572
Langmuir 1990, 6, 572-578
by the accumulated conduction band electrons is diffithe fact that overall free energy changes suggest that cult to calculate, since it depends upon the unknown cathodic decomposition is slightly more exoergonic than steady-state concentration of electrons on the particle and proton reduction. Although its wide band gap precludes their distribution within the particle. It should be noted its use as a sensitizer in solar energy conversion, it may that low doped oxides have donor densities < 1017 ~ m - ~ . provide a useful, inert redox carrier for photocatalysis. In tin dioxide, such a low donor density corresponds to about one ionized site in 2 X lo5. Sincethe average parAcknowledgment. The assistance of S. Bigger with ticle aggregation number is 390, only one colloidal partithe determination of the hydrogen yields is greatly apprecle in 500 will have one ionized impurity donor. The addiciated. This work was supported by grants from the Austion of just one electron to a particle of aggregation numtralian Institute of Nuclear Science and Engineering. Work ber Nagg= 390 corresponds to an impurity concentration at Argonne National Laboratory is performed under the of 9 X lof9 cm-3 and may therefore substantially raise auspices of the office of Basic Energy Sciences, Division the quasi-Fermi level of the parti~le.'~The overpotenof Chemical Sciences, US-DOE under contract no. W-31tial for both H,discharge and lattice decomposition may 109-ENG-38. P.M. acknowledges the receipt of a Combe easily reached in this case. monwealth Postgraduate Research Award.
Conclusions Transparent colloidal SnO, has been shown to be cathodically stable under reducing conditions. This is despite
Registry No. EDTA, 60-00-4; TEOA, 102-71-6;MV+, 2523955-8; MV+,4685-14-7; Ru(bpy),2+,15158-62-0; SnO,, 1828210-5; H,, 1333-74-0; propan-2-01, 67-63-0; oxalate, 144-62-7.
Characterization of the Electrical Double Layer of Montmorillonite S. E. Miller and P. F. Low*>+ Department of Agronomy, Purdue University Agricultural Experiment Station,$ West Lafayette, Indiana 47907 Received July 27, 1989 and {, the The primary objective of this paper was to determine the relative magnitudes of $o, electrostatic potentials in the plane of the clay-water interface, the outer Helmholtz plane, and the plane of shear, respectively. Another objective was to determine the relative magnitudes of uo and 0 6 , the charge densities in the first two planes, respectively. Four different methods were used to achieve these objectives. All of them gave the same results. It was found that was much smaller than $o but was equal to C also, u6 was much smaller than uo. Moreover, it was found that $a was independent of electrolyte concentration, pH, and uo but dependent on the nature of the exchangeable cations. On the other hand, a6 varied linearly with the square root of the electrolyte concentration. Nevertheless, it remained much smaller than u,,. These results were interpreted to mean that most of the exchangeable cations are condensed on the montmorillonite surface in a Stern layer and that adjustments in the ionic occupancy and/or thickness of this layer maintain $a at a constant, critical value that cannot be exceeded.
Introduction Electrical double-layer theory had its inception with the work of Gouy' and Chapman.' It was extended by L a n g r n ~ i rDerjaguin? ,~ and others and was refined and integrated by Verwey and Overbeek.' Especially since the latter work, it has become the fundamental theory of colloid chemistry. Although modern statistical mechanical methods have been used to further extend and refine Former graduate assistant and Professor of soil chemistry, respectively. Contribution No. 12088. (1) Gouy, G. J.Phys. 1910, 9, 457. (2) Chapman, D.L. Philos. Mag. 1913,25, 475. (3) Langmuir, I. J. Chem. Phys. 1938, 6, 873. (4) Derjaguin, B. V. Trans. Faraday SOC.1940,36, 203. (5) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids;Elsevier: New York, 1948.
*
0743-7463/90/2406-0572$02.50 f 0
the theory: its essential features have remained unchanged. The application of electrical double-layer theory to clays was initiated primarily by Sch~field,~?' but many have used the theory to explain their observations, e.g., Bolt,g Bolt and Miller," Warkentin et al.,ll Norrish,12 Kemper,13 Van Olphen,14 Q ~ i r k , Friend '~ and Hunter," ~
(6) Carnie, S.L.; Torrie, G. M. Adu. Chem. Phys. 1984, 56, 141. (7) Schofield, R. K. Trans. Faraday SOC.B 1946, 42,219. (8) Schofield, R.K. Nature 1947, 160, 408. (9) Bolt, G. H.J. Colloid Sci. 1955, I O , 206. (IO) Bolt, G. H.; Miller, R. D. Soil Sei. SOC.Am. Proc. 1955, 19, 285. (11)Warkentin, B. P.; Bolt, G. H.; Miller, R. D. Soil Sci. SOC.Am.
Proc. 1957,21, 495. (12) Norrish, K. Faraday SOC.Discuss. 1954, 18, 120. (13) Kemper, W. D. Soil Sci. SOC.Am. h o c . 1960,24, 10. (14) Van Olphen, H.An Introduction to Clay Colloid Chemistry;Interscience Publishers: New York, 1963. (15) Quirk, J. P. Isr. J. Chem. 1968, 6, 213.
0 1990 American Chemical Society
Langmuir, Vol. 6, No. 3, 1990 573
Electrical Double L a y e r of Montmorillonite
IL
ILr
Table I. Values of Specific Surface Area S, Cation-Exchange Capacity w, and Surface Charge Density q,for Montmorillonites Used in This Study montmorrilonite Na-Upton Na-Otay Na-Texas
lo-%', cmz/g w , mequiv/g 8.0
6.34 5.68
10-~~,," esu/cmz
0.90 1.12
3.25 5.11 3.90
0.76
a Values in this column were obtained by dividing w by S and converting the result to the appropriate units.
I
,/
Stern Layer
:
,..-Plane
of Shear
Diffuse Layer
Figure 1. Model of the electric double layer of clays.
and Barclay and 0 t t e ~ i l l . lFor ~ convenience, and in the absence of substantial evidence to the contrary, it has generally been assumed that the diffuse layer of counterions begins at the clay-water interface and that this interface is a plane of constant charge but variable potential. However, more recent evidence reported by Low1' and Chan et E11.l' indicates that the diffuse layer begins beyond a Stern layer and that the boundary that separates these two layers, i.e., the outer Helmholtz plane (OHP), is a plane of variable charge but constant potential. Now, double-layer theory applies to the diffuse layer only, and we must know the conditions a t its boundaries if we are going to integrate the relevant equations and make any theoretical predictions. For the sake of clarity, consider Figure 1,where uo is the charge density at the clay-water interface, us the charge density a t the OHP, $o the electrostatic potential at the clay-water interface, the electrostatic potential a t the OHP, j- the electrostatic potential a t the plane of shear, 6 the distance between the clay-water interface and the OHP, and T the distance between the OHP and the plane of shear. Note that uo has a fixed value for a clay mineral because it is governed by ionic substitutions within the crystal structure. Also note that the OHP is the plane in which the diffuse layer originates and, as such, is the origin of the coordinate system that is used in any mathematical treatment of this layer. With reference to Figure 1, we need to know the magnitudes of $* and ug. In addition, we need to know how relates to $o and j- and how u6 relates t o uo. In order to satisfy these needs, we conducted the following experiments.
natant solution. This procedure was repeated 5 times. Thereafter, the montmorillonite was freed of electrolyte by dialyzing it for 24 h and washing it repeatedly in distilled water by centrifugation and decantation. Washing was continued until the decanted solution showed no evidence of C1- as indicated by the AgNO, test. Water remaining in the montmorillonite was removed by freeze-drying. Samples of t h e freeze-dried montmorillonite were suspended in solutions containing the chloride salt of the exchangelo-,, 5 X 5X able cation a t concentrations of W4, and lo-* M. The concentration of the montmorillonite in the resulting suspensions was 0.1% by weight when the mobility of the particles was measured. Otherwise, it was 0.5% by weight. These suspensions were used for the determination of +6 by the following methods. Method I. The fundamental equation of electrical doublelayer theory is the Poisson-Boltzmann equation. When a single symmetrical electrolyte is present, this equation may be written5
a
d2$jdX2 = 7 tirevno sinh ve+
+
where is the electrostatic potential, x is the distance from the OHP, e is the electronic charge, v is the ionic valence, no is the ion concentration in the external solution, t is the dielectric constant, k is the Boltzmann constant, and T is the absolute temperature. For nonoverlapping double layers, integration of eq 1 yields tanh ( v e q j 4 k T ) = tanh (ve+&j4kT)e-"l:
(2)
in which K = (8nv2e2n0jtkT)'/2 (3) If eq 2 is expressed in logarithmic form and applied to the plane of shear, the result is
In tanh (veCj4kr) = In tanh ( v e q b / 4 k T )- KT
(4)
Thus, if In tanh (veCj4kT) is plotted as a function of K and a straight line is obtained, the slope and intercept of this line should yield values of T and +a, respectively. Equation 4 was derived originally by Eversole and Lahr.21 I t was used subsequently by Eversole and Boardman22to determine 7 and for glass and by Hunter and Alexanderz3 to determine the same quantities for kaolinite. For colloidal particles, the value of f a t any value of K can be calculated from the electrophoretic mobility, p , of the particles by means of the Smoluchowski equation
Experimental Section
{ = 4rt)vjtE = 4rt)pjt
The montmorillonites that we used in our experiments were the Na-Upton, Na-Otay, and Na-Texas montmorillonites prepared and described by LOW.'^,^^ Their properties are given in Table I. For some of the experiments, the Na-Upton montmorillonite was converted to the Li- and K-saturated forms by dispersing it in 1.0 M solutions of LiCl and KCl, respectively, centrifuging out the montmorillonite and pouring off the super-
in which t) is the viscosity of the interparticle solution, u is the velocity of the particles, and E is the voltage gradient causing them to move. In order to obtain { as a function of K so that eq 4 could be utilized, we determined p a t several values of K in two ways, namely, by microelectrophoresis as described by Lowz4 and by a modification of the moving-boundary method as described by Allen and MatijevkZ5 Since our modification of the latter method had some unique features, it will be described in detail.
(16) Friend, J. P.; Hunter, R. J. Clays Clay Miner. 1970, 18, 275. (17) Barclay, L. M.; Ottewill, R. H. Spec. Discuss. Faraday SOC. 1970, I , 138. (18) Low, P. F. Soil Sci. SOC.Am. J. 1981,45, 1074. (19) Chan, D. Y. C.; Pashley, R. M.; Quirk, J. P. Clays Clay Miner. 1984,32, 131. (20) Low, P. F. Soil Sci. SOC.Am. J. 1980,44,667.
(5)
(21) Eversole, W. G.; Lahr, P. H. J. Chem. Phys. 1941, 9, 530. (22) Eversole, W. G.; Boardman, W. W. J. Chem. Phys. 1941,9,798. (23) Hunter, R. J.; Alexander, A. E. J. Colloid Sci. 1963, 18, 833. (24) Low, P. F. Soil Sci. 1954, 77, 29. (25) Allen, L. H.; Matijevic, E. J.Colloid Interface Sci. 1969,31, 287.
574 Langmuir, Vol. 6, No. 3, 1990
Miller and Lou! substituting the right-hand side of the first integral of eq 1 for d$/dx, eq 6 can be integrated and then multiplied by S / n o to give
nCdde
/Ill
Vex= r-S/no= (2S/K)[1- exp(ve$,/2kT)]
A
Figure 2. Moving-boundary apparatus. Figure 2 shows the apparatus that we used. It consisted of a cathode chamber and a n anode chamber connected to each other by glass tubes joined by a stopcock. The tube leading to the anode chamber was a precision-bore capillary tube with a cross sectional area, A , of 0.0575 cm2. It was in this tube that the boundary between the suspension and solution was followed. Prior to being admitted into the apparatus, the suspension and solution were equilibrated with each other by placing them on opposite sides of a porous membrane (pore diameter = 0.025 bm) that separated the two compartments of a membrane cell and by shaking the cell for -60 h. Equilibrium was regarded as being established when the emf between a Naglass and a Ag,AgCl electrode was the same in both phases. Thereafter, the cathode chamber and the bore of the stopcock were filled with the suspension, and the anode chamber was filled with the solution. Some of the solution was also introduced into a calibrated conductance cell, and its specific conductance, L , was measured by means of a Wheatstone bridge. With the stopcock closed, a Pt cathode and a Cd anode were inserted into their respective chambers. Then, after the fluids in these chambers were adjusted to the same level, the stopcock was turned to connect the two chambers, and a sufficiently large voltage drop was established between the electrodes to make E approximately 10 V/cm. _The exact value of E was calculated by means of the equation E = I / A L in which I is the current. The value of I was measured by placing an ammeter in the circuit, the value of A was 0.0575 cm2, and the value of L was assumed to be equal to that of the solution. This assumption was reasonable because the suspended particles were too few in number to contribute significantly to L. However, the paucity of particles made it difficult to see the suspensionsolution boundary. T o make this boundary visible so that it could be detected with a cathetometer, we adopted a suggestion of A.H. Beavers of the University of Illinois and used a 0.95-mW helium-neon laser. When the beam of the laser passed from the solution to the suspension, light was scattered by the suspended particles and the suspension was illuminated. Once u was determined from the rate of movement of the boundary at any value of E , the corresponding value of {was determined by means of eq 5 with 9 = 0.89 X lo-' P and t = 80. In addition to determining at different electrolyte concentrations, we determined it a t a constant electrolyte concentration M) and different pH values. The p H was adjusted with either HCl or NaOH at a concentration of 0.1 M. These determinations were made by microelectrophoresis only. Method 11. When a single symmetrical electrolyte is present, r-, the deficit of anions per unit area of surface, is given by
r- = Ja(no
- n.) dx
(6)
where n- is the local concentration of anions a t any given value of x. By employing the Boltzmann equation, viz. n, = noexp(=ive#/kT) (7) to express n- in terms of no,replacing d r by d$/(dJ./dx), and
(8) where S is the specific surface area and Vex is the exclusion volume per unit mass of montmorillonite. This equation was derived initially by Chan et a1.l' Unlike earlier equations for Vex,s~26-28 it does not rely on the questionable assumption that > 100 mv. According to eq 8, $6 can be calculated from the slope of the relation between Vexand 2 / if~ the value of S is known. T o obtain the data necessary for the application of eq 8, we equilibrated 50 cm3 of the suspension with a n equal volume of the solution with which the suspension was originally prepared. Hereafter, this solution will be called the original solution to distinguish it from the external solution, Le., the solution in equilibrium with the suspension. We determined the C1- concentrations in both of these solutions by the method described below. Then we multiplied the C1- concentration in the original solution by the total volume of the system and divided the product by the C1- concentration in the external solution. The quotient was the volume that the C1- would have occupied had its concentration everywhere been equal to that in the external solution. Subtraction of this volume from the total volume of the system and division of the difference by the mass of montmorillonite gave Vex a t the given K . Subsequently, the same procedure was repeated a t different values of K . The C1- concentrations in the original and external solutions were determined by the method of Kolthoff and K ~ r o d a . ~In ' applying this method, we used a Ag,AgCl electrode, prepared as described by Smith and Taylor,,' with a Corning Ag,AgCl double-junction reference electrode. The outer compartment of the reference electrode was filled with a 2.0 M solution of KNO,. Since the C1- titration was conducted in a supporting electrolyte consisting of KNO, and HNO, a t concentrations of 0.25 and 0.05 M, respectively, the liquid-junction potential of the reference electrode was small. During titration, the solution was stirred a t a constant rate. Method 111. According to the Debye-Huckel theory, the electrostatic potential, Gr, at a distance r from a spherical particle having a charge Q is given by31
&-
ex(o-r)
tr (1+ ~ a )
where a is the distance of closest approach to the particle. Electrostatic potentials are additive. Therefore, if the electrostatic potential in the external solution is assigned a value of zero, E,,,, the difference in potential between this solution and the suspension in equilibrium with it, should equal the summation of the potentials at any point in the suspension due to the surrounding particles. Provided that n,,, the number of particles per centimeter cubed, is small enough to prevent the electric field of one particle from interfering appreciably with that of another, E , is given by
E, =
d r = 4 ~ Qexa n Xae-..r d r e(1
+ Ka)
(10)
With regard to eq 10, it is helpful to note that 4nn&,.r2dr is the electrostatic potential a t the center of a spherical shell of radius r a n d thickness d r due to the particles in that shell. Integration of eq 10 yields E,=-
4*n,Q tK2
(26) Bolt, G. H.; Warkentin, B. P. Kolloid-2. 1958, 156, 41. (27) Shone, M.G . T. Trans. Faraday SOC.1962, 58, 805. (28) Van den Hul, H. J.; Lyklema, J. J. A m . Chem. SOC.1968, 90,
3010.
(29) Kolthoff, I. M.; Kuroda, P. K. Anal. Chem. 1951,34, 1304. (30)Smith, E.;Taylor, J. K. J. Res. Natl. Bur. Stand. 1938,20, 837. (31) Mac Innes, D.A. Principles of Electrochemistry; Reinhold Publishing Co: New York, 1939.
Langmuir, Vol. 6, No. 3, 1990 575
Electrical Double L a y e r of Montmorillonite The above derivation of eq 11is based on that of Another derivation of the same equation was provided by Adair and Adair.,* The value of u6 is related to npQ by the expression u6 = n,Q/
o
n
u
0
Li-Upton
WS
(12) where W is the mass of montmorillonite per centimeter cubed. by Also, for nonoverlapping double layers, u6 is related to the following equation of double-layer theory5 u6 =
-m
-0.5
9 sinh (ve&/2kT) 2nve
-,,.I,
(13)
Therefore, measurements of E , at different values of K allowed from us to construct a plot of us versus K and to calculate the slope of the resulting curve. We equilibrated suspensions of Na-Upton montmorillonite with the solutions used in preparing them, as described earlier. After equilibrium was reached, we measured the respective values of E , by the method of C h e r n ~ b e r e z h s k i .For ~ ~ this measurement, we used a Beckmann p H meter with a Ag/AgCl electrode and a Corning reference electrode. A 1.0 M solution of KNO, was in the outer compartment of the latter electrode. Thus, we obtained the data necessary for the calculation of Method IV. The theory of the Donnan membrane equilibrium shows that, in a system containing a single symmetrical electrolyte
0
IO+K
K-Upton
2
3
I
,
(crn-')
Figure 3. Relation between In tanh (uef/4kr) and K for Li-, Na- and K-Upton montmorillonite in chloride solutions of the respective exchangeable cations. -0.5
5 ? u
J
1 Na-Otay
u -07
0
w
0
-
.c
e
n,n- = n2n-O (14) where n+O and n-' are the local concentrations of the cation and anion, respectively, in the external solution. However, analytical determinations of ion concentrations provide only average values. Now, if $ is small (525 mv), we can relate A+ and A_, the average concentratio9s of the respective ions, to the average electrostatic potential, $, by the equation34 A, = no exp(we$/kT)
I
,
No-Texas
-"
0
-C
0
-0.9
"
0
w
I
I
I
(15)
which is analogous to eq 7. Multiplication of eq 15 for the cation by the same equation for the anion gives A+A- = n+ko
which is analogous to eq 14. However, electroneutrality requires that n,Q=-ve(fi,-A-)(V,-
VJIV,
(17)
where V, is t h e volume of the suspension and V, is the volume occupied by the particles in the suspension. If the suspension is dilute, V, >> V, and eq 17 reduces to npQ = -ue(fi, - A _ )
(18)
Substitution of the right-hand side of this equation for npQ in eq 12 shows that u6 = -ue(ri, -
p determined by microelectrophoresis T, nm ILA,mV
(16)
%.)IW S
(19)
Recall that A- is the average concentration of the anion in the diffuse layer. Since an anion is not adsorbed onto the negatively charge clay, Le., it does not occupy the Stern layer, A- is experimentally determinable. The same is true of n+' and n-'. Once values of A-, n+', and n-' are known, eq 16, 19, and 13 permit the calculation of A,, u6, and qatrespectively. We used t h e membrane cell described previously to equilibrate suspensions of montmorillonite with the NaCl solutions used in preparing them. Then we determined the value of Ain each suspension by potentiometric titration and the values of n+' and n-' in each external solution by immersing a Naglass and a Ag/AgCl electrode in the solution and referring the emf produced to a previously prepared calibration curve of emf versus NaCl concentration. Hence, we were able to obtain data for the calculation of $sby another method. (32) Adair, G. S.; Adair, M. E. Trans. Faraday SOC.1935,31, 130. (33) Chernoberezhski, Y. M. In Surface and Colloid Sci.; Matijevic, E., Ed.; Plenum: New York, 1982; Vol. 12. (34) Overbeek, J. Th. G.h o g . Biophys. Biophys. Chem. 1956,6, 57. (35) Schramm, L. L.; Kwak, J. C. T.Colloids Surf. 1982,3,43.
clay mineral montmorillonites Li-Upton Na-Upton K-Upton Na-Texas Na-Otay kaolinite Na-Victoria a
0.026
0.050 0.015
-0.002 -0.108 0.360a
-71.1 -59.0 -48.9 -49.4 -61.7
p determined by moving boundary T, nm & A , mV
0.056 -0.115 0.075 -0.340 0.480
-70.3 -59.0 -48.1 -50.2 -58.8
-55.0"
Data from Hunter and Ale~ander.'~
Results Figures 3 and 4 show graphs of In tanh ( v e r I 4 k T ) vs K from which, in keeping with eq 4, the results in Table I1 were obtained. Note that these results did not depend on the technique by which p was measured. Also reported in Table I1 are the results obtained for Na-kaolinite by Hunter and Alexander.23 The values of at different pH values are tabulated in Table 111. Figures 5-9 show the relations between Vex and 2 / ~ for the different homoionic montmorillonites. Since we had the pertinent values of S (Table I), we were able to use these relations and eq 8 to obtain the values of $* listed in Table IV. Also listed in this table are values of $a that were obtained from graphs of Vexvs 2 / pub~ lished by other investigators. In the past, such graphs were constructed for the determination of S by Schofield's method.* Plots of u6 vs K are shown in Figures 10 and 11. The data for Figure 10 were obtained by method 111, whereas
r
Miller and Low
576 Langmuir, Vol. 6, No. 3, 1990 Table 111. Effect of pH on Electrophoretic Mobility, w, and f Potential, f, of Na-Upton Montmorillonite* PH 5.71 6.31 6.70 7.40 7.48 7.80 a
i04p, cmZ/Vper s
i,mV
-4.607 -4.803 -4.896 -4.791 -4.598 -4.795
-58.0 -60.5 -61.7 -60.4 -57.9 -60.4
4 0 0
In a lo-, M solution of NaC1.
0
200
400
600
2/K ( A ) F i g u r e 8. Relation between Vex and Z / K for Na-Texas montmorillonite in solutions of NaCl.
2/K (A) F i g u r e 5. Relation between Vex and 2 / K for Li-Upton montmorillonite in solutions of LiCl.
2 / K (A) F i g u r e 6. Relation between V and 2 / K for Na-Upton montmorillonite in solutions of NaCf. 7 "
I
I
2/K(A) Figure 7. Relation between Vexand 2 / K for K-Upton montmorillonite in solutions of KCl.
those for Figure 11 were obtained by method IV. The values of Ga, calculated from the slopes of these plots in accordance with eq 13, were -59.1 and -55.5 mV, respectively. For the purpose of comparison, the values of $6 obtained by the different methods are accumulated in Table V.
Discussion One of the primary objectives of the present study was to obtain reliable values for Therefore, let us turn our attention first to Table V. Note that the values of obtained by the four methods were remarkably consistent. In no case did a result obtained for a given montmorillonite by one method differ by more than 4% from
"0
200
400
600
2/K (A) Figure 9. Relation between Vex and Z / K for Na-Otay montmorillonite in solutions of NaC1. Table IV. Values of Obtained by Method I1 for Different Homoionic Clay Minerals clay mineral IO-'%,cm2/g *a, mV montmorillonites -67.4 Li-Upton 8.00 -56.8 Na-Upton 8.00 -51.6 8.00 K-Upton -46.0 5.68 Na-Texas -60.7 6.34 Na-Otay -90.0 (-76.7) Li-Upton 7.5 -69.0 (-60.7) Na-Upton 1.5 -44.0 (-39.8) 7.5 K-Upton -21.0 (-19.4) 1.5 NH,-Upton -12.0 (-11.1) 7.5 Cs-Upton -61.9 Na-Upton 8.0 -86.1 8.0 Li-Belle Fourche -64.1 8.0 Na-Belle Fourche -25.2 8.0 K-Belle Fourche -25.2 8.0 ",-Belle Fourche -2.6 8.0 Cs-Belle Fourche illites 1.10 -65.0 Li-Fithian 1.10 -51.0 Na-Fithian 1.10 -19.0 K-Fithian -11.0 ",-Fithian 1.10 -5.0 1.10 Rb-Fithian 0.0 1.10 C,-Fithian
ref a a
a a a
b b b b b C
d d d d d
b b b b b b
This study. * Chan et al.I9 The values in parentheses were calculated from the original values by changing S in eq 8 from 7.5 x lo6 to 8.0 x IO6 cm2/g. Calculated from the original data of Bolt and Warkentin.26 Calculated from original data of Schramm and K ~ a k . ~ ~
the average of the results obtained for that montmorillonite by all the methods. We conclude, therefore, that the reported values are reliable. Their significance with regard to the structure of the electric double layer will be discussed hereafter. Reference to Table I1 shows that, within experimental error, T equaled zero for every homoionic montmorillonite. This means that the OHP coincides with the plane of shear and that +6 = c. As a result, we can regard a measured value of f as being the value of $&.
Langmuir, Vol. 6, No. 3, 1990 577
Electrical Double Layer of Montmorillonite
------0 4 -
n
i 0 - O ~ (ern-')
Figure 10. Relation between u6 and K for Na-Upton montmorillonite as determined by method 111. 0
1
6ooo-
-
5
(rnv)
Figure 12. Frequency distribution of { for 34 Na-saturated montmorillonites from different sources.
determined by method clay mineral
I"
I1
111
IV
Li-Upton Na-Upton
-70.7
-59.1
-55.5
K-Upton Na-Texas
-59.0 -48.5 -49.8
-67.4 -56.8 -51.6 -46.0
Na-Otay
-60.2
-60.7
" Data in this column are averages of the data in Table 11. Table I11 shows that [ (and, hence, $J was independent of pH. It follows, therefore, that the planar surfaces of the montmorillonite particles did not have a pHdependent charge and that, if their edges had such a charge, it was effectively screened by the charge on the planar surfaces. In this regard, recall that the edges of montmorillonite are far less extensive than the planar surfaces. The results in Tables I1 and IV establish the fact that the values of follow the lyotropic series, namely, Li > Na > K. Consequently, we conclude that the degree of hydration of the exchangeable cations affects either their dissociation from the Stern layer or the thickness of this layer. Such a conclusion is reasonable because the energy released by the hydration of an exchangeable cation can be utilized to dissociate it from the charge site on the adjacent surface." Also, the size of the hydration shell of an exchangeable cation in the Stern layer should influence the thickness of the layer. (36) Zhang, Z.
Z.; Low, P. F. J. Colloid Interface Sci. 1989,133,461.
Observe that the variables used in constructing Figures 3-11 were linearly related to each other. In accordance with the respective equations on which these figures were based, we conclude that $a was independent of K and, consequently, of electrolyte concentration in and lo-' M. the range of concentrations between Not only was independent of electrolyte concentration, it was also largely independent of uo and of other characteristics of the clay mineral on which it developed. This is demonstrated by the narrow range of values reported in Tables I1 and IV for different clay minerals having the same exchangeable cation. For example, compare the values of $areported in Table I1 for the three sodium montmorillonites and the sodium kaolinite. They fell within a narrow range of -12 mV. Also reported in Table IV for the compare the values of two sodium montmorillonites and the sodium illite. They fell within a similar range. The lack of dependence of on the characteristics of the clay mineral is even more strikingly demonstrated in Figure 12, which shows the frequency with which the value of [ fell within the specified intervals for the 34 Na-saturated montmorillonites studied by Low.lS In considering this figure, it is important to realize that [ was not related to uo, the only inherent electrical property of the montmorillonite. The coefficient of correlation between [and uofor the 34 montmorillonites was only 0.19. Obviously, most of the values of [were distributed normally within a narrow range about a modal value. We interpret such a distribution to mean that all sodium montmorillonites, regardless of their values of uo, tend to have a common value of f and, therefore, of $a. This common value is the modal value of the distribution. In view of the lack of dependence of on environmental factors such as electrolyte concentration and pH and on characteristics of the clay mineral such as uo,we hypothesize the following: (1) montmorillonite and other clay minerals have a critical value of $* such that, when this value is exceeded, exchangeable cations are unable to leave the Stern layer. (2) The critical value of depends on the nature of the exchangeable cations. (3) The critical value of $a is maintained, once it has been reached, by adjustments in the Stern layer. In this regard, it is note-
578
Langmuir 1990, 6, 578-582
worthy that the critical value of $* is relatively small. If all of the exchangeable cations left the Stern layer, the value of $6 would become equal to that of $o which, for Na-Upton montmorillonite, is 270 mV. Theoretical evidence in favor of a critical surface potential has been provided by Plesner and M i ~ h a e l i . ~ ~ If $ais constant, eq 13 requires that ug be a linear function of ti. The experimental evidence in Figures 10 and 11 shows that this requirement is satisfied. Consequently, montmorillonite is not a colloid with a constant surface charge and variable surface potential as hitherto supposed. It is a colloid with a constant surface potential and variable charge. The net space charge in the Stern layer per unit area of surface is equal in magnitude but opposite in sign to uo - u6. Therefore, (uo - u,)/uo = 1 - u g / u ois the fraction of the permanent charge of the montmorillonite that is neutralized within the Stern layer. Since it is highly unlikely that anions can enter this layer against the Coulombic repulsion of the negatively charged surface, 1 u 6 / u o can also be regarded as the fraction of exchangeable cations that it contains. Accordingly, u s / u ocan be regarded as the fraction of exchangeable cations in the diffuse layer. If we let have a constant value of -57.6 mV, which is the average of the values for Na-Upton montmorillonite in Table V, and let uo have a value of 3.25 X lo4 esu/cm2, which is the value reported for this montmorillonite in Table I, we can use eq 13 to derive the relation
-
.a/uo = 4.59 x lo-%
(20) From Figures 10 and 11, we see that ti varied from 3.25 (37) Plesner, I. W.;Michaeli, I. J . Chem. Phys. 1974,60,3016.
lo5 to 32.55 X lo5 cm-'. It follows, therefore, that u6/ uo varied from 0.015 to 0.15. Evidently, only a very small
X
fraction of the exchangeable cations is in the diffuse layer. Almost all of these cations are in the Stern layer. The same conclusion was reached earlier by M a t t ~ o n , ~ ~ Low," and Chan et a1.l' As we have seen, u6 increases linearly with K . Such an increase could be caused by expulsion of cations from the Stern layer, by adsorption of anions into it, or by a decrease in its thickness. On the basis of spectroscopic evidence, Gan3' concluded that the increase in a6 was due primarily to the latter cause. This conclusion is consistent with the results of Friend and Hunter,16who showed that changes in electrolyte concentration induce structural changes in the Stern layer of vermiculite, a phyllosilicate like montmorillonite. In summary, we have shown that montmorillonite has a well-developed Stern layer in which most of the exchangeable cations reside and that the outer boundary of this layer, i.e., the OHP, is a plane of constant electrostatic potential and variable electric charge. The magnitudes of the potential and charge in the OHP are far smaller than those that would exist at the clay-water interface in the absence of a Stern layer. Moreover, the potential in the OHP and the { potential have a common value because the OHP and the plane of shear are coincident. To explain the constancy of this value, the hypothesis is proposed that it is a critical value which cannot be exceeded and which is maintained by adjustments in the Stern layer. Registry No. Montmorillonite, 1318-93-0.
(38) Mattson, S.Soil Sci. 1929,28, 179. (39) Gan, H.MSc. Thesis, Purdue University, May 1987.
Surface Pressure Gradients Formed during the Compression of Poly(viny1 stearate) Monolayers J. B. Peng and G. T. Barnes" Department of Chemistry, University of Queensland, Brisbane, Australia Received August 31, 1989. I n Final Form: October 11, 1989 Surface pressures have been measured at various positions along the center line of the trough during the compression of monolayers of vinyl stearate (VS) and poly(viny1 stearate) (PVS). With VS there was no appreciable inhomogeneity, but with PVS a significant surface pressure gradient formed. This exhibited an approximately linear decrease in surface pressure from the moving barrier to the end of the trough. The inhomogeneity of the PVS monolayers during compression depends on the technique of spreading and on the method of compression. No technique was found which would eliminate the surface pressure gradient. Even when the film was held at a high surface pressure for 90 min, there was still a significant surface pressure gradient. Much of the earlier data on PVS monolayers, particularly the apparent annealing effect, can be explained by the present findings. Introduction
It is almost a half century since the Langmuir technique was first used to study the behavior of polymer
mono layer^.'-^ Usually a polymer monolayer has been regarded as a homogeneous film during compression, like (1)Katz, J. R.; Samwel, P. J. P. Naturwissenschaften 1928, 16, 592.
~743-7463/90/2406-0578~02.50/0 0 1990 American Chemical Society
