sequences can occur throughout the reaction chamber thereby increasing the ob- served emission intensity.

Like atomic absorption, the atomization process is separate from the excitation process; however, in most atomic emission sources the atomization and excitation processes are the same due to the high energy used for the atomic excitation. This high excitation energy produces a complex atomic emission spectrum with numerous lines present for each element. As an atomic emission source for the low-temperature excitation of metallic spectra, this chemiluminescent detector has less complex emission as well as a lower spectral background than a flame, a microwave torch, or an inductively coupled plasma. Further, the requirements for chemiluminescence confer a degree of specificity while the negative interference of quenching is predictable and can usually be accommodated.

The need for ultratrace metal analysis in biological and environmental systems is well established and reviews (39,40) of existing techniques indicate that they are a t best satis- factory. The increased use of fossil fuels and organometallic combustion catalysts makes the development of a gas-phase ultratrace metal analyzer desirable for monitoring pollution levels. Data from the prototype instrument clearly indicate that an active nitrogen catalyzed chemiluminescent detector would provide the needed low limit of detection for this and other ultratrace metal analytical applications. The dielectric discharge generator also affords a large dynamic concentration range for metal analysis thereby permitting sub-part-per- billion to part-per-hundred gas-phase concentrations to be measured directly without dilution in the same instrument. Since the active nitrogen generator can be run a t higher pressures, direct atmospheric sampling is no problem. Finally, the low cost for building and operating this system make it attractive for many applications.

LITERATURE CITED ( 1 ) Strutt, R. J. Proc. R . SOC. London 1911, 85, 219-229. (2) Golde, M. F.; Thrush, 6. A. Rep. Prog. Phys. 1973, 36, 1285-1293.

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1286 Anal. Chem. 1981, 53, 1286-1291

(3) Meyer, J. A.; Setser, D. W.; Clark, W. G. J. Phys. Chem. 1972, 76, 1-9.

(4) Wrlght, A. N.; Winkier, C. A. “Active Nttrogen”; Academic Press: New York, 1968.

(5) Meerk, T. D.: Oskam, H. J. Int. J. Mass. Smctrom. Ion Phvs. 1972. . . 9(4), 387-395.

(6) Capeile, G. A.; Sutton, D. G. Appl. fhys. Lett. 1977, 30, 407-409. (7) Capeiie, 0. A.; Sutton, D. G. Rev. Sci. Instrum. 1978, 49,

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(11) Duthier, C. J.; Broida, H. P. “Chemiluminescence and Bioluminescence”; Lee, J., Hercules, D. M., Comeir, M. J., Eds.; Pie- num: New York, 1973.

(12) Yamashita, T. Sci. Light(Tokyo) 1972, 21, 44-52. (13) b u g , R.; Rappenecker, G.; Schmidt, C. Chem. fhys. 1974, 5 ,

(14) Duthier, C. J.; Broida, H. P. J. Chem. fhys. 1973, 59, 167-174. (15) Young, R. A.; St. John, 0. A. J. Chem. Phys. 1967, 48, 2572-2574. (16) Baker, R. R.; Jacob, A.; Winkier, C. A. Can. J. Chem. 1971, 49,

(17) Thrush, 8. A.; Wild, A. H. J. Chem. Soc., Faraday Trans 2 1972, 68,

(18) Shemansky, D. E.; Cartton, N. P. J. Chem. fhys. 1969, 51, 689-700. (19) Davis, J. A. Ph.D. Thesis, University of Virginia, 1980. (20) Pearse, R. W. B.; Gaydon, A. 0. “The Identification of Molecular

Spectra”; Chapman Hall: London, 1950.

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(21) Suchard, S. N., Meizer, J. E., Eds. “Spectroscopy Data ”, Plenum: New York, 1976; Voi. 2.

(22) Stedman, D. H.; Setser, D. W. J. Chem. fhys. 1969, 50, 2256-2258. (23) Hays, G. N.; Tracy, C. J.; deMonchy, A. R.; Oskam, H. J. Chem. fhys.

Lett. 1972, 14, 352-355. (24) Ung, A. Y.-M. Chem. Phys. Lett. 1975, 32, 193-196. (25) Stedman, D. H.; Setser, D. W. Chem. Phys. Lett. 1966, 2 , 542-544. (26) Gross, R. W. F.; Cohen, N. J. Chem. Phys. 1966, 48, 2582-2588. (27) Oldenberg, 0. J . Opt. SOC. Am. 1971, 61, 1092-1098. (28) Young, R. A.; St. John, G. A. Adv. Chem. Ser. 1969, No. 80. (29) Stevens, R. K.; Hodgeson, J. A. Anal. Chem. 1973, 45, 443A-449A. (30) Lampert, M. A.; Mark, P. “Current Injection in Solids”; Academlc

Press: New York, 1970. (31) Borst, W. L.; Weiis, W. C.; Zipf, E. C. Phys. Rev. A 1972, 5 ,

1744-1747. (32) Borst, W. L.; Chang, S. L. J. Chem. Phys. 1973, 59, 5830-5836. (33) Borst, W. L. Phys. Rev. A 1972, 5, 648-656. (34) Dodge, W. 8. Ph.D. Thesis, University of Virginia, 1980. (35) Kawaguchi, H.; Atsuya, I.; Vaiiee, B. L. Anel. Chem. 1977, 49,

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RECEIVED for review May 22,1980. Accepted April 22,1981. Presented in part at the 1978 FACSS-V Meeting, Boston, MA.

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Uncertainty in Calculated Values of Uncomplexed Metal Ion Concentration

Richard J. Stolzberg Department of Chemistty, University of Alaska, Falrbanks, Alaska 9970 7

A function descrlbing the minimum uncertainty in calculated values of the negative logarithm of the uncomplexed metal ion concentration (pM) has been derived for the interaction of a metal Ion wlth a single ligand to form a strong complex. Two factors have been considered: the uncertainty of measured metal and ligand concentrations and the uncertainty of the values of thermodynamic constants. This function can be used as an aid in deslgnlng and interpreting experiments where the uncomplexed metal ion concentration (rather than the total metal concentratlon) is the variable of interest. Representative calculations have been made for solutions where both the metal and llgand are present at trace levels. Uncertalnty In calculated pM values typically will be between 0.2 and 1 pM unit for solutions prepared In the laboratory and will be slgnlflcantiy larger when equilibrium calculations are applled to natural waters.

Interactions between metals and ligands form the basis of a number of challenging problems in environmental and analytical chemistry. Many of these are based on an interest in bioavailability and transport of metals and in models used to calculate the chemical speciation of metals at equilibrium. The importance of chemical speciation of metals has been recognized for over a decade. It is now known that the bioavailability of a metal is not regulated by its total con- centration but usually by the concentration of the uncom- plexed species (1, 2). Sorption of metals onto particulate matter, and therefore metal transport, also depends on metal speciation (3).

Recognition of these facts has led to the development of methods for calculating the concentration of uncomplexed and complexed species of metal in solution. Some are sophisticated computer programs (4 ,5) . Others rely on the use of chemical intuition and valid simplifying assumptions so that approx- imate values may be calculated easily (6, 7).

Experimental verification of the accuracy of calculations of this type has rarely, if ever, been done for a natural water system. This is due in part to the difficulty in measuring the true concentrations of metal species present in trace quantity (8). This is unfortunate since an estimate of the uncertainty of these calculations would aid in interpreting experimental results.

Since experimental verification of the reliability of calcu- lations is impractical, a theoretical approach is necessary. In this paper we have taken a first step by deriving a simple function which can be used to calculate the minimum expected value of pM, the negative logarithm of the uncomplexed metal ion concentration, when the total concentrations of the metal and ligand are small. We have considered only two sources of error: the inherent uncertainty in analytical concentration measurements and the uncertainty in the thermodynamic constants used. These factors are present in all systems and are independent of the computational technique. Other factors, such as the nonequilibrium state of natural waters and sorption or precipitation reactions can also be important. Therefore, the values calculated here are conservative esti- mates and must be considered a minimum.

Ringbom’s conditional constant method (9) has been used to calculate an expression for pM. This equation has been treated mathematically, using a propagation of variance ap-

0003-2700/81/0353-1286$01.25/0 0 1981 American Chemical Society