A modified McClelland method for measuring ionic mobilities

Journal of Atmospheric and Terrestrial Physics, 1952, eel. 2, pp. 266 to 271. Pergamon Press Ltd., London

A modified McClelland method for m e a s u r i n g ionic mobilities and P. J.

P. J. NOLAN

KENNY

U n i v e r s i t y College, Dublin

(Received 18 February 1952) ABSTRACT T h e limits of the large ion group s p e c t r u m in room air are investigated b y a modification of the McCLELLAND mobility m e t h o d . A n aggregation scheme based on these limits is suggested. This scheme accounts to some e x t e n t for t h e large ion grouping previously observed.

In the course of work on large ions in room air we have recently used a modification of the McCLELLAN])mobility method. The modified method possesses several interesting features which seem w o r t h y of record. The method first used by MCCLELLA~D [1] is well known and is usually attributed to RUTHERFORDand ZELENY. There are m a n y published accounts which include the unnecessary and unjustifiable assumption t h a t the air velocity in the cylindrical condenser is independent of the distance from the axis of the cylinders. ORIGINAL McCLELLAND METHOD

A steady current of air containing ions is drawn through a cylindrical condenser, the inner and outer radii of which are a and b. The length of the inner electrode is 1 and the potential difference between the electrodes is V. The radial field at a distance r from the axis is V/r loge ((b/a) and the radial velocity at t h a t point of an ion of mobility k is k V/r loge(b/a). If u is the air velocity at a distance r from the axis, taken as the axis of x, then the differential equation of the loath of an ion is u r dr loge (b/a) ~-- ]c V d x . We now write three equations with increasing values of V y

loge (b/a)

fur a

dr -~ k V 1 ,

(1)

log s (b/a) f u r dr = h:V1,

(2)

b a b

log~ (b/a) f u r d r = k V x .

(3)

a b

The saturation voltage is given by eq. (2). Since 27e fur dr = Q, the volume of air per second we obtain the standard formula Q loge(b/a) --: 2 ~ k V1 which m a y be written Q = 4 ~ k V C where C is the capacity of the inner electrode. Distortion of the field is taken into account by using the experimental value for this capacity. If the value of the field is less t h a n the saturation value the ions reaching the electrode come from a smaller area .of the cross-section. The volume of air from which y the ions are collected in unit time is 2 ~ f u r d r so that, provided the ionic cona

centration is uniform, the current is proportional to the applied field and OHM's Law 266

A modified MCCLELLAND method for measuring ionic mobilities

lmlds [eq. (1)]. This gives the theory of the aspiration method of measuring the conductivity of the atmosphere. If the value of V is greater than the saturation value, eq. (3) applies. The ions are collected on a length x less than 1 and the current remains constant. T,vo distinct groups of ions will give a cur- ~ ~ M 8 ~' rent-voltage curve of t y p e OABC of Fig. 1. The s . / / ~ voltages for points A and B give the saturation voltages and the relative charge concentrations are given b y OR and RS. The average mobility can be obtained from the voltage for the point M. With three or more groups corresponding con0 ~ [~0~l siderations apply. Fig. 1. •

~/~ODIFIED ~][ETHOD

The modified McCLELLA~D method now described consists in using a fixed high voltage and measuring the current to the inner electrode for various air-currents through the tube. A graph of current against air-blast is plotted. If only one group is present the current-blast curve consists of two straight lines, one through tile origin and one parallel to the blast axis. For low blasts the fixed voltage is sufficient to produce saturation and eq. (3) applies. The quantity of electricity collected is directly proportional to the blast. When the blast is increased, saturation ceases at the Pcritical blast given b y eq. (2). , M For larger values of the blast, eq.(1) applies ~s and the electric current is constant as it is proy

portional to f u r dr. As u varies y varies so as

f

to keep this quantity constant. This region of the current-blast curve corresponds to the initial OHM'S Law or conductivity straight line of the ordinary ~CCLELLAND method. The initial straight line of the current-blast curve corresponds to the saturation region of the ordinary method. The current-blast curve of two groups is Fig. 2. shown in Fig. 2. The critical blasts are given b y points A and B; the relative contribaltions are given b y RS/CQ~ and CR/CQt or since .RS/CQ~ = RP/CQ1 the ratio of the contributions is .RP/CR. If three or more groups are present the relative contributions are given b y intercepts on C P b y lines through the first corner B parallel to the various straight lines on the current-blast curve. The average mobility m a y be deduced from point, M. The portions CB of Fig. 1 and 2 are the saturation regions and the parts OA the conductivity regions. COMPARISON OF T w o

METHODS

With the current-voltage method it is necessary in ensuring that the lowest mobility present has been detected, to adjust the blast so that the point B, Fig. 1 occurs well below the highest voltage used. In other words, the line BC Fig. 1 must extend over a considerable voltage range. In the variable blast method the highest voltage nmy be used as the fixed voltage. 267

P. J. NoLa_w and P. J. K E ~ N Y

One of the great difficulties in experiments with natural ions is that the quantity of electricity is small with consequent trouble ca~sed b y drifts, leaks and unsteadiness in the high voltage supply. With the variable blast method, full use is made of the highest suitable voltage for all groups so that the currents measured are much larger. This is especially the case with the smaller ions. The method is particularly useful for detecting the sniallest ion present. The diagrams in Figs.1 and 2 have been drawn to illustrate these feat:ires. Two groups of mobility ratio 2/1 and concentration ratio 3/4 give in Fig. 1 a saturation current of 7 units. The fixed voltage of :Fig. 2 is that of point C of Fig. 1 and is 3/2 the saturation voltage. As a result tl~e blast at point B of Fig. 2 is 3/2 the fixed blast of Fig. 1 and the contribution of the slower group is 6 units instead of 4 units. As the fixed voltage of :Fig. 2 is three times that of point A of Fig. 1 the contribution of the faster group is 9 units instead of 3units. The maximum current in the variable blast method is thus 15 units in contrast with 7 units of the other method. We have taken a simple case as example; in practice the current magnification is larger as the ratio of the extreme mobilities if of the order 30. One of the advantages of the variable blast method is that the high voltage applied to the outer tube is not changed during an experiment. This increases the probability of steadiness in the voltage and entails constancy in drift corrections. The time which the ions spend in the field is much shorter in the variable blast method. Errors caused b y diffusion and mutual repulsion are as a consequence reduced. This consideration applies more to small ions than to intermediate or large ions. The variable blast method cannot obviously be applied to the examination of artificial ions in cases in which the time between formation and measurement must be constam,. With natural ions and long inlet tubes allowance m a y have to be made for diffusion with slow blasts and for turbulence with fast blasts.

ZELI~INY METHOD WITH VARIABLE BLAST Resolution of groups.in the ZELE~Y method depends on the ratio of the total length of the central electrode to the length of the insulated portion. It is desirable that ~ ~ this ratio should at least be larger than tile ratio ] xB ~ / / ~ of adjacent mobilities. In Fig. 3 tile current-blast curve for two groups with a ZELENY tube is given. The ratio total length to insulated length is 3/1" B/os7 the mobility ratio is 2/1 and tile concentration Fig. 3. ratio 3/4. )~Iobilitics can be deduced from points X and B and from points Y and A. The maximum current is one-third the maximum current of :Fig. 2. In the ZELENY method with variable blast a stepped curve will be obtained if the ratio total length to insulated length is greater than the ratio of adjacent mobilities. LARGE IONS I ~ ROOM AIR The modified I~¢[CCLELLAND method as outlined was applied to the examination of large ions in room air in University College, Dublin. The dimensions of the apparatus were as follows: Length of inner electrode = 80.5 cm External diameter of inner electrode = 1.90 cm 268

A modified McCL~LLAND m e t h o d for measuring ionic mobilities

Internal diameter of outer electrode -~ 2.91 em Measured capacity of inner electrode = 98.6 cm. Small ions were removed by a short ion tube with low voltage at entrance. The air-blast was obtained from a rotary pump driven by an electric motor. Blasts of from 2 to 60 1 per rain were used. Two rotameters of different ranges measured the air-blasts. The current to the inner electrode was determined by a balance arrangement similar to t h a t used by J. J. NOLA~ and P. J. NOLAN [2]. A LINDEMANN electrometer was employed as a null instrument. During a measurement the needle of the electIometer was maintained at zero by adjusting the potential of the outer eleetiode. Owing to fluctuations it is impossible to perform mobility measurements on outside air with one ion counter. With room air satisfactory results can be obtained but it is important t h a t conditions should be steady before beginning the experiment proper. Draughts, the opening and closing of doors and all such disturbing influences must be eliminated. I t was found advisable to allow about ten minutes to elapse from the time of starting the r o t a r y pump in order t h a t the air circulation caused by it should become regular. I t was not our intention to catalogue all the groups in room air. Our purpose was to apply the variable blast method to the determination of the lowest and the highest mobility present. As we have seen the method is particularly suited for the latter determination. Using a fixed field of 600 v we made six satisfactory measurement of the lowest mobility, the values lying between 1.0 × 10 -4 cm/sec/v/cm and 1.8 × 10 -4. This ion group represented about 30 % of the total ionisation. We consider t h a t ion groups of lower mobility would have escaped detection if present up to say 5 % of the tot)d ionisation. BOYLAN [3] examined the mobility spectrum of atmospheric large long paying particular attention to the question of the largest ion. In addition to an ion of mobility 1.3 × l0 -4 he found ions in the range 0.9 × 10 -4-0-5 × 10 -4 corresponding to ions found in artificial ionisation by MCCLELLANDand ~NOLAN [4]. NOLAN and DEIGNAN [5] using the nucleus-field method which is not suited for detecting ion groups in small concentration found t h a t t h e limiting mobility in air stored for one or two hours was 1.0 × 10 -4. Nuclei stored for 45 hrs gave as the limiting mobility 0.35 × l0 -a, corresponding roughly to BOYLAN'S minimum value. In the determination of the largest mobility a. fixed voltage of 120 volts was used. The largest mobility was found to be 41 × 10 -a and the group represented about 5 % of the total ionisation. On two occasions there were indications of the presence of more mobile ions; on one occasion the limiting mobility was 18 × 10 -4. Our result agrees with the previous Dublin observation [6] t h a t in room air the ion of mobility 43 × 10 -4 is the fastest ion present in any considerable quantity among the large ion group. This does not exclude the possibility of the presence of intermediate ions of mobility about 500 × 10 -4 in small concentration. In room air in Dublin the large ion concentration is of the order 10 000 and the small concentration of the order 200. The fastest group found by NOLAN and DEIGNAN in air stored for one or two hours was 6 × 10-4; but as we have stated their method is not suitable for the detection of groups in small concentration and the faster ions disappear by coagulation during storage. HOGG [7] found in atmospheric air at Kew t h a t the intermediate ion spectrum extended to about 150 × 1()-4. 269

P. J. N O L A N and P. J. K E N N Y

EXISTENCE OF DISTINCT GROUPS OF IONS

The production of groups of ions by spraying water, by bubbling air through liquids and by passing air over phosphorus has been observed by J. J. NOLA~ [8] and by J. A. McCLELLAND and P. J. NOLAN [4]. The existence of such groups of ions has been questioned b y BLACKWOOD [9] and by BUSSE [10]. BLACKWOOD using the MCCLF.~AND method did obtain breaks in the slope in the current-voltage curve with ions produced by spraying water. He worked over 59 of these in detail and decided that t h e mobilities did not fit into any group system. The mobility values are recorded in his paper. Omitting a few outlying values there are 52 mobilities lying between 6 × 10 -4 and 170 × 10 -4. It is interesting to note that despite BLACKWOOD'S failure to find evidence of grouping 12 of these mobilities are in the range 35 × 10 -4 to 45 X 10 -4, constituting apparently a group corresponding to the largest mobility in room air. Distinct groups similar to those produced artificially were found by BOYLAN in atmospheric air. The existence of the groups produced by spraying was confirmed by NOLA~ and O'KEEFFE [11 ]. The mobility of the ions in the corona discharge was investigated by Y o u n g [12] and a large number of distinct groups was observed. It is possible that these groups are not formed in the same way as the previous groups. The corona ions m a y be solid particles; it is probable that all the other ions are liquid. The production of discrete groups by spraying liquids was confirmed by CHAPMAZ~[ 13 ]. HOGG showed t h a t the intermediate ions of the atmosphere exist in separate groups with distinct mobilities and that the variation of these mobilities with humidity indicate that the ions are composed of some hygroscopic substance probably sulphuric acid. He further showed t h a t in the range investigated there are 15 distinct group sizes of volume ratios 1, 2, 3 . . . 15, resulting from agglomeration. VASSAILS [14] has examined the nuclei produced by ultra-violet light in air. The mobilities of the charged nuclei form a discontinuous series often linked by simple ratios (2/1, 3/2, 4/3). He points out that this result suggests that distinct groups are due to multiple charges of ions of the same size. This suggestion has previously been made (IsEA~L and SCHULZ [15]). The experiments of VASSAILS are noteworthy in that distinct mobilities are obtained by a statical method, that is a method not involving air flow. I n a review of the question of ion groups in "Conduction of Electricity through gases" (J. J. THOMSON and G. P. THOMSON, 1928) the verdict is against the reality of groups; it is suggested that the observation of groups is associated with eddies in the air-flow. In our opinion the exact opposite is to be expected; the mixing produced by turbulence would tend to obliterate evidence of any groups present. I n the variable blast method however, the onset of turbulent flow might give a kink in the current-blast curve and a second kink might occur at the "slip" velocity (DOWLn~G [16]). It is obvious from the investigations quoted that the existence of discrete groups of large and intermediate ions is beyond question. On the part played by size and charge in prodmcing the various mobilities we are able produce some fresh evidence. We assume in spite of some striking evidence to the contrary [11] that the mobility is proportional to the charge. The experiments described earlier were carried out during an investigation on the average charge on large ions in room air. These results are not yet published. The median value of 40 determinations of the average charge was 1.67 electronic charges; this average charge showed no marked dependence on 270

A modified McCLET~T.A~D m e t h o d for measuring ionic mobilities

mobility. As the ratio of the limiting mobilities 41 x 10 -4 and 1-5 × 10 -4 is 27 the theory of a single size is excluded. Using (1) the equation k = 40 D applicable to singly-charged ions .where k the mobility is expressed in cm/sec/v/em and D is the diffusion coefficient and (2) the STOXES-CV~I~G~AM-MILLIKA~ relation between D and the radius we have calculated the radii corresponding to mobilities 41.6 × 10 -4 and 1.52 × 10 -4. The radii 1.13 × 10 -e am and 7.05 × 10 -e give a volume ratio 35. In Table 1 we have inserted between these limits mobilities corresponding to volumes in geometrical progression with a ratio of three. We have also extended the series to ultra large ions of mobilities 8-5 × 10 -5 and 5.0 × 10 -5 which have been found in air passed over phosphorus and in atmospheric air. In this scheme the LA~GEWN Table 1 ion of mobility 3"3 × 10 -4 appears with mobility 2.8 × 10 -a. However in view of HoGG's con10'k 108D 106r Volume clusions with regard to the effect of relative h u m i d i t y we cannot expect exact agreement. 4.16 104 1.13 1 The scheme gives roughly the 2/1 relation bet2.06 51,5 1.63 3 1.04 26.0 2.35 3I ween adjacent mobilities found in this region 0.53 13.2 3.39 3s for prominent ion-groups especially in the alcohol o.28 7.0 4.89 34 and phosphorus experiments. 0.152 3.8 7.05 3i I t must be a d m i t t e d t h a t the value 1.67 which 0.085 2.12 10.2 34 we have obtained for the average charge raises 0-050 1.25 14.7 3T several difficulties; we do not intend to pursue t h e m at present. One difficulty for example is t h a t the room nuclei investigated have an average radius of about 3 × 10 -e whereas the critical radius at which doublecharging begins is 1.5 × 10-e (BRICARD [17]) or 4× 10 -e (NOLAN and K E ~ A ~ [18]). F r o m BRICARD'S figures we deduce t h a t the average charge for radius 10× 1 0 -6 is 1.47; NOLAN and KE~NAN find for the same radius an average charge 1.29. If we ignore this difficulty and assume t h a t a considerable number of the smaller nuclei have double charges we m a y attribute the prominence of the groups of Table 1 to the 2/1 ratio between neighbouring mobilities. This consideration applies especially to the groups in the upper portion of the Table. The suggested volume ratio 3 m a y be associated with the fact t h a t a fraction of the nuclear coagulations, those between large ions of opposite sign, entail the disappearance of an ion. These two considerations m a y in the mobility region under review account for the absence of evidence of intermediate aggregations. I t is noteworthy t h a t although HOGG'S scheme is a 1, 2, 3, 4, etc. type of aggregation the groups in a n y particular experiment had a wider separation. REFERE:NCES [1] •cCLELLAND, J. A.; Phil. Wag. 1898 46 29. [2] NOn_N, J. J. a n d NOLAN, P. J . ; Proc. Roy. Irish Acad. 1935 49. 15. [3] BOYLAN, R. K.; Proc. Roy. Irish Acad. 1931 40 76. [4] McCI,Er.LAND, J . A . a n d 1 % o ~ , P. J . ; Proc. Roy. Irish Acad. 1916 33 24; 1918 34 51; 1919 35 1. [5] NOLA~, P. J. and ~)EIG.I~AI%J.; Proc. Roy. Irish Acad. 1948 51 239. [6] NOLO, J. J. a n d DE SAC~r, G. P.; Proc. Roy. I r i s h Acad. 1927 37 71. [7] H o o a , A . R . ; Proc. Phys. Soc. 1939 51 1014. [8] No~_~, J. J . ; Proc. Roy. Irish Acad. 1916 33 9. [9] BLaCXWOOD, O.; Phys. Rev. 1920 16 85. [10] Buss~., W.; Ann. der Phys. 1925 76 493; 1927 82 697. [11] N o L o , J. J. a n d O'I~EEFFE, J. Cv.; Proc. Roy. Irish Acad. 1933 41 25. [12] YOUNG, W . M . ; Phys. Rev. 192628 129. [13] CHAPM~, S.; Phys. Rev. 193752 184. [14] VASS.~LLS, G.; Ann. de Phys. 1949 4 125. [15] ISRAEL, H. a n d SCHULZ, L.; Terr. Mag. 1933 38 285. [16] DOWLrNG, J. J . ; Proc. Roy. Dub. Soc. 1912 18 375. [17] BRICARD, J . ; Jour. Geophys. Research 1949 54 39. [18] I~OLA~, P. J. a n d KENYA,, E. L.; Proc. Roy. Irish Acad. 1949 52 171.

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