T H E MAGNITUDE OF SURFACE CONDUCTIVITY1
J. W. McBAIN
J. F. FOSTER Department of Chemistry, Stanford University, California AND
Received J u n e 14, 193'4
The only measurements of surface conductivity on surfaces of approximately known area measured with alternating current are those carried out during a period of ten years a t Bristol and Stanford Universities and finally published in 1929 (8, 9). They comprise measurements made with optically polished glass and with ordinary Pyrex tubing in contact with aqueous solutions of potassium chloride and, in addition, measurements of the surface conductivity of an insoluble film of stearic acid on water. All yielded results of the same magnitude, namely, several mhos X when referred t o 1 square centimeter of surface. Nevertheless, many writers have decided to reject these results for two reasons. In the first place, the conductivity is far larger than can be accounted for by current theories in which the phenomena are referred wholly to the outer portion of the diffuse part of the double layer. I n the second place, the only other measurements from another laboratory (11) with approximately known area of surfaces in contact with solutions of potassium chloride have yielded little or no surface conductivity. These other measurements by White, Urban, and collaborators are characterized by three important features. First, the measurements are made with direct current. Next, the liquid was kept in motion by applied hydrostatic pressure, streaming through the capillary. Lastly, almost alone amongst those who have measured the conductivity of salt solutions since the time of Kohlrausch, these authors have not seen fit to correct the observed conductivity of potassium chloride solutions for the conductivity of the solvent. This correction nullifies the very slight surface conductance which they report, rendering it zero or negative. We have now repeated with every precaution measurements with alternating current on systems consisting of tubing in contact with solutions of potassium chloride, and we have also extended and developed the measurements of surface conductivity of films of stearic acid, oleic acid, and palmitic acid on water. The results substantially confirm the previous measurements with alternating current, which would now appear to be Presented before the Eleventh Colloid Symposium held at Madison, Wisconsin, June 14-16, 1934 331
332
J. W. MCBAIN AND J. F. FOSTER
fully established and to require modification of any theory with which they are not in accord. We also emphasize what has been implicitly known but not fully realized or explicitly expressed except in papers from this laboratory (1, 6, 7), namely, the free mobility of the mobile ions of the double layer. In other words we stress the importance of the recognition of the fragility of the double layer. Attempts to measure electrokinetic properties of the double layer easily tend profoundly to modify or to destroy the object of measurement. Mobile ions lie passive in the liquid which surrounds them and in the absence of an applied force have neither any definite tendency towards directed movement nor, apart from discontinuities in the nature of the surface, any tendency to resist being carried along when the liquid in which they are embedded is moved parallel to the double layer. Any streaming of the liquid therefore, whether produced by applied hydrostatic pressure or induced by the application of direct current as in electrosmosis, sweeps along with it the mobile ions of the double layer. These would have to be replaced if the double layer is not to remain depleted. Surface conductance as measured can only be due to the physical presence of bodily carriers or ions free to move under the conditions of the experiment and in numbers greater than that corresponding to the ordinary bulk conductivity of the unchanged liquid or solution. If the mobile ions are being ejected from the outlet of the capillary system, the surface conductivity will disappear unless they are replaced. Only immobile ions are left upon the surface. The replacement has to occur in the stream of liquid a t the inlet. Ordinary electrolysis cannot accomplish this, because it merely discharges a space charge without in any way altering the concentration of the intermediate liquid through which the current is carried, as is well known in the field of transport or migration measurements. Especially is this evident with potassium chloride where both ions move with equal velocity in opposite directions, so that electrolysis through the entering stream of liquid cannot affect the total number of ions present, since a gain of one ion is exactly compensated with a loss of another of opposite charge and equal conductivity. Hence any loss of ions in the effluent cannot be replenished by ordinary electrolysis in the inflowing liquid. The depletion must be made good by diffusion, which requires time. The time required may be too great when the liquid is moving with appreciable velocity. Electrokinetic phenomena need not by any means disappear when, through streaming, the surface conductivity is thus partially or largely eliminated. Redistribution of the available charges within the capillary system in a direction perpendicular to the double layer will be almost instantaneous, and streaming potential or electrosmosis will remain
MAGNITUDE O F SURFACE CONDUCTIVITY
333
prominent. Thus, even surface conductivity will be actually present, although practically masked by the corresponding depletion of the bulk solution available within the capillary. An especially illuminating case for consideration is where there are no electrokinetic phenomena, either because the number of positive and negative points on the surface is equal, or because the surface is not charged anywhere but there is a general accumulation of ions in the neighborhood. I n both cases there would be observable surface conductivity as long as the total number of ions in the solution exceeded that in the same volume of liquid outside the capillary system. Rapid flushing out with that liquid would sweep away the excess carriers and with it the observable surface conductivity. It follows from the considerations outlined above that one should not expect exact concordance between electrokinetic effects measured by different procedures which directly modify the preexisting double layer. The most striking instance of this is that observed by DuBois and Roberts (private communication) in one and the same system in which a l-potential was positive and equal to $32 millivolts as measured by streaming potential, but negative and equal to -47 millivolts as measured by electrosmosis. The measurements were made in immediate a1ternation without any other interference with the system. Finally, it is possible that certain ions in the double layer may be capable of a restricted excursion and so may contribute to conductance as measured with alternating current, whilst not being measured by direct current. A careful examination of Ohm’s law and comparison of the two kinds of current should determine this point. EXPERIMENTAL METHODS*
Three experimental methods were employed, and in each case a whole series of cells was designed successively to eliminate difficulties of measurement or interpretation. The last cells actually used in each series were of Pyrex glass and are illustrated in figures 1 , 2 , and 3. Figure 1represents a cell containing seven concentric tubes between platinum electrodes which fill the cross section of the cell and are plane polished on the surfaces facing the concentric tubes. They are sufficiently far apart to permit of the tubes being slid in and out of each other without quite coming apart.3 The distance between electrodes was checked by measurement with a travelling microscope in each experiment. The tubes were settled by gravity on the plane surface; in every case a measurement was made before Experiments by J. F. F. The electrodes should not be much further apart than their own diameter, and the inner tubes replaced by a single solid cylinder. Then each would rest firmly upon its base without danger of tilting.
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J. W. MCBAIN AND J. F. FOSTER
and after agitation, tapping, standing undisturbed, sliding the tubes in and out, etc. The tubes were originally cleaned with chromic acid solution,
FIQ.1. CELLWITH CAPILLARY SPACES BETWEEN CONCENTRIC TUBES
FIG.2 FIG. 3 FIG.2. CELLFOR DETERMINING SURFACE CONDUCTIVITY OF THE AIR-WATER INTERFACE BY ELIMINATING THE EFFECT OF BULKCONDUCTIVITY FIG.3. CIRCULAR TROUGH FOR MEASURING INSTANTANEOUS PRODUCTION OF SURFACE CONDUCTIVITY The cell is shown empty
but were kept under constant changes of water or solution for periods of months. The final measurements were taken after a year of continuous
339
MAGNITUDE O F SURFACE CONDUCTIVITY
use since the last cleaning with chromic acid s ~ l u t i o n . ~Recleaning was effected by heating to 400-500°C. The cell in figure 2 was heated in a blast flame. That in figure 3 was likewise heated in a free flame and in a muffle furnace. Figure 2 for insoluble or slightly soluble films on water is a modification of that used by Peaker. The cell is first measured full of conductivity water; then again, without opening, with the meniscus immediately above the electrodes but not touching them, The ratio gives the ratio of bulk conductivities for the two positions. Without moving the meniscus, the film is placed upon the surface and ample time is allowed for equilibrium. The additional conductivity consists of surface conductivity and additional bulk conductivity. The latter is determined by raising the meniscus to the top position, applying the ratio previously determined. The cell is opened only to introduce the surface film. Excess liquid is stored in the side arm. The two essential points are that neither the electrodes nor their supports should come into contact with the surface, which might cover them with an insulating film. This requires correct adjustment of the size and position of the side arm. Figure 3 is for nearly instantaneous observations of the production of surface conductivity. Here again neither the electrodes nor their supports touch the surface. The diameter is a t least 12 em. to avoid alterations in level a t the electrodes due to surface tension changes a t the walls. Measurements were in all cases made by the latest Leeds and Northrup equipment, the Grinnell Jones bridge. Any supplementary resistances used were Curtis wound coils. The oil thermostat was adjusted to 25.00' & 0.005"C. Potassium chloride solutions were made up by weight by the method of Parker and Parker. The specific conductivity of the water was 0.4-0.5 X mho. Kahlbaum's best stearic and palmitic acids were used, together with sonie specially pure fatty acids made by Dr. Lepovsky of the University of California. I n all cases they were repeatedly extracted with conductivity water before use. EXPERIMENTAL DATA WITH CONCENTRIC TUBES (FIGURE
1)
The value of observed resistance represents in the case of each concentration a mean of many separate determinations which agree very closely among themselves. The cell was emptied and refilled with fresh solution several times, and the tubes were slid back and forth between individual measurements. The cell was always placed accurately vertical in the oil thermostat. At the end of measurements on one concentration the tubes were removed and the cell constant measured or remeasured before proceeding to the next higher concentration. I n each instance the measured Compare the similar prolonged treatment described on p. 3299 of a previous communication (9).
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J. W. MCBAIN AND J. F. FOSTER
resistance without tubes agreed with the resistance calculated from the dimensions of the cell within 0.1 per cent. Dimensions of cell and tubes were as follows: cross section of tubes, 0.959 sq. cm.; length of tubes, 2.94 cm.; cross section of cell, 1.246 sq. cm.; distance between electrodes, 5.450 cm. ; %urface cross section,” 18.50 cm. (sum of circumferences). Observed values of specific surface conductivities are high because the microscopic surface of the tubes is much larger than the apparent area. These results were confirmed with a complete series of measurements with the same set of tubes in an earlier design of cell which, however, did not allow as exact an evaluation of IC, because it was not truly cylindrical. Rapid streaming of the liquid through the tubes always caused a rise in resistance which continued usually to a point a t which there was no surface conductivity, thus demonstrating the fragility of the double layer. EXPERIMENTAL DATA ON INSOLUBLE FILMS IN CLOSED CELL (FIGURE
2)
This cell gives consistently reproducible results for surface conductivity of acid films on water. It was cleaned by heating in an oven a t 450-500”C., then filled with conductivity water to the proper level, closed and placed in a thermostat a t 25°C. to come to equilibrium. The cell was carefully levelled so that the tops of the electrodes were horizontal. I n general the contents of the cell reached equilibrium with the enclosed atmosphere in about twenty-four hours, a t which time it was possible to pour the water back and forth without changing the resistance of the cell by as much as 0.1 per cent. Two resistances were measured: (I) resistance of the cell with all the water in the main cell and the meniscus far above the tops of the electrodes, and (11) resistance of the cell with part of the water poured into the side bulb so that the surface of the liquid was just above the upper edges of the electrode^.^ Care was taken so that no part of the electrodes or supports broke the surface. After completion of the first two measurements, the cell was opened and the surface of the liquid in both the main cell and side bulb coated with the acid film, Again the cell was closed and allowed to stand for twenty-four hours to come into equilibrium with the surface film, Extreme precautions were observed to change neither the position of the cell nor the height of the meniscus during contamination. With equilibrium reestablished, two more resistances were measured : 111,resistance of the cell with the meniscus unchanged since measurement 11, but with the addition of the surface conductivity of the film and a certain bulk conductivity due to a slight solubility of the fatty acid, and IV, resistance of the cell with the meniscus again raised above the edges of the electrodes as in position I. Resistance I V is lower than resistance I 6. No difference was observed in the ratio of resistances I and I1 using conductivity water and using N/lOOO potassium chloride.
MAGNITUDE OF SURFACE CONDUCTIVITY
337
because of the conductivity of the small amount of dissolved fatty acid, and also probably because of a certain amount of contamination from the atmosphere when the cell was opened. The total surface conductivity is deduced from resistance I11 by calculating from resistance I V and the ratio between I1 and I the value for bulk conductance only, and hence necessarily taking the difference as surface conductivity. This is then corrected to specific surface conductivity from the dimensions of the electrodes. For example, in the first experiment in the table, calculated resistance = (46,970 X 72,450)/59,350 = 57,340; observed (III), 56,140. Difference in conductivity = 1/56,140 - 1/57,340 = 37.3 X lo-+' mho. Hence specific surface conductivity = 3.73 X lob8 mho. EXPERIMENTAL DATA ON INSOLUBLE FILMS IN CIRCULAR TROUGH (FIGURE
3)
The experiments of this section are presented in the form of three graphs, representing the effect of a film of oleic acid upon the time-resistance curves of conductivity water in the cell. After long investigation it was discovered that it is necessary to stir the surface thoroughly before the film is placed thereon; otherwise the mechanical disturbance accompanying the spreading of the film affects the resistance so seriously as to mask any surface conductivity which may be produced. When the uncontaminated surface is stirred vigorously with a clean glass rod, the resistance rises immediately to a maximum and falls rapidly again after agitation ceases. The reason for this is either that atmospheric impurities are absorbed to form a t the surface a thin conducting layer of solution which is replaced by pure water from the lower part of the cell during stirring, or that the highly cleaned surfaces of glass and platinum adsorb the impurities from the liquid in contact with them. After the cell had been heated in a free flame, allowed to cool, and filled with conductivity water, tests with flowers of sulfur showed repeatedly that the surface of the liquid was clean and free from any premature contamination; the small particles could be blown about freely and without hindrance. Consequently the prior technique of brushing the surface with a paraffined rod was discontinued in the final experiments as probably superfluous. Upon contamination with the oleic acid there is a rapid drop in resistance which is partly or wholly due to the surface conductance of the film. It has often been observed that a surface film tends to prevent Contamination from the atmosphere, so that the total drop may be caused by surface conductance and not partially by solution of carbon dioxide or other contaminants from the enclosed atmosphere. When the acid film is disturbed by further stirring after contamination, a momentary rise in resistance takes place, which is attributed to a partial destruction of surface con-
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J. W. MCBAIN AND J. F. FOSTER
\ 4 7 49 51 53 55
545
TIME,
TIME, MINUTES
MINUTES
FIG.4 FIG.5 FIG.4. CHANGEIN RESISTANCE WITH TIMEIN CELL (FIGURE 3) Showing effects of stirring and instantaneous production of surface conductivity upon adding insoluble fatty acid. FIG.5. CHANGE IN RESISTANCE WITH TIMEIN CELL (FIGURE 3) Showing effects of stirring and instantaneous production of surface conductivity upon adding insoluble fatty acid.
TIME, MINUTES
FIG. 6. CHANGE I N RESIBTANCE WITH TIMEI N CnLL (FIGURE 3) Showing effects of stirring and instantaneous production of surface conductivity upon adding insoluble fatty acid.
MAGNITUDE OF SURFACE CONDUCTIVITY
339
ductivity by disturbance of the double layer of ions at the interface, which is of course immediately restored. Calculation of specific surface conductivity involves a selection of values of resistance which represent (I) resistance of the cell without surface conductivity, and (11) resistance of the cell in the same condition as in (I) except for the addition of a surface film imparting a certain amount of surface conductivity. Such a selection is obviously somewhat arbitrary, although the order of magnitude of the surface conductivity thus calculated is unaffected by any reasonable choice. The experiment is too rapid for appreciable diffusion or alteration of bulk conductance, more especially as the oleic acid is practically insoluble. It should again be emphasized that surface conductance so measured is merely the amount by which the surface conductance of the oleic film exceeds that of the uncontaminated air-water interface. DISCUSSION
The outstanding result is the magnitude of the surface conductivity which uniformly exceeds mho per square centimeter, sometimes by a very large factor, as in the last line of table 1,p. 7. This fully confirms the previous findings of ,McBain, Peaker, King, and collaborators. The results with glass tubing are very high on account of the microscopically visible irregularities of the surface. The previously reported results for optically polished glass did not exceed 10 X mho. Of course all glass which has ever been exposed to water or even water vapor is superficially decomposed and corroded chemically upon a molecular scale. This would tend to increase the effective above the apparent area, although, as has been pointed out (6), it is essentially only the projection of the molecular discontinuities in the direction of the current that is effective, and for the most part continuous passages of adequate cross section will be lacking. Hence this would not appear materially to affect the magnitude of the results. Another communication by DuBois and Roberts will present comprehensive electrokinetic studies with these same optical surfaces. The t-potential found by DuBois and Roberts with 0.001 N potassium chloride by measurements of electrosmosis in the optically polished glass slit is -50 millivolts; DuBois (1) had used the value -78 millivolts derived from the data of Powis (10). No uncertainty attaches to the similar results with the air-water interface, which is ideally plane. The surface conductivity therefore exceeds in order of magnitude that currently calculated6 for the mobile ions of the diffuse part of the double layer. For example, Bikermann (e.Elektrochem. 38,763 (1932)) and Cole (Cold Spring Harbor Symposia on Quantitative Biology 1, 27 (1933)). Bikermann in attempting
340
J. W. MCBAIN AND J. F. FOSTER
It is now well known ( 5 ) that the so-called double layer in its classical continuous form cannot exist, but that charges on any surface are far apart and often of different sign. Hence the continuous distribution postulated in the cloud of ions in the diffuse double layer, based upon Poisson continuity of electrical charge in the surface, does not in general occur in the neighborhood of the surface where strictly localized conditions prevail, although it may be built up at relatively remote distances. This is one more reason for disbelieving the real occurrence of the j--potentials classically or currently calculated. TABLE 1 Deduction of surface conductivity in mhos X IO8 of solutions of potassium chloride i n contact with glass, assuming that the conductivity of 1 N potassium chloride is not appreciably influenced by surface conductivity CONCENTRATION REMARKS
N/1000 N/100
N/1
N/10
---Observed R . . . . . . . . . . . . . . . 33,825 8,850 Conductivity of solvent ( X 109 . . . . . . . . . . . . . . . . . . 0 . 5
980.4 114.24 Measured on bridge
Observed R corrected.. .... 54,110 8,850
0.7 0 . 7 Measured in another cell 980.4 114.24 Corrected for conductivity
Calculated R in tubes
795.5 91.72 Calculated from cross sec-
0,4
of solvent i9,878 7,263
tion, length, specific conductivity 195.3 22.52 22.52 X ratios of specific conductivities 785.1 91.72 (Total observed R ) - ( R outside tubes)
R outside tubes.. . . . . . . . . . . 17,160 1,783 Observed R tubes .....
i6,950 7,067
Surface conductivity, K , ... 62.6 1382
11,660
Specific surface conductivity, ks. . . . . . . . . . . . . . . . . . 9.961 60.8
1
264
1
I
I
K , X 0.159 = k,
Surface conductivity is undoubtedly exhibited by all mobile ions whether in the diffuse part of the double layer or not, and also (Laing paradox) by all unbalanced ions attached to or within the surface. DuBois (1) has t o defend the classical theory made the very serious error of abandonning in his calculation the well-known distinction between the Nernst potential E and the electrokinetic potential taking the r-potential as 1 volt. His conclusions are therefore fallacious, A r-potential of 50 millivolts in his calculation would lead t o the requirement that a film of water 0.4 A. U. thick had the viscosity and dielectric constant of water, although such a conclusion can carry but little weight if molecular dimensions retain any physical significance.
r,
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MAGNITUDE OF SURFACE CONDUCTIVITY
calculated from the data of McBain, Peaker, and King the individual surface conductances and mobilities which appear in the systems here considered. TABLE 2 Surface conductivity of acid films on conductivity water (figure 8) Cell constant (for surface conductivity) : 1/10. Dimensions of electrodes (measured by Cambridge cathetometer): outer electrode (inside diameter), 1.932 cm.; inner electrode (outside diameter), 1.037 cm.
I
~~~~
POHITION
~
REBISTANCE
POSITION
Stearic acid I I1 I11 IV
IC,
=
3.73
IC.
=
RESISTANCE
59,350 72,450 56,140 46,970
I I1 I11 IV
x
k , = 3 98 X 10-6
10-8
POSITION
107,330 150,360 138,260 104,450
I I1 111 IV
I
k , = 8.30 X 10-8
4.18 X- 10-8
X
Oleic acid
49,785 64,150 55,640 45,270
I1 I11 IY
RESISTANCE
43,720* 48,610* 45,320* 41,490*
k, = 3.87
Oleic acid
51,174* 57,003* 48,642* 44,574*
I
Palmitic acid
Stearic acid
Palmitic acid I I1 I11 IV
I
I I1 I11 IV
44,546* 50,110* 43,757* 40,400*
k. = 8 . 4 8 X
* Cell + 100,000 ohm shunt. TABLE 3 Surface conductivity of a f i l m of oleic acid in a circular trough Cell constant: 1/27. Resistance for continuous overflow, 170,000. Surface conductivity of oleic acid in closed cell (figure 2) was 8.4 X F1ouRE
4 5 6
No'
I
RDURING STIRRING OF CONTAMINATED BURFACE (I)
54,000 74,500 74,000
I
DISTURBING ACID FILM
k, X 10s
R BEFORE CONTAMINATION (I)
R AFTER CONTAYINAT I O N (11)
2.6 3.1 3.5
60,000 78,000 78,000
53,700 71,100 70,600
E;;BR
52,000 70,100 69,100
k, X 1oB
7.2
If this surface conductance is not sufficient there remain but two alternatives. The first is that which was suggested as reasonable by Horace Lamb (4),namely, that slip or sliding occurs between the two parts of the double layer, or between ions and the surface with which they are in
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J. W. MCBAIN AND J. F. FOSTER
contact, making all such ions mobile. Later authors have not endorsed this point of view, although some, like Smoluchowski, suspended judgment. The other alternative, toadopt the terminology of Frenkel (2,3) who has used it for explaining conductivity of dielectrics and supraconductivity of metals is “polarization current” carried by discontinuous jumps of otherwise sessile ions, the charge being thus transmitted from place to place. I n the introduction we mentioned that a variety of polarization current might be exhibited with alternating current when it could not be produced by low voltages of direct current. SUMMARY
Measurements extending over the past two years demonstrate the large surface conductivity per square centimeter exhibited by potassium chloride solutions in contact with glass surfaces, and likewise by films of fatty acid at the air-water interface. The specific surface conductivity of close packed films of stearic acid is 3.8 X mho, that for palmitic acid mho. mho, and that for oleic acid 8.4 X 4.0 X New designs of cells have been developed which permit a ready demonstration of these results. These results are much too high to be attributable solely to the mobile ions in the outer portion of the diffuse double layer. REFERENCES
(1) DUBOIS:Z.Elektrochem. 38, 764 (1932). Proc. Roy. SOC.London 140A,505 (1933). (2) FOWLER: Nature 132,312 (1933);133,730 (1934). (3) FRENKEL: (4) LAMB:Brit. Assoc. Advancement Sci. Rept., p. 495 (1887). (5) MCBAIN:J. Phys. Chem. 28,706 (1924). (6) MCBAINAND DUBOIS:Z. Elektrochem. 37,651 (1931). M. E. L.: Z. physik. Chem. 161A,279 (1932). (7) MCBAIN,J. W.,ANDMCBAIN, (8)MCBAINAND PIAKER:J. Phys. Chem. 34, 1033 (1930);Proc. Roy. SOC.London 126A,394 (1929). (9) MCBAIN,PEAXER, AND KING: J. Am. Chem. SOC.61, 3294 (1929). (10) POWIS:Z. physik. Chem. 89,91 (1914). (11) WHITE,URBAN, AND VANATTA: J. Phys. Chem. 36,1371 (1932).
