An interpretation of Electrochemical Measurements on a

Publication Date: October 1959. ACS Legacy Archive. Cite this:J. Phys. Chem. 63, 10, 1659-1662. Note: In lieu of an abstract, this is the article's fi...
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Oct., 1959

ELECTROCHEMICAL MEASUREMENTS ON A MONTMORILLONITE CLAY

1659

AN INTERPRETATION OF ELECTROCHEMICAL MEASUREMENTS ON A MONTMORILLONITE CLAY1 BY K. B. DESHPANDE AND C. E. MARSHALL Deparlmmt of Soils, University of Missouri, Columbia, Missouri Received March 8, 1969

Changes in (1)conductivity, (2) pH, (3) cation activity, (4) migration velocity of clay particles and (5) cation-halide ion pair activities during the titration of an acid-montmorillonite clay were studied. An attempt has been made to inter ret these by considering charge distribution around clay particles and by the application of the double layer theory. !!he agreement between the charge densities on the clay particles and the total of the charge densities on the various ‘ planes” is striking.

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Introduction The interfacial properties of clay suspensions are determined partly by the atomic structures of clays and partly by the nature of the ionic surroundings in the suspension. The correct interpretation of the phenomena involved would greatly benefit colloid chemistry and clay technology. The study of such systems requires, in the ultimate analysis, the consideration of single ion activities by both experimental and theoretical approaches. Such systems have so far been studied by thermodynamic, quasi-thermodynamic and conductometric methods. Davis2 employed the cell Ag. AgCl/Clay suspension IIXCl/Ag.AgCl which effectively measured the chemical potential of the Na-, K- or other chloride in the clay system. Using the same proportions of clay, water, salt and varying the nature of the salt to correspond to the cation on the clay, the chemical potential of KC1 was found to be significantly different from that of NaCI. The use of tertiary electrodes operating through the ionic equilibrium set up by two sparingly soluble salts with a common ion3 also gives a measure of the chemical potential of the molecular species involved. Both of these methods lead to an indirect determination of the surface properties through their effect on the chemical potential of a soluble molecular species. What is needed for the structural interpretation is the relation between the silicate surface and the individual ions which balance its charge. This can be obtained by a quasi-thermodynamic route which involves certain plausible but not strictly proved assumptions. The quasi-thermodynamic method, like conductivity, affords data which can be interpreted directly in terms of single ions. I n such an interpretation the activity which is a geometric average is treated like concentration in its conversion to conductivity. This is permissible in the case of very dilute systems where the activity and concentration are about the same. As one of the authors4 has pointed out, a combination of transport number, conductivity and activity determinations for a series of clay suspensions should lead to a more accurate evaluation of the electrochemical properties of cations in (1) Contribution from the Missouri Agricultural Experiment Station, Journal Seriepl No. 197%. Approved by the Director. ( 2 ) L. E. Davis, Null. Acad. Sei. Natl. Res. Council, 895, 290 (1955). (3) E. W. Russell and G . A. Cox, Fourth Internotl. Cow. Soil Sci., Amsterdam, Trans., 1, 138 (1950). (4) C. E. Marshall, Noli. Acad. Sci. Nail. Res. Council, 416, 288

(1956).

the clay systems. Use of silver halide electrodes in addition to calomel electrodes will throw further light on the ionic distribution in such systems. In the present investigation an attempt has been made to study the titration of a dilute acid-clay suspension in a limited pH range by measurement of (a) conductivity, (b) pH, (c) cation-activity, (d) migration velocity of clay particles, and (e) cation-halide ion pair activity with the corresponding Ag-Ag ‘halide electrodes. The results obtained in these last determinations will be discussed separately since they show a number of features at low salt concentration, quite different from those of D a v k 2 In this paper we shall offer an interpretation of conductance in bentonite clay, based on a combination of conductometric, quasi-thermodynamic and cataphoretic measurements. In this clay, Bloksma’s diffusion experiments5 indicate a value for the mean activity coefficient of the sodium ion in close agreement with membrane electrode results.

Experimental (1) Preparation of the Acid Clay.-The clay, Wyoming bentonite (Belle Fourche, .American Colloid Company) was similar to the material used by previous workers in this Laboratory.6 A 1% suspension was prepared and the fraction lesb than 0.2 p in equivalent spherical diameter was separated using a Sharples supercentrifuge. This fine suspension was then electrodialyzed using a cell of the type reported earlier,e until it reached the p H of about 2.5. This stock suspension, about 2%, was diluted from time to time as required for the titrations. The p H of the suspension was checked at frequent intervals and showed very little variation. (2) The exchange capacity of the clay was determined by the batch method’ and was found to be 80.0 meq. per 100 g. of dry clay. (3) The titration was set up by weighing out accurately the same amount of suspension in a series of flasks and adding to each the requisite amounts of water, alkali and dilute K-halide solution. In all the systems the final volume was maintained the same. Systems with 5, 10 and 20 ml. of 0.00065 N halide solution were investigated. After about 48 hours of standing, the following measurements were made on each system. (a) Conductivity was measured at 10,000 cycles/sec. (b) pH and K ion activities were measured in the same way as reported previously.6 (c) The cation-halide ion pair activity: This was measured by use of Ag-Ag halide electrodes. Each of these electrodes AgAgCI, Ag-AgBr, Ag-AgI was tested at frequent intervals, with solutions of known concentrations of the corresponding K-halides on the two sides of a clay membrane. (d) Mi(5) A. H. Bloksma. J . Colloid Sci., 12, 40 (1957). Sci. SOC.Amer. Proc., 13, 179 (1949). (7) D. R. Lewis, Prelim. Rep. No. 7. A n . Patr. Inat., Pro., 49. 9 1 (1950).

(a) E. 0. McLean and C. E. Marshall, Soil

K. B. DESHPANDE AND C.E. MARSHALL

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Vol. 63

TABLE I Weight of clay = 0.3867 g., final volume = 100 ml. Meq. KOH added/g. clay

PH

“K

Specifia conduotivity Measured Calcd. hm X 106 Xa X 106

X 10‘

Qm

x

-

Xo) lo(

Series 1 MI. of 0.00065 N KC1 added = 5.0

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0.13 .26 -39 .52 .65 .78

0.13 .26 .39 .53 .66 .79

0.13 .27 .40 -53

.66 .80

5.38 6.00 6.28 6.51 7.52 8.69

2.738 3.018 3.419 4.322 5.678 10.980

3.95 4.53 5.18 6.66 9.89 13.88

3.11 3.29 3.66 4.48 5.96 11.46

0.84 1.24 1.52 2.18 3.93 2.42

5.20 5.92 6.20 6.52 7.32 8.91

Series 2 M1. of 0.00065 N KC1 added = 10.0 2.869 1.419 4.43 3.200 1.645 4.85 3.727 1.860 5.55 4.859 2.293 6.91 6.955 2.617 10.44 10.900 3.480 16.38

3.48 3.62 4.14 5.28 6.42 11.58

0.95 1.23 1.41 1.63 4.02 4.80

5.02 5.91 6.23 6.60 7.67 8.60

Series 3 M1. of 0.00065 N KC1 added = 20.0 3.329 1.900 5.72 3.770 1.920 5.94 4.092 2.070 6.35 4.934 2.239 7.38 7.233 2.689 11.00 10.850 3.321 16.16

4.39 4.52 4.82 5.66 8.02 11.77

1.33 1.42 1.53 1.72 2.98 4.39

1.413 1.555 1.760 2.099 2.655 3.473

gration velocity of the clay particles. This wa8 measured by using Engel and Pauli’s method.8 The results obtained are reported in tabular form in Table I.

depending on the frequency of the ax. The frequency above which this happens is given by Y thus:

Discussion of Results The conductivity measurements bring out an important fact. If the various ions are attributed their mobilities at infinite dilution, the corresponding conductivities can be calculated from their respective activities. This requires evaluation of conductivity due to the clay particles which can be done using the fact that the algebraic sum of the charges on the positive and negative ions per unit volume of suspension is equal to the sum of the charges on all the clay particles in it. The migration velocities for all systems were found to be very close to 3 p per sec. per volt per cm. The values for conductivities of suspension obtained from such calculations are given in Table I.Q It is observed that the measured conductivities are higher than those calculated in all systems. One possible cause can lie in the fact that the migration velocities at infinite dilution used for the various ions and that for the clay are those obtained by application of a direct current, whereas the measured conductivities are obtained by using a high frequency ax. According to Debye-Falkenhagen” the latter should give higher values as the relaxation effect disappears more or less completely (8) W. Pauli and E. Valko, “Elektrochemie der Kolloide,” Vienna, 1929, p. 165. (9) It is assumed that the activity of H measured represents its concentration and that the chloride is negatively adsorbed.’@ (10) S. Mattson, SoiE Sei., 88, 179 (1929). (11) P. Dehye and Falkenhagen, Phyaik. Z.,!29, 121, 401 (1928).

Y

= CZh/71.3 X 1010 for a binary electrolyte

where C = g. moles of the electrolyte/per 1. Z = valency of the ions h = equivalent conductance

In the case of clay particles all the corresponding terms cannot be defined under given conditions. Hence, one has to consider other related aspects of the situation. The clay particle is much larger than an ion and hence will have a much larger volume for its ionic atmosphere. The low clay concentration contributes further to the extension of the latter. The charge required to decay during the relaxation time is much larger than that for a monovalent negative ion in a solution of the same concentration as the clay. The conductivity of a clay particle is much less than that of an ordinary ion. This implies that the delay time for the ionic atmosphere of a clay particle is much longer than that for the ionic atmosphere of a monovalent negative ion. Hence, the abnormality appears at a much lower frequency than for ordinary electrolytes. The cause of this abnormality or difference in conductivity from the expected value is attributable to those double layer ions which are physically adsorbed to the surface. Those adsorbed chemically will form a part of the surface (as far as conductivity is concerned), reduce its charge. density, and will not contribute to the process of building and decay of ionic at-

ELECTROCHEMICAL MEASUREMENTS O N A MONTMORILLONITE CLAY

Oct., 1959

1661

TABLE I1 All charges described are coulombs/cc.

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Molesfl. K in Stern layer x 104

Molesp. K chemisorbed

x 104 1.48 5.70 9.96 13.20 14.50 19.30 1.57 5.94 10.25 13.92 13.63 13.71 1.30 5.88 10.55 14.58

1.15 1.69 2.07 2.97 5.37 3.30 1.30 1.68 1.92 2.21 5.48 6.54 1.81 1.93 2.08 2.34 4.06 5.98

15.71 15.32

4Jharge/cc.

in Stern layer

X

0.011 .017 .021 ,030 .054 ,034 0.013 .017 .019 ,022 .056 .067 0.018 .019 .021 .024 .041 .061

lap

=

0.01 X c

X f Y

0.024 .026 .030 .039 .052 .lo2 0.022 .025 .030 .041 ,061 .098 0.021 .024 .027 .035 .057 .092

mosphere. This means that the K + ions equivalent to the defect in conductivity are situated in the physically adsorbed layer (Stern layer), whereas the rest are in the chemisorbed state. The above consideration leads to an approximation as to the nature and extent of distribution of the ions around the clay particles. Table I1 gives the values of ionic concentrations for each of these layers. The figures given in this table are the relative concentrations of the ions in a unit volume of the suspension and not in terms of the actual concentration in each layer. The latter can be obtained by taking into account the surface area of the particles and by considering that the depth of the adsorbed layer is about twice the ionic diameter, Le., about 5 A. The validity of such an ionic distribution can be tested by examining the charge distribution in each system. The surface charge density and the number of clay particles in a unit volume of the suspension can be found as described by Olphen.12 The entire surface area of a gram of clay is 750 m.2. The exchange capacity, showing the charge on 1 gram, is 0.8 meq. Hence, the charge density is about 10.32 pcoulombs ( = coulomb) per cm.2. The number of particles is given by N

Charge/cc. on clay after neutn.

Charge/cc. in Gouy

1 + Adps -

where A = surface area of the flat side of a clay plate (cm.) p = no. of unit layers per particle s = denaity of dry clay (g./cc.) c = g. clay per 100 ml. of suspension d = thickness of a unit layer of bentonite (cm.)

In calculating the surface charge on the clay particles, account has been taken of the hydrogen neutralized by hydroxyl ions added and also the H in the ionized form as shown by the pH measured. The charge on the clay surface is partly neutralized by the chemisorbed ions and the rest is balanced by the ions in the Stern layer and the diffuse part of (12) H. Van Olphen and M. H. Waxman, NatE. Acad. Sci., Natl. Rea. Council 566, 61 (1958).

0.035 .043 .051 .069 .lo6 .136 0.035 .042 .049 .063 .117 .165 0.039 ,043 ,048 ,059 .098 .153

XI

0.048 ,097 .145 .194 .242 ,291 0.049 .098 ,147 ..186 .244 ,283 0.050 ,099 .148 .198 .247 ,297

Charge/co. due t o sorbed K

YI

0.014 .055 .096 .127 .140 .186 0.015 ,057 .099 ,134 .131 .132 0.013 .057 .lo2 .141 .151 ,148

XI

-

Y1

0.034 .042 .049 .067 .lo2 .lo5 0.034 .041 .048 .052 .113 .151 0.037 .042 .046 .057 .096 .149

the double layer, to be called “Gouy layer” in what follows. Table I1 gives the charge densities in various parts, the charges mentioned being coulombs in respective parts per ml. of suspension. The application of the Donnan principle to the Gouy and the Stern layers will give the relative amounts of K and H in each. However, the pH in each system is high enough to render this discrimination unimportant. It can be seen that in most cases the surface charge is balanced by the layer-wise charges which is, in part, a test of the validity of the distribution arrived at. Application of the theories of charge distribution around a colloid particle can now be considered. The Gouy-Chapman theory would lead to an abnormally high concentration of ions in the proximity of the surface of clay particles. Also it does not consider the possibility of adsorption. The Stern theory with its modification by Grahamela takes into account such a possibility and could well be applied t o the case in point. The potential at the outer surface of the Stern layer (“outer Helmholtz plane”) is given by gC. Thus N

E

Noie-Zel+u/kT

Where N = no. of ions adsorbed per ml. in Stern layer Noi = no. of ions per ml. away from clay surface

z

K

T

el

valency of the ion concerned Boltzmann constant = absolute temperature = electronic charge = =

The surface charge density of the Gouy layer14 is given by m ,thus Where (13) D.C. Grahama, Chem. Reus., 41, 441 (1947). (14) E. J. W. Verwey and J. Th. G. Overbeek, “Theory of the Stability of the Lyophobic Colloids,” Elsevier Pub. Co., New York, N. Y.,1948, p. 144.

K. B. DESHPANDE AND C. E. MARSHALL

1662 E

=

dielectric constant of medium and other symbols have the same meaning as before

The charge density in the adsorbed part is given by GI, thus

-

= 2Zelrn0ie ( Z e d i f 9)/k T ni = 2rnoie-ze~+i+vp/kT concn. of adsorbed ions per sq. cm. ionic radius adsorption potential potential in the inner part of Stern layer (“inner Helmholtz plane”) U,

ni = r

=

rp ~i

= =

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The quantities $i and cp are inaccessible with the measurements made. However, ni is known from the balance of K between that added to the acidclay and the concentration of (I in Gouy layer; TABLE IT1 All charges described are pcoulombs/cm.a Moles/l. K adsorbed

x 104 2.63 7.40 12.04 16.18 19.87 22.61 2.87 7.62 12.18 16.13 19.12 20.25 3.11 7.81 12.63 16.93 19.77 21.29

Cl

CI

0.880 2.473 4.026 5.378 6.645 7.558 0.958 2.548 4.070 5.393 6.392 6.774 1.040 2.611 4.228 5.651 6.612 7.129

0.842 1.029 1.124 1.376 1.849 2.044 0.899 1.047 1.102 1.187 1.862 2.081 0.838 1 * 100 1.147 1.219 1.609 1.952

CI

+

02

1.722 3.502 5.150 6.754 8.494 9.602 1.867 3.595 5.172 0.580 8.254 8.855 1.878 3.711 5.365 6.870 8.321 9.081

C

1.669 3.360 5.044 6.732 8.418 10.090 1.708 3.391 5.087 6.527 8.484 9.987 1.730 3,420 5.150 6.860 8.570 10.310

u1 can, therefore, be calculated. The values of (r1 and GZ obtained thus are given in Table IJI. I n comparing the total of these figures in each system with (r, the surface charge density of clay (taking into account the H presumably still on it), it should be noted that the theories applied give approximation of the magnitude of the surface charge distribution in each of the three layers. The agreement between the G and u1+ ( r z values is striking. Since acidic clays are commonly hydrogen-aluminum systems, possible errors caused by disregarding the Al+++ ion should be mentioned. Table I indicates that no systems under study had pH values below 5.0, even in presence of salt. The p K , value for aluminum hydroxide is 32.7 a t 20”. Thus a t pH 5, pAl would be at least 5.7, and a t p H 6 at least 8.7. Hence dissociated aluminum ions would not contribute measurably to the conductivity nor to the activity measurements. Any exchangeable aluminum present must thus be either in the Stern layer or the solid. The high bonding energy of trivalent aluminum would be equivalent to chemisorption, that is, to association with the solid surface. I n view of the likelihood of its reincorporation in

Vol. 63

the octahedral layer of the silicate structure with increasing pH, we believe that our interpretation is not materially affected by disregarding the exchangeable aluminum. Cation-Halide Ion-Pair Activities.-It was observed that the use of silver bromide and iodide electrodes yielded results very close to those given by silver chloride electrodes. The figures given in Table I are, therefore, the mean of such readings obtained by the use of all three electrodes. The measurements show the measure of the product of K) ion activity and halide ion activity (H in each suspension. The fact that the substitution of bromide and iodide for chloride electrode does not change the results shows that the solubility differences between the three silver halides do not have appreciable effect on these measurements. The interpretation of these results appears to require further experimental data, particularly regarding the possibility of halide ion adsorption by the clay. This is being further investigated.

+

DISCUSSION C. T. O’KONSKI(University of California a t Berkeley).What concentration of electrolyte did you have in your system? K . B. DESHPANDE.-Around lo-‘ molar. C. T. 0’KoNsm.-Then I agree that the counterion relaxation, or polarization of the ion atmosphere, will be an important effect. But the Debye-Falkenhagen theory is not adequate to treat it in the present case because particle size and shape are clearly very important factors and the theory treats only point charges. I n a polyelectrolyte, the counterions are restrained in their motion by the high central charge of the charged particle, but they may move relatively freely in the vicinity of a surface; therefore, i t appears that an appropriate model to employ is one in which the conductivity of the solvent and the high localized conductivity at the interface are both taken into account. I have treated the complex dielectric const,ant of polyelectrolyte systems, Le., the frequency-dependent dielectric constant and conductivities on the basis of a model incorporating a surface conductivity, A, which may be evaluated from the ion distributions and mobilities. Arbitrary internal and external dielectric constants and bulk conductivities also are taken into account. The resulting equations resemble the Maxwell-Wagner equations, although the latter do not allow for an interfacial conductivity. For spherical particles with a thin ion atmosphere, the effective conduct,ivity turns out to be the internal volume conductivity of the spherer 4, plus 2X/a, where a is the radius. As a result of this localized conductivity an induced dipole is set up, the field in the sphere and its vicinity is decreased and, thus, the contribution of the cqunterions to the conductivity is reduced a t low frequencies. At high frequencies, where the induced polarization does not have time to build up completely, the local field is greater and the counterions contribute more fully to the conductivity. Thus the conductivity undergoes a dispersion characteristic of any lossy dielectric, including simple electrolytes. This is the effect you observed. If the particles are not spherical, the effect of shape upon the effective conductivities along the various axes must be considered, and the appropriate depolarization factors must be introduced to take iato account the effect of sha e on the internal field, in the treatment of the electric fie& problem. This is a rather intricate problem, but fortunately it can be solved b introduction of some simplifying ap roximations whicg seem reasonable. The magnitudes of t i e conductivity and the dielectric dispersions turn out to be shape dependent, so that with your system, which I believe consists of platelike particles this must be taken into account. A manuscript descridng this contribution to the theory is in preparation for publication in THISJOURNAL.