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Anal. Chem. 1984, 56, 186-193
Signal Detection of Pulsed Laser-Enhanced Ionization George J. Havrjlla,’ Peter K. Schenck, John C. Travis, and Gregory C. Turk*
National Bureau of Standards, Washington, D.C. 20234
A point charge model based upon charge induction theory has been developed to describe the proposed detection mechanisms of laser-enhanced ionization (LEI). The model predictions are in good agreement with experlmentaiiy observed LEI electron and Ion signal pulses. The predicted effects of alkali metal matrix concentration and laser beam position are also conflrmed by experimental results. The development of this model provides a basis for establishing experimental methodology that is nwessary for the development of LEI as a technique for trace metal anaiygis.
Laser-enhanced ionization (LEI) spectrometry is one of the most sensitive methods available for trace metal analysis. The method is based upon the enhanced rate of thermal ionization of an element in a flame, resulting from the population of an excited state of that element by the resonant absorption of light from a tunable dye laser. This enhanced ionization can be detected as an increase in a current passed through the flame by the qpplication of a high voltage across the flame. Published reports have appeared regarding the application of LEI fOF chemical analysis (1-4) as well as for combustion diagnostics (5-8). Fundamental studies on the mechanism of the LEI process (9-12) and on the collection of ions produced by contiquous wave (CW) LEI have also been published (12,13). This paper will deal with the details of how an LEI current pulse is generated in the high-voltage circuit as a result of pulsed laser excitation in the electrically perturbed flame and with the experimental variables which affect the detection process. Pulsed dye lasers have thus far proven to be more versatile and effective excitation sources than CW dye lasers for chemical analysis by LEI. Fundamental differences in the signal detection behavior of pulsed and CW LEI have been reported (13). An improved understanding of the pulsed detection mechanism is important, particularly since matrix interferences have been observed which are largely related to the detection process (14-17). Most prior research on pulsed LEI has utilized signal processing optimized for sensitivity. The filtering and amplification procedures used substantially distorted the temporal shape of the LEI pulse, and much information regarding the signal detection process was thus lost. Only recently were high bandwidth measurements of the LEI temporal pulse profile first reported by Berthoud et al. (18). In this work, such measurements of the LEI signal pulse under a variety of experimental conditiops have been made with a minimum of temporal distortion for comparison with theoretical predictions. A mathematical model of pulsed LEI in an idealized electrically perturbed flame is presented in this report. This model predicts the motion of the charged species produced by LEI and therefore the magnitude and shape of the LEI current pulse. Comparison with experimental data confirms that the National Research Council Postdoctoral Research Associate. Present address: The Standard Oil Company (Ohio), Research Center, Cleveland, QH 44128.
model can be used to systematically predict the effect of experimental variables such as applied voltage, flame background current, and laser beam position on the LEI signal.
THEORY Electric Fields in Flames. When a voltage V , is applied across an idealized pair of plane parallel electrodes of infinite extent in two dimensions and separated by a distance Win the third dimension, a uniform field strength of V,/W is predicted if the space between the electrodes is evacuated or air-filled. However, when a weakly ionized plasma such as a flame fills the space, a very different behavior results, as described in some detail by Lawton and Weinberg (19). Pertinent aspects of this theory (19) are briefly reviewed in this section and illustrated in Figure 1. In the idealized, one-dimensional, diffusion-free approximation of a flame under the influence of an applied potential, the field is found to be modified by a positive ion space charge, or sheath, adjacent to the cathode. The space charge and the resulting field modification are a natural consequence of the fact that electrons travel much faster than positive ions in response to a given electric fieid (see below), requiring a large imbalance in number density to equalize the removal rate at steady state. For sufficiently low applied voltages (see below), the field magnitude, E , has its maximum value, E,,, a t the cathode, decreasing linearly with distance from the cathode, x, to zero at the edge of the space charge, x = X,, so that E = 6(X, - x), x IX, = 0, x > (1)
x,
The position of the space charge boundary (X,) and the values of the negative field slope (6 = -dE/dx) and maximum field (E,,, = 6X,) depend on V , as well as on the mobility of the positive ions which constitute the space charge, K,, and the volume ionization rate of the flame, rc
x,= [2Va/6]1/2 (3)
E,,
= [2Va6]1/2
(4)
where e is the electronic charge and to is the permittivity of free space. The upper bound on applied voltage for eq 1-4 to be valid is set by the requirement that the sheath boundary (X,) occur between the plates, or X,< W , where x = W is the anode position. Higher voltages imply a condition of “electrical saturation” (19), with nonzero fields and positive space charge at all positions in the flame. At voltages above the saturation voltage, V , > Vsat,the current drawn from the flame becomes voltage independent, characterized by a saturation current density, jsst,given by j s a t = ercW (5) This relationship is convenient for estimating r, values for actual flames (12). The saturated regime is largely ignored in the present treatment for two reasons: (1)it is a relatively trouble-free experimental regime for analytical LEI, and (2) the depen-
This article not subject to US. Copyright. Published 1984 by the American Chemical Society
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proaches the virtual anode asymptotically. The condition XL < X , in eq 9 requires that ionization occur in the region of nonzero field for a signal current to be generated. A somewhat more realistic electron pulse shape may be modeled by considering the effect of amplifier risetime ( T J on the input pulse shape given by eq 7. By convoluting an exponential response function with i-(t), we find the amplifier-modified current function
SIGNAL 4
I
0 CATHODE
w (cm)
ANODE
Figure 1. Pictorial representation of the point charge model for LEI current induction. A uniform flame is bracketed between a cathode at x = 0 and an anode at x = W . A voltage V , applied across the flame resuits in a field, E(x),which decreases from a maximum at the cathode to zero at x = X , , as predicted by eq 1-4. An ion and electron were generated at the position of the laser, X,, at time t = 0, and have drifted to positions X + ( t ) and X J t ) at the time (>O) illustrated.
dence of field on position is more complex than eq 1, yielding differential equations for signal current which are not amenable to analytical solution. Point Charge Model for Charge Transport and Current Induction. Under the influence of a field in a flame, electrons and ions move in opposite directions with velocity magnitudes proportional to the field, E. The constant of proportionality is called the mobility, p+ or p, for ions and pfor electrons, and represents collisional resistance to the field-induced motion (“friction”). Mobilities are mass-dependent, causing electrons to travel at much greater velocities than positive ions (20) as mentioned in the discussion of the positive ion sheath above. Because of the mass dependence of ion mobilities, the mobility of the positive ions forming the sheath, ps, may not be the same as that of the positive ions formed by the laser, p+. As a first approximation to predicting ihe temporal LEI current pulse profile, we consider a point charge model, yielding current (i) due to a single ion (i+) and electron (i-) generated at t = 0 by a laser positioned at x = XL,and moving in an idealized electric field. Figure 1illustrates the positions of the electron ( X - ) and ion ( X + )a t a time t > 0, when each has drifted in the appropriate direction from x = XL. Included in the point charge model is the assumption that the field-free region of the flame, between the sheath and the anode, behaves as an electrical conductor. Thus, the sheath boundary becomes an effective anode, in place of the burner head. Without this assumption, discrepancies arise between experimental observations and theoretical predictions. The time derivative of the charge induced on the virtual anode by the free ion and electron (21) may be solved to yield
i(t) = i-(t)
+ i+(t)
where
i-(t) = e ( X , - XL)X,~T--~exp[-t/~-]
(7)
r- [p-S]-l (10) In eq 6-8, i- and i+ represent the electron and ion components of the induced current. The ion current is truncated a t t = t , by the neutralization of the ion as it arrives at the cathode. The electron pulse is not truncated, since the electron apT+
[p+S]-l a n d
where the response function has been normalized to yield the same area (charge) under i and i (22). The integral of eq 6 over all time may be found to yield e, the original charge on each member of the ion pair. However, by integration of the electron and ion current components separately, it is found that the fraction of the total charge arising from each species is a function of the beam position. If a large number of ion pairs, N , is deposited a t t = 0 and x = XLby LEI, yielding an initial charge Q = Ne of each species, we find that
Q = Q+ + Q-
(12)
4-/Q= ( X s- X L ) / X , , Q+/Q = X L / X ,
(13)
and
where Q- and Q+ are the integrals of the electron and ion current pulses over all time, multiplied by N.
EXPERIMENTAL SECTION LEI Pulse Shape Measurements. The LEI spectrometer is identical with the system described in ref 4 with the exception that only one dye laser is used. A KDP crystal is used to frequency-double the dye laser output to provide the desired wavelength of 296.69 nm for the model analyte, iron. Sample solutions of 100 pg mL-’ Fe containing 0,30,100,300, and 1000 pg mL-’ Na are aspirated at -3 mL min-I into a premixed C2H,/air flame. The flame gas flows are -1.5 L mi& for CzHzand -15 L m i d for air. The burner head serves as the anode of the LEI high-voltage circuit and is coupled to ground through a 1-kQload resistor. The water-cooled cathode (15) is positioned inside the flame at various heights from 1 to 2 cm to provide different cathode-anode spacings. A cathode potential of -1500 V is used throughout this work. The laser beam, which is limited by an aperture to about 0.1 cm in diameter, is positioned by using a 2.08 cm square by 1.2 cm thick quartz block as a refractor plate. The refractor plate is mounted on a shaft connected to a microcomputer-controlled stepper motor. The beam is first aligned normal to the plate and the position recorded. The computer then calculates the necessary number of motor steps to move the beam to the desired position. By rotating the refractor plate about the short axis, the beam can be moved over a range of about 1.2 em. The LEI pulse is detected with a minimum of pulse shape distortion by using a Tektronix signal probe (Model P6057,100X, 5 kQ, 0.5 W, Beaverton, OR) connected across the 1-kQ load resistor on the burner head. The signal is amplified (Princeton Applied Research, Model 115, Princeton, NJ), directed to an oscilloscope (Tektronix, Model 475), and then processed by a boxcar integrator (Princeton Applied Research, Model 162/ 165). The pulse shape is recorded by stepping the boxcar gate position under computer control. The data are digitized and stored on disk for later display and further processing. The boxcar averager time constants were chosen to provide optimum signal averaging with minimum distortion for each aperture duration used. Potential Measurements. The floating potential of a 0.013 cm diameter iridium wire immersed in the flame is determined as a function of position. The wire is oriented parallel to the cathode and immersed about 1 cm into the flame at one end of the burner head. The wire probe is connected to a calibrated high-impedance (1000 MQ)probe rated to 40 kV. The measured
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-5000
24000 P
4
I
;
I
i
i o \
2 3 4 5 Distance Below Cathode (rnrn)
J
I
6
Flgure 2. Experimentally measured electric field in an acetylene-air flame for a 100 pg mL-' Na solution, 1 cm cathode-anode separation, and applied voltages of (A) -250 V, (B) -1000 V, and (C) -1500 V.
! .
2
3
4
5
6
Distance Below Cathode (rnm)
Flgure 3. Effect of sodium on the electric field measured in the acetylene-air flame for -1000 V applied, a 1-cm electrode spacing, and matrix concentrations of (A) 10 p g mL-' Na and (B) 1000 pg mL-' Na.
potential is input to a digital panel meter that is sampled by the microcomputer which accumulates and processes the data. Potential profiles were taken at 0.05-cm intervals for the voltages and solutions given in the text.
RESULTS AND DISCUSSION Electric Field Profiles. Since the movement of LEIproduced ions and electrons is controlled by the electric field, it is important to know the magnitude of the field, and how it is distributed in the flame. Numerical calculation of the first derivative of the floating potential experimentally measured as a function of position gives the electric field profile. The measurement is simple to perform, but the intrusive nature of the voltage probe in the flame is a possible source of error. Localized cooling of the flame near the probe, thermal electron emission from the iridium, and insufficiently high meter input resistance could also affect the measurement. Even with these limitations, the results obtained appear reasonable in most cases. When the air-acetylene flame was not seeded with alkali metal, however, the resistivity of the flame was too high for accurate voltage measurement by the voltage probe. Also, it was not possible to place the Ir probe into the primary reaction zone of the flame, and measurements made in the region very close to the water-cooled cathode were often erratic. The Theory section of this paper discusses the electric field distribution for an idealized flame of uniform composition between infinite parallel electrodes. Despite the obvious differences between the actual LEI flame and the idealized one, measured electric field profiles show trends which are consistent with model predictions. According to eq 2, the extent of the ion sheath X , should increase as the square root of V,. Figure 2 shows the measured field profile for three cathode potentials. The bottom edge of the cathode was positioned 1 cm above the burner head, and a solution containing 100 pg mL-' of Na was aspirated into the flame. With -250 V applied to the cathode (curve A), the field was found to drop linearly from the cathode to a point 0.18 cm below the cathode. When the cathode potential was increased to -1000 V (curve B), the sheath extended, as predicted, almost to the primary reactioll zone 0.68 cm below the cathode, and when further increased to -1500 V (curve C), the field was still present at the limit of the measurement capability near the tip of the primary reaction zone. At the higher applied potentials, the field vs. position function was found to be nonlinear, and in the case of the -lo00 V cathode potential a sharp discontinuity was observed at 0.45 cm below the cathode, unlike the theoretically pre-
i
"OOk, 4000
i
l
ob
1
i
4
A
A
I
10
i i Distance Below Cathode (rnrn)
iPiL o
Flgure 4. Effect of cathode-anode separation on electric field in an acetylene-air flame for a 10 p g mL-' Na matrix, -1500 V applied, and separations of (A) 1 cm and (B) 2 cm.
dicted linear function. These deviations from theory are not surprising considering the nonuniformity of the temperature and composition of the flame between the electrodes, particularly a t the primary reaction zone of the flame. The dependence of the field on the volume ionization rate, r,, can be tested by the addition of alkali metals to the airacetylene flame. At alkali metal concentrations above about 1 ppm, the ionization rate of the metal exceeds the natural rate of the flame, and r, is nominally proportional to the alkali concentration. Equation 2 shows the value of X,to be inversely proportional to the fourth root of rc. An increase in the level of alkali metal in the solution being aspirated into the flame should thus shift the space charge boundary toward the cathode, resulting in a higher average field value within the sheath. Figure 3 shows the measured effect of the sodium concentration on the electric field distribution a t a fixed cathode potential of -lo00 V. With 10 yg mL-l of Na aspirated (curve A), the region of the flame with nonzero field includes most of the area between the cathode and the primary reaction zone. When the Na concentration is increased to 1000 pg mL-' (curve B), the field distribution shifts dramatically. As predicted by theory, the edge of the sheath moves closer to the cathode and the average value of the electric field within the sheath increases accordingly. An additional experimental variable which affects LEI signal detection is the distance between the burner anode and
ANALYTICAL CHEMISTRY, VOL. 56, NO. 2, FEBRUARY 1984
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I
0
I
0
.I
I
.2
.3
Time (ps)
.4
0
2
4
6
8
10
Time (p)
Flgure 5. Experimental (solid line) and theoretical (dashed line) LEI pulse shapes for 100 pg mL-' Fe in a C,H,/air flame, with a 2-cm electrode spacing, -1500 V applied, and the laser beam located 0.3 cm below the cathode. (a) Axes scaled to emphasize the high current, short duratlon electron contribution. Trailing edge of theoretical pulse is shown reproduced with a 75 ns time offset to show agreement with experimental trailing edge. (b) Axes scaled to emphaslze the low current, long duration ion contribution (electron pulse, t < 1 ps, deleted).
the water-cooled cathode. Figure 4 shows the field distribution that was measured for both a 1-cm (A) and a 2-cm (B) electrode spacing with -1500 V and a 10 pg mL-l Na solution. As expected, the closer alignment results in an increased field strength between the electrodes. LEI Electron and Ion Pulses: Comparison of Point Charge Model and Experimental Results. The point charge model for LEI signal detection can be utilized to generate theoretical time histories of the LEI current pulses using eq 6-11. The shape of these theoretical pulses, and their response to the variation of experimental parameters such as beam position and flame ionization rate, can be compared to experimental observations as a means of evaluating the accuracy of the model. For a more realistic prediction of experimental results, the amplifier-distorted electron current of eq 11 is used in place of i-(t) in eq 6. An instrumental risetime ( r 3 )of 0.02 ps matches the specified response of the amplifier used in this work. The solid lines in Figure 5 show the experimentally measured current response for the single color (A = 296.69 nm) excitation of Fe (100 ppm solution) in a CzHz/air flame, a cathode biased at -1500 V and positioned 2 cm above the burner head (anode), and the laser beam centered 3 mm below the cathode. Figure 5a is scaled to display the contribution of electrons to the LEI pulse, and Figure 5b is scaled to best display the ion contribution, with the offscale (t < 1 ps) electron pulse deleted. From the standpoint of signal-to-noise ratio, the ion pulse has no analytical utility and is normally ignored by the gated integrator. The dashed lines in Figure 5 represent point-charge theory for theoretical parameters intended to closely approximate the experiment, as described later. The most persistent constrasts between theory and experiment, illustrated in Figure 5 and in further data to be presented, are near the maximum of the electron pulse and in the trailing edge of the ion pulse. The latter discrepancy is readily interpreted as the result of the finite size of the laser beam and of ion diffusion. In the case of Figure 5b, the placement of a 1-mm diameter laser beam 3 mm from the cathode readily explains a *33% smearing of the ion arrival times. Diffusion has more opportunity to dominate for greater laser-cathode separations. The origin of the electron pulse shape distortion is more obscure and is the subject of continuing theoretical studies. Similar pulse shapes have been observed by Berthoud et al.
189
(18) and characterized as double pulses. The amplitude of the theoretical electron pulse in Figure 5a is derived from the single-point normalization of the theoretical ion pulse of Figure 5b to the experimental data. Figure 5 suggests that the area of the electron pulse (charge) may be a more accurate analytical parameter than the amplitude. In spite of the distortion at maximum current, the trailing edge of the pulse decays in the predicted exponential manner, though delayed in time. To illustrate this point in Figure 5a, a portion of the theoretical plot is reproduced with a time shift of 75 ns, showing close agreement with the experiment. Our tentative interpretation of the electron pulse distortion is based on Coulombic effects within the laser-generated ion and electron distributions are relatively high analyte concentrations, such as used for these studies. Specifically, if the ion density produced by the laser exceeds the ion density present in the sheath before the laser pulse, the steady-state field distribution will suffer a transient perturbation due to the laser-produced charges. The nature of this perturbation will be such that the Coulombic attraction between the ions and electrons produced by the laser will retard the process of charge separation by the external field. For the natural CzHz/airflame, the ion density in the sheath is about lo9 ~ m - ~If .we assume that lo9 electrons are generated over a 0.1-cm3active volume in an LEI event, resulting in a 200-11s electron current pulse (see Figure 5a), then a pulse amplitude of 0.1 X lo9 X (1.6 X C) X (2 X s)-l = 80 pA would be expected. From the figure, it is clear that we are well above the perturbation threshold. If our 100 ppm Fe solution yields 1013atoms ~ m -we ~ ,would enter the Coulombic perturbation regime for any LEI ionization efficiencies above Testing the above hypothesis will require more sensitive 100-MHz bandwidth detection electronics than those employed in the present work. Our conventional preamplifier ( I ) , used for trace element analysis, is capable of detecting about lo4electrons per pulse (23),but at a bandwidth of about 1MHz. For analytical purposes, the bandwidth of the analytical preamplifier is actually advantageous, since the output pulse is of reproducible shape and proportional to the integral of the input pulse. A second reason to expect departure of both electron and ion pulse shapes from the theoretical ideal is that the electric fields show significant deviation from theory, as shown in Figures 2-4. Since the electric field spatial profile is reflected in electron and ion current pulses, pulse shape measurements at concentrations low enough to avoid Coulombic distortions could be used as nonintrusive probes of the electric field distribution. Position Effects. The position of the laser beam has an important effect on LEI signal detection and, consequently, LEI analytical performance. As beam position is varied, the distance of the LEI ion-electron pairs from their respective destinations is varied. This variation affects the arrival time of the ions, and therefore the ion current pulse duration. As arrival time increases, the effect of diffusion becomes more pronounced. In addition, the electric field experienced by the traveling charge carriers changes as the beam position is varied. Finally, there are the normally encountered position effects of flame spectroscopy, i.e., variation in analyte and matrix concentrations and temperature. Figure 6 shows electron current pulse shapes for the same conditions as for Figure 5a, but with the laser centered 1,5, and 9 mm away from the cathode (as opposed to 3 mm for Figure 5a). The distortion discussed above is still present, and appears to depend on beam position. From eq 8, it may be seen that the amplitude of the electron pulse as a function of beam position is expected to mimic the
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 2, FEBRUARY 1984
4
2
z 3
I
/ I
I x L = 9 mm
0
c
C
; 2 a
0
0 2 100
XL - 9 mm
\
\\ \
\ -\
0.0 0.1
0.2
0.3
0.4
0.5
Time (ps)
0
10
20
30
40
50
Time (ps)
Figure 6. Experimental (solid line) and theoretlcal (dashed line) electron pulse shapes for the same conditions as Figure 5a, except for the laser beam position. Distance of laser below cathode is 1 mm (top), 5 mm (middle), and 9 mm (bottom).
Figure 7. Experlmental(solid line) and theoretical (dashed line) ion pulse shapes for the same conditions as Figure 5b, except for the laser beam position. Distance of laser below cathode is 9 mm (top), 7 mm (mkklle). and 5 mm (bottom).
electric field behavior, i.e., decrease linearly from a maximum at the cathode to zero at the sheath edge. Because of the pulse distortion the amplitude behavior is difficult to demonstrate. However, the dashed theoretical calculations of Figure 6 are calculated for an assumed sheath edge 16 mm below the cathode, yielding amplitude ratios behaving as (16 - XL)(mm), or 1511:7 for the cases shown. Overall normalization of theory to experiment for Figure 6 was simply done by scaling the theoretical pulses for the best fit of the 1-mm curve to the first peak of the corresponding experimental data, instead of the method used for Figure 5a. The theoretical electron pulses of Figures 5a and 6 were all generated with an electron time constant of T- = 0.06 ps in eq 11. As in Figure 5a, the trailing edges of the pulses in Figure 6 are shown to agree reasonably well with theory if the theoretical trailing edge is translated an arbitrary amount of time (different for each position). Indeed, the electron time constant was extracted from semilogarithmic plots of the data shown. The dependence of ion current pulse on laser beam position is illustrated in Figure 7 for laser-cathode separations of 5, 7, and 9 mm, for the same conditions otherwise as in Figures 5 and 6. When the laser beam is aligned near the cathode, as recommended for analytical measurements (13,15),the ion pulse becomes difficult to resolve from the electron pulse. Yet in terms of relative area, when compared to the electron pulse, it is still a minor component of the signal. The theoretical ion pulse shapes superimposed (in dashed lines) on the data of Figure 7 and Figure 5b were generated by using parameters obtained from the experimental data. Ion arrival times were extracted from five ion pulse shapes for five laser positions, including the four data sets shown in Figures 5b and 7. For this purpose, the ion arrival time was taken to be the time corresponding to the intensity halfway down the trailing edge of the ion pulse. (One assumes that the ions approach the cathode in a symmetrical spatial distribution, e.g., Gaussian, such that half of the ions have been neutralized when the maximum reaches the cathode.) A nonlinear least-squares curve fitting routine was used to fit the arrival time expression given by eq 9 to the data. This fit yielded estimates of T + = 22 f 4 ps and X , = 12.5 f 1.2 mm for the characteristic ion time constant and the sheath edge position.
These parameters were then used to determine the theoretical shapes plotted in Figures 5b and 7, using eq 8 and 9. The amplitudes of the theoretical functions were independently normalized to each data set at one point, indicated by arrows in Figure 7. From the agreement of the rising edge of the theoretical and experimental traces, it may be seen that the T + value extracted from the arrival times is reasonably consistent with the pulse shapes, as well. The primary departure of the ion pulse theory from experiment concerns the pulse amplitudes. If the same number of ions were created at each position, a single amplitude normalization should suffice for all beam positions. The amplitudes for the 5-, 7-, and 9-mm beam positions in Figure 7 employ amplitude factors in the ratio 1:0.760.6, respectively. Thus, the 9-mm data appear to represent a 40% charge reduction over the 5-mm data. This discrepancy is not understood but may result from the inadequacy of a one-dimensional model for a three-dimensional problem. A further discrepancy exists, this time between the electron and ion data. We have used the electron pulse amplitudes of Figure 6 to estimate a sheath edge at 16 mm, and the ion arrival times from Figure 7 to extract a sheath edge of 12.5 mm. Given the electron pulse distortion, this is not a surprisingly large disagreement. However, using the value extracted from the ions for the electron theory would have reduced the 9-mm theory by 35% and the 5-mm theory by 11% in Figure 6. Given the distortions of the measured fields of Figures 2-4 from the theoretical ideal, one might expect somewhat conflicting field measurements from ions and electrons. Electron pulse amplitudes are proportional to the field at the laser beam, while ion arrival times involve an intergral over the field from the beam position to the cathode. Thus, the field extracted from ion data is weighted toward the cathode from the field extracted from electron data. The steeper field slope implied by the smaller X,as measured by the ions, relative to that measured by the electrons, is consistent with the field shape of Figure 4b, the experimental field measurement which most nearly corresponds to our pulse measurements. Matrix Effects. The primary motivation behind the present work has been to better determine the relationship between the LEI signal detection mechanism and the alkali
ANALYTICAL CHEMISTRY, VOL. 56, NO. 2, FEBRUARY 1984
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-
Table I. Comparison of Theoretical and Experimental Charge Apportionment
Q-IQ predicted exptl
100 p g
100 p g mL-' Fe t 1000 p g
mL-' Fe
mL-' Na
0.94 0.92
0.66 0.72
.-__________.-___
0.0
0.1
0.2
0.3
Time ()IS)
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
Time (p)
Figure 8. Theoretical (a)and experimental (b) studies of the effect of Na matrix on the LEI current pulse for (A) 0, (B) 30, (C) 100, (D) 300, and (E) 1000 pg mL-' Na matrix and 100 pg mL-' Fe analyte. Dashed lines show running integrals to illustrate area effects.
metal interferences observed in LEI spectrometry (14-17). As discussed earlier, the addition of alkali metals to the flame results in an increased flame background ionization rate, which in turn affects the electric field distribution. The space charge boundary in the flame shifts toward the cathode, resulting in a higher average electric field in the new sheath, and a larger field-free zone. Earlier papers describe how this may result in loss of signal in the presence of alkali metals if the laser beam is not aligned near the cathode; otherwise, the presence of the alkali metal may shift the sheath edge beyond the laser beam, leaving it in the field-free zone (13,15). If the beam is aligned near the cathode, and is still within the sheath after the addition of the alkali metal, the total loss of signal is avoided. However, signal detection is still affected in two distinct ways: (1)the electric field distribution within the new sheath changes, and (2) the charge induction characteristics of the LEI flame cell change. The electric field as a function of distance from the cathode has been calculated by eq 1 for an applied voltage of -1500 V at two different flame background ionization rates (r,). An effective natural ionization rate of r, = 2 X 1013cm-3 s-' is used for the air-acetylene flame without alkali metal present. Using a value of r, = 8.7 X 1015 cm-3 s-' simulates the effect of aspirating 1000 pg mL-' Na solution into the flame. [These values are derived from measurements made of the background saturation current as a function of Na concentration in the aspirated solution.] An Na+ mobility of 25.8 cm2 V-l s-l (6) is taken as p8 for the indigenous flame as well as the seeded flame. The calculation predicts that the addition of 1000 pg mL-' of Na to the solution being aspirated into the flame will shift the position of the sheath boundary from 15.9 mm below the cathode to 3.5 mm below the cathode. Location of the laser beam further than 3.5 mm from the cathode will result in complete loss of LEI signal with the lo00 pg mL-' Na matrix. A much different response to the addition of the 1000 pug mL-l Na matrix is observed if the laser beam is located 1mm below the cathode. The electric field strength increases from 1.76 kV cm-l to 6.17 kV cm-l at x = 1mm when the Na is added. The increased field strength results in faster
moving charges and, consequently, higher peak currents and sharper pulses. Figure 8a shows 0.5 p s of the LEI current predicted by the point charge model for charge creation by pulsed LEI at 0.05 p s for simulated Na matrices (bottom to top) of 0, 30, 100, 300, and 1000 pg mL-'. The laser beam location is 1 mm below the cathode and the applied potential is -1500 V. The most obvious effect of the Na matrix is the sharpening of the electron pulse to give a higher peak current for a shorter duration. The other effect of the increased field strength at the point of laser interaction involves the ions. In the 1000 pg mL-' Na matrix, the peak of the ion pulse occurs at 0.65 p s . In the Na-free case, the maximum does not occur until 2.6 ps. The importance of this shift in the ion arrival time lies in the fact that most of the analytical LEI work utilizes a high gain preamplifier with 1MHz frequency response and 1-ps gated integration of the LEI pulse. Therefore, in the Na-free case, most of the ion current is not measured, but with the 1000 pg mL-' Na matrix, all of the ion and electron current is measured. Integration of eq 6 from 0 to 1ps predicts a 4% signal enhancement in the presence of a 1000 pg mL-' Na matrix under the conditions defined above. The signal enhancement results from the increased percentage of ion signal integrated due to the presence of the Na. Indeed, signal enhancement has been observed experimentally under conditions which these calculations have attempted to simulate (14-17). Running integrals, shown by the dashed lines, illustrate the increased ion charge observed within the 0.5-ps window a t the higher levels of Na. The ion charge is that which continues to accumulate after the decay of the electron current, This is more evident in the integral than in the slight offset of the base line after the electron pulse. The field-induced matrix effects predicted in Figure 8a have been experimentally verified, as seen in Figure 8b. This figure shows a series of LEI pulses for 100 pg/mL Fe in the presence of the same Na matrices as Figure 8a. Running integrations of the current again superimposed on the current pulses show the expected ion contribution a t high matrix concentration. Even with modest concentrations of Na present, the predicted sharpening of the electron pulse is observed. A 2-cm electrode spacing was used, rather than the 1-cm spacing recommended for analytical work (15). The increased spacing tends to exaggerate the alkali matrix effect, because the electric field in the flame is lowered as seen in Figure 4. Besides the matrix effects resulting from electric field strength changes, another effect arises from changes in the charge induction characteristics of the flame cell. This effect is best illustrated by eq 19, which predicts the apportionment of the total signal charge between the electrons and ions based on the position of the laser beam within the sheath. The addition of alkali metal to the flame lowers the value of X,. This results in a decreased fraction of the electron-carried signal and a corresponding increase in ion-carried signal. Therefore not only does the ion signal arrive faster in the presence of alkali metal matrix but it comprises an increasing percentage of the total available signal. Table I contains both predicted and experimental measures of the fraction of the total charge resulting from electron motion for a Na-free matrix and a 1000 pg mL-' Na matrix. LEI currents were
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 2, FEBRUARY 1984
_-___
-I_._-___
Table 11. Percent Signal Recovery as a Function of Sodium Matrix Concentration and Boxcar Gate Duration matrix Na % analyte signal recoverya concn, - ____ pg mL-' 0.05 ps 0.5 p s 5 PS 0 -100 =loo =loo 30 1 3 6 - 7' 94i 7 103 i 7 100 211 I 1 3 94 + 9 99 -r 7 300 321 r 20 l O O i 10 107i8 1000 2 9 4 r 22 114i 13 1 2 4 5 20 a Relative to the signal with no Na present for each of the three boxcar averager gate durations. Quoted uncertainties are + 1 standard deviation calculated from 1 0 replicate readings. .
--
-_
-.
- --
- - - __ .___
recorded and integrated up to 5 p s after the laser pulse. The fraction of electron charge ( Q . / Q ) was determined from the area under the electron pulse relative to the total signal area. This measurement is subject to some uncertainty in deciding a t which point the current becomes predominantly ion- and not electron-carried. Agreement between theory and experiment is quite good. The measurement of QJQ can be used with eq 19 to give an experimental measure of the value of X,.This can in turn be used in eq 2 and 3 to give a value of r,. In the Na-free case this procedure yields a value of X,= 13.2 mm and a value of r, = 4.2 X 1013cm-3 s-l. The values utilized for generating the theoretical electron pulse shapes of Figures 5a and 6 with the point charge model were X , = 15.9 mm and rc = 2 X 1013 s-l, and ion arrival times (Figures 5b and 7 ) yielded X, = 12.5 mm. For the 1000 pg mL-' Na case, values of X,= 3.6 mm and r, = 7.7 X 1015~ m - are ~ obtained from QJQ, compared to the values of X,= 3.5 mm and rc = 8.7 X 1015 cm-3 used in the matrix-effect model calculations. LEI electron and ion pulse shapes have been shown to be quite sensitive to the presence of alkali metal matrices. In order to avoid analytical interferences, as much of the total LEI signal as possible should be integrated, since (according to the point charge model) the total LEI charge is matrix independent. However, longer integration times (boxcar averager aperture durations) result in more electron shot noise from the background current of the flame (23),particularly when the background current is increased by the presence of an alkali metal matrix. Gated aperture durations fall into three categories for LEI signal detection: (1) incomplete integration of the electron pulse; (2) complete integration of the electron pulse, but incomplete ion pulse integration; and (3) complete integration of both electron and ion pulses. The actual time values for these categories depend on applied voltage, beam position, and flame background ionization rate. For -1500 V, with the laser beam aligned 0.1 cm below the cathode, the anode (burner) aligned 2 cm below the cathode, and no alkali metal present in the aspirated solution, aperture durations of 0.05, 0.5, and 5 ps would fall into categories 1, 2, and 3 respectively. Signal recovery percentages for 100 pg mL-l Fe in the presence of increasing concentration of Na matrix were measured by using these three gated aperture durations. The results are presented in Table 11. Under category 1 aperture conditions, large enhancements are observed in the presence of even moderate levels of Na as the electron pulse sharpens, allowing a greater percentage of the signal to fit within the aperture. These drastic interferences are avoided with category 2 and 3 apertures, where the total electron signal is integrated, making changes in the electron pulse shape irrelevant. As discussed earlier, a less drastic enhancement effect is expected if the addition of alkali matrix allows a more complete integration of the ion pulse within the aperture duration.
A category 3 aperture should avoid this problem, but at the expense of decreased signal to noise ratio. However, as seen in Table 11,a -20% signal enhancement is still observed in the presence of 1000 pg mL-' Na with the 5-ps aperture duration. This discrepancy can also be seen in Figure 8b. The integration of the electron pulse in the 1000 pg mL-' Na case shows an enhanced electron signal relative to the other cases, but the point charge model predicts that electron pulse area should decrease under such conditions. Apparently another mechanism Df signal enhancement occurs at this level of alkali metal matrix. One reasonable possibility is the occurrence of secondary ionization gain under the high electric field conditions within the sheath at such high alkali levels. With the single exception of the above-described anomaly a t very high concentrations of ionizable matrix, the signal detection mechanisms described herein are in good agreement with observed LEI electron and ion pulses, for a variety of experimental conditions. Efforts are currently under way in this laboratory to achieve even closer agreement between theory and experiment by including such effects as diffusion, coulombic interaction, convection, temperature variation, and spatial distribution of the laser beam in a computer-based model of the signal detection process. Even so, the functional expressions developed here using the point charge model should be of long range utility to practitioners of LEI.
ACKNOWLEDGMENT The authors wish to thank James R. DeVoe, W. Gary Mallard, Thierry Berthoud, Pierre Camus, and Jean-Louis Stehle for fruitful discussions. LITERATURE CITED Turk, G. C.; Travis, J. C.; DeVoe, J. R.; O'Haver, T. C. Anal. Chem. 1978. 5 0 . 817-820. Turk,'G. C.; Travis, J. C.; DeVoe, J. R.; O'Haver. T. C. Anal. Chem. 1979, 51, 1890-1896. Turk, G. C.; Mallard, W. G.; Schenck, P.K.; Smyth, K. C. Anal. Chem . 1979, 5 1 , 2408-2410. Turk, G. C.; DeVoe, J. R.; Travis, J. C. Anal. Chem. 1082, 5 4 , 643-645. Schenck, P. K.; Travis, J. C.; Turk, G. C.; O'Haver, T. C. Appl. Spectrosc. 1982, 36, 168-171. Mallard, W. G.; Smyth, K. C. Combust. Flame 1982, 4 4 , 61-70. Smyth, K. C.; Mallard, W. G. Combust. Sci. Technol. 1981, 2 6 , 35-41. Lin, K. C.; Hunt, P. M.; Crouch, S. R. Chem. fhys. Lett. 1982, 9 0 , 111-116. Travis, J. C.; Schenck, P. K.; Turk, G. C.; Mallard, W. G. Anal. Chem. 1979, 57, 1516-1520. van Dijk, C. A,; Alkemade, C. Th. J. Combust. Flame 1980, 38, 37-49. Smyth, K. C.; Schenck, P. K.; Mallard, W. G. I n "Laser Probes of Combustion Chemistry"; Crosley, D. R., Ed.; American Chemical Society: Washington, DC, 1980; ACS Symp. Ser 134, Chapter 12. Schenck, P. K.; Travis, J. C.; Turk, G. C ; O'Haver, T C. J. fhys. Chem. 1981, 85, 2547-2557. Havrilla, G. J.; Weeks, S. J.; Travis, J. C. Anal. Chem. 1982, 5 4 , 2566-2570. Havrilla, G. J.; Green, R. B Anal. Chem. 1980, 52, 2376-2383. Turk, G. C. Anal. Chem. 1081, 53, 1187-1190 Green, R. 8.; Havrilla, G. J.; Trask, T. 0. Appl. Spectrosc. 1980, 3 4 , 561-569. Green, R. B. Anal. Chem. 1981, 5 3 , 320-324. Trask, T. 0.; Berthoud, T.; Lipinsky, J.; Camus, P.; Stehle, J. L. Anal. Chem. 1983, 55,959-963. Lawton, J.; Weinberg, F. J. "Electrical Aspects of Combustion"; Clarendon Press: Oxford, 1969; Chapter 8. Nasser, E. "Fundamentals of Gaseous Ionizatlon and Plasma Electronics"; Wiley-Interscience: New York, 1971; Chapter 6. Glllespie, A. B. "Signal, Noise and Resolution in Nuclear Counter Ampliflers"; Pergamon Press: New York, 1953; Chapter 2. Malmstadt, H. V.; Enke, C. G.; Crouch, S.R.; Horlick, G. "Electronic Measurements for Scientists"; W. A. Benjamin: Menlo Park, CA, 1974; pp 818-819. Travis, J. C. J. Chem. Educ. 1982, 5 9 , 909-914.
RECEIVED for review February 28,1983. Resubmitted October 27, 1983. Accepted October 27, 1983. G.J.H. acknowledges the support of the National Research Council as a NRC-NBS Postdoctoral Research Associate. This effort was supported in part by the Defense Nuclear Agency through the NBS Law
Anal. Chem. 1984, 56, 193-196
Enforcement Standards Laboratory; DNA Task B990MXPF, Work Unit 00064, William J. Witter, DNA Task Manager. Presented in part at the 9th Annual FACSS meeting in Philadelphia, PA, September 1982. Certain commercial equipment, instruments, or materials are identified in this
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paper to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.
X-ray Diffraction Spectrometry for the Analysis of Crystalline Solid Phases J. R. Garcia, Marta SuPrez, C. G. Guarido, and Julio Rodriguez* Departamento de Quimica Inorgbnica, Facultad de Qufmica, Universidad de Oviedo, C/ Calvo Sotelo sln, Oviedo, Spain
X-ray dlffractlon In the quantitatlve analysis of crystalline solid phases was used. A nonconventionai method of callbrallon for mlxtures of materials with the same chemical composttlon and isomorphic structure Is reported. Thls method, whlch can be used when some of the components cannot be obtained In pure form, was applied to the evolution study of a-titanlum phosphate In the H+/LI+ and H+/Na+ Ion exchange. Dlstrlbutlon curves of solld phases were obtained.
The first synthetic ion exchangers for commercial applications were inorganic materials. After the initial development of fusion permutites and gel permutites (1, 2) for use in water-softening processes, a rapid expansion of organic ionexchange materials developed (3). In contrast, the study of inorganic solids was undertaken almost solely in relation to problems of structural chemistry and diffusion in solid systems. Due to new technical problems, such as the separation of ionic compounds in radioactive water, there has been a resurgence of interest in inorganic exchangers. In these operations, highly selective materials which have stability against high temperatures in acid medium and against strong ionizing radiation are required. Organic resins are not adequate for these applications because their selectivity and exchange capacity are altered by the presence of ionizing radiation. The fact that many insoluble oxides absorb anions or cations from an aqueous solution leads to problems in analytical separations. This has been attributed to several causes but it was not studied in the ion-exchange field until the use of an insoluble zirconium phosphate in the separation of uranium and plutonium from fission products was reported (4,5). As a result of the renewed interest in inorganic materials, the study of the insoluble acid salts of tetravalent metals has developed considerably. Compounds with a great variety of metals (Zr, Ti, Sn, Ce) and anionic groups (phosphate, arsenate, vanadate) were used, and the behavior of their amorphous ( 1 , 6) and crystalline (7-10) forms was studied. The most widely studied compound, among these materials, is a-zirconium bis(monohydrogen orthophosphate) monohydrate (a-ZrP), a lamellar solid (11). As a consequence of its special arrangement, the reflection in the X-ray diffraction powder pattern, at lower angular values, corresponds with the value of the spacing between layers (12, 13). Control of the saturation degree of ion-exchanger material is usually carried out by conventional methods of chemical analysis. They are slow procedures but their accuracy is great. However, in industrial processes, where there is a need to know
the actual degree of ionic conversion a t a fixed moment, the speed of the determination may be more decisive. Ti(HP04)2.H20(a-Tip) is isomorphic with a-ZrP (14)and both show cation exchange properties. a-TiP is an adequate material for retaining Li+ and Na+ ions (15-20). In this process, it behaves as a bifunctional exchanger, the presence of distinct crystalline phases being observed: TiHM(P04)2-xH20 and Ti(MP0&.yH20, where M = Li, Na (17-20). When the hydrogen ion is substituted by another cation in a-Tip, the spatial arrangement of each layer remains unaltered (21). Nevertheless, the layers will be situated a t different distances, the value of which will be a function of the size of the substituted ion and the degree of hydratation of the crystalline phase formed (10, 17, 18). The present paper reports the quantitative determination of the concentration of solid phases on samples of a-TiP unsaturated in Li+ and Na+ by measuring the intensities of the X-ray diffraction lines characteristic of the interlayer spacing and the most adequate conditions for their realization. In the following discussion, for the sake of brevity, the various ionic forms are simply indicated by their counterions (under a bar) and water content, while their interlayer distances are reported in parentheses (8). Thus, for example, Ti(HP04)2.H20and Ti(NaP04)2-H20will be written as ".H20 (7.6 A) and " a . H 2 0 (8.4 A). EXPERIMENTAL SECTION Reagents. All chemicals used were of reagent grade. The NaOH solutions were standardized with HC1, which had previously been standardized against Na2C03. The a-TiP was obtained following the method of Alberti et al. ( I @ , using 10 M H3P04and reflux times of 50 h. The titanium phosphate gel was prepared by precipitation from a hydrochloric solution of TiC14with diluted H3POI. The crystalline solid (a-Tip) was washed with deionized water until free of chloride (test with AgNO,), dried at 60 "C, and ground to a particle size of less than 30 fim. This solid was then characterized by chemical analysis, thermal analysis (DTA and TGA), IR spectrometry, and X-ray diffraction. Analytical Procedures. The determination of the concentration of phosphorus and titanium in the solids was carried out gravimetrically (22). The released phosphate groups were measured spectrophotometrically (23),using a Perkin-Elmer Model 200. The lithium and sodium ions in solution were determined by atomic absorption spectrometry, using a Perkin-Elmer Model 372. The diffractometer used was a Philips Model P V 1050/23 (A = 1.5418 A; (28) scan rate, 0.25'/min; chart speed, 2 cm/min). Ion Exchange Studies. The exchanger was equilibrated with the 0.1 M (MC1 + MOH) solution at 5.0 and 25.0 "C (f0.1), following a variation of the procedure described by Clearfield et al. (24). The hydroxide was added with additions of 1 mL (5 "C) or 2 mL (25 "C) (every second addition was followed by a 60 (5
0003-2700/84/0356-0193$01.50/00 1984 American Chemical Society
