TIVITY AT SOLID-LIQUID INTERFACES'

CONTRIBUTION TO THE THEORY OF SURFACE CONDUCTIVITY AT SOLID-LIQUID INTERFACES’ FRANK URBAN, H. L. WHITE,

AND

E. A. STRASSNER

Department of Biological Chemislry and Department of Physiology, Washington University School of Medicine, S t . Louis, Missouri Received J u n e 14, 1934

The double layer theory of Otto Stern may be briefly summarized as follows (7, 12, 14). The theory of Helmholtz gives values for the capacity of the double layer which agree approximately with those obtained from electrocapillary experiments. However, owing to kinetic heat motion, the double layer ions facing the liquid cannot have the distribution postulated by Helmholtz. On the other hand, GOUY’S(6) theory, which is based on t.he existence of a diffuse double layer, gives values for the capacity which are far too great. Stern develops his concept of the double layer in this manner: under the influence of the electrostatic forces of the wall, one type of ion forms a sheet of charges of constant density ( - m ) directly on the surface of the solid phase (inner Helmholtz layer). A sheet of positive charges (+ UO) (outer Helmholtz layer) would be located a t a distance 6 from the negative layer providing the kinetic heat motion did not exist, say a t a temperature of zero degrees absolute. At room temperature this charge will acquire a certain depth. A fraction, +ul, of the positive charges will face the sheet of negative ions, the rest ( + p , in a column of liquid of 1 cross section) extends into the interior of the solution with an asymptotically decreasing charge density (diffuse layer). go

=

Q1

+p

The electrokinetic potential, je, is the potential drop across the mobile component of the positive layer. According to Gouy all of the double layer ions, except those on the wall, are mobile with respect to hydrostatic forces, while according to Stern both sheets of ions comprising the Helmholtz layer are immobile with respect to hydrostatic forces. In the present communication the equation for surface conductivity is developed, based on the layer of Stern, so as to include not only the diffuse 1 Presented before the Eleventh Colloid Symposium held a t Madison, Wisconsin, June 14-16, 1934. The work reported in this paper has been aided by a grant made by the Rockefeller Foundation to Washington University for research in science. 311

TEE JOURNAL OF PHYSICAL CEEYISTRY, VOL.

39, N O . 3

312

FRANK URBAN, H. L. WHITE, AND E. A. STRASSNER

layer ions, but also t,hose of the outer Helmholtz layer.3 The equation thus becomes applicable to concentrated solutions, in which the surface conductivities predicted by the double layer theories of Stern, on the one hand, and of Gouy, on the other, would be expected to show a more marked disagreement. By comparison with experimental surf ace conductivity values, it should then be possible to choose between the theories. The following cases are theoretically possible: (A) The ions attached to the wall possess no electrical mobility. The surface conductivity is due to those components of the double layer which lie in the liquid phase. Electrosmose, by increasing the velocity of double layer ions, these being carried along by the moving column of liquid, will increase surface conductivity. Case A would be expected to occur when the conductivity is determined with D. c. (B) The same as case A, except that no electrosmose O C C U ~ S . ~(C) All double layer ions, including those on the wall, conduct; a The simplified equation proposed last year (J. Phys. Chem. 36, 3157 (1932)) did not include the Helmholtz layer ions, nor an electrosmotic correction. It agrees with equation 20, independently derived by Bikerman (Z. physik. Chem. 163A,378 (1933)), except for the mobility factor. Bikerman's equation 20 is as follows:

(a) Surface conductivity per 2 om*#= A, I , f A,l,

I , and la are the ionic mobilities of cation and anion, while

For potassium chloride, since I , = I , (d) Surface conductivity per 1 cm2. =

(e) Surface conductivity per 1 cm2. =

r -

--F

If e 4 R T can be neglected-large

t

-

( f ) Surface conductivity per 1cma. =

- e

e

dz

c e%.

1,

1,

* The surface conductivity measurements reported below were carried out with 1000-cycle A.C. From The Svedberg and Hugo Anderson's paper on electrophoresis (Kolloid-Z. 24,156 (1919)), we have drawn the conclusion that no significant electrosmose is likely to occur a t this frequency. If this conclusion is correct the attempt made by some authors to explain A.C. surface conductivity data by the von Smoluchowski equation-which is equivalent to the electrosmotic component of surface 3onductivity-is meaningless.

SURFACE CONDUCTIVITY AT SOLID-LIQUID INTERFACES

313

there is electrosmose. (D) All double layer ions conduct; there is no electrosmose. The experimental data do not permit a clean-cut choice between A-C, B-D to be made. Since A and B are the more conventional assumptions, the surface conductivity equations for these cases will be developed. The equation for the Stern layer is:6

KO

(E

- {)

=

FZ

1

-

1

1 1+-e 18c

6

*-+Fr RT

1

Symbols used: a = area of glass particles enclosing 1cm3. of 5 X lO-*M potassium chloride. Ft -

-.

2RT

A =

+1

e Fr -

'e

2RT

-1

c = concentration in moles per cm3. cI = 5 x lo-' moles per cm3. c I I = 3 X lovs moles per cm3.

cIII = D = D* = F =

1X moles per cm3. dielectric constant. dielectric constant in Helmholtz layer. Faraday (96,500 coulombs). K O = capacity of Helmholtz layer. I , = mobility of anion. I , = mobility of cation. R = gas constant (8.324 X lo7 ergs). T = absolute temperature. u = electrosmotic velocity (cm. per second). uo = electrosmotic velocity between Helmholtz and diffuse layer. urn= electrosmotic velocity in center of slit of thickness 1. uh = electrosmotic velocity of outer Helmholtz layer. = UhF, when E (electrical field) = 1. a = number of ions per cm2. of outer Helmholtz layer. Z = moles of ions per om2. of outer Helmholtz layer.

UT

a=-

2Fd2irc

Z/ET 6 = a = 5 = 9 = ++ = @- =

'

thickness of Helmholtz layer ( 5 X 10-8 cm. assumed). potential drop across entire double layer. potential drop icross diffuse layer. viscosity coefficient. adsorption potential of cation. adsorption potential of anion.

314


I t follows from the equation that the outer Helmholtz layer contains

z *,--FS

1 1+-e 18c

= moles of cations per cme2of surface

(2)

= moles of anions per cm.2 of surface

(3)

RT

and -0

1 1+-e 18c

RT

Equations 2 and 3 may be simplified; the wall is assumed to be negatively charged.

-r -*++F RT

18cZe

= moles of cations per cm.2 of surface

(2%)

= moles of anions per cm.2 of surface

(3%)

and f

-*---F

UT

18cZe

The concentration of cations and anions in the diffuse layer is:

dm dm DRT

c

DRT

c

- l} moles of -

1>

cations per cm.2 in excess of those normally present.

(4)

moles of anions per cmn2in excess of those normally present. (5)

Since the Stern layer consists of a diffuse (Gouy) layer and a Helmholtz layer, we can use, for the value of the conductivity of the former (uniunivalent salts), the sum of Bikerman's (1) equations 19 and 23. It is: Specific surface conductivity of diffuse layer (with electrosmose) =

The specific surface conductivity expressed in equation 6 is based on the assumption that, at the boundary of the diffuse layer near the wall (z = 0 ) , the electrosmotic velocity u = 0. This is not the case for the Stern layer, for we have, a t the boundary of the diffuse layer (x = 0 ) :


315

This is the velocity of the outer Helmholtz layer. This means that integration of Bikerman's6 equation 10 now involves the boundary conditions du & when x =

=0

'

2, where the thickness of the Helmholtz layer is neglected;

when 2 = 0. Performing the integration, Bikerman's equation 12 now becomes (see footnote 7) urn =

+

E D* E * D" * ( E 4v 4iv

- f)

(9)

The increase in conductivity ( A h ) of the diffuse layer, caused by the movement of the outer Helmholtz layer, is

When the potential ( E - p) in equation 7 is expressed in terms of charge (equations 2a and 3a, multiplied by F) and capacity of the Helmholtz condenser, we get

uh =

- e 11

(11)

The conductivity of the diffuse (Gouy) layer is the sum of equations 6 and 10; or, substituting equation 11 in equation 10,

The left-hand side represents the electrical force causing osmosis which is exerted on a volume of solution of 1 X 1 X dx 01113. The right-hand side is the frictional force counterbalancing the electrical force. 7 From equation 9 the important conclusion follows that electrosmose may still occur when = 0, since the Helmholtz layer still exists. See Monaghan, White, and Urban: J. Phys. Chem., May, 1935.

r

316

FRANK URBAN, H. L. WHITE, AND E . A. STRASSNER

Specific surface conductivity of diffuse (Gouy) part of Stern layer (with electrosmose)

The conductivity of the outer Helmholtz layer has to be added to the diffuse layer conductivity expressed in equation 12. The former is composed of two parts: the conductivity of the outer Helmholtz layer ions; the excess conductivity shown by these ions because the liquid moves. The total conductivity will be equal to: Moles of anions in outer Moles of cations in outer Helmholtz layer lo + Helmholtz layer Moles of cations in outer - Moles of anions in outer + Helmholtz layer Helmholtz layer

}

{

} ux

{

u; =

@, where E is the E

(13)

applied potential.

Substituting from equations 2a, 3a, and 11: Specific surface conductivity of outer Helmholtz layer (with electrosmose) = --O++F RT

18cZe

-*---F

. E, + 18cZe

5

-+++F f RT

RT

->

-@--PY

- 18cZe

2

(14)

The specific surface conductivity of the entire (Stern) double layer is the sum of equations 12 and 14. When no electrosmose occurs (high frequency A.c.), the specific surface conductivity becomes : Specific surface conductivity (no electrosmose)

EXPERIMENTAL

The surface conductivity was determined in the following manner. Pyrex glass particles were equilibrated with potassium chloride and sodium


317

chloride solutions (1.25 X M to 1 X 10-1 M ) , transferred to a conductivity cell, and the conductivity as well as the volume of the particles carefully determined, After deducting bulk from observed conductivity, the difference represented the total surface conductivity. The surface area of the glass particles being known,8 the specific surface conductivity (conductivity per cm.2) is also known.

FIQ.1 The experimental determination of specific surface conductivities will now be discussed. 1. Apparatus

The measurements were carried out in a kerosene bath (9) a t 25.000' f. 0.002'C. The conductivity cell was constructed of Pyrex glass and had a ground glass joint stopper (figure 1). It was graduated and carefully 8

See section 10, below.

3 18


calibrated. The Wheatstone bridge was a 5-dial Gray instrument, coils accurate to 0.025 per cent. The current was supplied by a Leeds and Northrup 1000-cycle motor generator. The cathetometer used read to 0.02 mm.; 0.01 mm. could be e ~ t i m a t e d . ~This permitted the volume of the Pyrex glass particles (52-55 cc.) to be read to f 0.005 cc. The volume readings were taken with the conductivity cell in the constant temperature bath. The salts used were Kahlbaum’s “Zur Analyse” grade. The interferometer was a Zeiss instrument. The need for careful measurements is obvious, as surface conductivity is obtained by subtracting bulk conductivity from observed conductivity. Dividing total surface conductivity by the area of the glass particles gives of surface. As was pointed out previously, the the conductivity per micro surface structure should not affect this calculation. 2. Volume occupied by constant m o u n t of Pyrex glass particles as a function of electrolyte concentration

We early noticed that a given amount of Pyrex glass particles does not occupy the same volume in solutions of different electrolyte concentration.10 This phenomenon had already been observed by Wo. Ostwald and von Buzagh (5, 11, 16). The latter observed a volume change of as high as 55 per cent, when quartz particles were transferred from water to benzene. Neglect of this factor may lead to serious errors in surface conductivity ineasurements.ll 3. Eflect of the amount of Pyrex glass particles in the cell on the cell constant

When a small amount of Pyrex glass particles is used, such that the electrodes are just covered by the particles, a value for the cell constant is obtained which is less than the one found when more particles are placed in the cell. In both cases the remainder of the cell volume is filled with solution to the same mark. As more and more particles are added, the differences in cell constant grow less. Finally a region is reached where the cell constant is unaffected by further addition of glass particles. The measurements must be performed with amounts of glass particles which lie in this region. Otherwise the volume changes discussed in section 2 will bring about unknown changes in the cell constant. We are indebted to Prof. A. L. Hughes for the loan of this instrument. The effect of vibration on sedimentation volume must not be confused with the above effect. 11 Fairbrother and Balkin (J. Chem. Soc. 1931, Part I, 1564-78) obtained their cell constant in aqueousO.l M potassium chloride and applied this value t o measurements in benzene solutions. They make no mention of a volume correction. 9

10

SURFACE CONDUCTIVITY AT SOLID-LIQUID

4. The size of

319

INTERFACES

the Pyrex glass particles and its influence on the reliability of the measurements

The particles were obtained by grinding Pyrex chemical glassware in a mortar and sieving. The fraction between 100 and 200 mesh was retained, weighed, washed one hundred times with boiling distilled water, equilibrated with potassium chloride solution, and transferred to the conductivity cell. Under these conditions it was difficult to duplicate our readings. Some improvement was noted after the cell and contents had been shaken vigorously and after the powder had settled spontaneously in the thermostat. But as the powder surface was still cloudy and uneven, the volume measureTABLE 1 Constancy of sedimentation volumes and resistance ~

RESIBTANCI

VOLUME

SOLUTION

ohms

CC.

1.25

x

10-4 M KCI

52.06, 51.97, 51.92, 51.92, 52.09,

1

X

M KCl

51.82, 51.853 51.84, 51.94, 51.89, 51.810 51.80,

8.975 x 9.055 X 9.075 X 9.044 X 9.024 X

104 lo4 lo4 lo4 10'

1408.9 1406.5 1409.8 1406.4 1405.0 1409.2 1409.0

ments were of doubtful value. Finally the difficulty was overcome b y ' using only the particles which settled within 1 minute. This powder gave sharply defined horizontal surfaces and reproducible volume and conductivity measurements, as shown by a representative experiment (table 1). The estimate of the area of all the glass powder, based on microscopic observation of about two hundred particles, is 20,000 cm2. This value is probably too low, as no correction for surface curvature was applied. The area determined by surface conductance is 27,000 om2. 6 . Change in cell constant (Parker e$ect)12

The Parker effect of a conductivity cell comprises a set of factors, such as construction of the cell, bridge set-up, etc., which result in a variation G. Jones and G. M. Bollinger (J. Am. Chem. SOC.63, 411 (1931) made a careful study of this effect. All references will be found in their paper.

320


of cell constant with concentration. The effect was evaluated from conductivity measurements in 2.5 X 1x 3X 3X 7X 1 X lo-], and 2.5 X 10-1 M potassium chloride. The values 9X for the specific conductivity of these solutions were taken from a paper by Shedlovsky (13).13 The observed resistances of these solutions in our cell covered the range 56-44,000 ohms. The cell constant is expressed by the empirical equation Cell constant = 0.6970

- 0.00265 log R

from which the percentage change of the cell constant at two different resistances can be calculated. The equation holds to about 60 ohms. Below this value, polarization of the electrodes begins to exert an influence on cell constants. It should be shown next that the percentage change of the constant with resistance is uninfluenced by the presence of glass particles between the electrodes. On account of surface conductivity, cell constants cannot be calculated from conductivity measurements, except in concentrated solutions. Hence the following procedure was adopted. The glass particles and solution were placed inside of a sealed, flat-bottomed glass tube which was coaxially cemented inside the conductivity cell. The annular space between the conductivity cell wall and the glass tube was then filled with a series of known solutions and their conductivities determined. The percentage variation of the cell constant was found to be the same as before. 6. Equilibration of electrodes

It is known that platinized platinum electrodes may retain adsorbed electrolyte with great tenacity (2). The effect is particularly noticeable when dilute solutions are placed in cells previously containing concentrated The electrodes were carefully equilibrated with the solution ’ solutions. before conductivity measurements were taken. 7. EquiliSration of Pyrex glass particles The particles were freed from electrolyte by repeated washing with boiling distilled water each time, before being equilibrated with a given electrolyte solution. The latter was decanted and renewed until the conductivity of the supernatant liquid or its refractive index (interferometer) was the same as that of the solution taken from the volumetric glassstoppered Pyrex flask. A rubber bulb was used for operating a wash bottle, thus preventing contamination by exhaled carbon dioxide. 1s For a discussion of Shedlovsky’s values see G. Jones and B. C. Bradshaw (J. Am. Chem. SOC.66,1780 (1933)). We are indebted to Prof. Grinnell Jones for a resume of specific conductivity measurements (private communication).


INTERFACES

321

8. Conductivity of the water

The latter was always determined and the surface conductivity measurements of the powder were corrected accordingly. This is important in dilute solutions, such as 1.25 X 10-4 M potassium chloride, where the specific conductivity of the water amounted to 8 per cent of the specific conductivity of the solution. 9. Determination of the density of the Pyrex glass particles

The density was calculated from the volume increase in our cell, when a known weight of powder was added to a known volume of water. We found d2$ = 2.225 f 0.005. 10. Determination of egective surface area of Pyrex particles

The effective surface area of the particles which are in contact with 1 c m 3 of solution was calculated according to the expression: Cell constant = bulk specific conductivity f effective surface Observed resistance area (cm.2) x specific surface conductivity (16) In this equation all quantities, except the area, are known for 5 X lov4M potassium chloride, the specific surface conductivity being 4 . 3 X mho, which is the value obtained with slits of known dimensions using A . c . ~ ~ The effective surface area may be defined as the area of that portion of the surface in contact with 1 ~ r nof. ~solution (interstitial liquid) which contributes to conductance. 11. Change of cell constant with concentration

The cell constant of the conductivity cell containing the glass powder is calculated from the observed conductivity in 1 X 10-I M potassium chloride. The bulk conductance is so great in this solution that the contribution of the surface may be neglected. At all other concentrations, the cell constant is found by applying the percentage correction outlined under section 5. 1.2. Correction of cell constant when the glass powder volume changes

It has been tacitly assumed so far that a given quantity of glass powder, when settling spontaneously, will always occupy the same volume, irrespecl4 See Urban, Feldman, and White (J. Phys. Chem., April, 1935). The older figure of 2.24 X mho, obtained by White, Urban, and Van A t t a (J. Phys. Chem. 36, 1371 (1932)) does not apply in this calculation, owing to the operation of Bikerman's membrane potential factor, discussed by Urban, Feldman, and White, and of electrosmose.

322


tive of the nature and concentration of the solution in which the powder is suspended. This is not the case (see section 2). For instance, the volume of glass powder solution was 51.759 cc. in 5 X M potassium chloride, but 53.482 cc. in 1 X 10-l M potassium chloride (see column 2, table 3a). I n order to carry out the calculations outlined under sections 10 and 11, it is necessary to determine what the cell resistance in 1 X 10-l M potassolusium chloride would have been if the volumes of the glass particles tion had been 51.759 CC. (instead of the observed 53.482). The correction has been made by equation 17

+

+

+

where R = calculated resistance at volume V (glass powder interstitial liquid), r = observed resistance a t volume V,, g = volume of glass particles (weight + density). Equation 17 can be tested. Thus we found that 24.79 cc. of particles suspended in 0.1 M potassium chloride solution gave a V , reading of 54.28 cc. in one determination, and 53.48 in another, probably due to vibration. The corresponding (observed) resistances were 146.44 and 150.49, respectively. The resistance a t the larger volume, calculated from the resistance a t the smaller volume, is 146.48 ohms (observed 146.44 ohms). The factor of non-homogeneous packing does not enter into the surface conductivity measurements, because the particles were always allowed to settle spontaneously. After one determination, the cells were shaken and both volume and resistance were redetermined. This was repeated from five to ten times. The volume and resistance measurements agreed closely, indicating that the same kind of packing always occurred under our experimental conditions. DISCUSSION

Calculations The observed specific surface conductivities (tables 3a, 3b, column 14) were next compared with the ones calculated according to equations 12 + 14, and 15, respectively, after appropriate values for { and the constants had been substituted. The (-potentials were those of Lachs and Biczyk (lo), calculated from their experimentally determined stream potentials. The following values were obtained (table 2). Since Lachs and Biczyk gave the stream potentials only for 1 X 1 X and 1 X M potassium chloride, it was necessary to interpolate. When the log of the potassium chloride


INTERFACES

323

concentration is plotted against the log of the stream potential, a nearly straight line is obtained. The interpolated (-potentials may, therefore, be considered as reasonably accurate. The interpolated Lachs and Biczyk ( value for 5 X M potassium chloride is 0.1209 volt; our (experimental) value is 0.1214 volt (17). The adsorption potentials, a+ and @-,15 have also been treated as constant and independent of the concentration. This seems permissible in the present concentration range. -a+ -

-*-

The values for Ze RT and Ze R T were determined by solving two simultaneous equations, obtained by substituting ( and specific surface conductivity (the experimental value) for the two concentrations 3 X M and 1 X M potassium chloride, in equations 12 14 (assumption A, electrosmose), and in equation 15 (assumption B, no electrosmose). These two solutions possess a Helmholtz layer conductance which is high com-

+

TABLE 2 Values of {-poiential at various concentrations POTENTIAL

CONCENTRATION OF POTASSIUM CELORIDE SOLUTION

1.25 X 2.5 x 5 x 1 x 3 x 1

x

0.1100 0.1160 0.1209 0.1226 0.1113 0.0816

10-4 10-4 10-3 10-3 10-2

pared with that of the diffuse layer. For this reason the uncertainty in the value of the (calculated) diffuse layer conductivity cannot greatly affect the fraction of the observed surface conductivity which is assigned to the Helmholtz layer.16 A tentative value (7 X 1.2) was used for the vis16 @+ and @ - signify adsorption "potentials" in the outer Helmholtz layer. They are of the same kind as those encountered near crystal surfaces. W. H. Zachariasen (J. Am. Chem. Soc. 64,3841-51 (1932)) has recently developed a picture of the atomic arrangement in oxide glasses. He finds that atoms in glasses are linked together by forces essentially as i n crystals. There are extended three-dimensional networks. The principal difference between crystal and glass networks is symmetry and periodicity i n the crystal and their absence in the glass network. I n this connection, the discussion of surface forces by Irving Langmuir (J. Am. Chem. SOC.40,1361 (1918)) is of interest. It may be further pointed out that the {-potential a t fused and unfused glass surfaces is the same. See Monaglian and White (J. Phys. Chem., in press), 16 Solution of these simultaneous equations (KC1):

A (electrosmose) B (no electrosmose)

z = 9- = 9, = @- = Q+

=i

1 x 1015 - 2.5 X 10" - 8.0 x 1010 - 2.5 X 10" - 6.9 X lo1'

Solution of the two simultaneous equations (NaCl):

z = 1.27x 1015 - 2.4 X 10"

- 6.1

X 10'' - 2.5 X 10"

- 7.4 x

10"

3 24

FRANK URBAN, H. L. WHITE, A N D E. A. STRASSNER

cosity coefficient of the Helmholtz double layer. The correction was made according to the H. A. Lorentz equation, cited by Bikerman. A similar correction has been developed by The Svedberg and Hugo Anderson (15).

Sedimentation volume The regular decrease of the values for the interstitial solution (table 3a, column 4) indicates a closer approach of the particles with increasing electrolyte concentration. The interpretation of this phenomenon by Zocher (18) is this: “Beim Entladen durch Elektrolyte nimmt der Abstand zwis.” We do not believe that this shrinkage dechen den Schichten ab. pends on l-potential changes alone. If the volume decrease effect were associated only with l-potentials, the two should run parallel, which is not the case.17 The effective particle volume falls progressively beginning M potassium chloride, until a second effect appears which with 1.25 X again causes a rise in sedimentation volume. The (-potentials, however, do not decrease progressively, but go through a maximum. The sharp rise in sedimentation volume beginning between 3 X M and 1 X 10-2 M potassium chloride is probably not due to a “Hafteffekt” (4),since the glass particles were far from dehydrated, as evidenced by the fact that in 4.5 X loF4M thorium chloride solution the volume of interstitial solution is about 2 cc. less than in 3 X M potassium chlo-

...

(no electrosmose)

@- =

- 2.6 X

1011

a+ = - 8.1 X 10”

- 2.5

X 10“

- 7.5 x

10’0

--o+

--o+

Solving for ZeRT and Ze R T , instead of for a+ and @-, offers the advantage that 2 does not have t o be evaluated separately. -a+

--o-

The ratio ZeRT /.ZFTcorresponds to the ratio of anions t o cations in the outer Helmholtz layer, i n the absence o f a double layer electrical field, i.e., if van der Waals forces alone were operative (E. Hueckel, reference 8, p. 57). For potassium chloride, it is 0.001, i.e., for 10,000 C1- there are 10 K + i n the outer Helmholtz layer. For the time being only approximate values can be assigned to Z . Stern uses the lo’‘ value Since the glass particles are hydrated, Z can be approximately 6.06 x 1023‘ calculated by using Tammann’s (Z. anorg. Chem. 168, 1 (1926)) value of 0.992 for the specific volume of depolymerized water. The number of water molecules per cm3. is “06 = 3.4 X 102*. The approximate number of lattice points I is = 0.992 X 18 1 X 10‘6, compared with a value of 1.27 X 1016 for the number of lattice points per om*.i n a potassium chloride crystal. 1 7 It may be concluded t h a t the electroviscous effect must be due to more than one factor, in agreement with Bungenberg de Jong, Kruyt and Lens (Kolloidchem. Beihefte 37, 395 (1933)).

4-


-1

"? = 32

2

S3131d - a V d S S V l D do

awnlon

325

326



INTERFACES

327

ride. The cause for this rise demands further investigation. It may possibly be connected with a rigidity change of the lyosphere which accompanies the increase in double layer field strength. This has shrunk to a thickness of 2 X lo-' cm. in 1 X 10-1 M potassium chloride, compared with a thickness of 55 X lo-' in 1.25 X M potassium chloride (see below). For purposes of the work presented here, an exact knowledge of the mechanism producing these changes is not necessary. The conductivity of the diffuse layer (for potassium chloride E, = E,) without electrosmose is, per cm.2 of surface,

This is the difference between total diffuse layer ions, and the ions normally present. The latter quantity is

dz.

moles of solute

Inasmuch as 1 contains normally c moles, the thickness of the diffuse double layer must be

The following thicknesses have been calculated (table 4).

Accuracy of measurements The observed specific surface conductivities in 3.0 X M potassium M potassium chloride are believed accurate to chloride and 1.0 X f10 per cent. This percentage error is deduced as follows. The accuracy of the values in table 3a, column 9, is f 0 . 2 per cent; in column 10, f 0 . 0 2 per cent. The error in column 12 (total observed surface conductivity in 1 of solution) depends on how small a fraction of column 9 it is. If total surface conductivity is one-tenth of total specific conductivity, the error is f 2 per cent; if it is one one-hundredth, the error is f 2 0 per cent. In calculating specific surface conductivity, column 14, the effective surface area of the powder must be known. It is obtained by dividing total surface conductivity in 5.0 X M potassium chloride by 4.3 X 10-9. If f a is the error in total surface conductivity A , and = t b the error in the specific surface conductivity B, then the error in the area will be

328


On the basis of an error of f 3 . 5 per cent in total surface conductivity and f 7 . 5 per cent in the specific surface conductivity in 5.0 X M potassium chloride, the error in the area is f 8 per cent. The percentage error for all values in table 3, column 14, has been estimated by the above equation of Fenner (3). It is about f 1 0 per cent. It follows that the accuTABLE 4 Thickness of diffuse double layer in various potassium chloride solutions MOLES

KCI P E R

THICENES8 OF DIFFUSE L A Y E R

LITER

cm.

moles

1.25 x 2.5 x 5 x 1 x 3 x 1 x 1 x

5.5 x 3.9 x 2.7 x 1.9 x

10-4 10-4 10-4 10-3 10-3 10-2, 10-1

10-6

10-6 10-6

10-6

1.1 x 10-6 0.6 X

0.2 x 10-6 TABLE 5

MOLES OF EALT P E R LITER

3BSERYED 8PECIFIC BURFACE CONDUCTIVITY

mhos X 10-0

KCl 1.25 x 2.5 x 5.0 x 1.0 x 3.0 x 1.0 x NaCl 1.25x 2.5 X 5.0 x 1.0 x 3.0 x 1.0 x

10-4 10-4 10-4 10-3 10-3 10-2

2.17 3.73 4.30 7.39 16.23 37.20

10-4

2.15 2.83 3.30 5.84 14.53 36.74

10-4 10-3 10-3

10-2

CALCULATED 4CCORDING TO ! 2 14 (ELECTRO~MOSE)

+

mhos X 10-

0.93 1.85 4.18 8.52 (16.23) (37.20)

-

CALCELAPED ACCORDING TO GOUY'S >OUBLELAYER

(1)

mhos X 10-9

0.51 0.84 1.36 2.03 2.58 2.13

CALCULATED ACCORDING T O 16 (NO ELECTRO~MOSE)

mhos X 10-8

CALCULATED LCCORDINQ T O GOUY'S iOUBLE L A Y E R

(1)

mhos X 10-

0.94 1.97 4.36 8.61 (16.23) (37.20)

0.34 0.56 0.91 1.35 1.72 1.42

0.80 1.72 3.89 7.77 (14.53) (36.74)

0.27 0.44 0.72 1.06 1.36 1.13

racy of the calculated Ze RT values, allowing furthermore for the uncertainty in 6, the thickness of the Helmholtz layer, I = ionic mobility (assumed to be normal), and the value of [, must be of the order of f20 per cent. The error in the volume occupied by the glass particles practically cancels out in the division described in section 12.

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IXTERFACES

329

RESULTS

The experimental data have been summarized in tables 3a and 3b, which are self-explanatory. In table 5 observed and calculated specific surface conductivities have been tabulated for potassium chloride and sodium chloride.‘* The agreement between observed and calculated values is good, when the sources of error and the experimental difficulties are kept in mind. The values calculated according to Bikerman’s equations 19 and 26 have also been included. It is seen that they are far too low. We interpret these results as confirming the essential accuracy of the Stern double layer theory which has been tested here for the first time. SUMMARY

1. Specific surface conductivities of Pyrex glass particles in potassium chloride and sodium chloride solutions of concentration 1.25 X M to 1 X M were determined. 2. The surface conductivities represent the same fraction of total conductivity as in a glass capillary of about l o p diameter. 3. An equation, based on the Stern double layer, for calculating specific surface conductivities was developed. 4. The calculated values are in agreement with experiment; values calculated according to GOUY’Stheory are not. 5. Evidence is adduced to show that (a) electrosmose may occur when [ = 0; (b) a sudden increase in sedimentation volume need not be due to “Hafteffekt”; (c) the electroviscous factor contains more than one component. 6. The thickness of the diffuse layer has been calculated. REFERENCES

(1) BIKERMAN, J. J.: Z. physik. Chem. lMA, 378 (1933). L.: J. chim. phys. 26,294-9 (1928). (2) DE BROUCKERE, (3) FENNER, G.: Naturwissenschaften 19, 297 (1931). H.:Kapillarchemie, 4th edition, Vol. 11, p. 166. (4) FREUNDLICH, Akademische Verlagsgesellschaft, Leipzig (1932). (5) Reference 4, p. 169. (6) GOUY,G.: J. phys. 141 9,457 (1910). (7) Handbuch der Physik, Vol. XIII, pp. 370-4. Julius Springer, Berlin (1928). (8) HUECKEL, E.: Adsorption und Kapillarkondensation, p. 96. Akademische Verlagsgesellschaft, Leipzig (1928). G.,AND JOSEPHS, R. C.: J. Am. Chem. SOC.60, 1049 (1928). (9) JONES, (IO) LACHS,H., AND BICZYK, J.: 2.physik. Chem. 148A, 441 (1930). (11) OSTWALD, Wo.,AND HALLER:Kolloidchem. Beihefte 29, 354 (1929). (12) PHILPOT, JOHN ST.LEGER:Phil. Mag. 13, 775-95 (1932). 18 It has been assumed that ppotentials of sodium chloride solutions were the same as those of potassium chloride.

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FRANK URBAN, H . L. WHITE, A N D . E. A. STRASSNER

(13) SHEDLOVSKY, THEODORE: J. Am. Chem. SOC.64,1411 (1932). (14) STERN,OTTO:Z. Elektrochem. 30, 508 (1924). THE,AND ANDERBON, HUGO:Kolloid-Z. 24, 156 (1919). (15) SVEDBERQ, A.: Kolloidchem. Beihefte 32,114 (1930). (16) YON BUZAOH, (17) WHITE, H.L., URBAN,F., ANDKRICK, E. T.: J. Phys. Chem. 36, 120 (1932). (18) ZOCHER: Cited by Freundlich, reference 4, p. 166.

TIVITY AT SOLID-LIQUID INTERFACES'

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