Mica

Micas are classified according to the charge of the mixed layer per formula unit. This depends on the diadochy level of AF (or Fe or, more rarely, Be ) with in tetrahedral groups, and on the charge (and occupancy) of the cation in the intermediate octahedral sheet. 

In each 2 1 mixed layer, the upper tetrahedral sheet is translated by a/3 with respect to the lower one, thus creating the octahedral oxygen coordination around the cations of the intermediate sheet. Translation may occur along any positive or negative direction defined by structural axes Xj, X2, and X3 of a pseudohexagonal lattice, as shown in figure 5.43. 

The degree of freedom in the translational properties of the various sheets gives the polytypism of the phase. Polytypes are structures with layers of essentially identical composition but differing in translational sequence. Poly types usually have different symmetry and periodicity along axis Z). Smith and Yoder 

The intermediate octahedral sheet is normally made up of cations of charge 2 or 3 (Mg, Al, Fe, Fe, or, more rarely, V, Cr, Mn, Co, Ni, Cu, Zn), but in some cases cations of charge 1 (Li) and 4 (Ti) are also found. In the infinite octahedral sheet, formed by the sharing of six corners of each octahedron, there may be full occupancy of all octahedral sites ( trioctahedral micas ) alternatively, one site out of three may be vacant ( dioctahedral micas ). Nevertheless, the primary classification of micas is based on the net charge of the mixed 2 1 layer. In common micas this charge is close to 1, whereas in brittle micas it 

Micas are primary phases in several types of igneous, metamorphic, and sedimentary rocks. Table 5.54 furnishes a rough scheme of main mica occurrences. 

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While Eq. III-18 has been verified for small droplets, attempts to do so for liquids in capillaries (where Rm is negative and there should be a pressure reduction) have led to startling discrepancies. Potential problems include the presence of impurities leached from the capillary walls and allowance for the film of adsorbed vapor that should be present (see Chapter X). There is room for another real effect arising from structural peiturbations in the liquid induced by the vicinity of the solid capillary wall (see Chapter VI). Fisher and Israelachvili [19] review much of the literature on the verification of the Kelvin equation and report confirmatory measurements for liquid bridges between crossed mica cylinders. The situation is similar to that of the meniscus in a capillary since Rm is negative some of their results are shown in Fig. III-3. Studies in capillaries have been reviewed by Melrose [20] who concludes that the Kelvin equation is obeyed for radii at least down to 1 fim. 

This effect assumes importance only at very small radii, but it has some applications in the treatment of nucleation theory where the excess surface energy of small clusters is involved (see Section IX-2). An intrinsic difficulty with equations such as 111-20 is that the treatment, if not modelistic and hence partly empirical, assumes a continuous medium, yet the effect does not become important until curvature comparable to molecular dimensions is reached. Fisher and Israelachvili [24] measured the force due to the Laplace pressure for a pendular ring of liquid between crossed mica cylinders and concluded that for several organic liquids the effective surface tension remained unchanged... 

Fig. III-3. Comparison of Eq. III-18 (solid line) with experimental results for cyclohexane bridges formed between crossed mica cylinders the dashed line is the calculation including Eq. III-20 (from Ref. 19).

Fig. V-5. The repulsive force between crossed cylinders of radius R (1 cm) covered with mica and immersed in propylene carbonate solutions of tetraethylammonium bromide at the indicated concentrations. The dotted lines are from double-layer theory (From Ref. 51).

The measurement of the streaming potential developed when a solution flows through two parallel plates [74-76] allows the characterization of macroscopic surfaces such as mica. 

The flow can be radial, that is, in or out through a hole in the center of one of the plates [75] the relationship between E and f (Eq. V-46) is independent of geometry. As an example, a streaming potential of 8 mV was measured for 2-cm-radius mica disks (one with a 3-mm exit hole) under an applied pressure of 20 cm H2 on QT M KCl at 21°C [75]. The i potentials of mica measured from the streaming potential correspond well to those obtained from force balance measurements (see Section V-6 and Chapter VI) for some univalent electrolytes however, important discrepancies arise for some monovalent and all multivalent ions. The streaming potential results generally support a single-site dissociation model for mica with Oo, Uff, and at defined by the surface site equilibrium [76]. 

These effects can be illustrated more quantitatively. The drop in the magnitude of the potential of mica with increasing salt is illustrated in Fig. V-7 here yp is reduced in the immobile layer by ion adsorption and specific ion effects are evident. In Fig. V-8, the pH is potential determining and alters the electrophoretic mobility. Carbon blacks are industrially important materials having various acid-base surface impurities depending on their source and heat treatment. 

Fig. V-7. f potential of muscovite mica versus electrolyte concentration at pH 5.8 0.3. (From Ref. 76.)...

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

An assortment of values of the Hamaker constant A is collected in Table VI-4. These are a mixture of theoretical and experimental values there is reasonable agreement between theory and experiment in the cases of silica, mica, and polystyrene. 

Fig. VI-6. The force between two crossed cylinders coated with mica and carrying adsorbed bilayers of phosphatidylcholine lipids at 22°C. The solid symbols are for 1.2 mM salt while the open circles are for 10.9 roM salt. The solid curves are the DLVO theoretical calculations. The inset shows the effect of the van der Waals force at small separations the Hamaker constant is estimated from this to be 7 1 x 10 erg. In the absence of salt there is no double-layer force and the adhesive force is -1.0 mN/m. (From Ref. 66.)...

While evidence for hydration forces date back to early work on clays [1], the understanding of these solvent-induced forces was revolutionized by Horn and Israelachvili using the modem surface force apparatus. Here, for the first time, one had a direct measurement of the oscillatory forces between crossed mica cylinders immersed in a solvent, octamethylcyclotetrasiloxane (OMCTS) [67]. 

Fig. VI-7. The force between two crossed mica cylinders in dry OMCTS. The cylinder radii R were about 1 cm. The dashed lines show the presumed, experimentally inaccessible, transition between a repulsive maximum and an attractive minimum. (From Ref. 68.)...

The modification of the surface force apparatus (see Fig. VI-4) to measure viscosities between crossed mica cylinders has alleviated concerns about surface roughness. In dynamic mode, a slow, small-amplitude periodic oscillation was imposed on one of the cylinders such that the separation x varied by approximately 10% or less. In the limit of low shear rates, a simple equation defines the viscosity as a function of separation... 

Calculate A/Aq of Eq. VI-38 assuming that the mica cylinders are immersed in a dilute aqueous solution at 25°C and taking the parameters to have the indicated typical values. 

A direct measurement of surface tension is sometimes possible from the work of cleaving a crystal. Mica, in particular, has such a well-defined cleavage plane that it can be split into large sheets of fractional millimeter thickness. Orowan... 

Fig. X-7. Advancing and receding contact angles of octane on mica coated with a fluo-ropolymer FC 722 (3M) versus the duration of the solid-liquid contact. The solid lines represent the initial advancing and infinite time advancing and receding contact lines and the dashed lines are 95% confidence limits. (From Ref. 75.)...

Fig. XI-12. End-on view of the layer structures of clays, pyrophillite, and mica. (From Ref. 163.)...

The structurally similar molybdenum disulfide also has a low coefficient of friction, but now not increased in vacuum [2,30]. The interlayer forces are, however, much weaker than for graphite, and the mechanism of friction may be different. With molecularly smooth mica surfaces, the coefficient of friction is very dependent on load and may rise to extremely high values at small loads [4] at normal loads and in the presence of air, n drops to a near normal level. 

Klein and co-workers have documented the remarkable lubricating attributes of polymer brushes tethered to surfaces by one end only [56], Studying zwitterionic polystyrene-X attached to mica by the zwitterion end group in a surface forces apparatus, they found /i < 0.001 for loads of 100 and speeds of 15-450 nm/sec. They attributed the low friction to strong repulsions existing between such polymer layers. At higher compression, stick-slip motion was observed. In a related study, they compared the friction between polymer brushes in toluene (ji < 0.005) to that of mica in pure toluene /t = 0.7 [57]. 

The surface forces apparatus of crossed mica cylinders (Section VI-4D) has provided a unique measurement of friction on molecular scales. The apparatus is depicted in Fig. VI-3, and the first experiments involved imposing a variation or pulsing in the sepa-... 

Fig. XII-12. Top friction traces for two calcium alkylbenzenesulfonate monolayers on mica where the monolayers are in a liquidlike state. A—in inert air atmosphere B—in saturated decane vapor. Bottom contact radius-load curves showing adhesion energy measured under the same conditions as the friction traces. (From Ref. 53.)...

Derive Eq. XII-18. In an experiment using hexadecane and crossed mica cylinders, the circular flat contact area is about 10 cm in diameter and the two surfaces oscillate back and forth to the extent of 1 % of their diameter per second. The separation distance is 10 A and the yield pressure of the glue-backed mica is 0.1 kg/mm. ... 

The flotation of mica has been correlated to the adhesion force measured from surface force (SFA—see Section VI-4) experiments although, to these authors, it is clear that dynamic effects prevent an absolute comparison [69, 70],... 

Fig. XVin-3. AFM image of DNA strands on mica. Lower figure image obtained in the contact mode under water. The contrast shown covers height variations in the range of 0-2 nm. Upper figure observed profile along the line A-A of the lower figure. (From S. N. Magnov and M.-H. Whangbo, Surface Analysis with STM and AFM, VCH, New Yoric, 1996.)...

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