The Pulse-Sampling Technique for the Study of Electron-Attachment

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PULSE-SIMPLING STUDY O F

ELECTRON-ATTACHMENT PHENOMENA

445

The Pulse-Sampling Technique for the Study of Electron-Attachment Phenomena

by W. E. Wentworth, Edward Chen,’ and J. E. Lovelock Department of Chemistry, Uninersity of Houston, Houston, Texas

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~

~

(Received August 6, 1965)

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A study of the parameters characterizing the electron-capture detector operated in the pulse-sampling mode was carried out. The pulse width, -0.4 psec., applied voltage, -50 v., and the pulse period -1000 psec., necessary to collect all of the electrons and to achieve a steady state when argon-10% methane is used as a carrier gas were determined. It was assumed that the electrons acquired a thermal distribution when no potential was applied to the cell and that the results were independent of the pulse potential examined up to 80 v. A kinetic model of the processes occurring within the electron-capture detector operated in the pulse-sampling mode has been proposed. For the case in which the electroncapturing species is capable of forming a stable negative ion (in contrast to dissociative electron capture), the system of differential equations has been solved using the steadystate approximation. From this solution, one can obtain the previously defined electron capture coefficient in terms of the rate constants for the processes proposed in the model. In certain cases one can obtain values for the rate constants and/or the electron affinity of the molecule from the temperature dependenceof this electron-capture coefficient. Evidence is given for the validity of the proposed model, and the magnitude of the rate constants and the electron affinities are given for several aromatic hydrocarbons.

Introduction tion. The pulse-sampling method arose not from a perverse desire for novelty but as a simple and inThe phenomena associated with the attachment expensive qualitative detector for gas chromatography. of electrons to molecules in the gaseous state has Its later consideration as a potential method for eleclong been a subject for experimental and theoretical tron-attachment studies was made not because it was studies. The scope of these studies can be seen from the numerous reviews of this subject in monographs, such as those by Loeb,2Massey and B ~ r h o p , M ~ *a s ~ e y , ~ (1) ~ A portion of this work was done in partial fulfillment of the requirements of the Ph.D. degree, University of Houston, 1965. Healy and Reed,4 etc., and also from the numerous (2) L. B. Loeb, “Basic Processes of Gaseous Electronics,” University articles appearing in the literature. However, none of California Press, Berkeley, Calif., 1961. of these studies has been carried out under conditions (3) (a) H. S. W. Massey and E. H. S. Burhop, “Electronic and Ionic of atmospheric pressure, low fields, with low energy Impact Phenomena,” Oxford University Press, New York, N. Y., 1952; (b) H. S. W. Massey, “Negative Ions,” Cambridge Unielectrons, and in the presence of complex organic nioleversity Press, New York, N. Y., 1950. cules. These are precisely the conditions under which (4) R. H. Healy and J. W. Reed, “The Behavior of Slow Electrons the Lovelock electron-capture operates in Gases,” Amalgamated Wireless Press (Australasia) Ltd., Sydney, 1941. when the pulse-sampling mode is employed. There(5) J. E. Lovelock, Anal. Chem., 33, 162 (1961). fore, the interpretation of the physical processes oc(6) J. E.Lovelock, Nature, 189, 729 (1961). curring within the detector would clarify the phenom(7) J. E. Lovelock and A. Zlatkis, Anal. Chem., 33, 1958 (1961). ena associated with the attachment of electrons to (8) J. E. Lovelock and N. L. Gregory, “Gas Chromatography,” molecules under these unique conditions. N. Brenner, Ed., Academic Press, New York, N. Y., 1962,p. 219. (9) J. E. Lovelock, A. Zlatkis, and R. S. Becker, Nature, 193, 540 In view of the many highly developed and accurate (1962). techniques already the introduction of a (10) J. E. Lovelock, Anal. Chem., 35, 474 (1963). new method of measurement in electron-attachment (11) J. E. Lovelock, P. G. Simmonds, and W. J. A. VandenHeuvel, studies would seem to need more than usual justificaNature, 197, 249 (1963). Volume 70,Number 2 February 1966

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446

better able to perform the physical measurements, but because none of the methods previously described are able to satisfy the severe chemical constraints imposed during measurements of weakly volatile, highly polar, and possibly impure organic compounds, for example, steroids. The method is dynamic and designed for the observation of brief pulses of ultrapure, dilute vapor emerging from a chromatograph column. Static methods of observing electron attachment, although adequate with pure permanent gases, are quite unsuited for this purpose. The original electron-capture detector described by Lovelock and Lipsky12 was operated on the basis of a constant applied voltage, but it was soon discovered that the pulse-sampling technique offered many advantages over the original d.c. system.'j These advantages were briefly discussed, and the electroncapture coefficients for several compounds relative to that of chlorobenzene as unity were obtained using the pulse-sampling technique and were given in the references cited earlier. A more complete discussion of the advantages and a more detailed description of the pulse-sampling mode of operation is given by Lovelock.lo However, the exact physical mechanisms occurring within the electron-capture detector were deferred to a later date since they were still being studied. In a preliminary article, Wentworth and Beckeri3 have interpreted the electron-capture coefficients obtained for several aromatic hydrocarbons by using the pulse-sampling mode in terms of the electron affinities of the molecules by assuming an equilibrium between the attachment and detachment of thermal electrons to the aromatic hydrocarbon. This interpretation was supported by a correlation with the halfwave reduction potentials of the aromatic hydrocarbons, and a comparison of the experimental values with those calculated by Hoyland and G00dman.l~ I n a later article, Becker and Wentworth15 correlated the measured electron affinities and the 0-0 frequency of the aromatic hydrocarbons and also substantiated the theoretical prediction made by Hush and Poplel'j that the sum of the ionization potential and the electron affinity should be a constant for alternant hydrocarbon molecules and radicals. Scott and Beckerl' used the o technique to calculate electron affinities for several aromatic hydrocarbons. The calculated values were in good agreement with the experimental values. Wentworth and Chenl* correlated the change in free energy for formation of complexes of p-xylene with different aromatic hydrocarbons and the electron affinities determined by the pulse-sampling technique. These studies, taken together, represent a formidable The Journal of Physical Chemistry

W. E. WENTWORTH, E. CHEN,AND J. E. LOVELOCK

body of evidence in favor of the interpretation of the electron-capture coefficients in terms of the electron affinities of the aromatic hydrocarbons. Much of the existing information concerning the electron affinities of complex organic molecules has been summarized in ref. 13, 14, 15, 17, and 18. I n addition, Briegleblg has recently given a comprehensive review of the subject and has extended many of the techniques for estimating electron affinities of molecules. However, Briegleb applied the calculation of electron affinities from electron-capture coefficients indiscriminately to dissociative and nondissociative compounds. In the earlier reference,I3 it was emphasized that the interpretation was only applicable to compounds which were clearly nondissociative, such as the aromatic hydrocarbons. However, it was not clearly stated how one could distinguish between these two processes for all types of molecules. Results from this paper will assist in making the decision but will not in itself distinguish between nondissociative and dissociative electron capture. The purpose of this paper is to present a detailed model of the physical processes occurring in the electron-capture cell operating in the pulse-sampling mode and to verify this model with experimental observations. Except for the consideration of a few experiments with chlorobenzene where dissociative electron capture is used diagnostically to test for the presence of hyperthermal electrons, this discussion will be restricted to molecules which form stable negative ions upon electron attachment in contrast to compounds which undergo dissociative electron capture.

Experimental Section During the course of these studies, a variety of equipment was used, Le., different electrometers, recorders, ovens, etc. Since these variations in the ancillary equipment did not affect the results obtained, only one of the systems will be described in detail as an example of the type of apparatus used. The electroncapture cell and the electrical schematic were described in references cited earlier. An Applied Physics Corp. Cary Model 31 vibrating-reed electrometer with the (12) J. E. Lovelock and S. R. Lipsky, J. Am. Chena. SOC.,8 2 , 431 (1960). (13) W. E. Wentworth and R. S. Becker, ibid., 84, 4263 (1962). (14) J. R. Hoyland and L.Goodman, J . Chem. Phys., 36, 21 (1962). (15) R. S. Becker and W. E. Wentworth, J. Am. Chem. SOC.,85, 2210 (1963). (16) N. S. Hush and J. A. Pople, J . Chem. Phys., 51, 600 (1955). (17) D. R. Scott and R. S. Becker, J. Phys. Chem., 66, 2713 (1962). (18) W. E. Wentworth and E. Chen, ibid., 67, 2201 (1963). (19) G. Briegleb, Angew. Chem., 76, 326 (1964).

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PULSE-SAMPLIKG STUDYOF ELECTRON-ATTACHMENT PHENOMENA

turret input was used. The voltage source was a Rutherford Nodel B78 square wave pulse generator. The signal was recorded on a l-mv. Texas Instruments Servoriter recorder. A Tektronix Type RR135A oscilloscope was used to measure the pulse characteristics. One of the chromatographs used was a modified Aerograph Autoprep. The temperature in the detector cell was measured with a thermometer rather than the thermocouple which was provided. The chromatographic column used was packed with 1% SF96 on glass beads, in 4 ft. of 0.25411. copper tubing. The operating temperature on the column varied with the compounds but was held constant for a given compound. The flow rate was 135 nil./min. of argon through the column and 15 ml./min. of methane added to the system between the column and the electron-capture detector. The flow rates were measured with a stopwatch and a bubble flow meter. The argon was obtained from the Big Three Welding Co. and C.P. grade methane was obtained from the RIatheson Co. The gases were passed through an Illinois Institute Dri Pak, filled with Molecular Sieve Type 5A 0.07-in. pellets, before going through the column or to the detector. Except for naphthalene, triphenylene, phenanthrene, and azulene, the remaining aromatic hydrocarbons used in this work were obtained from Dr. R. S. Becker, and the purity of these materials has been given in an earlier paper.*O The triphenylene and phenanthrene was obtained from Dr. 11. S. Newman through Dr. Becker. The naphthalene was Baker and Adamson’s reagent grade, and the azulene was obtained from K and K Laboratories, Inc. The solvent used was Eastman’s spectroquality benzene. All of these compounds were used without prior purification since they were passed through the gas chromatographic column before going to the detector. The material was weighed out on a Cahn Electrobalance, and the solutions were prepared in a 10or 5-ml. volumetric flask. Further dilutions were made volunietrically. The samples were injected with a Hamilton 10-p1. syringe with 0.2-pl. divisions. The areas under the chromatographic peaks were obtained by triangulation and conversion of the signal.

Preliminary Experiments The parameters applicable to the pulsed voltage are the applied voltages, VA, the width of the pulse, tw,and the pulse period or essentially the time between pulses, tp. The current arising from the electron capture cell is measured as a voltage drop, VM, across known input resistance’ This current is an average value of the current obtained in each in-

447

2.0

4.0

t w ( p sec)

Figure 1. Electron concentration us. pulse width a t various argon-methane ratios.

dividual pulse; thus, the product, V ~ t pis, proportional to the number of electrons collected per pulse, ne-, or if the reaction volumn is constant, then V M ~ is P proportional to the electron concentration [e-] within the reaction zone. It will soon be shown that only electrons are collected and that other negative molecular ions could not be collected during the time, tw. The negative charge carriers when argon, or argon with methane added, is ionized are free electrons and these presumably are the species collected. This is confirmed by the evidence shown in Figure 1 in which ne- is plotted against the width of the applied pulse, t ~ Curve . A is for argon-lO% methane, curve B is for argon-5% methane, and curve C is for pure argon. The electron drift velocities in argon-methane and argon can be estimated in the following manner. The electron cloud extends approximately 2 mm. from the tritium foil, and since the metal gauze (electron collector) is separated by 1.0 cm. from the foil, the mean distance for electron travel is 0.9 cm. The time necessary for the collection of the maximum concentration of electrons (greatest first derivative of the curve in Figure 1) is 2.0 psec. in argon and 0.15 psec. in arg0n-57~ methane. Thus, the drift velocities, calculated under the above assumptions, a t 40 v. and 1 atm., are approximately 6.0 cm./psec. in argon-5% methane and 0.45 cm./psec. in argon and are in fair agreement with the previously measured drift velocities in a r g ~ n , ~ 0.2 l - ~cm./Xsec., ~ and in argon-5% meth(20) R.

S.Becker, I. S. Singh, and E. A. Jackson, J. Chem. Phys.,

38,2144 (1963).

Volume 70,Number 2 February 1966

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448

ane21,243.5 cm./psec., measured a t 0.06 v. cm.-' mm.-'. The drift velocity in argon-10% methane is approximately the same as it is in argon-5% methane. These values quoted from the literature were read from graphs and consequently are not extremely accurate, but the general agreement is good and the difference between the values in argon and in argonmethane are obviously significant. The high value in argon is almost certainly due to trace impurities which can profoundly alter the drift velocity in this gas. Thus, it is certain that the current being measured is due to the free electrons generated primarily during the time that the voltage is not being applied. Figure 2 shows the variation of ne-with pulse width at several voltages for argon-10% methane at a pulse time of 1000 psec. The appearance of a plateau on the graphs shown in Figures 1 and 2 is an indication that all of the free electrons have been collected. The plateaus are not perfectly flat but the increase in the current in the plateau region can be ascribed to the fact that the electrons produced during the pulse are no longer negligible. As a result, some of these electrons which would otherwise recombine with the positive species or react with radicals are collected. Furthermore it is obvious from the common plateau for the curves shown in Figure 2 that the degree of ionization is independent of the applied voltage. I n order to determine the dimensions of the reaction zone, the current was measured as a function of the pulse time at different electrode spacings. The curves are essentially the same up to a distance of 2 mm., which; indicates that this is approximately the depth of the reaction zone or a t least represents a maximum value for the depth. This is also in agreement with the limited range of the weak 0's from tritium. The value of the half thickness for tritium 0's a t 1 atm. pressure in helium has been determined to be 2.75 mm.25 It is to be expected that the value in argon would be smaller. The cross-sectional area of the reaction zone can be taken as the area of the tritium foil. One important factor which must be considered before the electrons can be completely characterized is the average energy of the electrons. The fl particles released from the tritium have a maximum energy of 17.6-18.9 kev. as summarized in a paper by Strominger, et a2.z8 However, these particles rapidly lose their energy by ionization of the argon and methane until their energy is less than that necessary for forma-. tion of an ion pair. The electrons produced by the 0's will initially have an energy in excess of thermal energies, but it is assumed that they will rapidly lose The Journal of Physical Chemietry

W. E. WENTWORTH, E. CHEN,AND J. E. LOFELOCK

5.0

ne-

2.5

t ll t i

A l il J tw $ s e d

Figure 2. Electron concentration us. pulse width a t various voltages.

energy in collisions, primarily with methane, until their average energy is thermal. I n pure argon, only elastic collisions can take place once the energy is below the excitation level of argon. However, in the presence of methane there are other possible modes for the loss of energy, such as vibrational and rotational excitation of methane. This difference is reflected in the large difference in the drift velocity of electrons in argon and argon-methane (see Figure 1). I n argon-10% methane the collision frequency, v,, a t STP is about 3 X 10l1 collisions/sec., and the fractional energy loss per collision, j , for elastic collisions is 2m/M = 2.73 X where m is the mass of an electron and M is the mass of an argon atom. If these quantities are constant, then the following formulasz7can be used to calculate the time necessary to cool an electron of energy uuto near thermal energies.

du dt where e is the electronic charge. Integration under the assumption above gives (21) T. Nagy, L. Nagy, and S. Desi, N u c ~In&. . iWethods, 8, 327 (1960). (22) T. E. Bortner, G. E. Hurst, and W. G. Stone, Rev. Sci. Inatr., 28,103 (1957). (23) L. Coli and W. Facchini, ibid., 23, 39 (1959). (24) W.N.English and G. C. Hanna, Can. J. Phys., 31,768 (1953). (25) W.F. Libby, Phys. Rev., 103,1900 (1956). (26) D.Strominger, J. M. Hollaander, nd G. T. Seaborg, Rev. Mod. Phys., 30, 585 (1958). (27) A. V. Phelps, 0. T. Fundingsland, and S. C. Brown, Phvs. Rev. 84,559 (1951).

PULSE-SAMPLING STUDYOF ELECTRON-ATTACHMENT PHENOMENA

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-

uo--

IcT

This value for f is certainly a lower limit, and the difference in the drift velocities in argon and argonmethane indicates that it should be higher. However, using these figures one obtains a value of 0.076 psec. to cool a 10-e.v. electron to 10% above thermal energies. This is much shorter than the pulse periods, t p , used in these studies. Although this calculation does not rigorously prove there is a thermal distribution, it, would seem reasonable to assume that in the period of 1000 psec. with no voltage applied that a thermal distribution could well be obtained. Another important parameter which must be considered is the average energy of the electrons during the application of the pulse. A very rough approximation to this can be obtained from the Langevin expression X2X% E = 0.33(3) v2m where X is the Ramsauer free path, X is the field strength, and v is the drift velocity. The free path is a function of the energy so that the energy must be estimated in order to choose the free path. Loeb2 states that data derived from this method should be good to 20%. Since it is anticipated that the average energy is going to be approximately thermal, the free path is chosen to be that at thermal energies. The free path is not known for argon-lO% methane but is known for pure argon to be l/2.1P.27 Using this value at atmospheric pressure, the average energy is 0.038 e.v., which is not much above thermal energies. The approximate nature of the free path used in this calculation does not warrant iteration. If the value for the drift velocity in pure argon is used, the average energy is 3.8 e.v., demonstrating that the methane does lower the average energy considerably. The latter point is in agreement with the calculations made by Uman,28which demonstrated that traces of molecular gases in argon lower the average energy of electrons in the presence of an electric field. An additional study of the effect of the energy of the electrons during the pulse with respect to electron capture was carried out. The capture coefficient for anthracene was measured as a function of voltage in argon and argon-10% methane. The value with the argon-10% methane and the pure argon did not vary as a function of voltage from 10 to 80 v., indicating that the portion of the reaction taking place during the

449

application of the voltage is either negligible or coincidentally the same as the capture of electrons when an electric field is not applied. In addition, the ratio of capture coefficient of chlorobenzene to that of azulene was measured as a function of voltage, methane concentration, and pulse time. Chlorobenzene probably undergoes dissociative capture in an endo chermic process, while azulene probably forms a stable negative ion in a thermoneutral or exothermic process of attachment. Under these assumptions it would be expected that the capture of electrons by chlorobenzene would vary quite considerably with electron energy while that of azulene would be relatively insensitive. In Figure 3, this ratio is plotted as a function of voltage at a fixed pulse time and pulse width for different carrier gas mixtures. For pure argon, this ratio reaches a maximum a t 50 v., whereas it remains relatively constant for argon plus methane. This type of behavior is qualitatively in agreement with the work of Stockdale and H ~ r s t , ~ ~ who have recently observed that the cross section for the dissociative capture of electrons by chlorobenzene peaks at a mean energy of 0.5 e.v. This substantiates the claim that the mean energy of the

3.0-

2.0RATIO CHLOROBENZENE MULENE

1.0 -

Argon S X CH4

0

I 20

40

60

80

IO0

v (volts) Figure 3. Ratio of the response of chlorobenzene to the response of azulene vs. voltage applied for different argon-methane ratios.

(28) M. A. Uman, Phys. Rev., 133, A1266 (1964). (29) J. A. Stockdale and G. S. Hurst, J . C h . Phys., 41,255 (1964).

Volume 70,Number B February 1066

450

W. E. WENTWORTH, E. CHEN,AND J. E. LOVELOCK

present and no field is applied, the loss of electrons can be due to recombination, diffusion, or attachment. The effect of diffusion is small as can be seen by consulting ref. 2, p. 203. With a capturing species present, two types of electron attachment may take place. AB+e-+AB(A'

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AB

(4)

- B)-

+ e- +ABetc. \ / ' A' + B-

(5)

In the first case, a stable negative ion is formed which will only recombine with tthe positive species or react with the radicals. In the second case, the negative ion dissociates and forms radicals and ions or a radicalion which can subsequently react further. tp (,used

Figure 4. Ratio of the response of chlorobenzene to the response of azulene us. the time between pulses for different argon-methane ratios.

electrons is higher than thermal in pure argon but is lowered by the addition of methane. Figure 4 shows the variation in the same ratio as a function of pulse time at a fixed pulse width and a fixed voltage for several carrier gases. The difference in the curves for pure argon and argon-lO% methane clearly emphasizes the previous point. In addition, this illustration demonstrates that the reaction taking place during the application of the pulse is negligible since, after 10 psec. pulse time, the relative response remains constant. Another indication of the presence of thermal electrons is the value of the probability for the attachment of an electron to a neutral molecule at thermal energies. I t will be seen in a later section that an estimate of this value can be obtained for some compounds and that this value is approximately unity. Higman and for SFB,and more recently, Asundi and Craggs13' for SFe and C7F13, have shown that the cross section for attachment in these gases reaches a maximum value corresponding to approximately unit probability around thermal energies and remains high for a narrow range of energies. In addition to the electrons, the p particles also produce positive species. I n the case of argon-10% methane as the carrier gas, these are probably CH2+, CHa+, and Ar+.32 Thus, if only the carrier gas is The Journal of Physical Chemistry

Description of the Model The description of the model for the events occurring within the electron capture cell in the pulse-sampling mode is probably best initiated by a discussion of the assumptions made in the model. As will be seen shortly, the justification for most of these assumptions can be found in the results of the experiments just described. The first assumption to be made is that the rate of production of thermal electrons is a constant which is not affected by the presence of the added capturing species. Next, it is assumed that the reaction zone is localized in the region about 1 to 2 mm. from the tritium foil. The reaction zone includes a cloud of ions, electrons, and radicals in addition to the argon-methane mixture and the electron-capturing species. Since the electrons are being continuously removed by the application of the pulse and the positive species are only removed by the much slower Aow out the end of the cell or by being collected at the other electrode, it is assumed that the cloud is not neutral but rather has an excess of positive species. I n addition, it is assumed that there is an excess of radicals in the cloud. The cloud is considered to be homogeneous, or if localized clusters of ions exist, the kinetics are valid in the localized region. The reaction zone can be treated as a static system with respect to the electron concentration since the flow out of the cell is much slower than (30) W. M. Higman and R. E. Fox, J . Chem. Phys., 2 5 , 642 (1956). (31) B.K. Asundi and J. D. Craggs, Proc. Phys. SOC.(London), 8 3 , 611 (1964). (32) F. H. Field, N. H. Head, and J. L. Franklin, J . Am. Chem. Soc., 84, 1118 (1962).

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PULSE-SAMPLINQ STUDY OF ELECTRON-ATTACHMENT PHENOMENA

the pulse times. The slow removal of material occurs by the flow of the carrier gas approximately parallel to the face of the tritium foil. The primary mode for the loss of electrons in the presence of carrier gas alone is the recombination of the electrons with the positive species and/or the reaction of electrons with radicals. It is assumed that diffusion losses are minor. It is not necessarily assumed that electron capture by an impurity in the carrier gas is absent. However, if such an impurity is present, it is assumed that the concentration of such a species is constant. This may arise, for example, from a small amount of bleeding from a gas chromatographic column or from 0 2 in the carrier gas. I n the presence of an electron-capturing species which has been deliberately added, electrons will be lost by the capture of electrons to form negative ions. If the negative ions are stable, then detachment of the electrons can occur or the negative ions can recombine with the positive species. If the negative ions dissociate, then a host of subsequent reactions are possible. The final assumption is that the amount of material which undergoes electron capture is small in comparison to the total amount of material present. The rate constant, kpR,, will be used to represent a composite process for thermal electron production. This process includes ionization of carrier gas by particles followed by numerous electron-carrier gas molecule collisions. Other variables are defined as : a, the concentration of the capturing species, AB; b, the concentration of electrons in the absence of a capturing species; [e-], the concentration of electrons in the presence of AB; the concentration of the positive species; [R‘1, the concentration of the radicals. The processes taking place in the cloud and their respective rate constants can be described as

[@I >>

451

[e-], the following differential equations can

be written

~d[e-l - k,R, - k~’[@][e-]- k~’[R‘][e-] (6) dt

d[o1~ ()

(7)

dt

If [R’] = cst, eq. 6 can be solved directly to give

I n the presence of a capturing species AB which does not dissociate and again assuming [@I >> [e-] and [AB] = a - [AB-] = a, [R’] = cst, eq. 6 becomes

dm= k,R, - k~’[@][e-] dt kla[e-]

+ k-1LAB-I

- k~’[R’l[e-l (9)

The equation for the rate of formation of [AB-] is d[AB-] ~- - kla[e-] - k-1[AB-l dt

[e],

p-

+ Ar + CH4 3 @ + e- + B-* @ + e- +neutrals R’ + e- +R AB + e-= ABkN’

d[AB-l ~dt

- kla[e-]

- k-l[AB-]

- ~ L [ A B - ] (14)

These equations can be solved simultaneously to give

kR’

ki

k- 1

AB-+@%,

fA’

+

B’

+

R’

LAB+ R* ABR-

AB-

+ R’ -% AB + R- + @ +neutrals AR

+ B-

I n the absence of a capturing species and assuming Volume 70, Number 8 February 1966

W. E. WENTWORTH, E. CHEN,AND J. E. LOVELOCK

452

d ( k l a 4-k-1 4- kL 4- kD)' - 4( ( k d ( k 1 a

+ kD) 4-k l k ~ )

AB, designated as Q, is bleeding into the gas stream the concentration of the electrons, b, is given by

(18)

K 1 and Kz are both negative quantities so that a t time infinity, eq. 15 becomes

then

If the impurity is different from the species being studied, then the processes of at,tachment, detachment, and recombination must also be considered for this species. Designating the impurity as C, the rate constants for these three processes can be symbolized by kIc, k-Ic, k m . It is assumed that the exchange of electrons between species C and AB is negligible. I n this case, b, the concentration of electrons before the addition of AB is given by

Equation 21 can also be obtained from eq. 13 and 14 by applying the steady-state criteria to the species [AB-] and [e-]. I n that case

I n both cases, the steady-state criteria lead to the equation

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and eq. 8 becomes

kLkla b b b - [e-] - = KU[e-] JCD(~L k-1) bo bo

+

k-1 [AB-]

d[AB-] --dt

(22)

- 0 = Ic~a;[e-]- kl[AB-] - ~ L [ A B - ] (23)

where bo is the maximum concentration of electrons and is given by

kPR, bo = kD

or solving eq. 23 for AB- gives

or substituting in eq. 22 and solving for [e-] gives

which is identical with eq. 19. I n a gas chromatographic system there is often bleeding of the liquid phase from the column, or when the temperature of the column is increased, there is bleeding of materials accumulated on the column from the numerous injections a t the lower temperature. I n addition, there may be impurities in the carrier gas which come through the column and pass through the detector. Thus, it is necessary to see how impurities of this type would affect the response of the detector for a particular compound. If the species is the same as the capturing species being studied, then no new processes would have to be considered. When a constant concentration of The Journal of Ph.ysical Chemistry

(28)

Thus, if the standing current varies owing to bleeding from the column, it is possible to correct the response to the maximum standing current from eq. 28. It must be emphasized that changes in the standing current due to variations in the degree of ionization or changes in performance of electronic apparatus should not be corrected in this manner. The correction is also valid if C has a large electron affinity so that if electron transfer occurs, it only occurs from AB- to C. In each of these three cases, the corrected response is proportional to the concentration of the electron capturing species which is being studied. Thus, the capture coefficient, K , can be determined from the slope of the linear graph of corrected response us. concentration of the capturing species. Since the capture coefficient, K , contains the term (kL k-J (eq. 21), it is convenient to consider the case where kL >> k , and the case when k-, >> kL, in order to examine the type of temperature dependency to be expected. If the temperature variation for the forward rate is slight, corresponding to no energy of activation for the addition of an electron, and if the

+

PULSE-SAMPLING STUDY OF ELECTRON-ATTACHMENT PHENOMENA

electron affinity of the molecule is appreciable, then the backward rate constant, k-,, must have a significant temperature variation. Thus, it is quite likely that there would exist a region at low temperatures where k ~ which , is relatively temperature insensitive, would be greater than k-, and a region at higher temperatures where the opposite would be true. In the latter region, designated CY, it is assumed that k-, >> k~ so that eq. 21 becomes

453

2.0

ne(arbitrary units)o

Downloaded by FLORIDA ATLANTIC UNIV on August 29, 2015 | http://pubs.acs.org Publication Date: February 1, 1966 | doi: 10.1021/j100874a021

10.0

or assuming an ideal gas and using the statistical mechanical expression for Keg

ne(arbitrary

units) 5.0 -

or EA + In A + kD kT

I

kL

In (KT”/’)= In -

(32)

1000

2000 tp

If it is assumed that k ~ / isk temperature ~ independent, then In KT”/‘is a linear function of 1/T with a slope of E A / k and an intercept of In ~ L / J C D In A. In the former region, designated p, it is assumed that kL