Anal. Chem. 1980, 52, 473-482
473
Improved Model of the Pulsed Electron Capture Detector P. L. Gobby, E. P. Grimsrud," and S. W. Warden Department of Chemistry, Montana State University, Bozeman, Montana 597 17
A physical model of the pulsed electron capture detector (ECD) for gas chromatography is described. This model ditfers from previous models in that the Incorporation of electrostatic forces between charged particles is shown to be a dominant force in determining the concentrations and location of charged particles within the ECD. The model applies to an ECD in which ionization by p radiation occurs evenly throughout the cell, a condition which is applicable to "Ni detectors of cylindrical geometry. Important aspects of this model include the following: (1) All thermal electrons are removed from the cell to the anode during the application of each pulse. (2) The corresponding positive charge created in the cell by electron removal tends to dissipate itself by space-charge-driven migration to all grounded surfaces of the cell during the period (3) The thermal electrons produced between pulses. throughout the cell during the period between pulses are concentrated in a localized zone in which charge neutrality exists (plasma). The sire of this plasma increases with time after the pulse. Two dlstinct regions of charge character are, therefore, thought to exist-a charge-neutral plasma and a region of positive charge completely void of electrons. This positive ion sheath separates the plasma from the cell boundaries and decreases in size with time after the pulse. (4) Positive ion density remains relatively constant throughout the 63Nipulsed ECD. This is because the loss rate of positive ions from recombination in the plasma is approximately equal to their loss rate by space-charge-drlven migration in the positive ion sheath reglon. New experimental tests of ECD events are reported and discussed relative to the model. The implications of new physical insights of the ECD provided here for its analytical applications are discussed.
Since its introduction some twenty years ago to the area of trace organic analysis, the electron capture detector (ECD) for gas chromatography has undergone several instrumental refinements. Perhaps the most important improvement made since the earliest days of the direct-current ECD occurred with the introduction of the pulsed mode of current measurement (1). In common use today is a further refinement of the pulsed mode, the variable-frequency or constant-current ECD ( 2 ) . It possesses the essential features of a good gas chromatographic detector: good sensitivity, stability, and a wide linear dynamic range. Another desirable characteristic of the pulsed mode is that the basis of its response to samples has been thought to be more completely understood than that of the dc mode. This has prompted the analyses of certain compounds using the measured response, directly, without calibration standards (3-6). Very recently, new applications of the pulsed ECD have been described where the responses observed are thought to result from negative ion-molecule reactions which indirectly affect the free electron concentration (7-20). As these and presently unforeseen sophistications are added to the already proven worth of the ECD, corresponding increases in our understanding of the basis of its response become desirable. Alongside the above analytical developments, a physical model of the pulsed ECD has evolved, largely owing to the 0003-2700/80/0352-0473$01 .OO/O
research of Wentworth and co-workers (11,12) who have used the ECD primarily for the fundamental studies of electron attachment reactions in the gas phase. The Wentworth model has been used successfully to explain the ECD response in many practical and fundamental applications, and has been used as the starting point in explaining the basis of new analytical configurations (references 2 and 3, for examples). A few characteristics generally associated with the Wentworth model which will be specifically addressed in this article are the following: (1) The negative current one measures with a pulsed ECD is due to the collection at an anode of all of the electrons in the cell during the application of short pulses. Positive and negative ions are relatively immobile and contribute little to the measured current. (2) Positive ions are always in large excess over electrons because of point 1, and also because during the period between pulses, their free diffusion to the cell boundaries is much slower than that of electrons. Because they are present in large excess, the concentration of positive ions within the ECD will remain relatively constant. (3) The ECD is assumed to be a well-mixed reactor where one concentration expression describes the presence of each species throughout the cell. (Concentration gradients are recognized to exist if spacially uneven ion-pair formation is caused by the /3 radiation.) Siegel and McKeown (13) have recently argued that the omission in previous ECD models of the effects of electrostatic forces between charged particles is not justified, and that these forces are sufficiently strong as to affect the concentrations of all charged species within the ECD. Siegel and McKeown demonstrated that in a field-free ionization cell, such as exists in their ECD-like, atmospheric pressure ionization mass spectrometer (APIMS), that overall charge neutrality will be maintained owing to the attractive forces between oppositely charged particles. They argued that the tendency of spacecharge effects to maintain charge neutrality within the ECD should be an integral assumption in any complete ECD model. Recently, Grimsrud, Kim, and Gobby ( 1 4 ) presented evidence which supported some of the concepts of the Wentworth model, but also demonstrated the importance of space-charge dynamics. By a combination of APIMS and ECD measurements, it was shown that in the pulsed mode, the applied pulse probably does remove all electrons from the cell resulting in a momentary excess of positive ions. However, during the period which follows the pulse, it was shown that space-charge interactions of positive ions with themselves and with negative ions and electrons strongly influence the fate of all charged particles. If the period between pulses is sufficiently long, a condition approaching charge neutrality as described by Siegel and McKeown was attained. Furthermore, these experiments suggested that the measured negative ECD current cannot necessarily be attributed to the collection of electrons alone. I t was shown that the positive space-charge force created by removal of electrons during the pulse causes the migration of positive ions to the cell boundaries during the period between pulses. A fraction of these excess positive ions strikes the anode (which is at ground potential between pulses) and causes a reduction in the time-averaged negative current indicated by the electrometer. In this article, a new description of ECD events is developed which is initiated at a point resulting from the insight provided C 1980 American Chemical Society
474
ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
by all of the ideas described above. This view is developed from basic principles where possible, and is tested against new experiments reported here. The model will be shown to be in harmony with the many tests successfully applied to the Wentworth model, because it leads to mathematical expressions for the time dependence of the electron population which is of the same general form as those derived from the Wentworth model. In spite of its similarities to the Wentworth model, however, this model results in significant differences which are of importance to certain analytical applications of the ECD, and will assist the future development of other high pressure ionization methods for trace organic analysis. The model developed here should be most directly applicable to the increasingly popular 63Nidetectors of cylindrical geometry.
THEORETICAL In the development and discussion of this model, a rather large quantity of notation will be necessary. The majority of the symbols will be defined a t this time. Only a few others will be defined as necessary in the text. It should be noted that throughout the theoretical development, the SI system of units is employed exclusively. However, in discussions of results and experiments, values for number densities will be quoted in terms of mL-' instead of the more cumbersome m-3. T h e symbol will be used to denote number densities, with subscripts e, +, -, or A denoting electrons, positive ions, negative ions, or sample molecules, respectively. Other symbols include: n e t charge density equilibrium positive ion density in plasma v+ O equilibrium thermal electron density in a sam'le ple-free plasma total n u m b e r of thermal electrons in E C D Ne e electronic charge (1.6 X C) t permittivity of medium (8.8 X F/m) J' current density U electrical conductivity E electric field K ion mobility S ion-electron pair production rate via ionization by 63Ni Vo total active volume of ECD R positive ion-electron recombination rate constant kA electron a t t a c h m e n t r a t e constant for species A T pulse period I instantaneous electrical current (I) time-averaged electrical current T h e main objective of this article is to present a more complete physical picture of the charged particles within the ECD. T o relate this model as clearly as possible, only the essential chemical events required to adequately describe an ECD response will be considered at this time. The chemical events t o be included here are: (la) 63Ni-inducedionization of neutrals to produce positive ions and electrons, (lb) positive ion-electron recombination, (IC)irreversible electron attachment by electron capturing species A to form negative ion B-, and (Id) destruction of negative ions via recombination with positive ions.
-2%
S
neutrals
P+ + e-
-
+ e-
(la)
neutrals
(1b)
pt
R
kA
e-
+ A B- + neutrals R P+ + Bneutrals
-
(IC)
(Id)
T h e rate constant for recombination reaction Id will be assumed to be approximately the same as the rate constant for
positive ion-electron recombination. This point has been considered in detail by Siegel and McKeown (231, and will be addressed further below. The neutral products of reactions Ib-ld are assumed to be incapable of further electron attachment. A relatively small fraction of A will be assumed to undergo electron attachment while A passes through the cell so that its concentration, qA, will be constant. We begin by considering the ECD described by Siegel and McKeown (13)with only clean carrier gas flowing through it and no fields applied. Under this condition, an essentially uniform plasma exists, consisting of electrons and positive ions in equal numbers diluted in a huge excess of neutral carrier gas molecules. Overall charge neutrality exists because a t the high ionization densities present in the ECD, the diffusion rate of all charged particles, positive ions, and electrons, will be described by one ambipolar diffusion coefficient (13). I t is assumed in this treatment that positive ion-electron pair formation is caused approximately uniformly throughout the cell by /3 radiation of "Ni. This assumption is reasonable because for our cells, 63Ni-impregnated platinum forms the cylindrical wall of the cell, and each p leaves a trail of ion-pairs where the point of maximum ionization in one atmosphere of nitrogen is calculated to occur a t a distance equal to about one half the diameter of our cells ( 1 5 ) . In clean carrier gas, the steady-state concentrations of positive ions and electrons will be controlled primarily by reactions l a and l b . Other possible loss mechanisms for ions and electrons besides recombination reaction I b , such as free diffusion to the walls or ventilation through the cell, have been shown to be insignificant relative to recombination in the field-free condition (13). T h e rate of change in positive ion or electron concentration within the plasma is then described by
Applying the steady-state assumption to Equation 2 and recalling that v+ = qe, the equilibrium concentrations of these species in the field-free ECD are calculated from Equation 3 for the no-sample condition. 8+O =
veo=
fi
The total W i activity of each ECD cell used here is 9 mCi. If one assumes that about one half of the ps are lost into the cell walls causing no ionization, and that the average energy of the @sis 17 keV (this approximation is made in reference 13, the maximum /j'energy being 67 keV (16)),and one charge pair per 35 eV is created (17), a value for S = 8.1 x 10" s-l is obtained. For our cells V, = 1.1mL. Choosing R = 3 X lo4 mL s-l (It?), the value used by Siegel and McKeown, v+O and ~2are calculated to be about 1.5 X lo8 mL-' throughout the ECD. (Of course, within a very small distance from all cell boundaries, v+ and ve must reduce to zero, owing to neutralization on the conducting surfaces. Because recombination losses of electrons and positive ions are fast relative to diffusion, however, the size of this region having nonuniform vi can be assumed to constitute only a small fraction of the entire ECD volume). When sample is added to the field-free ECD, reactions IC and I d must also be considered. If the rate of positive ionnegative ion recombination is also equal to R , the new equilibrium positive ion concentration will also be equal to v + O , since the rate of positive ion loss by recombination will be unchanged. Also, preserving charge balance, this assumption for reaction I d leads to v+' = ve + q-. We have measured total q+ and 7- in a field-free ECD under clean and sample-saturated conditions (91, and have found these mea-
ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
surements to strongly support the above approximations for the field-free condition. Returning to the no-sample condition, we now consider the disruption of this equilibrated plasma caused by a positive voltage pulse (-50 V, - 2 ps) applied to an electrode pin cent,ered within the active volume. The electric field produced during this pulse is sufficiently strong so that all thermal electrons are collected. The massive and relatively immobile positive ions, however, are essentially unaffected during the short pulse. The field resulting from the positive space charge left behind tends to hold electrons back from the pin. Previous calculations (14),however, show that the field due to the pulse actually exceeds the maximum space-charge field, so that all electrons will indeed be collected. Moreover, in the Experimental section we show new data which unambiguously support this claim. Therefore, immediately after the pulse, there exists an approximately uniform distribution of positive charge in the ECD with the walls and pin again at ground potential. During the period after the completion of the pulse, positive ions will tend to migrate through the positive space-charge field they generate to all grounded surfaces-the anode (which is now held a t ground potential), as well as the walls. The new set of electrons being created by p radiation will move in the opposite direction along the E field. This migration is governed by the continuity equation (19),
7-J+ ap/at
=0
(4)
which is the mathematical statement of conservation of charge. 0.J denotes the divergence of the current density, J , and p is the excess positive charge density, (v+ - ve)e,at any point. Equation 4 is exact and completely general. Consequently it applies to the ECD even when the ongoing ionization process is considered-a process which continuously provides additional electrons and positive ions in equal numbers. For electric conduction in gases, J is related to the electric field, E , by
J = (Kv++ K,q,)eE
(5)
where K is the positive ion mobility, K , is the electron mobility, and e is the electronic charge. However, since the electron mobility in an E field (20) is orders of magnitude greater than ion mobility ( K , I 103K),electrons will be swept away from any region experiencing a field in a time which can be considered instantaneous relative to the time in which significant ionic motion will occur Gust as electrons, only, are removed from the plasma during a short voltage pulse). Thus, as will become more evident below, it is useful to consider the motion of the positive ions, separately, in a volume which is envisioned to be continuously swept free of electrons. T o consider the motion of positive ions in an electron-free environment, let us consider for the moment, the hypothetical situation in which the p radiation is turned off immediately following a pulse when positive ions, only, are present. This exercise will be useful in developing equations to be used later, and also will provide a qualitative feeling for the rate with which the excess positive charge dissipates itself by spacecharge migration. We then have J = KpE where now p = v+e. Substituting for the first term in Equation 4 and applying a vector identity, we find
0.J = KpO.E+ K E - O p (7) But from Gauss’ law, O.E = p / t . Consequently, the continuity equation becomes
If the charge density is uniform,
Op = 0
and Equation 8
00
0
7
2
3
4
5
6
7
475
8
Time ( ms) Figure 1. Relaxation of excess positive charge, p , with time as calculated from Equation 10. I+ is the instantaneous current caused by the migration of this charge to any imagined container. Initial positive ion density is assumed to be v+O = 1.5 X IO8 mL-‘. A value for ion mobility of 2.0 cm2 V-’ s-’ is used
simplifies dramatically. For our case, p is uniform at least initially after the pulse. In order to maintain mathematical simplicity in describing this hypothetical case, the term involving O p will be neglected. (When we use an extension of this equation later for the complete model to be developed, this approximation becomes especially reasonable because the ionization process which is then added produces positive ions uniformly in space.) Our continuity equation is then Kp2/t
+ ap/at
=0
(9)
The solution to this differential equation is
where po is the charge density at t = 0. With Equation 10, one can calculate for the situation under consideration, the rate at which the positive charge would escape by space-charge driven migration out of any imagined volume. The expected change in charge density with time is shown in Figure 1,where the initial positive ion density has been assumed to be v+O, previously calculated. It is seen that only a few milliseconds are required for the bulk of the excess positive ions to be expelled. This time is very short relative to the residence time of the carrier gas molecules passing through the cell (about 1 s) and clearly suggests the fate of the excess positive ions. Also shown in Figure 1 is the dependence of the instantaneous current, I+, due to the positive charge migration to any imagined container. I+ is obtained from the slope of the plot of p with time since a p / a t is proportional to current. Figure 1 indicates that the current reflecting positive charge relaxation follows the electron-removing pulse even more rapidly than does the change in p , itself. While the above treatment is useful for illustrating the relatively short amount of time required for the relaxation of positive charge following the removal of electrons, a complete model of the ECD must also take into account the ongoing ionization process. By making what appears to be a reasonable approximation of this process, it will be shown that this situation is not unduly complicated. The geometry of the cell chosen for the discussion to follow is an approximation of that used in the experiments to be described. Consider a single ionization event occurring shortly after the termination of the pulse, while a positive space-charge E-field exists in the ionization volume owing to the presence of excess positive ions. For the conditions existing in our ionization cells, the potential across the cell cross-section is
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
Radius ' m T!
Figure 2. Calculated electrical potential due to the presence of positive ions and electrons within our cylindrical ECD as a function of distance, r , from the center of the central electrode at various times after an electron removing pulse. All potential curves were calculated in the same manner. The positive ion density is assumed constant at q+ = 1.5 X lo8 mL-' throughout the cell. All electrons in the cell at the times indicated are assumed concentrated in the region of highest potential creating a plasma in which electron density equals that of the positive ions. The cell volume is then divided into three annular regions: the sheath of positive ions between the pin and the plasma, the plasma, and the sheath between the plasma and walls. Using Gauss' law and assuming infinite cylindrical geometry, the electric field was calculated in the two sheath regions subject to the constraints that E = 0 in the plasma and V = 0 at the central pin and the walls. The potentials were E d r . The radii of the plasma-sheath then calculated from V ( r ) = interfaces thereby deduced are indicated on each curve. For curve A where the cell is void of electrons, this treatment reduces to Equation 1 of reference 14. The central pin is shown as the shaded area below r = 0.79 m m
Figure 3. An illustration of the condition thought to exist in the ECD at a time corresponding to curve B of Figure 2. Since the prior pulse, all electrons created by p ionization throughout the source have migrated instantly to the plasma-sheath interface, which thereby grows with time
-s
c 2n- L
L
,
-
2
i
shown as curve A of Figure 2. The region of maximum potential is a region of minimum potential energy for the electron which feels a force toward that region. Just as electrons move to the anode during the pulse, it is reasonable t o assume t h a t the electrons created between pulses move instantly to the region of maximum potential. The parent positive ions left behind become just another part of the positive charge of that region. This is all reasonable because K , >> K. As more ionizations occur, the region of maximum positive potential will become electrically neutral as more and more of the electrons released during ionizations flock to this region of maximum potential. At various times later during the same period, the potential will qualitatively begin to look like curves B-E in Figure 2. An illustration of the condition thought to exist a t a time corresponding to that of curve B is shown in Figure 3. T h e regions of maximum, but constant, potential shown in Figure 2 for various times after the pulse will contain an electrically neutral plasma in which an electric field no longer exists. All of the electrons released via ionizations throughout the cell since the last pulse go there and, therefore, the size of t h e plasma increases with time. T h e events which occur within this main volume of plasma will be similar to those described previously for the field-free ionization cell. Positive ion and electron concentrations will be equal and constant within the plasma region. The steady-state concentrations of each within the plasma tend toward q+O = qeo = 1.5 X 10' mL-' as calculated from Equation 3 for the no-sample condition. We will now consider how this ionization process affects the regions surrounding the plasma where excess positive charge resides. We call this region which separates the plasma from grounded surfaces, the positive ion sheath. The ionization process is assumed to occur uniformly throughout the
3
Time ( m s ) Figure 4. Calculated positive ion densrty, T+, in the sheath as a function of time following the removal of all electrons by a pulse according to Equation 12. The initial value of q+ is assumed to be T+' = 1.57 X l o 8 mL-'. The units of the mobility values, K , are cm2 V-' s-'
ECD volume. Since the electrons released through ionization within the positive ion sheath immediately leave the sheath, ?le remains zero in the sheath. The net effect of the ionization in these regions is to create positive charge density a t a constant rate. This situation can be described by altering Equation 9 t o
ap/at =
Se --
VO
Kp2/c
where e is the electronic charge, and S e / V , is thus the charge density per second being created in the sheath due to /3 ionization. T h e solution to Equation 11 is obtained by direct integration.
where CY = x / K S e / V , t , and po is the charge density immediately following a pulse ( p o = q+Oe). Equation 1 2 gives the charge density in the sheath surrounding the plasma as a function of time, where the time is measured from the instant all the thern.al electrons are removed by a pulse. (As previously mentioned, this sheath is shrinking in size as the plasma grows.) Since only positive ions exist in the sheath, q+ = p / e in the sheath. It is then possible to calculate the positive ion density, rl+, as a function of time after the pulse. This is done in Figure 4 for three
ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
different values of ion mobility. For each case, values for other constants, R , Vo,and S , are the same as used in Equation 3. Two values of mobility, 1 and 3 cm2 V ' s ~ l bracket , the range of normally occurring mobilities (21). Two important points are clear from Figure 4: (1)q+ asymptotically approaches the equilibrium value in the sheath, q+', in a few milliseconds, where
( 2 ) q+s is not much different than q+O, for all values of K (this result will also depend on the accuracy of the value of R used here). One can now imagine how the positive ion density varies a t some arbitrary point in the ECD. Immediately after the electron gathering pulse the positive ion density, q+, starts to change towards q+3 because the ion loss mechanism has changed from recombination to space-charge-driven migration. But a t some time later, if the pulse period is sufficiently long, the plasma again grows to include this point. Now the electric field is again zero and the positive ion loss mechanism is again dominated by recombination. The positive ion density then moves back towards q+O. Because q+' = q+* and also because the time required for the achievement of one state following the other may be longer than the period between pulses, relatively little change in q+ with time a t any given point within the ECD may be expected. As indicated in our previous discussion of Equation 8, an exact treatment of ECD events would be difficult if charge density were non-uniform in the ECD. Fortunately, however, the special case of q+ = v+O = q+' (i.e., R = eK/c) appears to be a reasonable approximation to reality. With this assumption, analysis of ECD performance, even with repetitive pulsing, becomes tremendously simplified, since q+ is now a constant in both space and time. The major parameter which is changing with time for the no-sample condition is the size of the plasma which contains the electrons. One can now consider the ECD with sample present. Since all the thermal electrons are confined to the plasma, only in t h e plasma can negative ions be formed, and only in the plasma can electron loss by recombination occur. Consequently the rate equation describing change in the total electron population, Ne, will be
where V , is the instantaneous volume of the plasma, and qe is the electron density within the plasma. Since sample is present, qe < :7 and q+ = qe + 7- a t every point within the plasma. However, q- is not expected to be constant throughout t h e plasma, so q , will vary within V , also. Therefore, the integral of electron loss processes throughout V, is taken to obtain the instantaneous total electron loss rate. Note that Equation 14 indicates that thermal electrons are created via ionization throughout the entire volume of the ECD, while losses of electrons occur only within the plasma. Equation 14 is simplified greatly by the realization that N e = JqedV,, since all electrons are in the plasma. Since Rq+ and k*q, are constant values, Equation 14 becomes
where N e , only, varies with time. (Recall the positive ion density in the plasma is the same with or without sample and is assumed to remain constant a t about q+O.) In the region of the positive ion sheath, some negative ions may now be present, left over from the previous cycles of plasma growth into this region. Thus, the loss of positive ions
477
via space-charge-driven migration will be somewhat lessened, but this change is offset by the addition in the sheath now of positive ion-negative ion recombination. Thus, the overall loss rate of positive ions in the sheath should remain approximately unchanged, and the same steady-state positive ion density as in the no-sample condition is expected. For the case of R = e K / c , it can be shown that, in fact, q+ = q+O = q+* in the sheath with sample present. With the entire factor ( k A q A+ Rq+)constant, Equation 15 can be integrated to yield,
Equation 16 shows Ne,the total number of thermal electrons in the ECD, as a function of the time elapsed since the most recent pulse. If T is the time between pulses, the time-averaged electron current, ( I e ) ,will be given by
In order to obtain a complete expression for the observed ECD current, the contribution from space-charge-driven migration must also be considered. 'This positive ion current arrives between pulses, as opposed to during the pulses for the electron current, but in normal ECD operation the overall integrated (or time-averaged) current a t the pin is measured instead of the instantaneous current. Consequently, the measured ECD current may be less than Equation 17 would suggest. For simplicity in considering the positive ion current, we will return to the no-sample condition. I t is the K p 2 / c term of Equation 11 that represents the change in charge density due to ionic migration. In our q+* := q+O case, dp/dt = 0 in the sheath, so Kp2/t = Se/ Vo. Therefore, the instantaneous positive ion current to all grounded surfaces, I+, is
I+ = (Kp2/e)Vs = ( S e / V o ) V s
(18)
where V , is the instantaneous volume of the sheath and is the only quantity changing with time. An expression for V , is now needed. Free electrons created in the sheath go to the plasma-sheath interface whereupon sheath is transformed to plasma. The rate a t which the sheath decreases in volume will be equal to the number of electrons produced in the sheath per second divided by the density of positive ions in the sheath. Mathematically, this is
dt This differential equation integrates directly to yield
V , = V , exp (;s$ Substituting into Equation 18, we obtain
(
I+ = Se exp o);; As with the electron current, an expression for the time-averaged current is desired.
One can compare Equation 22 to Equation 17 which gave ( I e ) . For the no-sample condition Rq, + k A q A = RT+O,and from Equation 3, Rq+O = S/v+OV,,. Making these substitutions into
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
Equation 17 and recalling that q+8 = q+O, it is seen that (I,) from Equation 22 is equal to ( I , ) from Equation 17. We previously demonstrated how space-charge migration of positive charge to the walls is fast relative to ventilation. The equality of Equations 17 and 22 indicates that even within the very short time of one period, the number of positive ions which migrate to all walls will equal the number of electrons removed by the prior pulse. Therefore, positive charge does not build u p successively with each pulse. T h e result that (I,) = ( I , ) demonstrates a n internal consistency in the model. I t must be so since we ignored the effects of ventilation (with justification), and demanded charge conservation by beginning our treatment with the continuity equation (Equation 4). The addition of sample will in no way alter these original assumptions. Therefore, (I,) must equal ( I , ) in all cases, from the no-sample to the sample-saturated conditions. Consequently, Equation 17 can be used to calculate (I,) as well as ( I , ) for all cases. T h e effect of (I,) on the observed ECD current, ( I , ) , will depend on the geometry of the cell and the choice of which of the two ECD electrodes is to serve as the anode. The entire ( I , ) is measured a t the anode, but only a fraction, 6, of ( I + ) arrives at the anode. Since ( I e ) = ( I + ) ,the current observed a t a n anode will be An approximation of the fraction that goes to the central pin in our cell designs can be deduced from Figure 2 where infinite cylindral geometry is assumed. Curve A showed the potential a t t = 0, just after the electrons have been removed. At approximately r, = 2.57 mm, the potential is at a maximum. Positive ions outside ro will begin to move toward the walls, while those inside ro will begin to move toward the central pin. T h e positive ion current arriving a t the central pin between pulses will then be proportional to the cross-sectional area in the annulus described by the radius of the cental pin and ro. T h e fraction of the total area inside r = 2.57 mm is (2.572 O . 7 g 2 ) / ( 5 . O 2- 0.79*) = 0.25. Consequently for this particular geometry, approximately 1 / 4 of the positive ions go to the central pin. The net time-averaged current, ( I o ) ,arriving a t the central pin (if it is used as the anode) is, therefore, predicted to be ( I o ) = (1 - 0.25)(1,) = 0.75(Ie) (24) From Equations 23 and 17, the complete expression for the current observed with the pulsed ECD according to our model becomes
I t is noteworthy that the model developed here was based on assumptions different from those of Wentworth (1I). However, the expression for ( I , ) in Equation 25 is of the same mathematical form as that obtained from the Wentworth model, showr, generally in Equation 26.
S ( I o ) = -- [ l - exp(-LT)] LT where L is the rate of electron removal by all processes. Thus, though quite different in detail, the two models predict the same form of signal variation with pulse period, T . As one last step in this theoretical treatment, Equation 25 will be applied to the case of the frequency-modulated, or constant-current ECD. In that mode of operation, the frequency, f = 1/T, changes as sample enters the cell (or as q A changes) in a manner which allows ( I o )to remain constant. Inspecting Equation 2 5 , one notes that this will be accomplished only if
41 i Flgure 5. ECD cells used in this study. All cells have identical 9-mCi e3Nifoils, equal active volumes, and similar concentric electrodes. I n configuration A, the entire cell block is electrically isolated from earth ground. I n configuration 6,a second interior electrode, a two-pronged fork, is included. I n configuration C, a pulsed ECD constitutes, also, the ion source of an APIMS
where 2 is a constant. If f o is the frequency corresponding to no sample ( q A = 0), we then have
This result describes the well-known response of the frequency modulated ECD. The shift in the pulse frequency required to maintain constant current is proportional to the sample concentration over a large range of sample concentration. Note that the success of this mode of operation is consistent with and possibly dependent on our prediction that the positive ion density remain relatively constant with respect to time and space for all sample sizes.
EXPERIMENTAL Three different ECDs are used. Each is shown in Figure 5. The active volume of each is 1.1mL. The cylindrical wall of each is formed by a thin Pt cylinder onto which 9 mCi 63Niis embedded (New England Nuclear, Boston, Mass.). In each case, a '/16-inch stainless steel pin protrudes into the cell as shown via a ceramic feedthrough. The diameter of the cylindrical cells is 1.0 cm. Their length is 1.4 cm. For cell configuration A of Figure 5, the entire cell block was electrically isolated. The stainless tubes shown for carrier gas entrance and exit are attached to the flow system via glass tubing. The entire cell is suspended in an oven which controls its temperature. In configuration B, a second interior electrode protrudes into the active volume as shown. This electrode is a %pronged fork, also made of '/,,-inch stainless rod which has been filed flat on the sides nearest the cell wall. In configuration C, an ECD is shown which simultaneously serves as an ion source for an APIMS. This instrument has been described in detail elsewhere (14, 22). A small fraction of the carrier gas flows into an adjacent vacuum envelope by passing through a 25-pm aperture. This aperture is centered on a 5/8-inch Ni disk (Perforated Products, Inc., Brookline, Mass.) of 25-pm thickness which forms the terminating wall of the cell. The tip of the central pin is 3 mm from the aperture. The gas flow through this aperture is calculated to be 5-6 mL atm min-'. The total gas flow through this cell is 40-60 mL min-'. AU ECD circuitry was home-built. When currents are measured at the electrode which is also receiving pulses, the circuit shown in Figure 2 of reference 14 was used. When currents are measured at the electrode which is not being pulsed, the same electrometer configuration, minus the pulser and associated isolation capacitor, is used. In the dual-pin experiments using cell configuration B, a specialized pulser was constructed using conventional logic
ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
circuitry by which the firing of the second pin relative to the first was continuously variable over the pulse period. Positive and negative ion measurements are made with the specialized ECD/APIMS apparatus previously described (14). The total ion signal is detected by turning off the dc component to the quadrupole rods. This signal is obtained by the ion-counting technique. This signal is fed to a rate meter when a time-averaged ion current is desired and to a multichannel analyzer (Nuclear Data, Model 1200) when resolution of the ion signal with respect to time following the ECD pulse is desired. In all experiments, nitrogen carrier gas (Matheson, ultra high purity) was used at flow rates of 40-60 mL min-'. The carrier gas was further purified by passing it through a filter containing CaS04 and 5A molecular sieve. In some experiments a constant level of "column bleed" was desired. This condition was established using a inch x 10 f t stainless column packed with 10% SF-96 on Chromosorb W and an oven heated slightly above room temperature. Where the no-sample condition was desired, the gas chromatographic column was eliminated from the flow system.
RESULTS AND DISCUSSION T h e set of ideas which led to the model of the ECD developed here was first prompted by measurements previously reported ( 1 4 ) . Those measurements offer considerable experimental support of the model, and will be briefly summarized. In that study the measurement of ions within an ECD was made by the technique of APIMS where the source was modified to be an actual ECD, such as shown in Figure 5 , configuration C. By observing the dependence of positive and negative ion mass spectral signals on 50-V, 2-ys pulses applied to an anode centered within the source, the effects of these pulses on the movement of ions to the cell boundaries were deduced. With frequent pulses applied to the pin, negative ions formed in the small-sample conditions were held within the ion source gas and caused no APIMS signal, while positive ions were observed to move unimpeded to the cell boundaries. Since results were independent of the polarity of the pulse, these effects were attributed to a positive space-charge field existing during the period between pulses, and not to the field produced by the pulse itself. In a simple experiment in which the central electrode was pulsed negative instead of positive, a sizeable positive current was measured at the central pin. A consideration of the magnitude of this current suggested that it results from the migration to the pin 3f a significant fraction of the total excess positive ions during the period between pulses. I t was also shown that the interdependence of the mass spectral ion signals and the ECD pulses was greatly lessened by using longer pulse periods, apparently because the longer periods allow charge neutrality to be achieved during the latter portion of each period. Also, little or no interdependence of the APIMS signal and the ECD pulses occurred when the ion source was saturated with sample. In this condition, few electrons exist and a pulse of 2-ys duration would be expected to disturb very little the charge balance now maintained by positive ions and negative ions. All of these previous measurements provide qualitative support of the proposed model. We will now report additional measurements which test some of the more detailed suggestions of the model. The model began by assuming that all electrons in the ECD are removed to the anode during each voltage pulse. This has been a generally accepted point of the Wentworth model and is strongly supported by experiments such as those of Wentworth, Chen, and Lovelock ( I I ) , Devaux and Guiochon (231, and Simmonds e t al. ( 2 4 ) in which the effects of pulse width and pulse voltage on the measured ECD current were examined. However, in lieu of Siege1 and McKeown's description of a n ECD (13) from which one might infer that charge neutrality is maintained a t all times, this point has not been taken for granted. As an additional test of this central point, we have performed an experiment using a unique ECD
.c51 0
100 P'JLSE
23c F'HASE
479
-
300
L A S ILsec
Figure 6. Currents measured at the central electrode (pin 1) and the forked electrode (pin 2) of ECD configuration B (Figure 5)as a function of the time elapsed between the firing of pin 1 followed by pin 2. The period between the application of positive pulses for each pin is 300 ps. No-sample condition, 200 O C which was modified to include a second interior electrode as shown in Figure 5 , configuration B. The second electrode is a two-pronged fork having a surface area about twice that of the central pin. The two pins were electrically isolated from one another and from the grounded wall. Each pin had its own pulse generator and electrometer. The two pins were pulsed (+50 V, 2-ps width) with the same period (300 ps), but with a variable phase relationship. T h e results of this experiment are shown in Figure 6. The currents a t the central and forked pins, called 1 and 2, respectively, are plotted as a function of At, the amount of time between the application of the first pulse at pin 1 and the second pulse a t pin 2. Note that with At = 0, I , is large, while Z2 0. (The slight positive current a t pin 2 for At = 0 is due to positive ion arrival at this electrode between pulses.) As At is increased, ZIdecreases by an amount equal to the increase in Z2.With At 150 pus, the two currents are equal, and as At approaches T , pin 2 is essentially being pulsed first, and nearly the total negative current is measured a t it. Furthermore, it was observed that the magnitude of current measured a t pin 2 was largely independent of the polarity of the pulse applied to pin 1. The most obvious interpretation of these results is that a pulse (of the magnitude and duration used here) clears the ECD of all of its electrons. Other experiments were performed with a single pin ECD (Figure 5 , configuration A) which was modifed so that the current to the walls as well as to the pin could be measured. Figure 7 shows a plot of the negative current a t the central pin which is being pulsed positive, and also the positive current at the walls of the cell measured simultaneously as a function of pulsing frequency. Note that regardless of the pulse period, the two currents have equal magnitudes. This supports our claim of charge conservation within the ECD and the equality of (Z+)and ( I e ) . The sum of all negative and positive currents due to collection of electrons during the pulse and migration of excess positive charge between pulses is equal to zero. The number of excess positive ions being swept through the cell by carrier gas flow appears to be negligible, as originally assumed. In the experiment of Figure 7, the pin was pulsed positive. Consequently the current a t the pin consisted of the total electron current, (I,), minus the fraction, 6, of ( I + ) . The wall receives 1 - 6 of the total positive current. At T = 300 ps, the net positive current measured a t the wall was 2.8 nA, so 2.8 nA = (1- 6) ( I + ) . Now if the pin is pulsed negatively, instead, the electrons are collected a t the walls, while the central pin will receive its normal ration of positive ions, 6 ( I + ) . With negative pulses of T = 300 ys applied to the pin, the measured current a t the pin was +0.7 nA (point b in Figure 7 ) . From . both measurements, this measurement, 0.7 nA = & ( I + ) From e=
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 3 , MARCH 1980
I
c
F
Posit v e
pulse I
0
T I V E +1
PULSE
2
3
PERIOD ( m s e c )
Flgure 7. Currents measured at t h e pin and t h e wails of ECD configuration A (Figure 5 ) as a function of pulse period for the no-sample
condition, while positive 50-V, 2-ps pulses are applied to the pin. Points a and b are the currents measured at the wall and pin, respectively, when the pulses to the pin are of negative polarity at T = 300 p s ; 200 OC
we find 6 = 0.20. This is in reasonable agreement with our prediction of 6 = 0.25 for our cells (Equation 24). Point a in Figure 7 indicates the current (-0.75 nA) measured at the wall while the pin is pulsed negative every 300 ps. This current is due to ( I e ) minus now a larger fraction, 0.80, of ( I , ) arriving a t the wall of the cell. The magnitude of this current using the wall as the anode is again essentially equal to the current simultaneously measured a t the other electrode (point b), as it must be since (Io)a = (1.0 - 0.80)(1,) = 0.20(1+) = (I&. We have performed additional experiments with the ECD/APIMS instrument previously described. As shown in Figure 5 , configuration C, this instrument is an ECD with a small aperture in its wall leading to a differentially pumped vacuum envelope and quadrupole mass filter. The positive and negative ion content of the gas which flows through this aperture can thus be monitored while various pulse frequencies are applied to t h e central anode. As will be explained in greater detail below, the ion signals thus obtained are thought to reflect the concentrations of positive and negative ions in a small volume immediately adjacent to the 25-pm aperture. In the experiments to be related, a condition close to the clean carrier gas condition is maintained where the predominant species present are positive ions and electrons. However, since t h e measurement of the negative ions also provides a n additional means of observing ECD events, a constant, low-level supply of electron capturing molecules was maintained in the carrier gas. This condition was easily achieved by allowing some “column bleed” to occur. A column temperature was established which caused the ECD standing current to decrease to a level equal to about 90% of that observed in the clean carrier gas condition. Also with this arrangement, the total negative ion signal as monitored by the APIMS function was equal to about 10% of that of the total positive ion signal. In one experiment, the positive and negative ions present in t h e small sample conditions were monitored with the ECD/APIMS and a multichannel analyzer (MCA). Using long 9-ms pulse periods, the mass spectrometer output pulses were fed to the MCA in a synchronized, repetitive manner. A dwell time per channel of 100 p s thus divided the 9-ms period between pulses into 90 channels. For both the positive and negative ions, 1-h data accumulation times were used. The results of this experiment are shown in Figure 8, in which the negative ion data have been scaled up by a factor of 10. The positive ion current remains relatively constant with time, increasing about 9% immediately after the pulse and returning to a value close to the field-free, steady-state level after 2 to 3 ms. T h e total negative ion signal shows a much more
IOPS,
I
, , , , , . , , I
9 msec
4
Figure 8. Instantaneous total positive and negative ion signals using ECD configuration C (Figure 5) as a function of the time elapsed relative
to the application of pulses to the ion source electrode. The period between pulses is 9 ms. A small-sample condition corresponding to 10% of saturation is continuously maintained. Ion source, 250 O C
dramatic reaction to the ECD pulse. It decreases quickly to value about 30% of its field-free, steady-state value and then returns more slowly than did the positive ions to the steady-state value. By applying the model developed herein, one can explain the data in Figure 8. (1)Positive ions: Prior to a pulse, the positive ion signal reflects the equilibrium positive-ion concentration in the plasma, q+O. (The total ion signal during this time will be proportional to q+O x F where F is the carrier gas flow rate through the aperture.) Immediately after a pulse and the removal of electrons, the space-charge electric field increases slightly the flow of positive ions through the aperture. (The magnitude of this increase is discussed below.) As the plasma grows, the space-charge E field decreases. In about 3 ms, plasma has essentially grown to the walls, and the E field-enhanced positive ion current through the aperture ceases. This is approximately the amount of time our model predicts. For example, using Equation 20, in 3 ms the volume of the positive ion sheath is calculated to be reduced to 25% of the total cell volume. (2) Negative ions: The space-charge E field present right after the pulse tends to pull the negative ions away from the aperture, thus quickly reducing the negative ion concentration in the gas flowing through the aperture. Furthermore, negative ions are no longer being produced in this region because it is void of electrons, and the negative ions remaining in the sheath are being destroyed by recombination with the positive ions. At about 3 ms the plasma has grown to the walls, but the negative ion density has not recovered. The rate constant for electron attachment, k A , is finite, so even after the arrival of the electrons with the plasma, a few milliseconds are required for the negative ion density to recover to its value prior to the pulse. From the data of Figure 8, it is clear that the instantaneous positive ion current through the aperture is only slightly increased immediately following a pulse. Upon first consideration, this result may seem surprising because after a pulse, our model suggests that a large positive-ion migration current to all cell boundaries (including the aperture) is to be expected. The small effect observed is the result of the very small size of the aperture (25 pm). From Equation 21 we can infer that the total positive ion flux to all grounded surfaces has a maximum value (at t = 0) of S (in ions/s). But only a small fraction of these ions pass through the aperture. This fraction will roughly be the ratio of the area of the aperture to the total surface area (walls and pin) inside the ECD, which for the detectors described herein is approximateiy lo4. So the maximum positive ion current through the aperture due t o the space charge field is on the order of lo4 S. On the other hand, following a pulse the positive ion current through the aperture due to gas flow is approximately q+’ X
ANALYTICAL CHEMISTRY, VOL 52, NO 3, MARCH 1980
; j
2-85
21 , l ; K \ e * e2 j ~ h
0 + -.
4 .
2
PdLSE
5 -~----6--T
P E R 1 0 3 Crnsec;
Total positive and negative ion signals measured using ECD configuration C (Figure 5) as a function of the period between pulses applied to the ion source electrode. A small-sample condition corresponding to 10% of saturation is continuously maintained. Ion source, Figure 9.
250 OC
F where F , the gas flow rate through the aperture, is about 0.1 mL s l. For values of S and vis used previously, we calculate the positive ion current due to the space charge migration to be only about l % of that due to gas flow. Considering the approximations used, this is in qualitative agreement with the relatively small value of 9% observed in Figure 8 and supports our interpretation that the positive ion signal of the APIMS reflects mainly the steady-state ion density of the gas near the aperture. The observation that the positive ion signal increases by 9% after the pulse instead of the calculated estimate of 1%probably results from gas-flow effects near the aperture where somewhat more of the space-charge driven positive ions than are calculated from the aperture area are swept into the vacuum envelope. Another experiment using the ECDIAPIMS was performed in which the pulse period was varied over a wide range while the time-averaged total positive or negative ion currents to the mass spectrometer were measured, again for the smallsample condition. This experiment provides an insightful test of the model because with long pulse periods, the region adjacent to the APIMS aperture should tend toward the plasma condition, while with short pulse periods, this region will be held continuously in a state reflecting the positive ion sheath condition. The data thus obtained are shown in Figure 9, with the negative ion intensities scaled up by a factor of 10. Let us first consider the negative ions of Figure 9. Note that as T gets large t h e negative ion current asymptotically approaches about 4000 counts s the value obtained when the pulser was switched off. Below T = 3 ms the negative ion current begins to decrease progressively more rapidly until, a t T r= 300 p s , the negative ion current is essentially zero. This observation can be readily explained in light of our model. With no pulsing, plasma equilibrium is achieved throughout the ECD. Negative ions are as numerous near the 25-pm aperture as elsewhere in the cell. The leak through this aperture carries positive ions and negative ions to the mass spectrometer in numbers basically representative of their respective concentrations throughout the cell. However, as pulsing commences, conditions near the aperture begin to change. After a pulse, the resultant space-charge field begins to "pull" negative ions away from the walls, and hence the aperture. The region directly adjacent to the walls will be void of thermal electrons a t least part of the time, so negative ions destroyed by recombination with positive ions cannot be replaced as rapidly by electron capture reactions in this region. The two effects combine to reduce the negative ion current through the aperture. With long pulse periods, the region near the aperture is void of electrons only for a small fraction of the time, so the overall effect is to only slightly reduce the
481
time-averaged negative ion current. For pulse periods approaching 1ms, the plasma probably never reaches the wall. Nevertheless, the gas flow through the aperture carries some negative ions from the plasma through the sheath and into the aperture. As the pulse period is further reduced, the time-averaged size of the sheath increases and the transit time for negative ions across the sheath increases so that a greater fraction of negative ions is lost to recombination with the positive ions in the sheath. A t T '= 300 p s essentially no negative ions survive the journey across the sheath. One can appreciate why the negative ion current drops off so fast below 1 ms by considering a simple model for the gas flow near the aperture. Assuming isotropic radial gas flow toward the aperture, one can write F = 2 r r 2 d r / d t , where F is the flow rate through the aperture and r is the distance from the aperture. This equation states that the quantity of gas flowing through the aperture must equal the quantity of gas crossing any hemisphere centered a t the aperture. The differential equation can be integrated to yield t = 2ar3/3F. During the transit time across the sheath, negative ions are lost to recombination, but none are created through electron capture. Therefore, the rate equation governing the negative ion density during this period will be d7 l d t = -RV+'~-.This equation has the simple solution, 9 = 7 O exp(-RV+Y), where 7 is the negative ion density in the plasma. The ratio 7-/7-' is the probability that a single negative ion starting a t t = 0 in the sheath will still exist at some later time t. Using the transit time across the sheath given above, the probability that a negative ion will survive the trip across the sheath to the aperture is given by
Equation 29 indicates that the negative ion current through the aperture is a very strong function of the sheath thickness, r , which occurs to the third power. As the pulse period is decreased slightly, the minimum sheath thickness is increased slightly, but the negative ion survival rate may decrease greatly. For values of all constants used throughout this model, Equation 29 predicts the precipitous drop in 8 - observed in Figure 9 to occur between about r = 0.1 mm (where 7-17 is calculated to be 0.99) and I' = 0.7 inn1 (where 7 / a ! = 0.01). These values seem reasonable sirice the pin to aperture distance in the source is 3 mm and the plasma growth initiates at a distance approximately midway between the pin and aperture. The positive ion data of Figure 9 are also informative. I t is noted that two distinct regions of intensity are observed. With 7' 2 1 ms, the total positive ion signal is approximately constant a t about 40000 counts s l , and with T 5 200 ~.tsthis signal is nearly constant again at about 30000 counts s I. As previously discussed, the positive Lon mass spectral signal largely reflects the ion concentration in the gas adjacent to the aperture. The observation of two distinct plateaus for the positive ion signal was predicted by our model where with slow pulsing the signal reflects q+O and with fast pulsing, 'I+'. I t appears that q+' is not exactly equal ti s+O as har been assumed here for the sake of mathematical simplicity, but is certainly sufficiently close ( q + s = 0.75 q+") as to strongly support the general validity of the model.
CONCLU SI C) N A new model for the pulsed ECL) has been described and tested. This model adds further detail to its predecessor by including the effects of electrostatic forces bet ween ions and electrons. The result bears both similarities and differences when compared to the earlier Wentworth model. The mathematical expressions for the time dependence of electron
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 3, MARCH 1980
buildup during the period between pulses are of the same form. In the new model, however, electrons are not distributed throughout the ECD volume at all times, but are located only in a central plasma zone which grows with time. In both models, the positive ion density throughout the ECD is assumed to be constant with time, but for different reasons and with different concentrations. The Wentworth model has them constant because they are in large excess of negative particles. The new model has them constant because of the near equality of two complementing loss mechanisms, recombination and space-charge migration. The new model does not insist that positive ions are always in excess of negative particles, but with reasonably long pulse periods, has the total number of negative species equal to the number of positive ions. An acceptance of this model does not require that fundamental reevaluations of the basis of most existing analytical forms of the pulsed ECD be made, since the mathematical form of the relationship between current and the pulse period will be thereby unchanged. However, the new model will be helpful in the future development of certain ECD methods, and in understanding chemical and physical details which might affect these. One example of such an application is the use of the ECD for gas-phase coulometry (3-6). In that use, i t is important to understand the positive-ion chemistry (and positive-ion concentrations) which may compete with an electron capture reaction (6). Also, for gas phase coulometry, this model would advise the use of relatively long pulse periods, so that the plasma is allowed to grow to a large fraction of the total ECD volume (otherwise, a significant fraction of the sample molecules may pass through the ECD without being exposed to electrons). Finally, for gas phase coulometry, it is essential to know that the observed current is not necessarily ( I , ) , but is (1 - 6) ( I , ) , where 6 is the fraction of excess positive ions which migrate to the anode. The value of 6 will be a function of cell design. Throughout the approximately 15-year period in which developments in the pulsed ECD have occurred, many different cell geometries and sources for ionization have been used or tested. How precisely the model developed here fits each of these probably will depend most strongly on the validity of one of our initial assumptions-that is, ionization by the 8s occurs evenly throughout the ECD cell. With some
ionizers and cell designs, ionization which is nowhere near uniform may cause behavior quite different from that described here. Even in the ECD cells used here, the ionization process is certainly not perfectly uniform, as assumed in our model, and small differences in experiments are expected. Nevertheless, since most of the new ECDs in common use today use 63Nisources of interior dimensions on the order of 1 cm, the quantitative aspects of theory developed here should be reasonably applicable to these, while the general forces and tendencies described will apply to any ECD configuration.
LITERATURE CITED (1) Lovelock, J. E. Anal. Chem. 1963, 3 5 , 474. (2) Maggs, R. J.; Joynes. P. L.; Davies, A. J.; Lovelock, J. E. Anal. Chem. 1971, 4 3 , 1966. (3) Lovelock, J. E.; Maggs. R. J.; Adbrd. E. R. Anal. Cbem. 1971, 43, 1962. (4) Lillian, D.; Singh, H. 6. Anal. Chem. 1974, 46, 1060. (5) Lovelock, J. E.; Watson, A. J. J . Chromatogr. 1978, 158, 123. (6) Grimsrud, E. P.; Kim, S. H. Anal. Chem. 1979, 57,537. (7) Grimsrud, E. P.; Miller, D. A. Anal. Chem. 1978, 50, 1141 (8) Simmonds, P. G. J . Chromatogr. 1978, 166, 593. (9) Miller, D. A.; Grimsrud, E. P. Anal. Chem. 1979, 57, 851. (10) Phillips, M. P.; Goldan, P. D.; Kuster, W. C.; Sievers, R. E.; Fehsenfeid, F. C. Anal. Chem. 1979, 51, 1889. (11) Wentworth, W. E.; Chen, E.; Lovelock, J. E. J . Phys. Chem. 1966, 70, 445. (12) Wentworth, W. E.; Chen. E. J . Gas Chromatogr. 1967, 5 , 170. (13) Siegel, M. W.; McKeown. M. C. J . Chromatogr. 1976, 122. 397. (14) Grimsrud. E. P.; Kim, S. H.; Gobby, P. L. Anal. Chem. 1979, 57,223. (15) "Handbook O f Radioactive Nuclides"; Wang, Yen, Ed.; The Chemical Rubber Company: Cleveland, Ohio, 1969; pp 73 and 579. (16) Ref. 15, p 38. (17) "American Institute of Physics Handbook", 3rd ed.;Marion, J. B..Gray, D. E., Eds.; McGraw-Hill: New York, 1972; Chapter 8, p 184. (18) "Defense Nuclear Agency Reaction Rate Handbook", 4th rev.; Biondi, M. A., Bortner, M. H., Baurer. T., Eds.; 1975; Chapter 16, pp 16-27. (19) Lorrain, P.; Corson, D. "Electromagnetic Fields and Waves", 2nd ed.; W. H. Freeman and Co.: San Francisco, Calif., 1970; p 422. (20) McDaniei, E. W. "Collision Phenomena in Ionized Gases", John Wiley and Sons: New York, 1964; p 490. (21) Karasek, F . W.; Tatone, 0. S.: Kane, D. M . Anal. Chem. 1973, 45, 1210. (22) Grimsrud, E. Anal. Chem. 1978, 5 0 , 382. (23) Devaux. P.; Guiochon, G. J . Gas Chromatogr. 1967, 5 , 341. (24) Simmonds, P. G.; Fenimore, D. C.; Pettit, B. C.; Lovelock. J. E.; Zlatkis, A. Anal. Chem. 1967, 39, 1428.
RECEIVED for review May 2, 1979. Accepted December 18, 1979. This work has been supported by the donors to the Petroleum Research Fund, administered by the American Chemical Society, by a n M. J. Murdock Charitable Trust Grant of Research Corporation, and by the National Science Foundation under Grant CHE-7824515.
