The Flame Ionization Detector

December 1, 2005
John V. Hinshaw

John V. Hinshaw is senior staff engineer at Serveron Corp., Hillsboro, Oregon, and a member of LCGC's editorial advisory board. Direct correspondence about this column to "GC Connections," LCGC, Woodbridge Corporate Plaza, 485 Route 1 South, Building F, First Floor, Iselin, NJ 08830, e-mail LCGCedit@ubm.com. For an ongoing discussion of GC issues with John Hinshaw and other chromatographers, visit the Chromatography Forum discussion group at http://www.chromforum.com.

LCGC North America

LCGC North America, LCGC North America-12-01-2005, Volume 23, Issue 12
Page Number: 1262–1272

Flame ionization detection (FID) is the most commonly used gas chromatography (GC) detection method. Flame ionization detectors respond to a wide assortment of hydrocarbons, have a large dynamic range, are...

Ionization detection methods include flame ionization detection (FID) and, among others, electron-capture, photoionization, and thermionic-specific — also called nitrogen–phosphorus — detection. Ionization detectors interact with solutes eluted from gas chromatography (GC) columns to produce a current that varies in proportion to the amount of solute present. FID is sensitive to molecules that are ionized in a hydrogen–air flame, including most carbon-containing compounds (with some notable exceptions; see Table I). The other detectors rely upon substance-specific ionization mechanisms and respond only to certain heteroatoms such as halogens, nitrogen, or sulfur for electron-capture detection; nitrogen and phosphorus for nitrogen–phosphorus detection; or to specific chemical structures such as aromatics for photoionization detection. As ions are formed inside the detector, they are impelled by an electric potential toward an electrode, producing a minute current on the order of picoamps (10-12 A) for FID. This current is converted to a voltage, filtered, and amplified as required.

John V. Hinshaw

Although these ionization detectors share several features, their implementations differ significantly. Detector performance characteristics (sensitivity, minimum detectable quantity, linearity, and selectivity) are affected strongly by the type of ionization mechanism, the internal electrode arrangement, and the electronics.

FID

The internal arrangement of a typical flame ionization detector is shown in Figure 1. Carrier gas from the column enters at the bottom of the detector and is mixed with hydrogen combustion gas plus optional makeup gas in the area below the flame jet. This mixture is then combined with air and burned just above the jet tip. A negative polarizing voltage is applied between the jet tip and a collector electrode; as electrons are formed, they are accelerated across the jet tip–collector gap by the electric field and sent to an electrometer. Depending upon the FID design, either the collector or the jet tip is kept at ground potential; Figure 1 shows a grounded collector design. Air, carbon dioxide, and water exhaust gases are vented from the top of the detector body. In some flame ionization detectors, a glow-plug operates momentarily to ignite the flame.

Table I: FID relative sensitivities for various compounds and classes

Figure 2 shows a schematic of detector electronics. From left to right: a 200-V polarization voltage is applied across the flame jet and the collector. Electrons formed in the flame by combustion of hydrocarbons are collected under the influence of the electrical field, and the resulting current is converted to a voltage by an electrometer that can have one or more operating ranges. The voltage is amplified and high-frequency components are filtered out. The detector signal is converted to discrete digital samples by an A/D converter and additional signal processing is applied as required. This is a typical implementation; there are many other possibilities. Several amplification ranges are available typically, ranging from about 1 pA (input)/mV at the highest output sensitivity to about 10 nA (10 X 10-9 A)/mV at the lowest output sensitivity. Some GC systems use a logarithmic amplifier that covers the entire dynamic range. The detector signal is filtered to remove unwanted high-frequency noise. Noise is produced by instabilities in the flux of ionizable compounds in the carrier gas, by the flame itself, by the electronic circuit, and by induction of stray electromagnetic signals (from cell phones, for example). The FID electrometer and amplifier circuits impose an electronic limit on the response speed, and additional, more sophisticated signal processing is carried out in the GC firmware as well as the data system. For most capillary GC peaks, a response time of about 200 ms is appropriate and will reject the majority of detector noise while delivering better than 95% peak-shape fidelity. A response time of 50 ms or lower is required for fast capillary peaks (width at half-height << 1 s) as encountered in high-speed or comprehensive GC X GC separations. A too-fast response will not affect peak shapes, but will pass extra noise through the system and potentially worsen minimum detectable quantities. The A/D conversion rate affects the signal fidelity as well. In general, the sampling rate should be twice the maximum frequency of interest in the signal. For example, a response time of 200 ms corresponds roughly to 5 Hz and, thus, would be sampled at 10 Hz or greater. A recent installment of "GC Connections" discussed signal processing and peak shape in more detail (1).

Figure 1: Flame ionization detector cross-section. 1 electrometer connection, 2 = effluent exit, 3 = igniter coil, 4 = igniter power connection, 5 = polarizing voltage supply connection, 6 = air input, 7 = column connection, 8 = hydrogen input, 9 = flame jet, 10 = collector electrode. (Derived from a figure courtesy of PerkinElmer Instruments, Shelton, Connecticut).

FID Sensitivity

Overall FID sensitivity depends upon the combustion gas flow rates, the carrier gas flow rate, the flame jet exit diameter, the relative positions of jet and collector, and — to a lesser degree — the detector temperature.

Combustion gas flow rates: Combustion gas flow rates must be set correctly for proper FID operation; follow the manufacturer's recommendations for air and hydrogen flow settings. In general, the air:hydrogen ratio should be approximately 10:1. A hydrogen flow rate of 30–45 mL/min with a corresponding air flow of 300–450 mL/min is common. FID sensitivity will be reduced as hydrogen flow deviates above or below optimum, as illustrated in Figure 3. The linear dynamic range is affected by hydrogen flow as well: higher flows tend to reduce the linear dynamic range. There is little reason to operate a flame ionization detector far off the manufacturer's gas flow settings; they have been carefully optimized for that specific detector. Air flow is less critical than the hydrogen flow, but too much air will destabilize the flame causing noise and possible flame-out. Not enough air will reduce sensitivity and shorten the linear dynamic range.

Figure 2: Flame ionization detector electronics.

Caution: Hydrogen is highly flammable and can cause a serious explosion if allowed to build up in an enclosed space such as the GC oven. Never turn on the hydrogen flow without a column or blank fitting attached to the detector's base to prevent hydrogen from leaking into the oven.

Jet diameter: Standard FID jets have exit diameters of approximately 0.5–0.7 mm, which is suitable for most applications. A smaller jet of about 0.3 mm i.d. is sometimes used with capillary columns to gain sensitivity (about 1.5X); rarely, problems can be encountered with solvent-peak flame-out. A narrow FID jet is not recommended for packed-column use because stray column packing support easily can clog the jet passage. Conversely, narrower jets prevent the tip of a capillary from accidentally protruding into the flame.

Carrier gas flow rate: The carrier gas flow rate is an important consideration for detector sensitivity. For packed or micropacked columns, carrier flow normally will be greater than about 8–10 mL/min. If the packed column flow is under 40 mL/min, then the standard hydrogen flow need not be changed. When the packed column flow rate exceeds 40 mL/min, it might be necessary to increase the hydrogen flow somewhat to achieve a stable, sensitive flame. Larger jet diameters (0.7 mm) are also beneficial at higher carrier flows. The choice of carrier gas — other than hydrogen — such as helium, nitrogen, or argon does not affect detector operation significantly.

Figure 3: Effect of hydrogen flow on relative FID sensitivity. This is a representation of typical results.

Different flow considerations apply for capillary columns. Chromatographers can choose to operate columns with inner diameters of 0.53 mm and greater well above their optima at relatively high carrier flow rates of 10–20 mL/min. Normally, a flame ionization detector does not require any special attention under such conditions. When capillary columns with inner diameters of 0.32 mm or less are used, or when wide-bore columns are operated closer to optimum flow rates of less than 10 mL/min, flame ionization detectors can benefit from the addition of makeup gas to the carrier stream before entering the jet area. Makeup gas has two important effects. First, it maintains optimum carrier gas flow through the jet and keeps the detector operating at the best sensitivity and linear dynamic range. Second, for some detectors makeup flow sweeps out the area under the jet and inside the detector base, alleviating any peak broadening that might be produced as capillary peaks encounter larger-diameter internal passageways. Follow the instrument manufacturer's instructions regarding makeup gas and its flow.

Hydrogen, while sometimes used as a carrier gas for packed columns, is commonly used with capillary columns. Hydrogen carrier gives a wider range of optimum linear velocities or flows, is less expensive than helium, and can be generated from water on-demand with an appropriate hydrogen generator. With FID, it is convenient to compensate for the added carrier gas hydrogen by reducing the detector hydrogen flow correspondingly. For a column flow rate of 5 mL/min, for example, detector hydrogen flow should be reduced by 5 mL/min so that the total hydrogen flow through the jet is at the optimum level.

Column oven temperature might affect carrier flow rates, depending upon the carrier supply operating mode. When changing the oven temperature, the total hydrogen flow through the detector should remain constant. Electronic pressure programming systems accomplish this by determining the carrier gas flow rate as the oven temperature changes and adjusting the detector hydrogen flow accordingly. If running in constant-pressure mode, the carrier gas flow will drop off as the oven temperature increases; the detector hydrogen flow would be increased accordingly. If running in constant carrier gas flow mode, then the FID hydrogen flow would remain constant as well.

Detector temperature: The sensitivity of a flame ionization detector does not depend strongly upon its temperature, provided some conditions are met. The appropriate detector temperature is determined by the greater of the following two conditions: a minimum temperature of 150 °C for stable detector operation and a minimum temperature of approximately 20–50 °C above the highest column temperature. The detector produces a large amount of water vapor, which can condense in the cooler upper areas around the collector if the detector base temperature is less than about 150 °C; this condensed water vapor can produce noise and baseline drift. On the other hand, the detector base must be hot enough to prevent condensation of peaks as they are eluted from the column, so it should be kept somewhat warmer than the highest operating column temperature.

If a capillary column is installed with its end inserted into the detector base up to the jet and is operated at oven temperatures approaching the column's maximum rated temperature, then it is possible that the end of the column will be overheated in a detector base that is another 20 °C warmer. Such overheating can produce excessive detector noise from decomposing stationary phase, cause solute adsorption onto subsequently exposed column surfaces, and reduce column life. A capillary column detector adapter that positions the end of the separation column in the oven and conducts carrier gas flow along a glass-lined tube or via a piece of deactivated fused silica into the detector jet will help alleviate such problems.

Setting Up a Flame Ionization Detector

Carrier and combustion gas purities, pressures, and flow rates as well as detector and column temperatures are all important considerations when setting up a flame ionization detector. There are several steps to follow. First, be sure that all gases are of sufficiently high purity and that their supply pressures are stable enough to provide reliable operation. Then, with the instrument turned on but unheated, set the required gas flows. Finally, heat the injector, detector, and column to their operating temperatures and ignite the flame. These steps are detailed in this section.

Gas Source

Flame ionization detectors are quite sensitive to hydrocarbon impurities that can be present in gas cylinders or connecting tubing. Hydrocarbon impurities in the combustion gases will cause increased detector noise levels as well as higher baseline signal levels. Hydrocarbon filters are recommended for installation at the external GC bulkhead fittings for air, hydrogen, makeup gas, and of course, the carrier gas. It is not necessary to remove oxygen from the FID hydrogen stream, but an oxygen filter on the carrier line is recommended highly as well, so be sure to trap oxygen if hydrogen flame gas is used as the carrier gas as well.

Hydrogen for FID alone should be of 99.995% purity or better. If used for carrier gas, then 99.999% or better purity is preferred. There are several excellent commercial hydrogen generators that can produce sufficient carrier-grade hydrogen to supply dual flame ionization detectors plus one or two carrier channels with split injectors. If an electrolytic hydrogen generator is used, be sure the water you add is free of hydrocarbon impurities.

Air for FID should contain less than 100 ppb of hydrocarbon impurities. Aside from standard compressed gas tanks, a variety of suitable purified air generators are available with capacities ranging from a couple of chromatographs up to an entire laboratory's worth. Older air compressors, or so-called "house" air supplies, should not be used with gas chromatographs except to supply operating pressure for pneumatic valve actuators.

Carrier-gas purity is also important for proper detector operation — with or without makeup gas. Makeup gas impurities affect the detector in much the same manner as combustion-gas impurities. Even without makeup gas, impurities in the carrier gas eventually can pass through the column and onto the detector. In temperature-programmed operation, such impurities might appear as broad ghost peaks during a run or as a steadily rising baseline similar to column stationary-phase bleed. In isothermal operation, impurities might appear as a slowly rising baseline with increasing noise, often over a period of hours to days. Unfortunately, a heavily contaminated gas chromatograph often proves difficult to clean up. Even though the column can be baked out or replaced, impurities can remain in the internal gas lines, valves, and regulators after the contamination source is corrected. The best procedure is to assume that there can be a gas purity problem right from the beginning and install appropriate filters. Bear in mind that the best filter is one that is never needed because the incoming gas is consistently pure. On the other hand, assume that there will be a problem with incoming gas purity at some future time. Filters are an excellent insurance policy against contaminating an instrument.

Connecting tubing from the gas source to the instrument also can sometimes cause problems with contamination. Be sure to use copper or stainless steel tubing specially cleaned for chromatographic applications. Never use plastic tubing because significant amounts of plasticizer or monomer can be present. In addition, all plastic tubing is pervious to atmospheric oxygen. Leaky fittings also can be a contamination source: they allow some atmospheric gases to enter the instrument gas stream inside. Avoid leakage by ensuring that all fittings and ferrules are in good shape and not over-tightened. It is better to cut off a few inches of tubing and install a new nut and ferrules than to try to seal a leaking connection by overtightening.

Setting FID flow rates: Two situations arise when setting FID flow rates, depending on whether the gases are electronic pressure controlled (EPC) or manually controlled. With EPC systems, the flows are set on the instrument keypad. Do not assume, however, that the flows are correct — regular flow calibration is highly recommended. I like to measure the detector flow rates anyway. Be careful to enter the related settings that control the carrier gas mode of operation (constant pressure, constant flow, or constant velocity) and makeup gas flow. Also, bear in mind that in some GC systems, the flow rates depend upon the incoming gas pressure — if the pressure changes, then the flow controllers should be recalibrated.

For manually controlled detector gases, as well as when directly measuring detector gas flow rates, it is easiest to operate with the column connection in the oven blocked off with a blank ferrule or plug fitting. If the column is installed, then carrier flow should be enabled for capillary column installations, in which the column end is in the detector. In this situation, the operator will need to correct measured combustion gas and makeup flows for the column flow rate. Attach a calibrated flow meter to the detector's exit with the appropriate adapter and turn off the air, hydrogen, makeup, and carrier gas flows at the instrument. Be sure to set the tank regulators to recommended pressures and turn on any in-line shutoff valves. The hydrogen flow is the first to set. Turn on the hydrogen and set the correct flow rate, following the adjustment instructions in the manual. After turning on the flow, be sure to wait a minute or so for air to be purged out of the hydrogen lines for a more accurate reading.

Next, set the makeup flow, if used. Turn off the hydrogen flow and then turn on, measure, and adjust the makeup flow. If the hydrogen cannot be turned off conveniently, then subtract the measured hydrogen flow to find the makeup flow rate. Be careful, however, when using an electronic flowmeter. If your meter has settings to select the type of gas being measured, then it will produce inaccurate readings for gas mixtures. This is not a problem for a simple soap-bubble flowmeter, although readings should be corrected for ambient pressure, temperature, and the vapor pressure of the soap-bubble solution. The details of using a bubble flowmeter are found in reference 3 as well as in many instrument manuals and other chromatography books.

Third, set the air flow rate. This might require a larger-volume flowmeter to accurately measure the 10-fold higher flow. Again, it is best to turn off the hydrogen and makeup flows, but you can correct the measured air flow rate if necessary.

Finally, if it is not already on, then set the carrier gas flow. If you want to measure the carrier gas flow rate directly at the detector, then turn off the air, makeup, and hydrogen flows. Adjust the carrier gas flow controller, pressure regulator, or EPC system as required. Once column flow is established, and not before, the column and detector can be heated to their operating temperatures.

Accurate direct measurement of capillary-column flow under about 5 mL/min requires a suitable, low-volume flow-measuring device. For an EPC system, remember that with a split inlet system in constant or programmed flow mode, the system maintains column flow by calculating and setting the pressure drop required to produce the desired column flow based upon the oven temperature, the type of carrier gas, and the column dimensions entered by the operator. If the entered dimensions do not reflect the actual dimensions accurately, then column flow and velocity errors will result. If there is any doubt, see the instrument manual for a procedure to set, measure, and correct the dimensions on the basis of the measured column average linear carrier gas velocity.

Ignition: While the instrument is heating up, turn the combustion gas and makeup flows back on if necessary. You can ignite the flame as soon as the detector temperature has passed 100 °C. Most flame ionization detectors require users to temporarily reduce the air flow during ignition. Like a choke on an automobile, this reduced air flow creates a momentarily rich mixture that is easier to ignite. Some instruments have built-in igniters that are operated by pushbutton or from the keypad, while others have manual igniters that must be held over the detector as an internal glow wire is heated electrically. Some rely on a piezoelectric igniter. In any case, ignition is most often accompanied by an audible "pop."

Caution: Do not lean over the FID to see the flame (it is invisible), and always wear appropriate eye protection. Do not allow any clothing to come near the detector exit.

After the flame appears to have been ignited, check for combustion water vapor by holding a cold, shiny object such as a mirror or the polished end of a wrench directly over the FID exit — you should observe "steam" condensing on the cold surface. If you do not, the flame probably has not ignited or has gone out immediately.

Flame ignition problems have several causes. Foremost is an incorrect flow setting — or possibly you forgot to turn on one of the flows. Make sure that all flows are correct and that the gases are connected correctly at the back of the instrument. Flame ionization detectors will produce a very loud "pop" on ignition if the hydrogen and air lines are reversed, but usually the flame will go out immediately. Be very cautious in such cases because a large, invisible hydrogen flame that extends several centimeters above the detector can result from reversed connections.

Continued ignition difficulty might be due to a defective igniter or other hardware problem. To check a built-in igniter, first turn off the hydrogen flow. Then press the igniter button while indirectly observing the inside of the detector with a small angled inspection mirror. For a manual igniter, observe the internal element; you should see an orange glow, or with a piezoelectric igniter you will see the spark. If not, then check the igniter connections and replace the igniter element if needed.

Other hardware problems that cause difficult ignition include a broken or cracked flame jet, poor detector or column installation causing leaks around the detector body, or a poorly fitting flow-measurement adaptor plug that gives inaccurate flow measurements. If the detector had been operating well and then suddenly quit, check for a blocked jet tip by measuring the hydrogen flow. If required, replace or remove and clean out the jet carefully with a cleaning wire, following the manufacturer's maintenance procedures.

Sometimes the flame can blow out just after injection; the solvent peak can be large enough to interrupt the flame. If this occurs often, change to a flame jet with a larger internal diameter if possible, and adjust the hydrogen flow to more closely match the carrier flow rate, being mindful of a possible sensitivity compromise. If the problem persists, you should try reducing the amount injected, using a lower carrier gas flow rate, or both. If you are using a 0.53- or 0.75-mm i.d. capillary column, the problem might be due to the proximity of the column exit to the flame jet. It might be helpful to withdraw the column somewhat or to install a glass-lined detector-column adapter or piece of deactivated fused silica between the column tip and the flame jet.

Routine Troubleshooting

Flame ionization detectors generally are reliable once they are properly set up. Operators can check a few key areas immediately when previously good detector performance falls below the minimum required for the application. Flame ionization detectors are subject to two broad trouble categories: contamination and electronics. Of these, contamination is by far the more common.

Contamination: Everything that passes through a flame ionization detector is burned in the hydrogen flame. For carbon-based substances within normal levels, carbon dioxide and water are formed. Large amounts of chlorinated compounds or carbon disulfide, however, are not burned as efficiently as hydrocarbons. These materials can produce significant quantities of carbon particles (soot) as well as hydrogen chloride in the case of the chloromethanes and carbon tetrachloride. Carbon particles tend to aggregate between the jet and the collector, forming an electrical leakage path, and the result is a high, noisy baseline. Hydrogen chloride from chlorinated solvents can be tolerated in small quantities, but after extended exposure in combination with the water of combustion hydrochloric acid, will begin to corrode the detector's inner surfaces, producing electrical leakage paths and a high, noisy baseline.

Another common contamination source is stationary phase bleed from the column into the detector. Although this is not generally a problem for most capillary columns, packed columns as well as thick-film capillaries can emit significant amounts of stationary phase during their life, especially at elevated temperatures. Siloxane polymers produce silica when burned in a hydrogen flame. In a flame ionization detector, these silica particles tend to adhere strongly to the jet and collector surfaces inside the detector. These, in turn, can reduce the detector's sensitivity and increase the background signal level.

To check for detector contamination, shut off the combustion-gas flows and turn off the power to the instrument. After the instrument has cooled sufficiently, remove the detector covers and examine the outside of the detector body near the detector exit. It should be clean and completely free of colored deposits. Look down into the detector. Again, the surfaces should be clean and free of deposits. If you observe some colored material inside the detector, remove the collector electrode for a closer look. A black deposit indicates carbon formation. White or gray deposits are typical of silica contamination, and green or blue-green deposits or corroded areas are a sign of excessive acid formation.

Light deposits of silicon dioxide or carbon usually can be removed from the collector by gentle scrubbing with distilled water and surfactants or in an ultrasonic bath. Be sure to first remove the collector electrode from any attached electrical connections. Ceramic insulators from inside the detector also can be cleaned in this manner. In general, follow the manufacturer's recommended maintenance procedures. Detector parts that have been corroded should be replaced as cleaning is usually ineffective.

When the detector is reassembled, be sure that internal connections for the polarizing voltage or the collector electrode are secure. Electrical contacts can be cleaned by gently wiping them with a clean pencil eraser. Do not use any abrasives or emery cloth on detector parts — you will cause more harm than good.

Electronic problems: Flame ionization detectors produce minute picoampere currents. The electrometer–amplifier circuit is thus very sensitive. Although modern amplifiers and power supplies are very reliable, they do fail occasionally. Often, however, what appears to be an electronic problem actually is due to operator error. Check all instrument settings and external connections before assuming that the problem is electronic. Most internal electronic failures require the attention of a trained service technician. However, you can investigate and possibly remediate some of them.

Polarizing voltage supply failure is indicated by reduced peak size and by widely varying responses for different substances. If your instrument has a discrete polarizing voltage connection to the flame jet, you can check the supply. Such instruments usually have one or two separate wires or cables going to the detector in addition to the igniter cable, if any. If there is only one cable, your detector probably has a grounded flame jet. Do not attempt to check this type of detector for the polarizing voltage, but instead try swapping out the amplifier for a good amp.

Caution: FID polarizing voltage is a high voltage and is potentially dangerous. Turn off the combustion-gas flows and disconnect the polarizing voltage at the detector before making any measurements.

Use a high-impedance digital voltmeter to measure the polarizing voltage relative to ground. Be sure that the instrument is turned on and the detector is activated (some gas chromatographs turn off the polarizing voltage when the detector is not active). If there is no voltage, the supply requires servicing by a trained technician. If a 180–250 V reading is obtained, turn off the instrument, disconnect the polarizing-voltage supply, and check the resistance from the polarizer connection on the detector to ground or from the flame-jet tip to ground. You should get an "open circuit" reading. There is a significant leakage path if the resistance is less than about 10 Mo, and the detector should be cleaned, the jet replaced, or both. If possible, you also can swap a suspected electrometer for one that is known to be okay.

Detector heaters and temperature sensors should be tested or replaced only by a trained service technician. If the detector does not heat or the instrument reports that the temperature sensor is defective, you should not attempt to fix the problem yourself. Call in a qualified technician.

Summary

FID is the most familiar and widely used GC detection system, if not the simplest. It provides high sensitivity to a wide range of compounds as well as reliable routine operation. Common FID problems are few and easily identified. However, it is very important to remember that a gas chromatograph is a system that relies upon the proper functioning of all of its discrete components. A problem that appears to be detector-related can in fact originate elsewhere. Perform at least a brief check of all related instrument components before concluding that the detector is at fault.

John V. Hinshaw "GC Connections" editor John V. Hinshaw is senior staff engineer at Serveron Corp., Hillsboro, Oregon, and a member of LCGC's editorial advisory board. Direct correspondence about this column to "GC Connections," LCGC, Woodbridge Corporate Plaza, 485 Route 1 South, Building F, First Floor, Iselin, NJ 08830, e-mail lcgcedit@lcgcmag.com

For an ongoing discussion of GC issues with John Hinshaw and other chromatographers, visit the Chromatography Forum discussion group at http://www.chromforum.com.

References

(1) J.V Hinshaw, LCGC 21(3), 268 (2003).

(2) L.S. Ettre and J.V Hinshaw, Basic Relationships of Gas Chromatography (Advanstar, Cleveland, Ohio, 1993), p. 36.

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