A CORRELATION O F STREAM POTEKTIALS AND SURFACE CONDUCTANCE BY H. L. TVHITE, FRANK U R B A S A N D E. A. VAX ATTA
At the 193 I Colloid Symposium we reported’ that the stream potential of pyrex capillaries with j X IO-^ iV KCl was independent of capillary size down to a bore of about 0.01 mm. Below this bore the potential decreased, being found about 7 5 % as great with a 0.005 mm capillary as with large capillaries, Le., of 0.1mm. McBain and Pealter2 had found a specific surface conductance of 1.3 X IO-’ mhos at an interface of pyrex and I x IO-^ N KCI; by interpolation from their data we calculate that this would be not less than I x IO-? mhos for j X IO-^ A7 KCl. If the mean conductance (resultant of volume and surface conductances) calculated on the basis of McBain and Peaker’s data is put into the stream potential equation E = f P D / 4 n y ~the calculated stream potential for a 0.005 mm capillary with 5 X IO-* N ICCI would be only 8.4% of that with a large capillary in which surface conductance can be neglected. This discrepancy might have any one or all of three explanations, I , that’ NcBain and Peaker’s surface conductance figures arc too high, 2, that the classical stream potential equation does not hold in the smaller capillaries and/or, 3 , that our previously reported stream potential figures for small capillaries are too high. We are now convinced that, all three explanations hold. First, we have shown3**that the specific surface conductance with pyrex and j X IO-* NKClisonlyz.z4 X ~ o - ~ m h o s , a b o u1/4jasgreatasfoundby t McBain and Pealter. If the classical stream potential equation holds this conductance would make the stream potentials with 0.00j mm capillaries about y j to 80% as great as with large capillaries, as we1 had found to be the case. This agreement, seems to be a gratifying confirmation of our stream potential results on .the smaller capillaries. We now recognize, however, that our figures of last year on stream potentials in the smaller capillaries are erroneous and ihat the apparent agreement is merely a coincidence. The error was due to our using a paper-paraffin condenser in the stream potential measurements. For the surface conductance work? a standard condenser was essential. Stream potential determinations have been repeated on capillaries of various sizes using the standard I mf. mica condenser obtained since last year’s report. I t is found that, the values for the larger capillaries, down t o about 0.03 mm diameter, are correct as previously reported; below this bore the potent’ialsfall off. With the smaller capillaries the potentials are not only very much lower than with the larger, but much less satisfactorily reproducible. It had been White, Urban and Krick: J . Phys. Chem., 36, 1 2 0 (1932). McBain and Peaker: J. Phys. Chem., 34, 1033 (1930). 1 White, Van Atta and Van Atta: J. Phys. Chem., 36, 1364 (1932). 4 White, Urban and Van Atta: J. Phys. Chem., 36, 1371 (1932). 1
2
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STREAM POTENTIALS AND SURFACE CONDUCTANCE
noted and reported last year that with the smaller capillaries reproducibility of results was much less satisfactory. This is now known to be due t o residual charges on the paraffin condenser; the lack of reproducibility with the smaller capillaries as reported in the present paper is not due to any fault in the method of measurement but to actual changes in the capillaries. I t has been found that the paraffin condenser gives the same readings as the mica with resistances up to about IO@ ohms. With higher resistances the potential readings with the paraffin condenser are too high and variable due to variations in the amount of residual charge. With the mica condenser also the readings with the smaller capillaries vary from one experiment to another but consecutive readings agree. Even with the paraffin condenser consecutive readings may show excellent agreement, giving a false sense of security. Only after beginning to use the mica condenser and finding that a small capillary which might, show a potential of 600 to 800 mv. with the paraffin condenser would at the same time show from o to zoo mv. with the mica did we realize that our earlier figures on small capillaries, with the paraffin condenser, are too high, although those on the large capillaries are correct. In Table I are shown a few stream potentials with the mica condenser.
TABLE I Cap. no.
Length cm.
58d 59 s7a 63a 60a 61 7oa 69a
1.1
4.66 = .97 0.25
Diameter mm.
0.0964 0.0405 0.039 0.0058
Stream pot,ential mv./cm. Hg X 1 0 - - 4 N KC1 5 x IO-^ N KCl
_-2.5
31.4 32.0
15.4 15.6
31 . o I .6
0.94
0.0055
5.8
0.76
0.0053
0.0
0.13 0.34
0.0050
0.0
2.2
0.0047
9.2
2
.o
The stream potentials on the smaller capillaries are much lower than can be accounted for on the basis of the classical stream potential equation by the specific surface conductance of 2.24 X IO-@ mhos which we have found; they are rather of the magnitude expected if McBain and Peaker’s values are correct. We thus have the paradoxical situation that with our surface conductance value the classical stream potential equation gives the stream potentials for small capillaries which we recorded last year but which are erroneously high, while the equation with McBain and Peaker’s value for surface conductance gives stream potentials of about the value reported in this paper, which we believe to be correct. Since we can find no fault with our value for specific surface conductance we conclude that the classical equation does not hold in the smaller capillaries. I t must be pointed out that the validity of the low stream potential values for small capillaries reported here depends upon the assumption that these capillaries have been satisfactorily treated. We have exerted every possible effort as to cleanliness of water, alternating periods of evaporation and con-
3155
H. L . WHITE, FRANK URBAN AND E. A. VAN ATTA
densation during steaming, protection of capillary from dust, etc., to ensure that the state of the walls of these small capillaries is the same for a stream potential experiment as it is with the larger capillaries. Furthermore, we have found that a brief period of heating a large capillary in a Bunsen flame, after it has had hot water sucked through it for an hour, will usually give a stream potential about the same as that after steaming. When a small capillary is so heated it still shows the low stream potential value, just as after steaming. We must state, however, that we cannot have the same degree of conviction regarding the adequacy of the steaming treatment with the small capillaries as with the large. When, however, a number of treatments and determinations are carried out on a given capillary and in no case does the stream potential exceed 30% of that shown by a large capillary it seems probable that the low values are not purely fictitious. Reichardt5 has attempted to develop an equation to express the influence of capillary diameter on the stream potential. His corrections do not bring the values down to those observed by us on the smaller capillaries. His equation E’ = E(I JJJ,) is equivalent merely to substituting for the bulk conductance the true conductance, L e . , resultant of surface and bulk conductances, of the solution in the capillary. His correction for the departure from laminar flow suffered in the initial segment of a capillary reduces the stream potential in even a 0.005 mm capillary by only a few per cent. Thus, for a capillary of 0.005 mm diameter and 4 mm length his equation (1*7a), using a Reynolds number of 1000,gives XI = 0.92, i.e., the stream potential would be lowered by only 8% due to this factor. We are not yet in a position t o present a theoretical treatment of our stream potential values on the smaller capillaries. Briggsh has pointed out that surface conductance may vary independently of zeta potential and has concluded that surface conductance is therefore not ionic conductance. He suggests that the effects of salts upon surface conductance are a function of their effects upon the equilibrium between monohydrol and polyhydrols. The former is supposed to be an electronic conductor; varying the nature or the concentration of ions affects surface conductance by affecting the concentration of monohydrol in the double layer. Briggs finds that the surface coiiductance with the tri and tetravalent cations, Al+++and Th++++,after passing through a maximum falls off with increasing concentration. This is attributed to their decreasing the concentration of monohydrol. Urban and Daniels’ have found, however, that bivalent cations decrease the partial specific heat of water more than do monovalent cations. The presumption is that the effect would be still more marked with tri and tetravalent cations. A decrease in specific heat indicates, znter alia, a decrease in polyhydrol concentration. This finding speaks against Briggs’ view that polyvalent ions reduce the monohydrol Concentration. With KCl Briggs found that surface conductance increased continuously with concentration while zeta passed through a maximum and then fell off
+
2. physik. Chern., 154, 337 (1931). Colloid Symposium Monograph, 6,41 (1928) Urban: ,J. Phys. Chem., 36, 1108 (1932)
STREAM POTENTIALS AND SURFACE CONDUCTANCE
3155
continuously. This lack of correlation, as well as the findings with polyvalent ions, led him to the statement that surface conductance is not a function of the zeta potential. The thesis developed in the present and the accompanying paper is that surface conductance is a function of zeta in the following sense, that a correlation between surface conductance and zeta exists only provided that the essential conditions for exhibiting a normal zeta potential are established. I n the case of glass capillaries, with the stream potential taken as an index of zeta, this means that the capillary must be of a t least 0.016to 0.02 mm. diameter and must have been subjected to a standardized treatment such that a maximum stream potential is developed.s If a capillary of proper size is so treated it will show with 5 X IO-^ N KC1 a stream potential corresponding to a zeta potential of about 120 mv. and a specific surface conductance of about 2 . 2 4 X IO-^ mhos. If the capillary is allowed to stand in the solution for several days or if it is used without having been first treated it will show a much lower zeta potential, which may drop even to zero, with practically no change in surface conductance. This looks like a failure of correlation between surface conductance and zeta potential. If, however, a normal zeta potential is established, the charge density calculated from this and the surface conductance calculated from the charge density, assuming normal viscosity, mobility and dielectric constant, the surface conductance so calculated agrees with the observed. We have interpreted these facts as meaning that with the untreated capillary the diffuse layer is absent or reduced while with the treated capillary the initially existing diffuse layer gradually collapses into the Helmholtz layer. The sum of the charges in the entire double layer remains constant; the ions in the Helmholtz layer can conduct electrical current but cannot contribute to stream potential, i.e., they can move in an electric field but not under hydrostatic pressure. The surface conductance is, therefore, unaffected by the distribution ratio of ions between diffuse and Helmholtz layers, but the zeta potential depends upon this distribution. If we establish the proper conditions practically all of the cations at a glass-aqueous interface are in the diffuse layer with concentrations of KCl not greater than 10-3 N . When a normal, L e . , maximum for that system, zeta potential exists the cation conductance in the diffuse layer (with concentrations of KC1 not greater than IO-^ N ) is therefore practically equivalent to the total cation conductance and can be calculated from the zeta potential. With increasing concentration, where it is no longer true that practically all of the cations are in the diffuse layer, one can still calculate surface conductance from normal, i.e., maximum for that system, zeta potentials if the distribution of cations between diffuse and Helmholtz layers is first calculated
* The determination of both surface conductance and stream potential on one and mme capillary is difficult but not impossibIe. The percentage of error is rather large since, if a capillary of diameter greater than 0.02 mm is used the ratio of surface to volume is too low for the most accurate determinations of surfare conductance while if the diameter is leas than 0.016 mm the stream potential is likely t o be too low. Numerous determinations on a capillary of 0.0186 mm diameter have shown marked fluctuations in stream potential depending upon its treatment, while the surface conductance remained constant. Furthermore, the type of treatment known to be essential to the establishment of a normal stream stream potential in large capillaries is known not to be essential to the maintenance of a constant surface conductance in small capillaries.
H. L. WHITE, FRANK URBAN AND E. A. VAN ATTA
3’56
according t o the method outlined in the accompanying paper, and allowance made for the conductance of ions which are no longer in the diffuse layer. While affording a satisfactory explanation of both Briggs’ and our results with monovalent cations this concept at first thought seems inadequate to account for Briggs’ finding that with polyvalent cations the surface conductance progressively decreases as concentration and zeta potential increase. We are not yet ready to discuss this situation fully. Insufficient knowledge of the work functions of adsorption of these ions makes it impossible to calculate satisfactorily the distribution between the diffuse and the Helmholtz layers. Until such calculations are possible we cannot judge of the applicability of our equations to the case of polyvalent cations. We may point out that McBain and Peaker, working with pyrex surfaces, did not find a decrease in surface conductance on increasing the concentration of A1C13, as did Briggs with a cellulose diaphragm. They found that the increase in conductance on increase of concentration was even greater with AlC18 than with KCl. Furthermore, Bull and GortnerO working with cellulose diaphragms found with ThCl, a fall in surface conductance followed by a rise, within the same range of concentrations used by Briggs. We are now investigating the surface conductances at pyrex surfaces of various concentrations of salts with ions of different valences but are not yet prepared to report our findings. summary
The stream potentials with capillaries of 0.005 mm diameter are from o to 2.5% as great as with large capillaries, instead of 75 to 85y0as great, as was reported last year. 2. These low figures cannot be accounted for by the classical stream potential equation or by any modification so far proposed. The possibility that unavoidable inadequacies of treatment of the smaller capillaries may be in part responsible for these abnormally low values cannot be excluded but it is believed that the low values are not entirely fictitious. 3 . A necessary and sufficient condition to a correlation between surface conductance and stream potentials is that the conditions essential to the exhibition of a normal stream potential be established. The zeta potential may fluctuate with no change in surface conductance but if a normal zeta is established surface conductance can be calculated from it and vice versa. 4. Briggs’ findings on monovalent cations which led him to the conclusion that surface conductance is not a function of the zeta potential can be interpreted as indicating that in his experiments the diffuse layer is less pronounced and varies more with concentration than is the case a t glass surfaces; under these conditions the zeta potential is not an index of the charge density until the distribution of charges between the components of the double layer is determined. The case of polyvalent cations is being further investigated. The work reported in this paper has been aided by a grant made by the Rockefeller Foundation to Washington University for research in science. I.
Department of Physiolooy and the Department of Biochemistry, Washington Uniuersity School of Nerlinine St. Louis, Missouri.
J. Phys. Chem., 35, 307 (1931).
