An Experimental Test of the Identity of Electrokinetic Potentials

AN EXPERIMENTAL TEST OF THE IDENTITY OF ELECTROKINETIC POTENTIALS ELECTROSMOSIS AND STREAMING POTENTIAL MEASUREMENTS WITH GLASSSLIT ROBERT DnBOIS AND ALEXANDER

A

HUNTER ROBERTS1

Departmnt of Chemistry, Stanford University, California Received April 11, 1986

Because of the extensive use and the great importance of electrokinetic methods in the study of adsorption from solution, the stability of colloidal systems, the electrical charges on colloids, living cells, etc., and a variety of other properties dependent on the existence of an electrical double layer a t an interface, it is of importance to know whether the results of different electrokinetic experiments can be compared with each other, or, more specifically, whether the electrokinetic, or zeta, potentials obtained by one type of electrokinetic measurement are identical with those obtained by another method. It has generally been assumed that cataphoresis, electrosmosis, or streaming potential experiments would yield identicel values of the r-potential provided the system being studied were in exactly the same condition in each case. This assumption is partly due to a rather prevalent notion that the classical mathematical formulations of electrokinetics require such an identity and partly to Sax6n’s (23) experimental demonstration of the socalled reciprocal relation between electrosmosis and streaming potential

which he showed must obtain if the identity assumption is made with regard to the l-potentials. Since the Sax& experiments of 1892 very little has been done to supply additional evidence on this important point. Thon (24) called attention to the fact that electrokinetic potentials calculated from cataphoresis measurements passed through maxima or minima at electrolyte concentrations considerably different from those a t which maxima or minima occurred in streaming potential or electrosmosis experiments. Kanamaru a Present address: Department of Chemistry, Fresno State College, Fresno, California. 543

544

ROBERT DU BOIS AND ALEXANDER HUNTER ROBERTS

(12) has made extensive electrosmosis and streaming potential measurements on cellulose and cellulose derivatives in contact with water and numerous electrolyte solutions, and reports that the streaming {-potentials were 2.6 times as large as the electrosmosis values. Since our own experiments were completed Bull ( 5 ) has reported a careful investigation of the same question. Electrosmosis, streaming potential, and electrophoretic measurements were made with Pyrex glass coated with protein. The {-potentials were found to be identical in the three cases. Briggs (4) measured streaming potentials produced by streaming buffer solutions through diaphragms made of quartz particles covered with egg albumin. The {-potentials calculated from his data are in remarkably close agreement with those reported by Abramson (1, 10) on the basis of measurements of cataphoresis of quartz particles coated with egg albumin. However, the buffer solutions used in the two sets of experiments differed in electrolyte content, and Abramson (2) repeated the cataphoresis measurements with protein-covered quartz particles and buffers identical in composition with those used by Briggs. The {-potentials were now found to be about 50 per cent higher than Briggs’ values, and Abramson concluded that the proteins used must have differed in some way. In addition to these direct comparisons of electrokinetic potentials, it may be mentioned that deviations from the Helmholtz equations have been reported and discussed by various workers, including Gosta Kohler (13), Manegold and Solf (le), H. Reichardt (20, 21, 22), and Ettisch and Zwanzig (7). H. B. Bull has recently repeated the measurements of Ettisch and Zwanzig (6) and finds the deviations not t o exist. I n order to provide a further, independent test of the identity of electrokinetic potentials we undertook t o make combined measurements of electrosmosis and of streaming potential on a single system. We chose for the experiments a glass slit made of optically polished glass and of known dimensions. This was generously put at our disposal by Professor J. W. McBain and was the largest (slit No. 10) of the glass slits used in his careful measurements of surface conductivity (15). A detailed description of the preparation of these slits is given in the paper referred to. The dimensions of the slit were checked by us and found to agree with those published: namely, thickness ( t ) , 0.00125 em.; width (w),1.001 em.; length ( I ) , that is, the thickness of the supporting block containing the slit, 0.5014 em.; cross section of slit (wt), 0.00125 cm.2 APPARATUS

The Pyrex glass apparatus in which the slit was mounted is shown in figure 1, the letters of which refer to the following parts: S, glass block containing the slit; BB, glass end blocks about 2.5 em. square, with an opening through them about 1.3 cm. square; F, ebonite clamps holding

IDENTITY OF ELECTROKINETIC POTENTIALS

545

together slit block, end blocks, and main cell; CC, capillary tubes about 30 em. long, graduated in millimeter scale divisions and calibrated at 1-cm. intervals along their length by a weighed mercury thread,-used for observing displacement of liquid through slit; E, saturated calomel electrodes, separated from the rest of the apparatus by porous plugs, PP, of sintered glass; E,,, probing electrodes of bright platinum; R, connections of rubber tubing; D, screw clamps. This apparatus (denoted cell IV) was designed to replace an earlier form equipped with platinized platinum probing electrodes and glass stopcocks throughout. The difficulties experienced with the earlier apparatus (denoted cell 111) were (a) contamination of the very dilute solutions by

Fxo. 1. Apparatus for electromosis and streaming potential measurements with glass slit. S, block containing slit; C,C, capillary tubes; E,E, calomel electrodes; E, and E,, platinum probing electrodes; F,F, ebonite clamps; B,B,glass end block; R, rubber tubing; D, screw clamp; P, P, porous plug of sintered glass.

foreign electrolyte previously adsorbed on the porous platinum surfaces of the probing electrodes, (b) persistent leakage through the glass stopcocks, and (e) contamination by stopcock grease. The new apparatus was entirely free from these sources of error. To test the rate of contamination from the rubber tubing and other sources in cell IV the solution used in experiments 21 and 22 was allowed to remain in the cell ninety-one hours and experiment 23 was conducted. The results showed that the rate of contamination was no greater than would be expected for conductivity water in any type of container. The rate of increase of the specific conductance of the conductivity water in the special Jena glass storage flasks was about 1per cent per day. At intervals the cell was cleaned with chromic acid without disassem-

546


bling, and then rinsed with conductivity water for a period of about three days before resuming measurements, the water being forced through the slit by pressure. Tine cell was cleaned as described between the successive experiments 26-27, 43-54, and 61-87. Dilute nitric acid was used for cleaning between experiments 113 and 114. Mercury for the electrode arms was cleaned by distillation in the absence of air. PREPARATION OF SOLUTIONS

The conductivity water used in these experiments was prepared in a special still (3) and was stored in Jena glass flasks properly protected against atmospheric contamination. The specific conductance was always determined immediately before use. The electrolyte solutions were made up to weight normality from samples of the salts, which were the purest obtainable on the market and were used without further purification. The glassware used was always steamed thoroughly and rinsed with conductivity water. The specific conductances of the more dilute electrolyte solutions were measured directly; the others were obtained from the International Critical Tables and the Landolt-Bornstein-Roth Physikalisch-Chemische Tabellen, were recalculated to 22OC., and were corrected for the conductivity of the solvent. The values are given in the later tables. METHOD OF MEASUREMEST OF ELECTROSMOSIS

The quantities directly measured in the electrosmosis experiments and the methods of obtaining them are indicated in what follows. Ti, the electrosmotic flow (cc. per second), was calculated from the average of the displacements of the liquid meniscuses in the two capillary tubes and the duration of the experiment. ET,the total E.M.F. applied at the calomel end electrodes, was obtained from 45 volt “B” batteries in series, which served excellently as sources of steady voltage because of the very slight current drain. EO,the potential drop across the probing electrodes. To measure this a compensating E.M.F. exactly equal and opposite to Eo was applied to the probing electrodes by means of a potentiometer supplied by “B” batteries and shunted a t the output terminals by a calibrated Weston voltmeter. Between one of the output terminals and its connection to the probing electrode was inserted a sensitive galvanometer. When the E.M.F.’S were balanced, as shown by the absence of any current through this galvanometer, the value of the compensating E.M.F. was read directly from the voltmeter. This method did not disturb the electrosmosis experiment in progress but, on the contrary] had a steadying effect on the working current, which had often varied considerably when a quadrant electrometer had been used to measure Eo. The values of Eo appearing in the tables are the means of three such determinations made during each experiment.

547


IO,the current passing through the slit during electrosmosis, was measured by means of a sensitive galvanometer connected in series with the slit and calibrated at frequent intervals. I n experiments with highly conducting electrolyte solutions a 0 to 999.9 ohms four-dial resistance box was used as a shunt around the galvanometer to bypass part of the current. E,z, the effective E.M.F. across the ends of the slit, was obtained by multiplying the current IO by the resistance of the liquid in the slit, Rsl (see below). It is important to note that the magnitude of the electrosmotic effect depends on the value of the electrical field within the slit, that is, on Esl/L,and the potential difference Est is somewhat less than Eobecause of the potential drops between the probing electrodes and the ends of the slit. I n order to evaluate these I R drops an extended study was made of the series resistances in the circuit. As a result it was possible to evaluate separately the resistance Rsl and thus the potential difference Esl ( = Io X Rsz). {-potentials were calculated from the experimental data by use of equation l, which was derived by Helmholtz for a capillary tube and can be shown to be applicable without change to a narrow slit: p = - 4n' D '&'E'

(all quantities in absolute units)

(1)

where 7 is the viscosity of the liquid within which the double layer lies (taken equal to the viscosity of the bulk liquid), D is the dielectric constant of the liquid in the same region (taken equal to 80 here), L is the length of capillary or slit, Q its cross section, E the potential difference at its ends (equal to ES2 here), and V the electrosmotic flow (cc. per second). With substitution of the numerical values and change to practical units, {

(in millivolts) =

4 X 3.1416 X 0.01 80

0.5014

(300)2

V

~l

0.001251

METHOD OF MEASUREMENT OF STREAMING POTENTIAL

The data obtained from the streaming potential experiments and the methods used were the following: V ,the rate of flow of the liquid through the slit during the streaming, was obtained from the observed displacement of liquid in t$hecapillary tube left open during the experiment. P, the applied hydrostatic pressure, was obtained by the use of mercury in a reservoir whose height could be adjusted and which was separated from the reservoir containing the streaming solution by a glass tube to which was connected a mercury manometer. The readings of the manometer were corrected for the difference in water levels in the reservoir and the outlet of the cell.

548


E,, the streaming potential, In the early experiments with cell I11 streaming potentials were measured directly by the deflections of a Compton electrometer connected to t'he calomel electrodes (one connection through ground). This was a sensitive quadrant electrometer (1000 mm. deflection per volt with scale at one meter), and although the instrument and all connections to it were carefully shielded, considerable difficulty was caused by the unsteadiness of the zero point arising from the large deflections obtained. I n the later experiments with cell IV this difficulty was avoided by the use of an improved method of measurement. Figure 2 shows the circuit arrangement. The streaming potentials were measured with a Leeds and Northrup Type K potentiometer with the Compton electrometer as a null instrument. By this method the electrometer vane was subjected to only slight displacements while a setting was being ELECTROMETER

TO CALOMEI. ELECTRODES

OF STREAMING POTEHTIAL APPARATUS

FIG.2. Electrical circuit for measurement of streaming potential

obtained, so that the zero point was very stable. It was necessary to operate the potentiometer a t the high range (0 to 16.1 volts) to accommodate the large streaming potentials often obtained. A group of 6-volt storage batteries supplied the working current for the potentiometer. These were always recharged slowly and gave a constant voltage over long periods of time. Calomel electrodes saturated with potassium chloride were used for all streaming potential measurements. The maximum error in the measurements of E , was not more than 0.1 per cent, except in the few experiments where E , was only a few millivolts. The potentiometer, cell, and reservoir were placed on plate glass resting on grounded sheet iron. K,, the apparent specific conductance of the liquid in the slit, was calcu-

549

IDENTITY O F ELECTROKINETIC POTENTIALS

lated from the known dimensions of the slit and the observed conductance of the liquid in the slit. This slit conductance (l/RsJ was determined before and after each set of streaming potential measurements. For this purpose the slit was flushed out with fresh solution, a known E.M.F. of, say, 90 volts, was applied to the calomel end electrodes (disconnected, of course, from the electrometer), and IO,EO,Eszrand Rsl were determined as in the electrosmosis experiments. TABLE 1 Electrosmosis experiments with conductivity water

- -

UEO

NO.

-

CM.? __

'EMP

'C

.

VOLT-8EC.

x

- -__________-

19 20 21 22

23 24 23 23

0.53 0.53 0.53 0.53

6.75 0.96 1.70 3.48

8.22 7.14 9.04 8.20

67.7 50.9 61.6 63.1

-95.8 -72.0 -84.7 -89.3

f2.5 14.7 f5.5 17.5

24 25 26

22 22 22

0.73 135 106.8104.2 -14.8 5.54 0.73 135 104.2101.7 -14.1 5.39 71.6 69.9 -8.8 3.62 0.73 90

8.97 8.71 8.21

57.2 55.7 50.7

-81.0 -78.8 -71.7

f4.8 f5.0 f4.7

27 28 29 30 31

22 22 24 24 25

0.56 225 122.3116.0 -23.610.70 0.56 180 115.5 87.8-16.0 8.09 0.56 135 72.0 68.3 -12.6 6.46 0.56 90 49.1 46.6 -8.2 4.43 0.56 45 25.4 24.1 -4.1 2.35

7.42 6.74 6.54 6.20 5.90

81 .o 72.3 73.4 71 . O 70.4

,.. . . . . . ... ....... . . . . .. . . . . . . . . . .

7.65

64.0

-

-

Mean..

135 105.0104.2 -17.2 22.5 16.7 16.1 -2.0 45 30.4 29.4 -4.6 90 56.7 54.6 -8.8

r

MILLIVOLT6

105

-114.6 1 7 . 3 -102.2 1 7 . 7 -103.9 f 1 1 . 9 -100.4 1 1 1 . 4 -99.5 1 1 9 . 0 -91.6

~4~7.2

The ratio V / I Ois in absolute units-cc. per second per ampere/3 X 109-in order to facilitate comparison with the streaming potential ratio E / P , also in absolute units

P-potentials were calculated from the experimental data by the use of equation 2, valid for slit or capillary: (all in absolute units)

or, in practical units,

(l in millivolts, E,in volts, and P in dynes per square centimeter). ELECTROSMOSIS EXPERIMENTS WITH CONDUCTIVITY WATER

Three series of electrosmosis experiments were carried out with thrce different lots of conductivity water of nearly the same conductivity

550


(0.5 to 0.7 X 10-6 mho per centimeter), fifty-seven separate determinations of 1 in a1L2 The results are given in table 1. Before making a set of measurements the apparatus and the slit were rinsed thoroughly (while assembled) with conductivity water whose specific conductance had just previously been determined. The positions of the water meniscuses in the capillary tubes were then read after previous observations had shown them t o be stationary without applied field. The desired voltage was then applied to the calomel end electrodes and the time noted to the nearest second. From two to four times during the ensuing electromosis the total current passing through the slit was read from the series galvanometer and the potential difference between the probing electrodes (EO) was measured without interruption of the experiment. At the end of from three to ten minutes the current was interrupted; the water meniscuses in the capillaries instantly became stationary, and their positions were read. Each set of data in the tables is the mean of the results of from four to six such experiments carried out in succession a t the same applied voltage and without refilling the apparatus. The last column in table 1 gives the mean deviation of the individual r-potentials from the recorded mean. The direction of electrosmosis was generally reversed in successive experiments by reversing the applied field. The mean of the {-potentials thus obtained was 11.7 per cent less for experiments in one direction (thirty experiments) than for those in the reverse direction (twenty-seven experiments), or 4.2 per cent less than the published mean for all experiments. The work with conductivity water was entirely completed before that with electrolyte solutions was begun, in order to avoid as far as possible contamination of the slit by foreign electrolyte. Relation of observed electrosmosis to strength of applied field

We were much interested in the possibility of finding a dependence of the {-potential on the applied field, which would show up in a variation of the quantity V I E . Toward this end the experiments were carried out over a tenfold range in the applied voltage. In figure 3 we have plotted the observed values of the ratio V/Esl against the effective voltage Esl, also the average values of the ratio V / E T, for all experiments at the same total voltage, against E T . The plot shows only a random variation in V I E s ! and only a very slight variation in V I E T. It is evident that in the range of these experiments the charge distribution in the electrical double layer at the glass-water interface has been unaffected by the increase in the strength of the external electrical field applied parallel to the interface. It would perhaps be more accurate to say that the highest field strengths used 2 These do not include twenty earlier and much less reliable measurements made with the same slit mounted in a different apparatus (cell 111,see p. 3).

551


were insufficient to effect a displacement of parts of the double layer which were sessile under the influence of the lowest fields. We are inclined to predict, however, that with su5ciently large applied electromotive force such a displacement, or slipping, might be brought about, with a consequent increase in the apparent value of the electrokinetic potential, 1.

Absence of time e$ect in electrosmosis In his early experiments on electrosmosis through a glass capillary tube Quincke (19) noticed that the electrosmotic flow was much more rapid just after the apparatus had been filled than after it had stood twenty-four hours. He attributed this fact to slow solution of the glass, which he actually demonstrated to have taken place. A parallel increase in the

I . - .

r*,

" ' 10 .0

'

E

-

' . 150 . . .

XI0

VOLTS

FIU.3. Relation of electrosmotic flow, V, t o applied field, E

TABLE 2 Absence of lime effect i n electrosmosis experiments

Hourly change.,. , , , . , . . . .. , . . . , . , . . , . . . . . . . . . . . . . . . . . . . , . ,

1

0 0004

1

0.28

electrical conductivity of the water was found. I n our own work each series of experiments with the same filling of conductivity water occupied an interval of several hours. In order to test for a similar source of error in our own work the following experiment was carried out. At the conclusion of experiment No. 22 the apparatus was allowed to stand without rinsing or refilling. At the end of ninety-one hours experiment No. 23 was performed, using water already in the apparatus and the same applied voltage. The results in table 2 show an almost negligible hourly change. The increase in the ratio Eo/E indicates the effect of passage of potassium chloride from the end electrodes into the tubes leading to the main cell; the constancy in the ratio Esl/Eo shows that the electrolyte did not reach the slit. Since examination of the results of the electrosmosis experiments fails to

552


show any regular dependence on applied voltage or conductivity of the water used, we shall take as the most probable values of the {-potential and related quantities the mean values of all of the fifty-six experiments of the three series (exclusive of No. 23). These are given in table 1. The final value of the {-potential for the glass-water interface thus calculated is - 92 millivolts. STREAMING POTENTIAL EXPERIMENTS WITH CONDUCTIVITY WATER

A t the close of the electrosmosis experiments just described the cell and slit were cleaned and rinsed thoroughly. An extended series of streaming potential measurements was then made at different pressures with various lots of conductivity water of about the same specific conductance (0.5 to 0.7 X 10-6 mho per centimeter); one hundred thirty-five separate measurenients were made in all. TABLE 3 Comparison o j the results obtained with the early cell and the improoed cell

’

ELECTROSXOSIS

Jsp

CELL

Number

Xumber

TEO

mv.

Cell I V ....... . . . _ ,. . . . . . , . , , , , . . . . . . . . Cell 111.., , . . . . . . . . . . . . . . . . . . . . . , . . . . . Both cells.. . , . . , , . . , , . , . , , . , , , . . , . , . , .

This number does not include two experiments which were evidently unreliable, and twenty earlier measurements with the slit mounted in cell 111. Table 3 affords a comparison of the results obtained with the early cell (No. 111) and the improved cell (No. IV). At the beginning of each set of measurements at a given pressure a preliminary measurement was made of the rate of flow over a period of about two minutes. Before streaming was started again a reading was made of the zero point of the electrometer connected to one of the calomel end electrodes and to ground (the other calomel electrode being grounded). This reading was repeated at the close of the measurements in order to check the absence of any potential differences due to difference in the condition of the electrodes. The reading was always found to be within three millivolts of the initial value. Streaming was then started a t the given pressure (always in the same direction in all experiments), and measurements of the streaming potential were made a t intervals of a few minutes,

553


Time effect in streaming potential experiments The streaming potentials were found to vary erratically during the first few minutes of streaming, but we found on continuing the measurements over an extended period of time that constancy was obtained after about ten minutes. In computing the published mean values of our results we have therefore excluded all observations made during the first ten minutes of ~treaming.~The collected results are given in table 4,each value given TABLE 4 Streaming potential experiments with conductivity water NO.

34 35 36 37 39 40 41 42 43 54 55 56 57 61.1 61.2 61.3 61.4

‘?z-c”p‘ 23 23 22 23 23 22 24 22 22 23 23 23 24 21 21 21 21

X./SEC.

-__0.53 6.57 0.53 6.57 0.48 6.12 0.48 6.52 0.66 6.97 0.60 6.35 0.60 6.17 0.54 6.87 0.54 6.03 0.56 5.48 0.56 5.48 0.56 5.48 0.56 5.48 0.58 2.60 0.58 2.60 0.58 2.60 0.58 2.60

2.74 5.60 2.78 5.62 51.7 2.73 5.66 5.81 2.78 48.8 23.4 7.90 3.21 48.90 22.10 7.94 3.26

__

v/p

V

x 108 0.515 1.047 0.466 0.977 9.30 0.474 1.210 1.15 0.556 2.56 5.32 1.92 0.709 1.71 5.32 1.93 0.711

Mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

b

0X.S

MILLIVOLTS

DYNE-BBC.

x

10s

1.88 1.87 1.68 1.74 1.80 1.74 2.14 1.98 1.99 2.57 2.27 2.43 2.21 2.39 2.41 2.43 2.18 2.08

_____ 0.4688 5.70 0.9026 5.37 0.4449 5.34 0.9702 5.82 7.563 4.87 0.4741 5 79 1.1165 6.57 1.1989 6.87 0.5686 6.80 2.4887 8.60 4.5713 6.34 1.480 6.25 0.5771 5.99 6.044 10.95 6.805 10.60 8.96 2.138 0.8318 8.48

-6.81

~

-158 -150 -139 -161 -145 -156 -172 -200 -174 -204 -151 - 148 - 143 -120 -113 -99 -94

-162 -

*K” and K~ are respectively the bulk conductivity of the water used, as measured outside of the slit, and the apparent conductivity of the same water in the slit, the increase being due to the surface conductivity.

therein being the mean of from six to ten observations made during the next ten to twenty m i n u t e ~ . ~ 3 Similar unexplained variations in the streaming potential have been observed by other experimenters. For example, Grumbach (11) was led to adopt a rule of selection similar to ours: “Je fus amen6 ainsi B m’imposer cornme rhgle de n’admettre cornme valable que les forces Blectromotrices qui demeurent fixes B pression constante pendant au moins 10 minutes.” As a matter of fact the average value of thus calculated from all measurements made after the first ten minutes of streaming (namely,-l62.2 millivolts) is identical with the average obtained from all measurements both before and after this ten minute mark (-162.0 millivolts).

r

554

ROBERT DU BOIS AND ALEXANDER HCNTER ROBERTS

Careful plotting of the observed values of the E / P ratio against the applied pressure shows only random variation with this factor. We have therefore taken the mean of all determinations as representing the most probable value of the {-potential for the glass-water interface derived from streaming potential experiments. This value is - 162 millivolts. Streaming rate and applied pressure The fundamental equations of electrosmosis and streaming potential are derived on the assumption that the flow of liquid through the slit, capillary, or porous diaphragm is non-turbulent. The usual experimental evidence of non-turbulence in streaming potential work is a constant proportionality between the rate of streaming (or the streaming potential) and the applied pressure. The data obtained from our own experiments (table 3, column 7) show that while the V I P ratio is satisfactorily constant in certain sets of measurements, it is not at all constant through the entire series of experiments. Now the rate of flow to be expected at any pressure can be calculated by use of the following equation derived for laminar flow through a slit in exactly the same way as is the Poisseuille equation for a circular tube:

V = -wt3P -

1271

where w, t , and 1 are respectively the width, thickness, and length of the slit, 7 is the viscosity of the liquid, P the difference in pressure at the ends of the slit, and V the flow rate in cc. per second. The value of the thcoretical ratio V I P in the case of our slit is 3.28 X l0Ws cc. per second per dyne per cm.* The observed ratio in most of our experiments is less than this; the average value is 2.46 X lo-* in the experiments with electrolytes and 2.00 X low8with water. This discrepancy is in the direction to be expected if the flow was turbulent. Davics and White (6a) have established that the flow of liquid through a narrow slit becomes turbulent only after the mean velocity exceeds the limit u = 890 7 / p t , where 7 is the viscosity of the liquid, p is its density, and t is the thickness of the slit. The flow rates in all our streaming experiments were far below the critical value, and we are therefore of the opinion that turbulence did not occur in the flow of Tvater through the slit. The discrepancy noted forces us to suspect that the actual cross section of the slit, &, was effectively smaller than that which we had calculated from the observed dimensions. Whether this was due to foreign intrusion in the slit, which resisted the repeated and thorough cleaning operations to which i t had been subjected, or to an error in measuring the width of the slit (an error of about 0.0005 em. would account for the discrepancy), we are unable to say. It is important, however, to point out (1) that all the [-potential values given here will be multiplied by a factor of 3.2SI2.00 or

555


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:+8 .g El ex

382

9

9

%Worn

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. . . I

.

... ... . ...

... ... .. ..

.

... ... .. ..

mmm

.. . ..

.. .. .. ... ... . ..

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hN03*N

.. . ..

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556


3.28/2.46 (1.6 to 1.3) if an empirical value of the cross section is calculated froin the observed B/P ratios, and (2) that both the electrosmosis and the streaming potential {-potentials will be multiplied by the same factor since both sets of values depend on the cross section, &, in the same way. The V I P discrepancy does not therefore invalidate our general conclusions regarding the relative values of the {-potential obtained from electrosmosis and from streaming potential experiments. COYIPARIhON O F ZETA POTENTIALS OBTAINED FROM ELECTROSMOSIS AND FROM STREAMIKG POTENTIAL MEASUREMEXTS

The principal results of our experiments with water and with electrolyte solutions are summarized in table 5 for the purpose of comparison. The {-potentials calculated from these are plotted in figure 4.

I

---

ELECTROSMOSIS STREAMINC

POTENTIAL

x

CONWCTIVITY WATER

0

KCL

FIG.4. Compaiison of electrokinetic potentials obtained from electrosmosis and streaming potential measurements

The results of the experiments with conductivity water show a striking discrepancy in the {-potentials obtained from the two types of electrokinetic measurement, the electrosmosis values (- 162 millivolts with cell IV and - 134 inillivolts wilh cell 111) being almost twice as great as the streaming potential values (-92 millivolts and -68 millivolts with cells IT' and 111, respectively), the differences being well outside of the experimental error. Such a difference in the {-potentials is not intrinsically a contradiction of the Helmholtz equations, for the following reason. These equations imply that-whatever the charge distribution in the electrical double layer-under the influence of an applied electrical field parallel to the wall


557

(electrosmosis) or of a mechanical force (streaming potential), a lateral displacement of a mobile part of the double layer takes place relative to a sessile part fixed on the wall, and that somewhere very close to the wall there exists a limiting plane of shear where the lateral velocity of the liquid with respect to the wall is zero. The difference in the electrical potential at this distance from the wall and that in the interior of the solution is the zeta potential. The {-potentials calculated from the results of electrosmosis and streaming potential experiments will be identical only if the limiting planes of shear lie a t the same distance from the wall in the two cases. There is no stipulation in the Helmholtz formulation that this condition shall be satisfied. We had indeed looked for some difference in the two (-potentials as an indication that the condition may actually not be satisfied. The discrepancy actually observed does not, however, allow a definite conclusion of this sort to be drawn, because of a certain internal inconsistency in our own results. The large ratio of the (-potentials obtained from the forty experiments with cell I11 corresponds, as it should, to a similar ratio of the quantities E / P and V / I and an equality of the observed apparent conductivities of the liquid in the slit. In the one hundred eighty-eight experiments with cell IV, however, we find a similar high ratio of the {-potentials coupled with practical equality of the ratios E / P and V / I . This is an apparent contradiction of the usual assumption that equality of E / P and V / I indicates equality of the {-potentials. The discrepancy is explained when we compare the measurements of the apparent slit conductivity made during the two sets of experiments and note that the value of K~ observed in the streaming potential experiments was twice as great as that measured in the electrosmosis experiments, although the procedures were identical and the bulk conductivities of the water were practically the same in both cases.6 Although the inconsistency noted robs our results of some of their theoretical import, it serves to point a warning that mere equality of the quantities E / P and V / I does not in itself demonstrate equality of the {-potentials without definite experimental proof that the specific conductances of the liquid in slit, capillary, or diaphragm are identical.

Identity of {-potentials obtained from experiments with electrolyte solutions The results of the experiments with electrolytes show on the whole that {-potentials obtained from streaming potential measurements were identical with those obtained from electrosmosis measurements. They there6 This increase i n I with increase in the specific conductance of the slit liquid is in the reverse direction from the effects noted by Lachs and Biceyk (14) with conductivity water, but is consistent with the initial rise i n the i--concentration curve commonly observed i n electrokinetic experiments.

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fore point t o the conclusion that the applied mechanical force acting on the liquid in the streaming potential experiment displaces the same fraction of the double layer as the applied electrical force in electrosmosis acting directly on the charged ions in the layer. The observed equality in the values of { is not a fortuitous result of a particular choice of applied field (electrosmosis) or of applied pressure (streaming potential), since the {-potentials were found to be independent of these factors.

Anomalous reversal of sign of the {-potential The conclusion just stated rests on a comparison of the average values of all experiments with the three electrolytes. When we consider the individual experiments at different concentrations, we find random variations such as are generally observed in similar work. The usual valence effects are observable, including charge reversal in the case of solutions containing the trivalent Ai+++ cation. The most surprising result of all our work with electrolyte solutions was the observation that the electrosmosis and the streaming potential effects were of opposite sign in the measurements with N aluminum chloride solution; that is, the direction of electrosmosis corresponded to a negative (-potential (-46 millivolts), while the streaming potential corresponded to a positive {-potential (+ 32 millivolts). This was so important a result that in order to establish the reality of the effect we disconnected the pressure apparatus just after completing the streaming potential measurement and immediately made another electrosmosis measurement. Electrosmosis again occurred as before in the direction corresponding to B negative {-potential. We are therefore forced to recognize that conditions may exist in an electrokinetic system where electrokinetic effects may differ not only in magnitude but even in sign. This suggests that in the neighborhood of the electrokinetic isoelectric point, where charge reversal takes place, the electrical double layer may have a complex structure involving several layers of charge of alternately positive and negative sign, as has been proposed by several writers (8, 9, 17). To complete the explanation of the effect we have observed it is necessary to suppose that when the tangential mechanical force was applied to such an interfacial layer in the streaming potential experiment, the limiting plane of shear (the “rigidity boundary” of Muller (18)) lay in a different part of this complex double layer than when the electrical force was acting in the electrosmosis experiment. That is, the rigidity boundaries in the two experiments lay in regions of the double layer where the electrical potential was of different sign. SUMMARY

1. Electrosmosis and streaming potential measurements have been made with an optically polished glass slit in contact with conductivity water and


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with solutions of electrolytes of different valence types. The measurements were made over the concentration range of lo-* N down to about N (conductivity water),-that is, the range in which electrokhetic effects change most rapidly with concentration. 2. The values of the [-potential for the glass-water interface were calculated from the results of these experiments. The electrokinetic potentials thus obtained from the electrosmosis experiments were nearly identical with those calculated from the results of the streaming potential measurements over most of the concentration range studied. 3. However, in the region of extremely low ionic concentrations large discrepancies were found. With water of specific conductance 0.6 X mho per centimeter the streaming potential effects were relatively almost twice as great as the'electrosmotic effects. The interpretation of the results, however, is complicated by the discrepancy in the observed values of the apparent specific conductance of the liquid in the slit. 4. With aluminum chloride solution of concentration 10-6 N a remarkable result was obtained when it was observed that the electrokinetic effects of electrosmosis and of streaming potential were of opposite sign, the values of the [-potential being respectively -46 millivolts and $32 millivolts. The two experiments were made in immediate succession without any reasonable chance for a change in the structure of the electrical double layer. We wish to acknowledge with thanks the grant of funds by the American Association for the Advancement of Science for the purchase of the Compton electrometer used in this work. REFERENCES ABRAMSON, H.: J. Am. Chem. SOC.60, 390 (1928). H., AND GROSSMAN, E. B.: J. Gen. Physiol. 14,563 (1931). ABRAMSON, J. M., AND LEE,A. R.: J. Chem. SOC.1927,2156. BENGOUQH, G. D., STUART, BRIGGS, D.: J. Am. Chem. SOC.60, 2358 (1918). BULL,H. B.: Colloid Symposium Monograph 11, 577 (1934). BULL,H. B.: Kolloid-Z. 66,20 (1934). (6a) DAVIES,s. J., AND WHITE,c. M.: Proc. Roy. soc. London 119A, 92 (1928). ('7) ETTISCH, G., AND ZWANZIQ,A.: Z. physik. Chem. 147A, 151 (1930). (8) EUCKEN, A.: Z. physik. Chem. l B , 375 (1928). H . : Kapillarohemie, 4th edition, Vol. 1, p. 357. Akademische (9) FREUNDLICH, Verlagsgesellschaft, Leipsig (1930). H., AND ABRAMSON, H.: Z. physik. Chem. M A , 51 (1928). (10) FREUNDLICH, (11) GRUMBACH, A,: Ann. chim. phys. [SI24,451 (1911). (12) KANAMARU, K.: Cellulose Ind. 7,3-16,29-52 (1931); Abstracts, 3-13 (in English); Chem. Abstracts 26, 3895 (1931). (13) KBHLER,G.: Z. physik. Chem. 167A, 113 (1931). (14) LACHB, H., AND BICZYK, J.: Z. physik. Chem. 14M, 441 (1930). (1) (2) (3) (4) (5) (6)

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(15) MCBAIN,J. W., PEAKER, C. R., . ~ Y DKINQ,A. MILLICENT:J. Am. Chem. Sac. 61,3294 (1929). (16) MANEGOLD, E., A N D SOLF,K . : Kolloid-Z. 66,273 (1931). (17) MUKHERJEE,J. N . : Trans. Faraday SOC.16, 103 (1921). (18) M~TLLER, H.: Cold Spring Harbor Symposia on Quantitative Biology 1,l (1933). (19) QUINCEE,G.: Pogg. Ann. 113, 513 (1861). (20) REICHARDT, H.: Z. physik. Chem. 164A, 337 (1931). (21) REICHARDT, H.: Z. physik. Chem. 169A, 417 (1932). (22) REICHARDT, H.: Z. physik. Chem. 166A, 433 (1933). (23) SAXON,U.: Wied. Ann. 47,46 (1892). (24) THON, N.: Z. physik. Chem. 147A, 147 (1930).

An Experimental Test of the Identity of Electrokinetic Potentials

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