3300
J . Phys. Chem. 1991, 95, 3300-3301
concerning the diffusion properties inside a cell and since Dell is assumed to be independent of the diffusion in the cell. In eq 2 this formula is applied to a micellar system where Deu is identified with Dmiccile and D(fixed cell) is expressed as Dicff. In the original paper on the cell-diffusion model, the two-region application described in section 2 was evaluated for a more general form a spheroidal cell. Consider the coordinates FI, u, and 4 defined through the relations x = a(FI2i 1)Il2 sin
Y
symmetry axis. The two equations for Un(tR),where 9 = z or 7 = x , may be written as
cos 4
y = a(FI f 1)i/2sin u sin 4 z = ati cos u where 2a is the distance between two foci of the prolate (- sign) or oblate (+ sign) ellip~oid.~' For prolate or oblate ellipsoids, the expression analogous to eq 7 then becomes y is finally given by
D(fR) C(tR) Uv(FR) D:f
=
(C)
('43)
where tRrepresents the boundary of the cell and the subscript 9 either represents the direction along the symmetry axis of the cell, in our case the z axis, or the direction perpendicular to the
If the directions of the spheroidal aggregates are isotropic, the average self-diffusion coefficient in the system becomes
(27) Arfken, G.Mathematical Methods for Physicists, 3rd ed.;Academic
('49)
Press: New York, 1970.
The Nature of "Contact" in Measuring the Forces between Muscovite Surfaces J. P. Quirk Soil Science and Plant Nutrition, School of Agriculture, University of Western Australia, Nedlands, Western Australia
and R. M. Pashley* Department of Chemistry, The Faculties Australian National University, Canberra, ACT, Australia (Received: August 7, 1990)
A mechanism is discussed for the interpretation of the values observed for the strength of adhesion of muscovite mica crystals
in various aqueous electrolyte solutions. In pure water the mica surfaces apparently contact at a separation of about 2.2 8, with the hydroxonium ion balancing the lattice charge.
Introduction In a relatively recent communication McGuiggan and Israelachvili' reported that the adhesion energy between molecularly smooth muscovite mica surfaces at "contact" in water of 7 and 10 mJ n r 2 depended on the rotational angle between the two surface lattices relative to the original crystallographic orientation in the uncleaved crystal. These values for adhesion are an order of magnitude less than that reported by Kay and Bailey2 of 107 mJ m-2 for the original cleavage of muscovite in water. Thus, the matched surfaces in the McGuiggan and Israelachvili experiments were considerably different in their relationship at "contact" from the pristine condition. We examine here the reasons for this difference. Significance of Hydroxonium Ions The surfaces investigated by McGuiggan and Israelachvili would have had the muscovite surface charge balanced by H30+ because of the ion exchange which occurs when 1 cm2of muscovite
(=3.4 X lo-'* mol of K+ cm-2) is immersed in 500 mL of water at pH 5.8. In addition, Pashley3 has reported a 1000-fold preference for protons as compared with alkali-metal ions for adsorption at the mica surface. Recently, Pashley and Quirk4 have discussed the reason for the strong affinity of H30+ for the mica surface as being due to the fact that the proton ion is able to reside in a water molecule in contact with the siloxane oxygens at the mica surface immediately above sites where AI3+ replaces Si4+ in the crystal lattice. By contrast, other inorganic ions including K+ because of their primary hydration shell can only approach the siloxane surface to a distance of the diameter of a water molecule (2.76 A); the hydroxonium ion is actually at the siloxane surface and very close (-2 A) to the aluminum ion tetrahedral sites of the lattice which give rise to the lattice charge. In a series of experiments at the Australian National Unive r ~ i t yit, ~has been shown that in water or dilute salt solutions, when the surface charge is balanced to a significant degree by H 3 0 + , opposing muscovite surfaces are pulled together from a separation of 20-30 A apparently into a primary minimum
( I ) McGuiggan, P. M.; Israelachvili, J. N. Chem. Phys. Lett. 1988, 149,
469.
(2) Bailey, A. 1.; Kay, S.M. Proc. R. Soc. London 1967. A301, 47.
(3) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531. (4) Pashley, R. M.; Quirk, J. P. J . Soil Sci. Soc. Am. 1989, 53, 1660.
0022-3654/91/2095-3300$02.50/00 1991 American Chemical Society
Forces between Muscovite Surfaces "contact". However, when sufficient quantities of alkali-metal ions' are present in the solution, strong repulsive forces are developed as the surfaces are brought together, and as a result this "contact" is not achieved. These forces are described as hydration forcesS or ion-mediated structural forces being generally similar to the structural forces, described by Derjaguin: which give rise to disjoining pressures between surfaces. It has been shown4 that these hydration forces are very much greater than the osmotic repulsive forces due to the diffuse distribution of counterions.'
van der Waals Forces McGuiggan and Israelachvili' have used the relationship E = -A/1 2rD2 to calculate the theoretical adhesion energy; A, the Hamaker constant, is taken as 2 X J, and for D,the separation of the surfaces, they use 2 A for the "cutoff" distance for molecular contact.8 The calculated value for the adhesion energy is 12.7 mJ m-2. The authors suggest that this agreement with their experimental results highlights the importance of atomic granularity. However, the difficulty remains that the adhesion energy at "contact" is much lower than the pristine condition when the surfaces are actually in contact; the feature responsible for this appears to be the "cutoff" distance. The H30+ ion could occupy one of two possible positions between the contiguous muscovite surfaces at "contact". This ion is similar in size to the potassium ion and could occupy a position between three oxygens forming the base of the Si-0 tetrahedra on one surface and a similar group of oxygens on the opposing surface. If we take 2.76 A (the diameter of the water molecule) as the diameter of H30+ (cf. K+ diameter 2.66 A) and note from a scale model that the H30+is sunk into each surface to the extent of 0.25 A, then the separation becomes, for the purpose of a van der Waals calculation, 2.26A; this is extremely close to the value chosen by McGuiggan and Israelachvili.' The other possible position for the hydronium ion is in the ditrigonal cavities in opposing surfaces; that is in the position occupied by K+ in the uncleaved crystal. The basal spacing is 10.2A and the thickness of the silicate layer itself is 9.5 A so that the siloxane surfaces are separated by 0.7 A; in this circumstance the van der Waals contribution to the adhesion is almost 100 mJ m-2, and this approaches the pristine value obtained by cleavage in watere2 It would thus seem that "contact" in the force measuring apparatus involves the separation of the surfaces by the diameter of the water molecule after allowing for some keying into the surface oxygens; that is about 2.2 A. The desolvation of the hydroxonium ion to achieve "contact" does not appear feasible since the enthalpy for the first water molecule hydrating the proton is 690 kJ mol-'? which for the number of protons involved (3.4X mol cm") would require 2350 mJ m-2. Hydration Forces and Surface Separation For sufficiently concentrated solutions of alkali-metal ions' and alkaline earth ionslO-" when the exchange sites of the muscovite (5) Israelachvili, J. N.; Adams, G. E. Faraday Trans. Chem. SOC.1978, 74, 975. (6) Dcrjaguin, B. V. Prog. Colloid Polym. Sci. 1987, 74, 17. (7) Venvey. E. J. W.; Overbeck, J. Th. G. Theory of fhe Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (8) Israelachvili, J. N . Intermolecular and Surface Forces; Academic Press: New York, 1985; pp 156-200. (9) Kebarle, P. Higher-Order Reactions-In Cluster and Ion Solvation. In Ion Molecule Reactions; Franklin, J. L., Ed.; Plenum: New York, 1972; Vol. 2, Chapter 10.
The Journal of Physical Chemistry, Vol. 95, No. 8,1991 3301
are predominantly occupied by metal ions, it is not possible to bring the surfaces into contact despite the application of large pressures; in the case of Ca-muscovite even though the pressure applied was 45 MPa the surfaces did not come into contact as revealed by the absence of an adhesive primary minimum. To clarify this situation, it is helpful to consider the crystalline swelling of vermiculite, a layer silicate closely related to muscovite. Muscovite has an excess of two electrons per unit cell based on an anionic framework of composition Om(OH)4,and vermiculites have a charge varying from 1.2 to 1.9 e per unit cell.12 Muscovite has a fixed d(001) basal spacing of 10.2 A, but vermiculites depending upon the vapor pressure and the ion balancing the charge adsorb water between the elementary silicate layers (9.5 A thick) to attain spacings of 12.5 and 15.5 A corresponding to approximately one and two "layers" of water between contiguous mineral surfaces.I2 Even on immersion in water, the spacing remains fixed at 15.5 A because the surfaces are in a primary potential minimum and are therefore adhesive. Van Olphen13*14 has studied the water vapor adsorption of the N a and Mg form of vermiculite at 25 OC and found that the 2 to 1 "layer" transitions take place a t relative vapor pressure values of 0.4 and 0.05,respectively. These relative vapor pressures correspond to disjoining pressures of 70 and 400 MPa, respectively. These pressures are much larger than those that can be applied in the force measuring apparatus, and hence it is possible that the muscovite surfaces do not approach closer than several water layers. Posner and QuirklS have reported that in electrolyte solutions similar minerals have a surface excess corresponding to two water layers, and it seems probable that at the pressures involved in the force measuring apparatus, there would be two layers of water on each muscovite surface; that is, the surfaces are separated by a proximately 4 times the diameter of a water molecule (2.76 ) or about 1 1 A from actual contact. At this distance of separation, each surface has its own set of counterions balancing the charge so that to bring the surfaces into the primary minimum would require pressures large enough to cause the interpenetration of the two sets of cations to form a single layer of ions between the two surfaces.16
K-
Summary and Conclusion By reference to the crystallography of muscovite and the behavior of the related vermiculite minerals in the presence of water as revealed by X-ray diffraction, the interpretation of McGuiggan and Israelachvili' of "contact" distance has been refined. The significance of the absence of an adhesive minimum when surface sites are occupied by hydrated inorganic cations is discussed. In these circumstances the closest distance of separation even at large pressures may well be about 11 A, and when replaced by hydroxonium ions, the surfaces move into a tential minimum with "contact" a t a separation of about 2.2 (IO) Pashley, R. M.; Quirk, J. P. Colloids S u r - 1984, 9, 1. (1 1) Pashley, R. M.; Israelachvili, J. N . J . Colloid Interface Sei. 1984,97, 44.
(12) Brindley, G. W.; Brown, G. Crystal Structures of Clay Minerals and Their X-ray Idenriflcation; Mineralogical Society: London, 1980. (13) Van Olphen, H. J . Colloid Sci. 1965. 20. 822. (14) Van Olphen, H. Proceedings of rhe Inrerotional Clay Conference, Tokyo, Israel University Press: Jerusalem, 1969; p 649. (15) Pwner, A. M.; Quirk, J. P. Proc. R. SOC.,London 1964, 2784, 35. (16) Slade, P. G.; Stone, P. A,; Radwlovich, E. W. Clays Clay Miner. 1985, 33, 5 I .
