CHEMICAL ACTION I N T H E GLOW DISCHARGE IX. Reaction in the Crookes Dark Space and Negative Glow* BY A. KEITH BREWER AND P. D. KUECK
In the previous articles of this series it has been shown that an Electrochemical Equivalence Law, analogous to Faraday’s Law for Electrolytes, holds for the chemical action in the electric discharge in gases. The definiteness of this law combined with the facts that the active states are easily identified, and that the reaction takes place in the gas phase without the presence of solvent, surface, or catalyst, makes the glow discharge an extremely fertile field for the study of chemical reactivity. The principal difficulty at present in this type of research results from a lack of understanding of the physics of the discharge. Until this is solved an accurate estimation of the ratio of molecules formed to reactive centers (M/N) cannot be given. The present research was undertaken to clear up the uncertainty regarding the relative ability of the various regions of the discharge to incite reactivity, special attention being given to the Crookes dark space and to the negative glow. Also, a new method is suggested which permits a more accurate estimation of the number of positive ions formed than has heretofore been possible. The Reaction The reaction chosen for this work was the synthesis of nitrogen dioxide from an N2/202 mixture since the previous study of this reaction’ yielded very clean cut results with no apparent complication. The technique was identical to that employed in the previous study. The Method The method of procedure employed was to measure the reactivity when various portions of the discharge were eliminated by moving the anode towards the cathode. In the glow discharge as the anode is moved through the positive column toward the cathode the rate of change of potential between the electrodes is constant until the anode reaches the Faraday dark space where the change in potential per cm. is usually slightly increased. As soon as the anode enters the negative glow, however, no change in potential between the electrodes is observed until it has reached a point near the edge of the Crookes dark space, where the voltage rises suddenly, changing from about 300 for the average discharge t o many thousand in a very short dbtance. The conditions
* Fertilizer and Fixed Nitrogen Investigations, Bureau of Chemistry and Soils, Wmhington, D. C. 1 J. W. Westhaver and A. K. Brewer: J. Phys. Chem., 34, 554 (1930).
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existing in the discharge Yhen the anode has reached the edge of the Crookes dark space are identical to those found in the gas-filled x-ray tube, similar voltages being necessary to maintain the current. From these considerations it will be seen that no difficulty is to be expected in measuring the reactivity in various regions of the discharge by changing the electrode separation until the anode approaches close to the edge of the Crookes dark space where the cathode fall of potential is no longer characteristic of the ordinary type of discharge.
Apparatus The discharge tube is illustrated in the insert in Fig. I . It consisted of a Pyrex tube 3.5 cm. inside diameter and 2 0 cm. long sealed to a 3 liter bulb. The cathode was made of an aluminum block turned to fit tightly into the bottom of the tube in order to confine the discharge entirely to the top surface. The position of the anode was adjusted by a stopcock suspension. The anode itself was made of two thin aluminum discs placed 0 . 5 mm. apart. The lower disc was 3.5 cm. in diameter with a I cm. hole in the center; the upper disc was a solid plate 2 . 5 cm. in diameter. It was found necessary that the outer disc fit the walls of the tube tightly to prevent the discharge from passing up along the walls when the anode approached the Crookes dark space. The 0.5 mm. separation between the plates was to allow fresh gas to diffuse into the discharge. The rates were measured a t 0.3 mm. pressure with the electrode separations from 0 . 2 cm. to 2 . 5 cm. The discharge current was maintained a t 5.0 m.a. The dark space measurements were made visually with a 2 . j cm. electrode separation, the distance between the cathode and the edge of the negative glow being taken as the dark space. The electrode separation, however, has no effect on the length of the dark space.
Results The pressure vs. time curves for the various electrode separations are given in Fig. I . The data show a decrease in the rate of reaction as the anode approaches the cathode. Especially it should be noted that there exists a definite pressure at which the rate becomes zero for each electrode separation; this pressure decreases for increasing separation. Further, the curves show that the reaction in each instance dropped to a negligible value when the dark space approached close to the anode. The voltage curve for various electrode separations are shown in Fig. 2 . The curves become practically asymtotic to the voltage axis where the dark space reached the anode. This is the same point at which the reaction rate became negligible. The reactivity, however, never entirely ceased as it was not possible to confine the discharge completely between the electrodes. When the electrode separation was just slightly greater than the length of dark space the high
CHEMICAL ACTION IN THE GLOW DISCHARGE
Pressure, mm.
FIQ.2 Pressure vs. voltage curves for various electrode separations.
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FIG.3 Curve showing the relation between the length of the Crookes dark space and the electrode separation for zero rate as a function of pressure.
voltage necessary to maintain the current tended to cause the discharge to leak by the anode; the observed rates, therefore, are doubtless slightly high under these conditions. The relationship between the Crookes dark space and the pressure a t which the reaction ceases is shown in Fig. 3 . The length of the Crookes dark space and the electrode separation a t which the reaction becomes zero are plotted against the reciprocal of the pressure. It will be noted that the points fall close to the same straight line passing through the origin. The per cent error for short distances is necessarily higher than for greater distances; hence the observed deviations are not surprising. It should be mentioned that the dark space length was measured simply by visual observation; in another type of lube, designed for more accurate measurement, the hyperbolic relationship between length and pressure held accurately. I n Fig. 4 are plotted the rates measured a t 0.3 mm. pressure for various electrode separations. The Crookes dark space at this pressure is very close to 2 . 0 mm. It will be Electrode Separaflon (mm) observed that the rate decreases rapidly FIQ.4 as the anode approaches the dark space. Rate vs. electrode separation curve.
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The rate of decrease in reactivity per unit volume of negative glow in moving from the Crookes dark space to the Faraday dark space is shown in Fig. 5 . When the log of the decrease in rate (maximum rate minus the observed rate) is plotted against the electrode separation the points fall on a straight line except where the anode is very close to the Crookes dark space. 0.030 was taken as the maximum rate, since it represented the rate
Current = 5.o ma
FIG.5 Curve showing the rate of decay in reactivity through the negative glow.
observed when the entire negative glow was included between the electrodes. Thus it will be seen that the reactivity in the negative glow decreases exponentially with distance from the edge of the dark space.
Discussion of Results Astonl has given the following expression for the Crookes dark space in the abnormal discharge,
A
ds=-+p
B
dT
in which d, is the length of the dark space in cm., p the pressure in mm. of mercury, i the current density, and A and B are constants. I n the present experiments the current density was maintained constant so the relationship between length and pressure is expressed by
+
d, = ki/p C IF. W. Aston: Proc. Roy. Soo., 87, 437 (1912).
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From Fig. 3 it will be seen that the electrode separation at which dp/dt also obeys the relationship 1 = kz/p C'
= o
+
where 1 is the electrode separation. Since the points for both distances fall on the same line kl is equal to kz, and C and C' are equal and negligible a t the low current densities used; hence d, = 1, Le., the electrode separation at which the reactivity ceases is equal in length to the Crookes dark space. From this it follows that the reactivity in the dark space is negligible compared to that in the negative glow. The mean path through which an electron is chemically active may be estimated from the rate of decrease of reactivity in the negative glow. Since the curve in Fig. 5 is exponential in character, except in the immediate neighborhood of the Crookes dark space, it follows from kinetic theory that for constant current and at a given pressure the decrease in the ability of an electron to induce reactivity can be expressed by
where x is the distance from the Crookes dark space, and X is the mean path over which an electron is capable of inciting reaction. The value of X obtained from the slope of the line is 2 . 5 mm. for I mm. pressure. The fact that the exponential decay curve does not hold a t the junction of the dark space may be due to several causes. When the anode is brought near the edge of the dark space the cathode fall of potential is not only materially raised, as is shown by Fig. 2 , but the anode itself receives the direct impact of high-speed electrons. This bombardment gives rise to secondary electrons which produce an abnormal ionization in the gas adjacent to the anode. Another possible cause, inherent to the discharge itself, will be presented later on. Interpretation of Results The results that have just been presented can be interpreted readily from the physics of the discharge. I n the discharge electrons are liberated from the cathode largely by metastable molecules and to some extent by positive ions and by photoelectric emission.' The electrons thus ejected are accelerated through the Crookes dark space by the cathode fall of potential. Very few positive ions are formed in the Crookes dark space since the length of the dark space is approximately equal to the mean free path of an electron between ionizing collisions. For instance, the dark spaces in nitrogen and oxygen a t I mm. pressure are given by Townsend as 0.113 cm. and 0.114 cm., respectively. At this pressure the ionization mean free path of an electron is 0.113 em. in nitrogen and 0.12 cm. in oxygen. These values as 1 Note. Linder and Davis (J. Phys. Chem., 35, 3649 (1931)) postulate that the current passing through the discharge is carried to the cathode almost entirely by positive ions falling in from the dark space. This conclusion apparently grew out of a misconception of the length of the dark space and the mean free path of an electron between ionizing collisions. Direct experimental measurements of the number of positive ions arriving a t the cathode (to be published shortly) shows the positive ion current to be less than 3% of the total current in N2 a t I mm. pressure.
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obtained from kinetic theory are equal to 4 4 2 times the molecular mean free paths times the probabilities of ionization upon collision. From this it follows that the average electron does not begin to ionize until it reaches the edge of the negative glow. I n spite of the fact that the edge of the dark space comes within a mean free path of the cathode a fraction of the electrons, as given by probability, will ionize in this region. The ions formed near the cathode give rise to the positive ion current received by the cathode; the ions formed near the outer edge of the dark space where the field is weak are apparently driven into the negative glow by the momentum of the electrons and thus give rise to the known increase in pressure of the gas a t this point. It is these ions driven into the negative glow from the dark space that may in part be responsible for the high reactivity observed a t the beginning of the glow. It does not seem probable that the positive ions arriving a t the cathode can contribute materially to the chemical action. The lowest pressure to which this reaction can be carried shows that an ion must make between I O and 15 colliPims with neutral molecules for reaction to take place. The mean free path of an ion in oxygen is 0.082 mm. a t I mm. pressure. Such an ion, therefore, would make less than 14 collisions in traveling completely across the dark space. However, as was just pointed out, it is doubtless only the ions formed near the cathode that ever reach that electrode; hence the probability of making the required number of collisions with neutral molecules is relatively small. For this reason it is not surprising that Fig. 2 shows the distance from the cathode where the reactivity becomes zero is equal to the length of the dark space. The number of positive ions formed per electron of current can be estimated from the exponential decay of reactivity in the negative glow. I n making this estimation it is necessary to assume that the rate of reaction is proportional to the rate of positive ion formation; the M/N ratio is not involved. The slope of the line in Fig. 5 gives the value X = 0 . 2 5 cm. for the mean distance over which an electron is chemically active in the negative glow. Since the electron has already traveled through the Crookes dark space or 0.11 cm. before entering the negative glow the total path of the average electron at I mm. pressure is 0.36 cm. The mean free path of an electron times the probability of ionization, as has been stated, is equal to the length of the dark space of 0.11 cm.; hence the average number of ionizing collisions made by an electron is 0.36 + 0.11 = 3.3. The total number of positive ions formed per electron under conditions quite similar to those found in the discharge can be estimated from an extrapolation of the results of Langmuir and Jones' or from the values given by G. A. Ans10w,2 both observers obtaining substantially the same results. Miss Anslow gives 3.7 positive ions for a 400 volt electron which is in reasonable agreement with 3.3 derived from the present data. 'Langmuir and Jones: Phys. Rev., ( 2 ) 31, 357 (1928). * G. A. Anslow: Phys. Rev., ( 2 ) 25,484 (1925).
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These values assume that the energy of the electron is given by the entire cathode fall of potential. It may be, however, that the actual energy is slightly less than this, due to the space charge in the region through which the electrons are accelerated. I n this connection it is interesting to note that Miss Anslow observed that an electron with 0.36 cm. range at I mm. pressure produced 3.4 ions, the required accelerating voltage being 347. Since 3.3 ions are obtained for a 0.36 cm. range in the present experiments, it might be inferred that the electrons in passing through the Crookes dark space failed by about 50 volts of receiving an acceleration corresponding to the entire cathode fall of potential. The value of the M/N ratio can now be placed within reasonably narrow limits. The time vs. pressure curves for 2 . 5 cm. electrode separation indicate a yield at 0.3 mm. pressure of 1.5 molecules of KO2 synthesized per electron of current. I n the first paper on oxidation of nitrogen it was shown that this reaction is initiated by Nfz ions, Of2 ions being relatively inert. Since the stopping powers of oxygen and nitrogen are very nearly identical, the ratio of N+zto Of2 ions is as I : Z . This gives an equivalent yield of 1 . 5 molecules formed per I . I K’z ions, assuming positive ion current to be negligible. The positive ion current at 0.3 mm., however, has been found by direct measurement to be 15% of the total current; thus the number of electrons producing ions IS reduced by IS%, and further the number of ions formed suffers an effective loss corresponding to 15% of the entire current since the positive ions arriving at the cathode do not contribute materially to the synthesis. Making these corrections the number of N+2 ions available for reaction is 0.73 per electron of current. The value of M/N, therefore, is 1.5/0.73 = 2 , approximately. S-ary
The chemical action taking place in the Crookes dark space and the negative glow of the ordinary glow discharge has been measured for the synthesis of nitrogen dioxide. The distance from the cathode within which no appreciable reactivity occurs is shown to be equal to the length of the Crookes dark space. The reactivity per unit volume of discharge is a maximum at the beginning of the negative glow and thereafter decreases exponentially through the glow. The average path a t I mm. pressure over which electrons ejected from the cathode are capable of inciting reaction is shown to be 0.36 cm., the reactivity being confined entirely to the last 0 . 2 5 cm. of path. The total number of positive ions formed per electron is given by dividing 0.36 cm. by the mean free path of an electron between ionizing collisions. Thus the measurement of the mean free path over which the electrons are chemically active enables the number of positive ions formed in the negative glow to be computed by a new and independent method. The value of 3.3 ions so obtained agrees fairly well with 3.7 reported by Miss Anslow for 400 volt electrons. The ratio of M/K = 2 for NLz ions is obtained by correcting for the loss of N+zions to the positive ion current.
