Measurement of Ion Swarm Distribution Functions in Miniature Low

Measurement of Ion Swarm Distribution Functions in Miniature Low-Temperature Co-Fired Ceramic. Ion Mobility Spectrometer Drift Tubes. Kent B. Pfeifer*...
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Anal. Chem. 2005, 77, 5215-5220

Measurement of Ion Swarm Distribution Functions in Miniature Low-Temperature Co-Fired Ceramic Ion Mobility Spectrometer Drift Tubes Kent B. Pfeifer* and Arthur N. Rumpf

Microsensor Science and Technology Department 1744, Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1425

Measurements of the performance of a miniature, portable 12-mm-diameter, 57-mm-length low-temperature cofired ceramic (LTCC) ion mobility spectrometer drift tube were undertaken to verify models of ion transport and determine the physical shape of the ion “swarms” in the LTCC tube. Simplified two-dimensional Gaussian models of ion swarm shape were fit to measured data to extract geometrical shape parameters. Results indicate that tubetransfer function effects that produce asymmetric ion swarms are minimized in the tube reducing temporal dispersion. Data are presented that illustrate the swarm shape as a function of gate time, electric field magnitude, and total charge in the ion swarm. Characterization and understanding of the ion transport mechanisms and effects that limit the resolution and other performance parameters of miniature IMS drift tubes is essential to the development of practical, robust, portable systems for “first responder” and homeland security missions. Sandia National Laboratories is developing a miniaturized explosives detection system that requires the development of a practical miniature ion mobility spectrometry (IMS) drift tube as its principle sensor subsystem. IMS is an attractive technology for developing a miniaturized explosives sensor.1-4 An IMS sensor system has the advantage of operating at atmospheric pressure and is able to detect trace quantities of explosives. We have demonstrated a miniaturized IMS drift tube design that is similar in construction to larger “stacked” drift tube designs found in commercial systems.5 However, performance requirements in miniaturized IMS systems are a complex tradeoff between the practical concerns of cost, physical size, and power consumption versus the limitations of resolution and sensitivity required to accomplish the sensing task. Thus, as a result of experience gained in operation of the “stacked” IMS systems, we have migrated this design into a simple-to-assemble IMS drift tube constructed from rolled, low-temperature cofired ceramics (LTCC) with integral potential resistors.6 * To whom correspondence should be addressed. Phone: (505) 844-8105. Fax (505) 844-1198. E-mail: [email protected]. (1) Matz, L. M.; Tornatore, P. S.; Hill, H. H. Talanta 2001, 54, 171-179. (2) Wu, C.; Steiner, W. E.; Tornatore, P. S.; Matz, L. M.; Siems, W. F.; Atkinson, D. A.; Hill, H. H. Talanta 2002, 57, 123-134. (3) Tabrizchi, M.; Abedi, A. Int. J. Mass Spectrom. 2002, 218, 75-85. (4) Cottingham, K. Anal. Chem. 2003, 75, 435A-439A. (5) Pfeifer, K. B.; Sanchez, R. C. Int. J. Ion Mobility Spectrosc. 2002, 5, 63-66. 10.1021/ac050149z CCC: $30.25 Published on Web 07/09/2005

© 2005 American Chemical Society

IMS drift tube designs for handheld instruments are constrained by several key areas of concern. First, the tubes must be small and lightweight enough for the application. Second, the sensitivity and resolution must be adequate for the application, and finally, the cost of the manufacture and assembly of the tube must be kept low enough to be practical. Our IMS subsystem design has an overall dimension of 10 cm × 5 cm × 5 cm and has a mass of fewer than 200 gm including its enclosure making the subsystem miniature and portable. In addition, our system employs a 20-µCi 241Am sample as the ionization source rather than the conventional 63Ni found in most commercial IMS systems. This eliminates many of the regulatory issues associated with transportation and storage of radioactive sources while still requiring no system supplied power for ion production. Stacked Drift Tube Design. We have previously reported the design and testing of a “stacked” 6-mm-bore, 37-mm-drift length tube that is contained on a small circuit board with dimensions of 6 cm by 10 cm.5 The board contains all of the electronics to operate the drift tube including a 1000 VDC supply and associated switching circuitry, resistor chain for development of IMS drift tube potential profiles, and a nine-pole, 1010 Ω gain transimpedance amplifier/filter circuit for IMS current detection. The band-pass of the filter is from ∼30 Hz to ∼5 kHz. The entire IMS subsystem has a mass of 0.06 kg. Miniature drift tubes require a high linear density of electrodes to increase the region of electric field uniformity in the drift tube. To maintain resolution in a drift tube, it is important that the local electric field be a constant over as much of the cylindrical cross section as possible. Since electric field is a vector quantity, this requires that the direction be parallel with the axis and the magnitude be constant. Uniform electric fields provide every ion with an equal probability of transport via electric forces to the detector at exactly the same drift velocity (vd) independent of its initial conditions. The motion is independent of the initial conditions because the mean free path at atmospheric pressure is on the order of 66 nm, implying that the ions reach terminal velocity very rapidly and their average drift speed and direction is dominated by the electric field direction and magnitude. If an ion is transported to the detector in a region of nonuniform field such as very near the tube walls, then intuition and modeling confirm that its path will be substantially longer (6) Peterson, K. A.; Rohde, S. B.; Pfeifer, K. B.; Turner, T. S. 204th Meeting of the Electrochemical Society, Orlando, FL, October 12-17, 2003.

Analytical Chemistry, Vol. 77, No. 16, August 15, 2005 5215

than an ion transported down the center of the drift tube. This results in spreading of the pulse in time or “temporal dispersion”. Temporal dispersion leads to a reduction in the resolution of the drift tube since ions closer to the walls will arrive at the detector later than the ions in the center of the tube resulting in spreading and asymmetry of the IMS pulse.7 Low-Temperature Cofired Ceramic Drift Tube. LTCC technology holds the promise of inexpensive automated drift tube production with minimal part counts and electrical connections to the control and detection circuitry.6 We have demonstrated an LTCC drift tube with dimensions similar to the “stacked” drift tube (bore of 6 mm and a 37-mm drift length). However, to produce a higher resolution tube, we have now produced a 12mm-bore and 57-mm-drift length LTCC tube. This tube has a high density of electrodes spaced at 0.75-mm pitch over the length of the drift tube to maintain a uniform electric field in the center of the tube and reduce temporal dispersion. The high-voltage dc power supply (EMCO CA20N8) employed in our circuitry is variable, and the electric fields obtained in the center of the tube can range from 0 to 18 kV/m. The detector circuitry has performance parameters similar to that of the amplifier developed for the stacked design and described above. LTCC allows simple screen-printing operations for the production of the electrodes, and on-board surface mount resistors fabricated directly on the tube reduce the number of electrical connections required without sacrificing the performance of numerous electrodes (80 electrodes) with small (0.75 mm) spacing. In addition, integral heating elements are incorporated into the structure for operation at elevated temperature. Most of the processing of the LTCC occurs during its unfired state during which it is still pliable. Thus, the processing can be done to flat sheets of material and the tube is then rolled onto a mandrel of the desired inner diameter and fired at 550 °C to burn off the organic binders in the material and then at 850 °C to complete firing of the tube. The LTCC shrinks ∼12% during the 850 °C firing, requiring that allowance in the size of the structures be made to accommodate the shrinkage. Fired tubes have the desired final dimensions required for operation and mechanical fit to circuit boards and housings. After firing, the resistors are laser trimmed to within 1% of the desired values and the tubes are dimensionally trimmed. Control structures constructed using LIGA (LIGA is a German acronym that stands for lithography, electroforming, and molding) processing are inserted into the tubes and form the gate structures of the tube. The end pieces containing the gas inlets, target, apertures, and 241Am sources were constructed from the LTCC and bonded to the tubes. The experimental setup consisted of a signal generator (SRS DS3459) used to set the overall timing of the circuit connected to a variable-width pulse generator (HP 8082A10). The output of the pulse generator was then used to trigger an oscilloscope (HP 54522A10) and the drive electronics of our custom IMS board. The (7) Pfeifer, K. B.; Rohde, S. B.; Peterson, K. A.; Rumpf, A. N. 13th International Society of Ion Mobility Spectrometry Meeting, Gatlinburg, TN, July 25-29, 2004. (8) EMCO High Voltage Corp., 70 Forest Products Rd., Sutter Creek, CA 95685; (209) 267-1630. (9) Stanford Research Systems, Inc., 1290-D Reamwood Ave., Sunnyvale, CA 94089. (10) Hewlett-Packard Co., 3000 Hanover St., Palo Alto, CA 94304-1185.

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Figure 1. Gaussian in the radial direction and Gaussian in the axial direction where w and a are the 1/e dimensions, respectively. The tube boundary and the detector diameter are illustrated for reference. As is clearly illustrated, the radius of the swarm is significantly larger than the tube diameter, implying that wall interaction must occur; however, our detector pin only samples near the center and thus observes an ideal Gaussian swarm shape.

IMS circuit board contains the necessary high-voltage supply for the tube potential gradient as well as switching circuitry that allows for development of 5-70-V potential wells in the tube. We have empirically determined that the highest signal-to-noise ratio occurs with a potential well on the order of 25 V and that is what was used for this experiment. The circuit board also contains a 200dB gain transimpedance amplifier (TIA) with a nine-pole bandpass filter (10-5500 Hz). The ion current is amplified by the TIA and displayed by the oscilloscope. Data from the scope are saved to its internal disk drive for later analysis. Drift gas is obtained by collecting room air through a small pump that can move ∼100 sccm through the drift tube. The drift gas was passed over the outlet of a diffusion tube that produces an estimated 300 ppm concentration of CH2Cl2 and is passed into the drift gas inlet of the drift tube. THEORY In the literature, it has been shown that the general charge density of the ion swarm in drift tubes, where the tube diameter is large compared to the ion swarm diameter and the electric field is constant, is of the following general form:11,12

F(z,r) ) Foe-[(r/w) +(z/a) ] 2

2

(1)

In eq 1, F(r,z) is the charge density as a function of radius (r) and axial direction (z), Fo is the initial charge density, w is the 1/e radius, and a is the 1/e width along the z-axis. Equation 1 is simply a Gaussian in the axial direction multiplied by a Gaussian in the radial direction with a scale factor that is set by the initial conditions (Figure 1). Integrating the charge density over a cylindrical volume with the radius of the detector element in the drift tube (R) leads to the following equation for the total charge (11) Mason, E. A.; McDaniel, E. W. Transport Properties of Ions in Gases; John Wiley and Sons: New York, 1988; pp 86-89. (12) Spangler, G. E.; Collins, C. I. Anal. Chem. 1975, 47, 403-407.

measured.

Q(z,r) )

(az )(1 - e

Qtot ) lim Foπ3/2aw2 erf

∫ F dV ) ∫ ∫ ∫ F re 2π

0

V

z

R

-z 0

-[(r/w)2+(z/a)2]

o

dφ dz dr (2)

Q(z,R) ) Foπ3/2aw2 erf(z/a)(1 - e-(R/w) ) 2

∫v

d

dt ) κEt + z0

(4)

with z0 the initial position of the ion “swarm”. Substitution of eq 4 into eq 3 and differentiation with respect to time leads to an equation for ion current:

i(t) ) dQ/dt ) 2πκEw2Foe-((κEt + z0)/a) (1 - e-(R/w) ) 2

2

(5)

Recognizing that the output from the IMS amplifier circuit is a voltage that is proportional to the IMS current multiplied by the transimpedance gain of the circuit (G ) 1010 Ω), we can rewrite eq 5 in terms of adjustable parameters that can be fit to the measured data using MathCAD.13 The form of eq 6 (all parameters represented by u0-4) is required by the structure of the curve-fitting routines found in MathCAD, where no additional constants can be independently passed to the curve fitting algorithm:

v(t) ) u0 + u1u42e-((t+u2)/u3) (1 - e-(1/u4) ) 2

2

(6)

In eq 6, u0 is the DC offset in the data whose origin is in the leakage current of the operational amplifiers that form the filter in the amplifier circuit and must be included as a DC error correction term. The other parameters are as follows where L is the drift length of the tube (57 mm) and td is the drift time:

u1 )

2πLR2F0G u 1t d f F0 ) td 2πLR2G

- (R/w)2

))

Foπ3/2aw2 f Qtot )

u1tdaw2π3/2 2πLR2G

(11)

(3)

Since z ) z(t) and recognizing that the standard ion mobility equation for drift velocity (vdzˆ ) κEzˆ) applies, where vd is the drift speed of the ions, E is the electric field vector, κ is the mobility of the ions, and zˆ is a unit vector in the axial direction along the drift tube. We can write the position of the ion swarm as a function of time:

z(t) )

zf∞ Rf∞

(7)

u2 ) z0td/L f z0 ) u2L/td

(8)

u3 ) atd/L f a ) u3L/td

(9)

u4 ) w/R f w ) u4R

(10)

In addition, it possible to calculate the total charge in the packet by taking the limit as z approaches infinity and R approaches infinity of eq 3 as shown below: (13) Mathsoft Engineering and Education, Inc., 101 Main St., Cambridge, MA 02142; (617) 444-8000.

By writing the parameters as in eqs 7-10, we are able to extract the physical shape of the charge swarm from known physical constants of the tube and electronics such as length, detector radius, and detector gain and measurable quantities such as drift time. The above arguments are predicated on the shape of an ion swarm fitting the data well, which implies that the swarm does not undergo temporal dispersion that results in an asymmetric pulse shape to any appreciable degree. This is the basis of the hypothesis of eq 1. Figure 2 is a plot of the time spectra of the 12-mm drift tube fit to eq 6 for various electric field magnitudes with a Cl- ion pulse derived from CH2Cl2 at room temperature. The CH2Cl2 is injected into the drift tube by way of a drift gas flow of ∼100 sccm room air (10-20% RH, 23 °C) that is first passed over a diffusion tube containing liquid CH2Cl2. This gives a CH2Cl2 concentration in the ionization chamber of ∼300 ppm. Figure 2 is data for a 500µs gate time; however, similar plots for other gate times illustrate similar data fits. Figure 3 illustrates the relationship between signal amplitude and gate time for the Cl- ion pulse derived from CH2Cl2 at room temperature. These data illustrate that there is not a linear relationship between ion pulse width and signal amplitude due to diffusion, electrostatic space charge effects, initial width of the pulse prior to release into the drift tube, and other broadening mechanisms. To achieve an appropriate balance between signal amplitude and pulse width, it is appropriate to measure the shape of the ion pulse as a function of various electric fields magnitudes and gate times in the tube. The symmetry of the pulses in Figure 2 verifies that there is very little temporal dispersion of the ion swarm in the 12-mm tube. This is potentially due to very little wall interaction by the swarm in the form of ions traveling in regions of electric field nonuniformity and very little trapping of ions in small surface imperfections of the inner surface of the tube. In miniature tubes where wall interaction is prevalent such as our stacked drift tubes and our 5-mm rolled LTCC tubes, there is an asymmetry in the shape of the pulse that is characterized by a more rapidly changing leading edge than trailing edge. This asymmetry has been observed in both 6-mm-diameter stacked tubes (with rough wall surfaces) and 6-mm-rolled LTCC tubes (with smooth inner wall surfaces).7 Since this temporal dispersion has been observed in tubes with smooth surfaces, we conclude that interaction with the nonuniform electric field at the walls on small-diameter tubes is the predominate temporal dispersion mechanism in these tubes. For this 12-mm-diameter LTCC tube design, symmetry in the data pulses implies that the low-interaction hypothesis is correct. RESULTS Detailed measurements of Cl- ion pulses were undertaken for the tube at several electric field strengths from 9.3 to 17.3 kV/m and gate times from 50 to 1400 µs. Typical operational gate times are limited to less than 1000 µs in order to maximize signal-tonoise ratio and tube resolution. Each measurement was then fit Analytical Chemistry, Vol. 77, No. 16, August 15, 2005

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Figure 2. IMS response for a 12-mm-diameter LTCC drift tube with a corresponding fit of eq 6 (solid line) to the data. This plot is for a Cl- reactive ion peak in the tube with a 500-µs gate time and various field magnitudes from 12 to 18 kV/m. Excellent fit to eq 6 implies that there is very little interaction between the walls and the ion swarm.

Figure 3. Data showing the response of the rolled IMS to a Cl- ion peak derived from CH2Cl2 for an electric field of 14 kV/m for various gate times. Data illustrate the tradeoff between signal and resolution. As the signal increases with gate time, the full width at half-amplitude of the pulse increases decreasing the resolution.

to eq 6 and the parameters u1-u4 were extracted from the model and converted to the geometrical parameters (a and w) and charge density (F) of eq 1. The geometrical parameters a and w are plotted in Figure 4 as a function of initial gate time. The 1/e parameter in the radial direction (w) is ∼8 mm for short gate times and increases linearly with gate time. Similarly, the axial 1/e parameter (a) is on the order of 3 mm for short gate times and increases linearly with gate time over the gate lengths measured. However, the a parameter data show a definite decreasing trend at any given gate time as the electric field strength is increased. Several observations can be made about the performance of the tube based on these measurements. First, the resolution, which for IMS is defined as the drift time (td) divided by the pulse width at half the maximum amplitude (∆t), is reduced as the gate time increases as is expected.5,14-16 Our shutter is of a design that relies on a potential well to capture ions rather than to block the (14) Xu, J.; Whitten, W. B.; Ramsey, J. M. Anal. Chem. 2000, 72, 5787-5791.

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Figure 4. Gaussian parameters a and w as a function of gate time for various electric field magnitudes. The shape and size of the ion swarms increase with gate time, but w appears to be roughly independent of electric field magnitude. The two solid lines in the a data are the linear regression of the 10.7 kV/m data and the 17.3 kV/m data illustrating the trend toward narrower width with increasing field strength.

flow of ions by annihilation as in the case of a Bradbury-Neilsen or a Tyndall gate. In these types of gates, the ion current density is not changed locally since there is no mechanism to concentrate ions. Ions are simply annihilated at the same rate that they drift into the gating structure. In our tube, we employ two conducting LIGA formed grid structures spaced 0.75 mm apart that form a uniform potential contour across the diameter of the tube at their respective potentials. The first grid structure is then actively switched to form a 25-V potential energy well in the potential field. The second grid is permanently biased such that it reestablishes the uniform electric field found in the rest of the tube and also tends to shield the detector pin from the field disturbance due to the gate switching. Ions of low kinetic energy are trapped in this potential well, and the charge density becomes locally higher resulting in electrostatic repulsion effects initially spreading the captured ion swarm when the potential well is released.17 While we are currently unsure of the exact charge distribution at the well, its initial width must be on the order of the spacing between the two LIGA grids (0.75 mm), otherwise ions would enter into the drift region and escape the well. The value of w appears to be independent of electric field strength over the gate times measured and within the measurement uncertainty. However, the value of a illustrates a definite trend toward a narrower pulse as the electric field magnitude increases. This is expected since diffusion and electrostatic repulsion have less time to act on the swarm as the drift speed increases (transit time decreases). The pulse width in an IMS has been related to several broadening mechanisms including (1) initial pulse width, (2) diffusional broadening, (3) electrostatic space charge repulsion, (4) capacitive coupling between approaching ions and the collector, (5) field gradients, (6) temperature gradients, (7) gate (15) Rokushika, S.; Hatano, H.; Baim, M. A.; Hill, H. H. Anal. Chem. 1985, 57, 1902-1907. (16) Revercomb, H. E.; Mason E. A. Anal. Chem. 1975, 47, 970-983. (17) Blanchard, W. C. Int. J. Mass Spectrom. Ion Processes 1989, 95, 199-210.

depletion/dynamic leakage, (8) pressure fluctuations, and (9) ionmolecule reactions in the drift space.18 Care was taken to avoid temperature gradients and pressure fluctuations in the drift tube by operating the tube with static heating and supplying gas from the pump through a pressure damper. In addition, our detection electronics have a pass-band that is from 20 to 5500 Hz, making it insensitive to dc ion currents that might be expected from dc gate leakage. Capacitive coupling should lead to asymmetry in the pulse on the rising edge, which we generally do not observe in our drift tubes, leading to the conclusion that this effect is small. The tube was designed with 80 rings spaced at 0.75 mm centerto-center to form the potential gradient. This was done to reduce the effect of ion interaction with nonuniform electric fields near the wall. Thus, we are left with initial pulse width, diffusional broadening, electrostatic space charge repulsion effects, and ionmolecule reactions in the drift space as the principle broadening mechanisms in the tube. The initial pulse width (ag), to first order, is ∼1.5 mm based on the spacing of the control grids, and the amount of diffusional broadening (ad) that is expected for a singly ionized species at 300 K is ∼1.0 mm.14 Since these effects are uncorrelated, we add them as follows:19

Figure 5. Total charge in an ion swarm as a function of gate time for various gate times and electric fields. The linear fit of the data indicates that the average Cl- ion current in the system is on the order of 20 pA and that the ion well is not becoming saturated.

Thus, the expected pulse width from diffusion and initial gate width alone is on the order of 1.6-1.8 mm for all the electric field magnitudes considered. This is less than the measured width for the limit of zero gate time (y-intercept of a data in Figure 4) in all cases. The limit of zero gate time implies zero ions in the swarm and allows separation of the effects of diffusion and initial swarm width from space charge effects. Thus, we must conclude that electrostatic space charge repulsion effects and ion-molecule reactions account for the rest of the broadening observed. Modeling of the electric field as a function of position in the tube when the capture well is active illustrates that for a potential well the initial space charge-induced fields are on the order of the potential well depth (25 V) divided by the control grid spacing (0.75 mm) or 30 kV/m, which is on the same order as the drift field. Thus, we cannot ignore the space charge effects with this type of gate as in the case of a Bradbury-Neilson or Tyndall gate. Initially, the space charge effect is large due to close spacing of the ions. However, this effect drops off as the inverse of the charge separation squared reducing its effect rapidly. We estimate from models published in the literature that the broadening due to space charge effects is on the order of 0.5 mm for an ion swarm of 20 fC (Figure 5).14 If we add a third term to eq 12 that is the widening due to space charge effects, the total swarm width becomes on the order of 2 mm; thus, we are left with an unaccounted 1 mm of widening that must be attributed to ionmolecule interactions. Figure 5 illustrates the relationship between the total ion charge (eq 11) as measured as a function of gate time. The total charge in the swarm increases at a rate that indicates that there is ∼20 pA of dc Cl- ion current being produced by the ionization

source and CH2Cl2. The actual current produced in the ionization region of the tube is larger than 20 pA, but some charge is lost during tube transit as expected. Thus, 20 pA is the effective dc current at the gate. Clearly, one substantial concern for field application of a miniature drift tube is the tradeoff between signal amplitude and resolution in these systems. For applications where the input chemistry is stable over long data acquisition intervals, the IMS can be operated at much shorter gate times, reducing the number of charges and hence increasing the resolution. However, to accomplish this with adequate signal-to-noise ratio (SNR), multiple scans must be averaged together. For applications such as explosive detection, a preconcentration scheme must be employed to capture trace material and then rapidly desorb it into the IMS, resulting in a transient chemical signature.20 This reduces the available time over which averaging can occur without reducing signal fidelity and requires IMS operation at longer gate times to improve SNR at the expense of system resolution. In addition, the radial Gaussian parameter (w) trends upward linearly over the measured gate times, implying a widening of the pulse with increased ion charge. This can be can be explained qualitatively by recognizing that the swarm will become larger in the radial dimension by way of the same mechanisms noted for the axial spreading. As the ion swarm becomes larger in the radial dimension, a larger fraction of the ions will begin interacting with the nonuniform electric field that does exist at the wall boundary. Thus, the swarm will deviate from the form of eq 1 and become wider due to temporal dispersion of the swarm near the edges. Our ion collector pin has a radius (2.5 mm) that is roughly half the overall 6-mm tube radius, implying that we are not measuring the ions in the outer 3.5 mm of the tube radius. We have intentionally chosen to measure only the center of the ion swarm at the expense of signal amplitude to reduce sensitivity to this wall-induced temporal dispersion. Because our collector pin is small compared to the diameter of the tube, our system tends to ignore temporal dispersion at the walls and appears to have a more ideal swarm shape.

(18) St. Louis, R. H.; Hill, H. H. Anal. Chem. 1990, 21, 321-355. (19) Siems, W. F.; Wu, C.; Tarver, E. E.; Hill, H. H. Anal. Chem. 1994, 66, 41954201.

(20) Hannum, D. W.; Linker, K. L.; Rhykerd, C. L.; Parmeter, J. E. IEEE 34th Annual 2000 International Carnahan Conference on Security Technology, Ottawa, ON, Canada, October 23-25, 2000; pp 222-227.

a2 ) ag2 + ad2

(12)

Analytical Chemistry, Vol. 77, No. 16, August 15, 2005

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An apparent contradiction is observed between the actual tube radius (6 mm) and the measured 1/e radius of the ion swarms (∼8 mm) as a swarm of this radius cannot fit into a tube of this diameter. Thus, there must be interaction between the edge of the swarm and the walls, and the Gaussian assumption must break down for any tube of finite radius. However, since our collector pin has a radius that is much less than the radius of the tube, we only sample that portion of the swarm that approximates a Gaussian of the form suggested in eq 1 and hence the model is approximately correct. CONCLUSION We have constructed a drift tube fabricated from low-temperature cofired ceramics and have measured its performance under various electric field magnitude and gate times to determine the physical parameters of the ion swarm. We have found, based on data fitting, that the ion swarms form a shape that approximates a two-dimensional Gaussian function in cylindrical coordinates (eq 1). The physical dimensions of the swarm trend upward in the axial direction as a function of gate time. The physical mechanisms that cause broadening in the tube were discussed and compared to the results. The broadening mechanisms of initial gate width, diffusion, and space charge repulsion account for the majority of

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broadening in the tube; however, the swarms appear to be ∼1 mm wider than what can be accounted for by these mechanisms, leaving ion-molecule interaction as the suspect mechanism. The radial 1/e dimension (w) also trends upward with gate pulse length and begins on the order of 8 mm. The w dimension of the swarm does not seem to vary with electric field within the limits of the experiment; however, slight narrowing is observed in the a dimension as the electric field magnitude is increased since the time of flight is reduced and hence the spreading time is reduced. In addition, the average ion current was measured using the fit parameters and found to be on the order of 20 pA with a 20 µCi 241Am source and 300 ppm CH2Cl2 dopant gas. ACKNOWLEDGMENT Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.

Received for review January 25, 2005. Accepted June 7, 2005. AC050149Z