Gas Analysis by Use of Microwaves

GlLLlS JOHANSSON

Department o f Analytical Chemisfry, University of Lund, Lund, Sweden

b The properties of microwave cir- cuits permit highly accurate measure- ments of dielectric constants. A simple arrangement of two cavities in series can be used for very sensitive relative measurements. Traces of one gas in another gas can be detected if the di- electric constants differ, which is gen- erally the case. The response law is derived and verified experimentally. The influence of selective absorption and dielectric loss i s discussed. The device will find application as a detector in gas chromatography, es- pecially at high temperature.

HE i-ery high &-value of a micro- T wave resonant circuit suggests that this technique might be used for measuring dielectric changes. Very small changes in the equivalent capaci- tance of such a circuit can be recorded. Dei-elopment of the gas chromatography technique has created an increased interest in the analysis of traces of gas in a carrier gas. To study the be- havior of micronave apparatus, a preliminary setup n-as arranged. If the experiments succeed, the apparatus might be used as a detecting device in gas chromatography.

Hershberger ( 7 ) , using the microwave technique for analysis of gases in the Haber process, based his method on the presence of absorption lines. His tech- nique is probably less sensitive than the present method. X gas chroma- tography detector based on changes in the dielectric constant has been de- wribed by Turner ( I S ) . His apparatus operates in the megacycle range. A more sensitive detector using the same principle has been constructed by Winefordner (14).

Microwave technique has been used earlier to measure dielectric constants. Birnbaum, Kryder, and Lyons (1) have measured the frequency change ob- tained n hen a previously empty cavity is filled with a gas. Crain (2) has also made such measurements. Crain (3)

ta"8'y tar, ,y osc 11oscope Modulation Ylllage

Figure 1. Block diagram o f micro- wave apparatus

and Crain and Dean ( 4 ) have developed their apparatus so that i t can be used as an airborne refractometer.

GENERAL PRINCIPLES

A klystron was used as a generator of microwave poiver. The porn-er nas fed through a ITare guide to a cavity of the transmission type (a standard wave meter). Another cavity was mounted in series n i th the first one, the t n o cavities being identical except that the second had an inlet and a n outlet for gas. It constituted the measuring cell. The microwave energy was fed from the cell into a crystal detector. -4 block diagram is shown in Figure 1.

Power can be transmitted from the generator to the detector only n hen the frequency of the transmitted signal is equal to the resonant frequency of the cavities. For maximum transniis- sion of energy the two cavities should be tuned to exactly the same frequency. The klystron is frequency modulated by means of a 50-cycle sine m v e voltage on the repeller. Thus, a burst of energy passes to the detector each t h e the generator frequency equals that of the cavities. The detector current is amplified and measured on an oscil- loscope. If the signal is rectified, the amplitude variations can be recorded by a pen-recorder.

At the beginning of a run the two cavities are filled with carrier gas, usually nitrogen. If the conipobition in one of the cavities is changed, the electrical size of the cavity will also be changed. This change has the same effect as a detuning of the cavity, and i t causes a decrease of the current from the detector.

EQUIVALENT CIRCUIT A N D RESPONSE L A W

The equivalent circuit of a cavity can be represented by lumped inductances, capacitances, and resistanccs. The coupling to and from the cavity may be represented by ideal transformers, and the load by a resistance RL. The representation shown in Figure 2 is valid (Or, 12) near resonance if the loss is small and the coupling between input and output elements can be neglected. The impedance of the resonant circuit expressed in terms of frequency ( w ) , resonant frequency wg. and Q-vnlce i?

Gereralor :av,,y Load

Figure 2. ator, one cavity, and detector

Equivalent circuit o f gener-

TThen the gas composition in the cavity changes, the dielectric constant is also changed-Le., the electrical length of the cavity is changed. The physical length of the cavity remains constant, however. Thus, the reso- nant frequency of the cavity is changed. The relation betiyeen resonant fre- quency, W O ~ and dielectric constant, e, in the t n o cases is

? E = + €1 (2) a02

The generator frequency is made equal to wol by mechanical tuning when the cavity is filled Tvith carrier gas, the dielectric constant of R-hich is el. The dielectric constant of the carrier gas plus the gas to be analyzed is € 2 . If Equation 2 is substituted into Equation 1 and the fact that E is close to unity is considered, the impedance of the cavity is obtained as a function of the dielectric constant.

A detector crystal follow the so- called square law-Le., the current is proportional to the square of the ap- plied microware voltage (6). This has also been yerified by means of a cali- brated attenuator in the transmission line. The quotient is taken between the reading Ao, measured a t resonant condition with carrier gas in the cavity and the reading A n ith a gas mixture in the cavity.

4 = 1 + Q2 (€1 - (4)

If the mole fraction of unknown gas in the carrier gas is IC, Equation 4 becomes

2 = 1 + ~2 (el - e2)2r2

-4

( 5 )

n here el = dielectric constant a t cavity

temperature and pressure of the gaseous compound to be ana- lyzed

e? = dielectric constant of carrier gas under the same conditions

914 0 ANALYTICAL CHEMISTRY

I n practice the generator frequency is not const,ant enough to allow direct feeding of the measuring cavity. Two cavities are mounted in series as shown in Figure 1, and the generat'or frequency is sn-ept back and forth by a modulation voltage. The first cavity can be considered as a monochromator that selects a burst of microwave energy only when this has the right frequency. The output from the detector then becomes an alternating current.

The int'eraction between the two cavities and between t'he cavities and the generator were not taken into account in the derivation of Equation 5 . Further, i t was supposed tha t the cavities Tvere unloaded, tha t no coupling between input' and output elements existed, and t'hat the frequency was fixcd. The interrelation may thus be more complicated than Equation 5 indicat'es. It gives, anyhon-, a n in- dication of the genersl form of the response. The relation between A and the mole fraction is shown in Figure 3.

ABSORPTION OF MICROWAVES

If the gas under investigation shows abrorpt,ion in the frequency band used, this will affect the measurement,s. Sevwd investigations of such absorption ha\-(, been made (IO, 11). A similar explcssion as Equation 5 may be derivcd for the case where the dielectric coiiqt:int is a complex number. The 1 0 s tmgent, is dpfined as t'he quotient bc,t[-;c.c$n the complex and the real part of rl!c, diclcct,ric constant. The total d ~ x : ( m e in nmplit'ude due to both al)+oyt ion and dielect,ric constant c1i:iiige is

r l I , - 11 = (1 + Q tsn 6 ~ ) ~ [ 1 -+ Q 2 ( e , - e2)2z2]

I t is evident that t'he increase in sensitivity due t'o absorpt'ion may be rnt1ic.r high for materials with high loss factor. Also, the shape of the response curve is different when the gas absorbs micioivave energy.

0 50mm u Figure 4. Section of Teflon tube insert in the cavity (choke flanges are shown to the left and the right)

0.4

< 0.6

d 2 8 a

i

Y 5 d0.8 z

1 .o

MOLE FRACTION, X

Figure 3. Relative amplitude as func- tion of mole fraction calculated for Q = 10,000 and el - e2 = 0.0 1

EXPERIMENTAL

The source of microwave power was a 2K25 reflex klystron delivering about 30 mn-. at 9700 Nc. , and the detector n-as a 2S21B silicon crystal. *One of the cavities was a surplus wavemeter employing the TE,,, mode of oscillation. The second cavity was made from brass which was silverplated. It had con- nections for tubings. The tuning plunger n-as fitted close enough to give a tight seal after lubrication. The cavi- ties were coupled to the wave guides with irises. The irises of the second cavity were sealed n-ith mica windows. An estimation of the Q L was made by tuning to half-power points. The rela- tion w 'h = Q then gave a Q L some- what lower than 3000.

The validity of Equation 5 was tested n ith volatile substances. Sitrogen was passed through a sintered-glass disk immersed in a vessel containing the sub- stance under investigation. This vessel n-as cooled with dry ice in an alcohol bath. K h e n thermal equilibrium was reached, the temperature TT as noted so that the amount of substance in the saturated nitrogen gas could be cal- culated with the aid of vapor pressure tables (9). Then the gas mixture was passed through one of the cavities. The detector amplitude was measured on an oscilloscope (Tektronix. Model 3101. The temperature was allom-ed t o rise, and a number of points were taken. K h e n the relation between the square of the mole fraction and the detector voltage ratio is plotted, a straight line results. The linearity of these plots was excellent. The slope Q2(el - eJz was evaluated with the method of least squares. Tabulated data on dielectric constants (8) were converted to room temperature and used for calculating Q. The value for Q obtained by this

method ranges from 2700 to 3700 for different substances. The variation in Q values might be due to some dielectric loss which is not accounted for in this calculation. The value agrees reasonably well with tha t obtained by tuning to half-power points. The cor- relation coefficient was in all cases higher than 0.99. This high value indicates that Equation 5 describes the behavior of the detector correctly.

The most serious disadvantage of the set-up described is the large volume of the cavity, 50 ml. It is not necessary, however, t o use the whole cavity. A Teflon tubing was pressed into the cav- i ty giving a cell with a volume of 4 ml. (Figure 4). The sensitivity n-as lowered 5 times by this arrangement.

The apparatus described was tested as a detector for gas chromatography using the Teflon insert in the cavity. The signal from the detector was am- plified, rectified, and bucked against the voltage from a mercury cell. The changes were observed on a recorder. The column, a C-shaped, 70 om. long and 4 mm. i d . , glass tube, was filled with firebrick, 35-60 mesh (Johns- Manville Co., C 22), containing 20% dinonylphthalate. A mixture of 2.5 pl. of dichloromethane and 2.5 PI. of di- ethylether was separated a t 25" C. The carrier gas was nitrogen, and the flow rate was 35 ml. per minute (Fig- ure 5 ) .

This device has also been used to re- cord the humidity of air. An air stream with constant humidity-5.g.. 35X-i~ passed over wheat plants and further into the caT-ity. The changes in the humidity level, caused by the transpiration of the plants, are recorded.

W 0) z 0

b a K w 0 K

W 8 a

L _L

TIME

Figure 5. Chromatogram of mixture of 2.5 pl. of dichloromethane and 2.5 pl . of diethylether at 25' C.

VOL. 34, NO. 8, JULY 1962 915

DISCUSSION

The cavity arrangement described here can be used to monitor changes in the dielectric constant of a gas mixture. The sensitivity is sufficient for detecting the components eluted from a gas chromatography column and is equal to or better than that of a thermal conductivity detector. The derived expressions show that the sensitivity can be increased further if cavities having a higher Q-value are employed. It is possible to get cavities with a Q-value more than 10 times higher than those used in these investigations. If shorter wavelengths are used, a small cavity volume without tubings is obtained. At 8.5 nim., for instance, the volume of the cavity will be about 0.8 ml.

The most obvious advantage with this detector is the possibility of working at high temperatures. The metal cavi- ties can withstand as high temperatures as any other parts of the chroma- tography system. As the temperature is increased, the resistivity of the metal increases, which results in a lower Q-value due to the change in surface resistance. The arrangement described

cancels out any temperature variations if both cavities are kept a t equal tem- perature.

This microwave detector is very rugged and trouble-free. After a warm-up period of about 20 minutes, the detector current is very stable. The drift during a day is about 27,. By selecting standard microwave com- ponents, this detector unit can be assembled a t relatively l o ~ v cost.

ACKNOWLEDGMENT

The author thanks K. J. Karrman for his advice and for the encouraging interest which he has shon-n throughout this investigation. He also thanks Sivers Lab, Stockholm, for calibrating an attenuator. The work on plant transpiration was made by S. Falk a t the Department of Plant Physiology, Lund, Sweden.

LITERATURE CITED

(1) Birnbaum, G., Kryder, S. J., Lyons,

(2) Crain, C. M., Phys. Rev. 74, 691 H., J : Appl . Phys. 22, 95 (1951).

(1948).

(3) Grain, C. Jl., Rev. Sci. Instr. 21, 456 11950).

(41 Grain, C. &I., Dean, -1. P., Ibid., 23, 149 (1952).

(5) Gina:pn, E. L., “Microwave Measure- ments, p. 354, McGran--Hill, New York, 1957.

(6) Zbid., p. 115. ( 7 ) Hershberger, W. D C. S. Patent

2,792,548 (May 14, li57). (8) Hodgman, C. D., “Handbook of

Chemistry and Physics,” Chemical Rubber Publishing Co., Cleveland, 1950.

(9) Jordan, T. E., “Vapor Pressure of Organic Compounds, Interscience, h-ew York, 1954.

(10) Krishnaji and Srrarup, P., J . - 4 p p l . Phys. 24, 1525 (1953).

(11) Millman, G. H., Raymond, R. C., Ibid., 20, 413 (1949).

(12) Montgomery, C. G., Dicke, R. H., Purcell, E. SI., “Principles of Micro- n-ave Circuits,” p. 236, M.I.T. Radia- tion Laboratory Series, 8, McGraw- Hill, Xew York, 1948.

(13) Turner, D. K., Satzire 181, 1265 (1958).

(14) Kinefordner, J. D., Steinbrecher, D., Lear, W. E., ANAL. Cmni. 33, 515 (1961).

RECEIVED for review February 19, 1959. Resubmitted March 9, 1962. Accepted March 26, 1962. Kork was supported bv grants from the Statens Katurveten- skapliga Forskningsrdd (Swedish Katural Research Council).

Electron Paramagnetic Resonance and Electroc hemistry

Studies of Electrochemically Generated Radical Ions in Aqueous Solution

L. H. PIETTE Instrument Division, Varian Associates, Palo Alto, Calif.

P. LUDWIG and RALPH N. ADAMS

Department of Chemistry, Universify of Kansas, lawrence, Kan.

b The electrochemical generation of radical ions directly in the microwave cavity of an EPR spectrometer (in situ technique of Maki and Geske) has been applied to a variety of processes in aqueous media with considerable success. Cyclic voltammetry coupled with the EPR technique is particularly useful in studying complex organic electrode reactions. Rather unusual stabilities for radical anions of aro- matic and aliphatic nitro compounds in aqueous solutions have been found. The utility of EPR in elucidating organic electrode reactions of electroanalytical significance is indicated.

HE electrochemical generation of T free radical ions directly in the microwave cavity of a n electron para- magnetic resonance (EPR) spectrom-

eter, introduced by N a k i and Geske (4 , f 0, f I ) , has pro\ ided electrochemists and EPR spectroscopists alike with a valuable new research technique. For the first time electrochemists are able to make positive identifications of short lived intermediates in complex electrode reactions. From the spectroscopy view- point both anion and cation radicals can be generated free of the possible inter- actions of chemical oxidants and re- ductants. The purpose of this report is to indicate the utility of the technique in aqueous solution studies and to demonstrate the applications of primary interest to electroanalxtical chemistry. A brief report of the aqueouq generations has been given ( I S ) .

Galkin, Shamfarov, and Stefanishina apparently carried out the first elec- trolysis experiments in an EPR spec- trometer ( 3 ) . They observed a reso-

nance absorption upon passage of cur- rent between two platinum electrodes immersed in a solution of sodium chloride dissolved in liquid ammonia. .lustin, Given, Ingram, and Peover showed aromatic radical ions could be generated electrochemically ( 1 ) . But the real value of the merging of electrochemistry and EPR spectroscopy R as realized with the in situ generation technique developed by Maki and Gesbe (4 , I O , 11). A11 the n-ork reported herein involved direct generation in the microwave cavity.

EXPERIMENTAL

The EPR spectrometer n-as a Varian Y-4500, X-band instrument employing 100-kc. field modulation. Electrolysis cells for reductions at a mercurj. cathode and oxidations a t a platinum gauze anode iyere made by slight modifications

916 ANALYTICAL CHEMISTRY