Microwave studies in the ionization of alkali metals in flame gases and related phenomena

SPECIALTECHNIQUES

406

37

MICROWAVE STUDIES IN THE IONIZATION OF ALKALI METALS IN FLAME GASES AND RELATED PHENOMENA By T. M. SUGDEN Introduction

contains no added alkali metal. This also reduces boundary self-reversal effects in the temperuture determination ~. The temperatures measured range from 2250~ down to 1800~ in which range there was no measurable ionization from clean (i.e., without added metal) flames. In this range even the alkali metals are only ionized to a small extent, which greatly simplifies the interpretation of the results. Work at higher temperatures ~, directed towards the ionization of clean flames, meets with very serious difficulties from adventitious traces of alkali metals, and will only become reliable under conditions where the total ionization is considerably larger than that which can be produced from these traces.

This paper is intended to provide a summarized account of measurements made by the author and various collaborators on ionization in flame gases, using the technique of microwave absorption to measure the concentration of free electrons. These electrons have in general been produced by the addition of controlled amounts of alkali metal to the premixed gases before combustion, and it has been shown that their concentration, in the systems which have been studied, are consistent with thermodynamic equilibrium. I t is, however, necessary to take into account various side reactions with other constituents of the flame gases, in particular reactions involving hydroxyl radicals, and it is with these that the main chemical interT h e M e a s u r e m e n t of Electron est of the work lies. Concentration The flames used are of hydrogen and air, The presence of free electrons in a gas gives sometimes further diluted with nitrogen, the prerise to an electrical conductivity ~, which is remixed gases being burned at atmospheric pressure lated to n, the number per cc, by in a M~ker type of burner. This produces a large number of small cones of primary combustion, in ne ~ r = (1) which no thermodynamic equilibrium is expected, and above them a more or less extended zone (interconal gases) which is only faintly where e and m are the electronic charge and mass luminous, and which is considered to be at or respectively, ~ is the angular frequency of the near to equilibrium. I t is with this extended zone applied electric field (microwaves), and r is the that this work is concerned. The temperatures collision frequency of electrons with gas molehave been measured by the sodium D-line re- cules. This equation is based on a very approxiversal method (see, e.g., Griffiths and Awberryl), mate derivation with inaccurate averaging over which is expected to be reliable under these con- the collisions, and a more accurate treatment has ditions. Recent measurements of James and been given by Margenau 7. It has, however, been Sugden 2 on flame gases of this type show agree- shown to be correct in form by measuring the ment of measured temperatures within experi- dependence of r on co over a wide range of fremental error for both the first and second quencies s, and since the quantitative values resonance lines of all the alkali metals, the sodium given by Margenau's much more complicated theory differ very little from those given by D-lines being the easiest to read (to within 5~ The measured temperatures differ from calcu- equation (1), the simpler expression has been lated ones on account of two effects, firstly heat used to derive n from a. I t will be seen that unless losses, mainly to the burner, and secondly the there is a very large excess of heavier ions, the effects of indrawn air, which in a hydrogen-rich small mass of the electrons makes them responflame may give rise to secondary combustion, sible for effectively all the conduction. I t is thereby making the gases non-uniform in tem- necessary to work at low microwave powers so perature cross-section. This latter effect may that the electrons do not become appreciably largely be eliminated by enveloping the flame hotter than the rest of the gases7. Two methods of measurement of r have been with nitrogen 3, or, in more recent work 4, b y sheathing the flame with a similar flame which employed; that of direct attenuation of micro-

407

MICROWAVE STUDIES IN IONIZATION OF ALKALI METALS

waves, and that of finding the effect of the flame on the characteristics of a resonant cavity at microwave frequencies. These are shown diagrammatically in Figures 1 and 2 respective]y. The simpler method is that of direct attenuation, in which a beam of monochromatic microwave radiation from a klystron, after suitable attenuation, passes through the flame gases a few cm above the primary cones, between two horns. After further attenuation, the microwaves are rectified by a crystal, and the resultant crystal current passed on to an amplifying and measuring system. I t is necessary to have the microwave line carefully tuned with the minimum of standing waves. If the attenuation brought about by introduction of a conducting f a m e in the gap is db/cm thickness of flame, then a, and hence n, may be obtained from the equation ~ = (17.4~r/c)z, where c is the velocity of light. This method is suitable for electron concentrations of Klystxon

~L'.3 Pa~ ~ m

Burner I I

becoming less sharp on account of the dielectric losses introduced. From these changes, knowing the geometry of the system, it is possible to deduce the conductivity of the flame gases, and hence the concentration of free electrons. The useful range of this method overlaps with that of the previous one, and extends down to l0 s electrons per cc. A valuable mode of calibration of this type of apparatus is to use the simple behavior of alkali metals as given by the more straight-forward attenuation method. The alkali metals are added to the gas stream in the form of finely divided sprays of one of their salts. The maximum added is of the order of 1 part in l0 ~ of the total gases, and at this level the corresponding amount of anion plays no effective role, i.e., all salts of a given metal produce the same electron concentration. Thus the amount added can conveniently be controlled by changing the strength of the solution in the

"~ ~.,

t'o arnpl1~ers & measunng System

FZG. 1. Direct attenuation apparatus-diagrammatic. the order of 101L1012/CC, working with flames of a few cm thick. Various refinements have been used to extend this to lower concentrations 6, but in Cambridge it has been found more convenient to use the resonant cavity method to achieve this. An account of such an apparatus is given by Sugden and Thrush 9, a rather similar device having been used by Adler1~ to study electrons in discharge tubes. In this case the microwave power passes through a cylindrical cavity, with apertures to allow ingress and egress of the flame gases axially. The klystron is frequency modulated by a low frequency saw4ooth voltage applied to its reflector plate, and the cavity tuned by a plunger, so that the frequency range used sweeps across the resonance point of the cavity in a suitable mode (TE011 is most convenient). By applying the saw-tooth voltage to the X plates of an oscillograph, and the signal transmitted by the cavity to the Y plates, a diagram of the resonance characteristic of the cavity is obtained on the screen. The shape of this is altered when a conducting flame is present in the cavity, the peak

Fla. 2. Resonant cavity method-diagrammatic. atomizer. The estimation of the total metal picked up can best be made from measurements of loss in the atomizer, coupled with careful estimations of any salt deposited on connecting tubing between the atomizer and the burner. I t has been found most convenient to express all concentrations in the flame gases in partial pressures in atmospheres, which will be expressed here by enclosing the appropriate symbol in square brackets--e.g., [e]--for electron concentration.

The Ionization o f Alkali Metals and Hydroxyl Effects When an alkali metal A is added to flame gases in small proportion, the following equilibrium m a y be supposed to be set up A~A

+ + ~;

K1 =

[A+IM [A]

(2)

The equilibrium constant K1 is given by a thermodynamic equation first put forward by SahaU: log]0K1

5050V T +

log~0 T - 6.50

(3)

408

SPECIAL T E C H N I Q U E S

where V is the ionization potential of the metal in electron volts and T the temperature in ~ Under present conditions the background ionization is negligible so we may put [A+] = [~] for charge balance, and the total ionization is small, i.e., [A+] << [A] so we may write [A] = [A0], where [A0] represents the total added metal expressed as a partial pressure. In this case equation (2) reduces to [E]~

K][Ao]

=

(4)

[A0] will be proportional to the concentration of the salt solution in the atomizer, so that a plot of log [~] against log (molarity of solution) should be a straight line of slope 0.50. This result is always

4o

4s

SO

I

I

I

Lz

FIO. 3. The relative ionization of the alkali metals in a hydrogen-rich flame of H~/air (sodium D-line reversal temperature 2245~ The dotted line through the -Na point has a slope corresponding with that predicted by the Saha equation for this temperature. found to be the case under the conditions used, and is equivalent to the Ostwald dilution law for a not too dilute solution of a weak electrolyte. This supports the idea of equilibrium, or at least of a steady state of balanced ionization and recombination. The next point is to consider the values of the constant K1 in the light of the Saha equation (3), but in order to do this it is necessary to examine two possible interactions with the flame gases, which might affect the final equilibrium position. These are the formation of gaseous alkali hydroxide AOH and negative hydroxyl ion OH-, by reaction with the free hydroxyl of the gases. AOH ~

A -I- OH;

OH- ~ OI-I + ~;

K2 Ka =

[AI[OH] [AOH----~

(5)

[OH][~]

[OH-]

(6)

If we write @ --- [OH]/K~, and r = [OH]/Ka, then @ and @' are parameters of the system, the first being characteristic of a given metal and flame, and the latter of a given flame. Since [OH] for the flames under consideration is at least 10 times larger than the amounts of metal added, it will be unaffected by the above two reactions. Assuming balance of charge and of mass: [A+] =

[~]+ [OH-] = [~] (1 + ~ ' )

(7)

[A0] = [A] -J- [AOH] = [A] (1 + r

(8)

and combining these last four equations with equation (2) the following result is obtained: [~]~ =

KI[A0] (1 + @)(1 -J- r

(9)

This equation still gives the observed dilution behavior but with a modified constant. A selection of actual results for various alkali metals in a given flame is shown in Figure 3, a n d for various hydrogen air flames (i.e., various temperatures) with a given alkali metal in Figure 4. Both of these diagrams show marked deviations from the Saha equation, which would predict straight lines, of slopes (5050/T) and (5050V) respectively in Figures 3 and 4. On the basis of interpretation of deviations from this behavior which has been adopted, then Figure 3 will show up the hydroxide (r effect only, since the hydroxyl ion (r effect, if present at all, will influence all metals in a given flame similarly. The extent 9f the deviations of Figure 3 suggests that LiOH is a very stable compound, followed by CsOH, RbOH, KOH and NaOH in decreasing order of stability. These molecules should be largely ionic in type, resembling the gaseous alkali fluorides and chlorides, whose heats of formation from atoms are shown in Table 1, and it is interesting to see that the sequence of these is the same as that suggested for the hydroxides, within experimental error. The tittle thermodynamic evidence which is available TM, suggests that the reaction K -J- OH ~ KOH is exothermic to the extent of 87 • 2 kcal, and a statistical calculation of the equilibrium constant of the same reaction for NaOH, assuming a heat of reaction of 5 kcal less than this, shows that NaOH should be so unstable as'to be effectively absent under the flame gas conditions used at equilibrium. On this basis that there is no significant hydroxide effect with sodium Smith and Sugden 13 have examined the

MICROWAVE STUDIES IN IONIZATION OF ALKALI METALS

409

deviations shown by LiOH and CsOH, and have hook in the case of flames containing sodium. A shown that they predict a difference of 11 kcal little more evidence is provided by the study of between the heats of formation, LiOH being the more stable, and a similar difference of 5 kcal -2.0 between CsOH and KOH. These differences closely resemble the halide data of Table 1. Further, the absolute value of q~ for Li, on the basis of ~ = 0 for Na, taken together with the calculated values of [OH] for the burned gas (based on the composition of the unburned gas and the measured reversal temperature) leads to a value of 102 kcal for the reaction Li -t- OH --+ LiOH, which with the above measured differences FIG. 4. The relative ionization of lithium in gives 86 kcal for KOH, compared with the value various hydrogen/air flames as a function of the of 87 kcal from independent estimation quoted sodium D-line reversal temperature. above. Thus the evidence on relative ionization of the TABLE 1. THE HEATS OF FORMATION OF GASEOUS ALKALI FLUORIDES, CHLORIDES AND HYDROX~lkali metals strongly suggests the correctness of IDES (THE LAST BEING DEDUCED FROM THE the equilibrium hypothesis, when this hydroxide PRESENT WORK) FROM ALKALI METAL ATOMS effect is taken into account. This interpretation is AND HALOGEN ATOMS OR HYDROXYL RADICALS. also in line with experiments of James and ALL IN KCAL/MOLE Sugden ~4on the intensity of emission of resonance lines of the various metals in flame gases. In more Alkali Metal Fluoride Chloride Hydroxide recent work 4, measurements of the relative Li 140 116 102 ionization of lithium and sodium have been used Na 122 96 83 over a much more extended range of flames than K 126 100 86 was used to arrive at the above viewpoint, rather Rb 124 104 88 to check whether the values of [OH] derived from Cs 128 105 91 them agreed with the theoretical ones for the measured temperatures. The results of this, which show good agreement, are shown in Table 2. TABLE 2. COMPARISON OF HYDROXYL RADICAL CONCENTRATIONS OF VARIOUS HYDROGEN/AIR Additional confirmation of effects involving hyFLAMES ON THE BASIS OF COMPARATIVE IONIZAdroxyl ion is given by the hook-shaped curves of TION OF SODIUM AND LITHIUM AND ON CALCUthe type of Figure '4, which show that an oxygenLATION OF FLAME GAS COMPOSITION rich flame always gives less ionization than a Sodiffm D-Line [OH] from Relative [OH] from Unburned hydrogen-rich one of the same temperature--in Reversal TemperIonization of Na Gas Composition and fact the calculated curve of [OH] against 1/T ature of Flame and Li Na Temp shows an inverted form of this hook-shape. The ~ arm arm hook is most marked for lithium but is still pres2150 4.0 X 10-4 5.6 X 10-4 ent for sodium, even though its hydroxide is so 2109 2.1 X 10-4 3.4 X 10-4 unstable. The explanation of this may lie in the 2063 1.7 X 10-4 2.1 X 10-4 possibility of formation of hydroxyl radicals (r 2010 9.6 X 10 -s 1.2 X 10-4 effect), as may the fact that values of K~ deduced 1965 6.3 X 10-5 7.3 X 10-5 without allowing for this are always about 5 times 1907 3.6 X 10-5 3.7 X 10-5 lower than those from the Saha equation. 1855 2.3 X 10-5 2.1 X 10-5 Both of these results are consistent with OH having an electron affinity of 62 ~- 6 kcal, but flames containing excess of halogen over the must be treated very cautiously. The use of equation (1) to determine absolute values of alkali metal. electron concentration is much less reliable than The Effects of Excess Halogen in the case of relative ones, and in any case comAlthough it has been demonstrated that an parison over a series of flames involves the simultaneous change of so many variables that there amount of halogen anion equivalent to 1 part in may be some other explanation for the residual 105 or less of the flame gases has no significant

410

SPECIAL TECHNIQUES

effect on the ionization of a corresponding amount of alkali metal, it has been found in more recent work by Page and Sugden ~5that if excess halogen is added to the extent of 1 part in 104-103 parts of

-tO

--

Rel~ttve s

AB ~ A + B;

K4 =

B- ~ - B + ~;

K5 =

HB ~ H + B;

Added

,4 o

~0

K~ =

t~.O

I I I I I I FIG. 5. The effect of the addition of chlorine on the ionization of potassium in a typical hydrogen/air flame.

/ --off

the gases, then a significant reduction in the free electrons from much smaller amounts of alkali metal occurs. This reduction may be the result of one or both of two effects--salt formation and negative ion formation, both of ~hich will be offset by the tendency of the halogen to combine with the hydrogen of the flame gases. These additional equilibria may be expressed as follows:

r

[A][B] [AB] [B][~] [B-] [H][B] [HB]

(10) (11) (12)

Combining these three with the previous three equilibria (B represents an atom of halogen), and introducing the ideas of charge balance, mass balance of metal and halogen, and small ionization of the metal as before, then provided that the total halogen [B0] is much greater than the total alkali metal [Ao], the addition of the halogen changes the electron concentration from a value [e0] (which is that given by equation (9)) to a value [e] such that

(I oJ?

1+

\[eli

K,(1 + r

+ O) (13)

1 + Ks(1 + r - -

where 0 ---- [H]/K6 is a flame parameter, characteristic of a given flame and halogen. This equation may be written simply

005

4

I

~elaCive Clz [[Bo]) 8 tz

I

E

I

I

([~0]/[~]) 2 = (1 + a[B0]) (1 +

I

FIG. 6. A plot to test the validity of equation (13) for the effect of chlorine on the ionization of potassium in a hydrogen/air flame. TABLE 3. A COMPARISON OF a' AS OBTAINED FROM THE EFFECT OF HALOGENS ON ELECTRON CONCENTRATION~ AND AS OBTAINED BY THEORETICAL CALCULATION

a' = (Ks (1 + r (1 + 0)). -1 r = 9 has been taken for the hydrogen/air flame used Halo- Electron gen _ _ _ _ A f f i n i t y 0

a' (exp)

C1 Br

I

I

85.8 80.5

/ 724

02 / 2 1 •

(14)

a' (theor)

= (a + a') + aa'[Bo]

(15)

alto

ar m

167 1.8 • 10-s 2.8 / 1.1 X l0 -3

/

a'[Bo])

where a = (/s + ~b)(1 + 0)) "1, and represents the reduction of electron concentration on account of salt formation (which is offset by the halogen acid (0) and hydroxide (r effects). Similarly a' represents the reduction due to negative ion formation (offset by halogen acid (0) and hydroxyl ion (~') effects.) These overall reductions will be called the salt effect and the halogen ion effect respectively. Equation (14) may be rearranged to [d~ - 1 ~

kcal

+ 0)

10-

3.9 X 10-a 0.4 X 10-a 0.7 X 10 -3

which should yield a straight line plot. The effect of chlorine in reducing the electron concentration given by the ionization of potassium in a t y p i e a l

MICROWAVE STUDIES IN IONIZATION OF ALKALI METALS

flame is shown in Figure 5, the maximum chlorine added being about 0.5 per cent of the total flame gases. A test of equation (15) for the same type of system is shown in Figure 6, which is a fair straight line, with a positive slope, indicating the existence of both salt and halogen ion effects. This is a very sensitive type of plot and better experimental accuracy is desirable. Values of a and a r may be obtained from graphs of this type, and are distinguished by the fact that, with a given flame, a' is independent of the alkali metal used. The values for the salt effect show reasonable agreement with the predictions of theory (K4 can be calculated for the salt, 0 can be obtained from the stability of the acid and the calculated composition of the flame gases at the reversal temperature, and 4) from the results of the previous section), but here we shall consider rather a'. Observed and calculated values of this for three halogens are given in Table 3. The last column was obtained using a value of r = 9, and the agreement with the last but one column, although not good, is markedly worsened by omitting this factor in a'. This value is consistent with an electron affinity of 60 :t: 5 kcal for the hydroxyl radical. Further work along these lines is proceeding. Free Electrons f r o m Solid Carbon Particles

The first observations on the free electrons produced by evaporation from carbon particles in acetylene flames by a microwave method were made by Sugden and Thrush 9, more recent data being given by Shuler and Weber 6. They indicate that the ionization occurring is not inconsistent with thermal ionization of the particles, with values of the work function as for graphite. Although these measurements do not throw any direct light on the mechanism of carbon formation in such flames, it is suggested that examination of the ionization, if any, in metal-free flames in the region of composition just outside that in which luminosity from solid particles appears

411

might provide some extra information. I t is well known that even quite small conjugated systems of carbon atoms have quite low ionization potenrials, rapidly converging to the work function of graphite. The presence of compounds of this type might be made evident by measurable ionization. Conclusion

This paper has attempted to demonstrate the uses to which the study of ionization in hot flame gases may be put in some selected problems of high temperature thermodynamics, and has indicared a fairly general consistency with thermal equilibrium under the conditions chosen. The method is not, however, restricted to such systems, and could disclose the absence of equilibrium. The main difficulty is that it only gives information about relatively extended volumes of flame. REFERENCES 1. GRIFFITHS, E., AND AWBERRY, J. H.: Proc.

Roy. Soc. (A), 123, 401 (1929). 2. JAMES, C. G., AND SUGDEN, T. M.: In course of

publication. 3. SMITH, H., AND SUGDEN, W. M.: Proc. Roy.

Soc. (A), 211, 31 (1952). 4. SUGDEN, T. M., AND WHEELER, R. C.: In

course of publication. 5. LEWIS, B., AND VON ELBE, H.:

Combustion,

Flames and Explosions of Gases. New York, Academic Press, 1951. 6. SHULER, ]/~. E., AND WEBER., J.: J. Chem.

Phys., 22, 351 (1954). 7. MARGENAU, H.: Phys. Rev., 69, 508 (1945). 8. BELCHER, H., AND SUGDEN, T. M.: Proc. Roy. Soc. (A), 201,480 (1951). 9. SUGDEN, W. M., AND THRUSH, B. A.: Nature, 168, 703 (1951). 10. ADLER, F. P.: J. Appl. Phys., 20, 1125 (1"949). 11. SAHA,M. N. : Phil. Mag., 40,472 (1920). 12. SMITH, H., AND SUGDEN, W. M.: Proc. Roy.

Soc. (A), 211, 58 (1952). 13. SMITH, H., AND SUGDEN, W. M.: Proc. Roy. Soc. (A), 219, 204 (1953). 14. JAMES, C. G., AND SUGDEN, W. M.: Nature,

171,428 (1953). 15. PAGE, F. M., AND SUGDEN, T. M. : To be pub-

lished.