(26) La Villa, R. E., Bauer, S. H., J . Am. Chem. SOC.85, 3597 (1963). (27) Mellor, J. W., “A Comprehensive
Treatise on Inorganic and Theoretical Chemistry,” Vol. 4, p 303, Longmans, Green, London, 1923. (28) Moffat, A. J., Solomon, P. W., U. S. At. Energy Comm., Res. and Development Dept., IDO-16732, 1961. (29) Nelson, F. M., Eggertsen, R. T., ANAL.CHEM.30, 1387 (1958). (30) Pimentel, G. C., MpClellan, A. L., “The Hydrogen Bond p. 255, W. H.
Freeman, San Francisco and London, 1960. (31) Zbid., p. 202. Y . Acad. (32) Purnell, J. H., Ann. Sci. 72,598 (1959). (33) Rogers, L. B., Altenau, A. G., ANAL. CHEM.35, 915 (1963). (34) Scott, C. G., “Gas Chromatography 1962,” M. van Swaay, ed., p. 36, Butterworths, Washington, 1862. (35) Smith, E. D., Johnson, J. L., ANAL. CHEM.35, 1204 (1963).
(36) Trapnell, B. >I “Chemisorption,” ., p. 143, Butterworths Scientific Publications, London, 1955. (37) Zbid., p. 6.
RECEIVED for review January 27, 1964. Accepted June 8, 1964. Supported in part by the U. S. Atomic Energy Commission, under Contract AT( 11-1)-1222. Presented a t 2nd International Symposium on Advances in Gas Chromatography, University of Houston, Houston, Texas, March 23-26, jY64.
Piezoelectric Sorption Detector WILLIAM H. KING, Jr. Analytical Research Division, Esso Research and Engineering
b Piezoelectric quartz crystals have long been used as frequency and time standards accurate to 1 part in lo* or better. These stable elements become selective gas detectors when coated with various materials. Crystals coated with gas chromatographic substrates produce gas chromatographic detectors which have several advantages: Sensitivity increases with solute boiling point, detectors can be made selective to compound type and respond in 0.05 second, and the output signal is a frequency which simplifies integration of peak areas and digital presentation of the datu. The crystals used in this work were quartz plates ‘/z inch in diameter, 7.3 mils thick, that vibrate at 9 Mc. A readily measured signal of 1 C.P.S. corresponds to a weight increase of about gram. Coated-crystal moisture detectors sensitive to 0.1 p.p.m. are now commercially available. Hydrocarbon detectors sensing as little as 1 p.p.rn. of xylene have been tested.
P
quartz crystals are used in great numbers for controlling frequency in communication equipment, and are widely used as selective filters in electrical networks. Special quartz crystals, are available which can control frequencies to 1 part in log and very accurate clocks can be run from this signal. Other less familiar uses include the generation of ultrasonic waves ( 7 ) and the measurement of temperature (S), thickness of evaporated metal films (X), dew point of gases ( 2 ) , and adsorption of gases on quartz (10). In the latter three uses advantage is taken of the very high sensitivity of a vibrating crystal to the presence of foreign material on its surface. Sauerbrey (9) developed a relationship between the weight of metal films deposited on quartz crystals and the change in frequency (Equation 1). IEZOELECTRIC
Co., linden, N. 1.
AF = 0.38 X IO6 X
F -
T
X
AW -
A
(1)
For common crystals this reduces to
can be made specific for certain vapors and are now employed on a commercially available A ater vapor detector (Gilbert and f3arker Manufacturing Co., West Springfield, Mass.) (6). SORPTION DETECTOR CRYSTAL
where AF = frequency change due to metal coating, c.p.s. F = frequency of quartz plate, Mc. T = thickness of quartz plate, cm. AW = weight of deposited film, gram A = area of quartz plate or electrode, sq. cm.
Equation 2 predicts that commercially available 1 5 3 I c . crystals having electrodes 5 mm. in diameter will have a mass sensitivity of 2600 c.p.s. per pg. It is therefore apparent that the vibrating quartz crystal can be an extremely sensitive weight indicator. The detection limit is estimated to be about 10-l2 gram. I n the manufacture of certain crystals, metals are often evaporated directly on the quartz plate to serve as electrodes. The amount of metal deposited is adjusted to bring the frequency to a desired point. Metals and many other solids do not greatly affect t h e crystal’s ability to vibrate. However, when liquids are deposited on the quartz surface, the ability to vibrate is often impaired, probably because the vibrating crystal surface is dissipating energy in the liquid. If a gas is allowed to absorb into the liquid coating, the amplitude of vibration is again further reduced. I n this way the amplitude of vibration can be used to detect gas composition. This paper presents information on the use of coated piezoelectric quartz crystals to detect and measure the composition of vapors and gases. Both the amplitude change method and the frequency change method were employed. These sorption detectors
Many sizes, shapes, and frequencies of quartz crystals can function effectively as sorption detectors. The most convenient type to use are thin disks vibrating in the thickness shear mode ( 7 ) . The sensitivity of detection is inversely proportional to the square of the electrode diameter and thickness of the crystal. Thus, the most sensitive disk would be infinitely small. Obviously, these parameters cannot be taken to their extremes and a compromise must be sought. We have found that a frequency of around 9 Mc. is convenient. This choice is a compromise of cost, sensitivity, and ruggedness. A typical 9->IC. crystal has a sensitivity of about .500 C.P.S. per pg. Sorption detectors have been ma-de from two types of commercidly available crystal mountings, plated electrode and pressure mounts. The plated metal electrode crystals rnost often used are designated as plated electrode, 9 Mc., AT cut, H C 6 i U holder. The quart,z plate is about 12 mm. in diameter and 0.15 mm. thick. Support wires provide electrical connection to the electrodes and maintain the quartz plate in the center of the holder. The volume of this housing is about 2 cc. Gas conduits are soldered to the brass can cover of this housing. Figure 1 is a drawing of the other type of mounting (FT-243), where the quartz plate is retained between two metal electrodes with tabs on each corner. The gas space between the electrode and the quartz plate is the order of 0 . 0 2 cc. Thus. this type of mounting provides the detector with a very small volume. Both types of crystal detector housings have been used with success. The only change VOL. 36, NO. 9, AUGUST 1964
1735
from the standard crystal housing is the addition of the gas conduits to bring the sample in and out of the detector. DETECTOR CHARACTERISTIC DETERMINED BY COATING
It is possible to relate the detector signal quantitatively to the sorption isotherm of the coating material. In the case of the frequency change signal, Equation 3 is helpful.
where frequency change due to application of coating A W o = weight of coating AF = frequency change due to sorption of solute vapor A W = weight increase due to sorbate AF,,
=
Of particular interest are the gas chromatography substrates, which show a linear relationship between the concentration of solute vapor and the fractional weight pickup, A H 7 / A l f * o ( 4 ) . Equation 3 may be used to get an idea of the detector's sensitivity with a particular coating. Coatings from AF0 = 1 kc. to 100 kc. can be obtained with many different materials. As mentioned previously, many types of materials may be coated on crystals to make detectors. Table I is a partial list of materials which the author has used to make selective gas composition detectors. I t is desirable to coat the surface evenly with the substrate. The usual amount to use is 5 to 50 pg. per sq. cm. The method of coating is not critical, if the crystal and coating remain un-
Table I.
Sorption Detector Coating Materials
Detector characteristic Hydrocarbon detection, nonselective to compound type Selective detection of polar molecules such as aromatic, oxygenated, and unsaturated compounds Water vapor
Coating material Squalane Silicone oil Apiezon grease
Polyethylene glycol Sulfolane Dinonyl phthalate Aldol-40 Tide (alkyl sulfonate) Silica gel Molecular Sieve Alumina Hygroscopic polymers" Hydrogen sulfide Lead acetate Metallic silver Metallic copper Anthraquinonedisulfonic acid a Natural resina, glues, cellulose derivatives, and synthetic polymers.
1736
ANALYTICAL CHEMISTRY
L, Figure 1
Pressure-mounted corner-clamped crystal used for low-volume detector Bakelite holder, 2 9 X 21 X 11 mm., FT-243 Front cover fastened with screws 3. Front electrode 4. Rear electrode with 2-mm. diameter gas tube connection 5. 1.2 X 1.2 X 0 . 0 2 cm. quartz crystal 6. Spring to maintain contact pressure 7. Detector volume of obout 0.02 ml. 8,9,10. Rear and side gas tubes 1. 2.
damaged after application. With a liquid, a typical procedure is as follows. Using a microsyringe, a few microliters of a solution containing a coating liquid dissolved in a volatile solvent are dropped on the surface of the electrode. When the solvent evaporates, the substrate spreads out slowly and covers the surface uniformly. With squalane this occurs in two or three days, depending on the temperature. This can be speeded up by applying heat. Solid substrates of many forms can be applied with glue or cement. Some very fine powders can be deposited from solutions or suspensions. If the coating material is a metal or a metal oxide, it is convenient to make the plated electrodes from the desired metal or convert the electrode metal to the oxide form. Other film-coating methods can also be used, depending on the type of material. DISPLAY OF DETECTOR SIGNAL
One signal from the detector crystal oscillator is a radio-frequency which can be measured with a high precision in a variety of ways. The greatest precision is obtained from the use of digital frequency counters which are available
from many manufacturers. These units can measure the signal frequency directly to 0.1 c.p.s. Remote reading of the signal can be accomplished with a communications receiver and a frequency meter. An audio-frequency can be obtained from the detector by heterodyning a second or reference crystal oscillator with the detector crystal oscillstor (Figure 2). The system consists of a detector oscillator which has a coated crystal detector in a vacuum tube or transistor oscillator circuit. The reference crystal oscillator is identical to the detector oscillator, except that its crystal is not coated. The two oscillator frequencies are fed to a mixer, where the difference in frequency between the two crystals is obtained. This difference frequency is in the audio range and can be readily displayed through the use of an audio-frequency meter or similar device. Specific circuits on the oscillators and other electronics are not given here, because of the wide variety that are available commercially. Electrical circuits are not critical to the art of detection and many types are well known in the field of electronics (6). The independence of the frequency
1
DETECTOR OSCILLATOR
I
I
REFERENCE OSCILLATOR
1
AUDIO = R F l - R F 2
DIGITAL OR ANALOG
W W
z
Figure 2. Heterodyne measurement
-I
X >
frequency
I
0
Audio-frequency signal obtained by Beoting detector oscillator with noncoated or reference oscillator
change signal with the electronic circuit was demonstrated by data gathered to confirm Equation 1 due to Sauerbrey (9). Quartz (cut) of different orientation and gold electrode crystals of different thicknesses, all having 0.64-sq. cm. area electrodes, were electroplated with copper and nickel. The weight increase was measured with a Metler M-5 microbalance, and the frequency change in several oscillators was observed. The data shown in Table I1 are representative of signals obtained from two of the most different electronic circuits. The series resonant data were obtained with a crystal impedance meter (Lavoi Laboratories, M organville, S . J., crystal impedance meter Model 51), while the anti resonant data were obtained with a 32-picofarad Pierce oscillator circuit (International Crystal Manufacturing Co., Oklahoma City, Okla., printed circuit oscillator, Model FO-1). Considering the accuracies of the area measurement by planimeter, the small weight measurements, and the micrometer thickness data, reasonable agreement was obtained among series, anti, and the theoretical value calculated from frequeney and thickness data. When it is desirable to use the amplitude of vibration as the detected sig~ial,we have found it convenient to employ the Pierce oscillator circuit (6). The amplitude of' vibration is adjusted to a convenient level by varying the plate voltage on the tube. The grid current of the oscillator is sampled and presented to a recor(1er. Steady grid
Table II.
t
t
t
t
4 MINUTES
3
2
I
Figure 3. Simultaneous recordings of thermal conductivity and squalane sorption detectors
currents of about 0.1 ma. are usually obtained with a grid leak of 47,000 ohms. When a solute gas enters the detector, it will immediately partition with the liquid coating on the crystal. which will be sensed as a reduction in the grid current of the oscillator circuit. The amplitude signal presentation is simpler than for the frequency signal, but it is neither as precise nor as accurate. Analog signals, in general, cannot be measured as accurately as time or frequency signals. RESPONSE CHARACTERISTICS OF SOME SORPTION DETECTORS
Sorption detectors made with various liquid coatings have interesting and unusual performance characteristics and can be used to determine solute concentrations in gas chromatography.
Weight Sensing Unaffected b y Electronic Circuit
Crystal" Frequency, kcs. 3490 4082 5058 6942 9019 9816
cut AT AT BT BT AT ET
Thickness, inch 0.0190 0.0160 0.0197 0.0155
0.0072 0.0112
t0
Weight added, !4
157 119 116 95 70 106
Frequency change, kcs. Series Anti Theo. 6.72 5.85 5.86 7.05 6.70 6.77 6.92 6.02 6.03 10.3 10.3 9.88 19.6 20.4 19.1 21.8 21.6 21.6
a '/z X '/rinch Quartz plate with 0.64-sq. cm. gold electrodes, 5/16-in~hdia. with '/&-inch tabs.
Sorption detectors are more sensitive at higher molecular weight, linear in response, selective, and fast. Support of some of these claims is evident from Figure 3, which is a dual recording of an eight-component blend of hydrocarbons run on an isothermal chromatograph. A sorption detector operating at room temperature was connected through 20 inches of '/*-inch tubing to the effluent of the thermal conductivity cell in a Perkin-Elmer Model 154 gas chromatograph. A two-pen recorder was used to obtain the signals from both detectors. Other details are given on the figure. As expected, the peak heights of the thermal detector fall off with increasing time, although the peak areas are fairly constant. However, the squalane sorption detector shows increased sensitivity with increasing time. A plot of solute boiling point us. the log of peak area is a straight line for the sorption detector. Further, this line is parallel to that drawn for solute boiling point us. log retention time of squalane. This is evidence aqain that Equation 3 is obeyed. Thus, the A l I - term in Equation 3 has a linear relationship to the partition coefficient of squalane and its specific retention volume. I t is therefore apparent that the performance of a sorption detector can be predicted from a knowledge of gas chromatograph data. The concept of the sorption detector response being proportional to the specific retention volume of the coating, V,, is valuable in estimating selectik ity, VOL. 36, NO. 9 , AUGUST 1964
1737
Table 111.
Carrier Gas Has No Effect on Sensitivity
Helium Air Peak, Time, Peak, Time, Sample sq. cm. sec. sq. cm. sec. 22 120 20 Pentane 112 48 596 44 Benzene 588 ~. 100 1968 Toluene 1856 110 5888 287 317 Xylene 5388 ~~~
Table IV.
Helium carrier solute gas
30 mole
air
2 mole
yo
toluene
~
Comparison of Detector Signals
Thermal o r p t i o n detector conducAF, tivity, C.P.S. A I , yo AI, 70 0.5 1660
15.3
33.0
35.2
6.4
sensitivity, temperature effects, and response speed. The effect of V , on the first three points is direct. Thus, polar substrates are more sensitive to polar solutes, and lowering the temperature increases the detector sensitivity. The effect of V , on speed is not so obvious; here it is convenient to assume that the sorption detector is a tiny chromatograph with a small but known substrate weight and then calculate the retention volume. For a typical squalane detector having 20 kg. of coating the volume of carrier gas required to displace benzene from the X 500 = squalane a t 25" C. is 20 X 0.01 cc., since V , is 500 cc. per gram a t 25' C. Thus, for a chromatograph using a flow rate of 1 cc. per second, sufficient gas volume is available to flush out the detector in a reasonably short time. The sorption detector described here should not be confused with the Brunel mass integral detector of Bevan and Thorburn ( 1 ) . These workers used several grams of absorbent with an automatic recording balance, the product of Ti, and substrate weight is very high and large volumes of gas are required to strip out the solute. This results in a quantitative integral detector which has several advantages as noted by Bevan and Thorburn. The work reported hcre for gaq chromatography stresses the advantage of a small amoiint of sorbent and instantaneous selective detection. Other work was done by the author in detecting H,S by reaction with silver and copper electrode crystals and the detection of polar compounds with a silica gel-coated crystal. These detectors behaved as integrators and specific data on this subject are not included in this paper. Another important advantage of the sorption detector is that different carrier 1738
ANALYTICAL CHEMISTRY
gases can be used without penalty. Data, to illustrate this point, are shown in Table 111. One-half-microliter samples of liquid hydrocarbons were injected into a short column chromatograph having approximately 180 plates. Either helium or air flowed through the chromatograph a t 38 cc. per minute. The detector was a 9-Mc., gold-plated crystal with a squalane coating. The peak area and retention times of helium and air carriers are very nearly the same. As the properties of helium and air differ greatly, this is a sensitive test of the effect of carrier gas. I t can be further illustrated that the squalane sorption detector can be insensitive to changes in the nonpartitionable carrier gas. I n this particular example, 'both the frequency change and amplitude change of the sorption detector crystal were measured and compared simultaneously with the response of a thermistor-type thermal conductivity detector. When the carrier gas was changed from helium to 30 mole % air in helium, the sorption detector showed almost no frequency signal but a marked change in grid current or amplitude signal. Table IV shows the signals obtained. For further comparison, 2.0 mole yo toluene signals are shown. The amplitude change signal and the thermal conductivity response are put on the same basis by expressing the data as the per cent unbalance of the bridge circuit. This is arrived a t by dividing the voltage output of the grid circuit of the detector by the no-signal voltage output. With the thermal conductivity detector, the output voltage is divided by the battery voltage supplied to the bridge. Linearity of response to solute concentrations is an important property of any detector. Good linearity is expected in the case of the liquid-coated sorption detector because the sorption of gases by liquids is linear at the lower concentrations (4). I n addition, Equation 3 shows that the frequency change of a crystal is a linear function of the weight increase. Many esperiments to determine the linearity of the liquidcoated sorption detector were performed by varying the amount of liquid injected into a gas chromatograph and plotting the peak area us. injected volume. These curves are not shown, since they are all straight lines over the range from 0.01 to 2.0 ~1 injected. The data were analyzed statistically. The peak area of the sorption detector showed a relative standard deviation, s, of +3.1%. Simultaneous readings on the thermal conductivity detector showed s = +2.5%, while the ratio of sorption to thermal showed s = f1.6%. These data suggest that both detectors are better than our ability to inject reproducible samples. High speed of response of the liquid-
i
,
l01/L+ EQUILIBRIUM
Or 0
I
I
I
20
40
60
MILLISECONOS RESIDENCE TIME
Figure 4. crystal
Response of liquid-coated
coated crystai is possible, since small detector volumes can be employed and the rate of solute partitioning into and out of the liquid coating is known to be high. To test this, a sorption detector having 0.02-cc. gas volume was employed (Figure 1). Equal samples of benzene and toluene were injected into the chromatograph over a wide range of gas flow rates. For an infinitely fast detector, a constant value would be expected when the peak area is divided by the retention time. Figure 4 shows the results of this experiment. Here, the peak area divided by the retention time is plotted against the residence time of the gas. These data indicate that the detector has a response speed in the order of 40 milliseconds. Probably the most unusual feature of the sorption detector is the ability to detect gases selectively. By using different coating materials the selectivity of the detector to composition changes can be measured. For example, the sensitivity ratio of benzene to cyclohexane with different gas chromatography liquid coatings was measured. This pair was chosen because they have the same retention time on a 180-plate column and almost equal boiling points. The ratios found were 1.0 for DC 200 silicone oil, 3.06 for U C O S polar, and 8.06 for 1,2,3-tris(2cyanoethoxy) propane. These data are consistent with published retention data observed when the same liquids are used on a chromatograph. CONCLUSIONS
Coated piezoelectric quartz crystals can be used as sensitive sorption detectors. The detectors are rugged and fast and can be used to detect a variety of gases selectively. GC liquid substrate-coated crystals are particularly interesting because the sensitivity increases with molecular weight of solute. Linear response is obtained and because the signal is a frequency it may be presented readily to many types of readout systems. Integrating peak areas is particulary simple because the total number of cycles generated during the passage of the GC peak may be readily indicated by digital equipment.
I n the case of detection of trace amounts of \vater, thr coated quartz crystal is now a commercial reality. Probably many other types of detectors will be developed in the future. LITERATURE CITED
D. E., “Improved Cryogenic Thermometer,” paper F-2, 1962 Cryogenic Engineering Conference, Los Angeles, Calif 1962 .. ~~. ., ~ - Inem lYJl.
( 5 ) King, W. H., Jr., paper C 19.11, International Symposium on Humidity and JIoisture. JIav“~ 20-23. 1963. ~
(1) Bevan, 8. C., Thorburn, Samuel, J . Chronlatog. 11, 301-6 [ 1963).
s., U. s. Patent 257,171 (July 4, 1945). ( 3 ) Flynn, T. >I., Hinriah, H., Newell, ( 2 ) Dyke, K.
-
(4) Keulemans, A. I. AI., “Gas Chromatography,” Reinhold, Xew York,
~~
~
~
and Their Application to Cltrasonics,” Tan Nostrand, Princeton, X. J., 1950. (8) Oberg, P., Longensjo, J., Rev. Sci. Instr. 30, N o . 11, 10.53 (1959). ( 9 ) Sauerbrey, G., 2. Physik. 155, 206 (1959). (IO) Slutsky, L. J., Wade, W.H., J . Chem. Phys. 36, N o . 10, 2688-92 (1962).
~~~~
Washington, D: C. (6) Landee, 12. W., Davis, D. C., Albrecht, A . P., “Electronic Designer‘s Handbook,” JIcGraw-Hill, Kew York, 1951. ( 7 ) JIason, W. P., “Piezoelectric Crystals
RECEIVEDfor review April 3, 1964. Accepted JIay 18, 1964. Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pa., 1963.
Electron Drift-Velocity Detector for Gas Chromatography V. N. SMITH and J. F. FlDlAM Shell Development Co., Emeryville, Calif
b The effect of trace impurities on the drift-velocity of electrons in pure argon has been exploited for the detection of trace concentrations of permanent gases in gas chromatography. The detector is a smallvolume, parallel-plate ionization chamber in which a tritium source is used to ionize the argon in a region near one electrode. Negative voltage pulses of short duration are applied to this electrode to drive electrons from the ionized region toward the opposite electrode. The pulse duration is selected so that not all electrons are collected in pure argon carrier gas. Trace concentrations of components eluted from a chromatographic column and passing through the detector increase the electron drift-velocity and thus increase the electron current to the collector electrode. Sensitivity has been measured for a iiumber of permanent gases and a few light hydrocarbons. The lower detectable limit for nitrogen is about 10-10 gram/second.
I
x X ~ N Y applications of gas chromatography a detector is required for trace concentrations cd the so-called permanent gases-e.g., He, Hz, N,, 02, and CO. Most of the available detectors, including the flame and argon ionization detectors, as well as ionization cross-section, thermal conductivity, or gas density balance detectors, are inadequate in this respect. Lovelock ( 2 >3 ) has described the application of both direct and indirect’ electron mobility t,echniques to the problem of detecting traces of the permanent gases, and, more recently, Shahin and Lipsky ( 4 ) have described a mode of operat,ion of a n ionization detector, using a low
d.c. potential and high operating temperature (150” to 200” C , ) j which exhibits high sensitivity to the permanent gases as a result of changes in electron drift-velocity . The authors have investigated the direct electron mobility or drift-velocity technique in some det’ail and have developed a detector system (cell, pulse generator, and commercial electrometer) which provides high sensitivity to the permanent gases and excellent base line stability. The ultimate sensitivity of t’he detector system has been determined for several permanent gases and light hydrocarbons. I n t’he course of this development the drift-velocity of electrons in pure argon was measured as a function of electric field strength. These measurements are discussed and the data are presented here to illustrate the characteristics of the cell and the effects of changing operat,ing parameters. THEORETICAL BASIS
When a uniform electric field is applied to a gas containing free electrons, the electrons are rapidly accelerated to a terminal drift-velocity toward the positive electrode. In general, the electric field increases the thermal agitation energy or temperature of the electrons to a value above that of the gas, and the directed drift toward the positive electrode is a diffusion phenomenon superimposed upon the thermal motions of the electrons. In a pure monatomic gas such as argon the drift-velocity is relatively low and is increased by the presence of traces of more complex gases .such as nitrogen, carbon monoxide, or hydrocarbons. This effect can be understood by considering the diffusion equations for electrons in a gas.
Healey and Reed ( I ) have used Maxwell’s diffusion equations to derive the following expression for the driftvelocity of electrons in a gas under the influence of an electric field.
w = -K S e E T*P where
K
= =
.I’
=
ZLI
e
=
E T*
= =
P
=
drift-velocity of electrons coefficient of diffusion for electrons in the gas number of molecules of gas in 1 cc. a t 760 mm. of Hg pressure and 15” C. electronic charge electric field strength ratio of mean agitation energy of.electrons to that of the gas a t 15” C. pressure of 760 mm. of H g expressed in dynes per sq. em.
The factor T* in Equation 1 is a measure of the electron temperature, which can be quite high in a monatomic gas because the electrons do not lose appreciable energy in collisions with these atoms. However, in gases having more complex molecules the electrons can lose energy in collisions with the molecules by exciting vibrational or rotational states. These inelastic collisions reduce the electron temperature, and since T* appears in the denominator of Equation 1, the drift-velocity is increased. Intuit’ively,this result may seem paradoxical, but the physical picture can be clarified by considering two extreme casesperfectly elastic collisions and completely inelastic collisions. I n the case of perfectly elastic collisions, the electrons bounce off the gas molecules lvith negligible energy loss because of the large ratio of molecular mass to elect,ronic mass. Thus, the direction of the electron’s travel is changed a t VOL. 36, NO. 9, AUGUST 1964
e
1739
