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pend upon the structure of the organic cation and the manner in which it is adsorbed upon the silicate surface. This dependence is elaborated into a method for the determination of molecular “thickness” for van der Waals adsorption. The structures of several molecules were studied by this method. It WM shown that fluorene and the purine bases adenine and guanine are “plane” molecules. A structure also was found for the nucleosides guanosine and adenosine, in which the plane of the ribofuranose ring is approximately parallel to that of the purine base. REFERENCES (1) GIESEKING, J. E.: Soil Sci. 47, 1 (1939). J. M., AND HOLIDAY, E. R.: J. Chem. SOC.1936, 765. (2) GULLAND, (3) GIJLLAND,J. M., A N D ROBINSOS,R.: J. Chem. SOC.128, 980 (1923). (4) HENDRICKB, S. B., AND ALEXANDER,L. T.: Soil Sci. 48,257 (1939). R. A., AND ALEXANDEE, L. T.:J. Am. Chem. SOC. (5) HENDRICKG, s. B., NELSON, 62, 1457 (1940). (6) HOFMANN, U.: Ergeb. exakt. Naturw. 18, 229 (1939). U.,ENDELL, K., AND WILM,D.: Z.Krist. 88,340 (1933). (7) HOFMANN, (8) IBALL, 3.: Z. Krist. 94, 397 (1936). , (9) LEVENE, P. A., AND BASS,L. W.: Nucleic Acid. The Chemical Catalog Company, Inc., New York (1931). These authors write the keto formula for guanine, as does also T. B. Johnson in Organic Chemistry (H. Gilman, Editor), Vol. 11, p. 1003. John Wiley and Sons, Inc., New York (1938). (10) PAULING, L.: The Nature of the Chemical Bond, pp. 174-8. Cornel1 University Prese, Ithaca, New York (1939). A discussion of van der Waals radii. (11) SMITE,C. R.: J. Am. Chem. SOC.66, 1561 (1934). (12) STOSICK, A. J.: J. Am. Chem. SOC.61, 1127 (1939).
STUDIES IN T H E DEGREE OF DISPERSION OF T H E CLAYS. IV
THESHAPESOF CLAYPARTICLES” * C. E. MARSHALL Department of Soils, Missouri Agricultural Ezperiment Station, Columbia, Missouri Received J u l y 3, IS@
The importance of particle shape was emphasized in the first paper of this series (6),which was concerned chiefly with the accuracy of the twolayer method for the centrifugal mechanical analysis of the clays. Since then many papers have been published on the crystal structures of the 1 Presented a t the Seventeenth Colloid Symposium, held a t Ann Arbor, Michigan, June 6-8, 1940. Contribution from the Department of Soils of the Missouri Agricultural Experiment Station, Journal Series No. 706.
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clays. In these the presence of a layer lattice is inferred from the similarity to other minerals showing ready basal cleavage. Frequently, therefore, we tacitly assume that clay particles too small to be measured visually as individuals are also platy in character. The purpose of the present pawr is, firstly, to show how far qualitative observations are in accord with this view,. secondly, to develop a method for the characterization of platy particles, and thirdly, to correlate the optical and electrical properties of clay particles with their morphology. I. QUALITATIVE OBSERVATIONS
A . U s e of the ultramicroscope The scintillation of rod- or plate-shaped particles in the slit ultramicro8cope has often been noted. It is due to great variation in the light diffracted from the particles as they turn into different orientations with respect to the incident beam. When the Szegvari diaphragm is used, the cardioid ultramicroscope shows the same effect. Clay particles whose settling velocities in water correspond to equivalent spherical diameters of from 2 p to 200 mp scintillate very well. This is true in particular of kaolinite, halloysite, beidellite, montmorillonite, and illite. Smaller particles down to the limit of resolution of the instrument are practically indistinguishable from spheres. In Part I ( 6 ) such observations led’to the conclusion that below 500 mp the particles were less markedly plate-shaped than those in the range of 2 p to 500 mp. However, it now seems more probable that the uniform appearance of the smaller particles is due rather to the extremely rapid Brommian movement of rotation. The Brownian movement of rotation of plate-like particles has not been evaluated mathematically. Microscopic observations on fine silt (10 p to 2 p ) and coarse clay (2 p to 1 p ) fractions of micaceous minerals indicate that the rotations about axes in the plane of the plates are very sluggish for particles whose equivalent spherical diameter is 4 p, whatever their linear dimensions. The fraction 2 p to 1 p , however, displays vigorous rotational movement. These observations agree qualitatively with the Einstein equation for spheres
where A is the angular displacement during an interval t, q is the viscosity of the liquid, and r is the radius of the sphere. The rotational displacement increases much more rapidly with diminishing particle size than does the translational displacement, for which the corresponding equation is
D”
RT
t
67rNqr
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We may conclude, therefore, that it is entirely reasonable to expect such high rotational displarements for particles less than 200 mp in equivalent spherical diameter that the scintillations in the ultramicroscope occur too rapidly to be observed by the eye. Thus, their appearance affords no certain guide as to shape. B. Experiments on dityndallism
As one would expect, the orientation of non-spherical particles in suspension produces variations in the intensity of the diffracted Tyndall beam. Diesselhorst and Freundlich (3) studied this dityndallism, using orientation by flow in a rectangular cell, and established the fact that both rods and plates tend to orient themselves so that their longer axes lie approximately in the stream lines of the liquid. By changing the direction of the light beam in relation to the lines of flow, they showed how it is possible to distinguish between rods and plates. It is by no means certain, however, that this apparatus would draw a clear-cut distinction between short rod-shaped particles and platy ones. I n the ideal case of flow between two large parallel plates there would seem to be no reason why rods should orient themselves in the direction of flow. They should simply lie in the stream lines, which are planes parallel to the two walls. In the actual apparatus devised by Freundlich, where the width of the cell is only about five times the distance between the plates, the lines of equal flow probably form surfaces approximating cylinders of elliptical cross section. In such an apparatus long rods would naturally set themselves more or less as they would in a circular tube, that is, with their axes parallel to the walls, phereas short rods might be expected to show good orientation at the sides of the cell and poor orientation in the middle. These considerations led to the study of dityndallism in flowing systems where the stream lines are circular cylinders. Because of the optical difficulties encountered with systems flowing inside glass tubes, it was decided to use jets of liquid projected from circular tubes into a large bulk of liquid contained in a rectangular cell. The Tyndall effects were investigated by using a narrow beam of light of rectangular cross section which could be focussed on any part of the jet. Figure 1 shows the experimental arrangement. The perfection of orientation a t different points in such a jet will depend on the rate of shear, which is zero a t the center of the tube and increases linearly to 2v/r at the wall (T being the radius of the tube and v the linear velocity of the liquid at the center). The movement of the jet in the surrounding liquid will modify the quantitative aspects somewhat, but the essential symmetry will remain unchanged. Thus a beam passing centrally through the jet at right angles will traverse regions of widely differing rates of shear, whereas one passing only through the outer portions of
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the jet will experience the maximum rate of shear and the least variation in rate of shear. Most of the observations therefore were made in a horizontal plane intersecting the jet a t about $r above the center. The depth of the beam was about tr. With rod-shaped particles of vanadium pentoxide this arrangement showed very marked increase in brightness over all the illuminated section of the jet when the liquid moved through the tube. Upon illumination parallel to the jet, by turning the cell through go", a corresponding decrease in intensity compared with that of the stationary liquid was observed. These effects agree well with a parallel orientation of rods along the stream lines. In the case of disc-shaped particles it is obviously impossible for the whole flat particle to be in the cylindrical surfaces of equal velocity, and the question arises whether the preferred orientation will be tangential. If it were, then the appearance of the Tyndall beam in the flowing jet
FIQ.1. (a) and (b), optical arrangement for observation of dityndallism; (o), enlarged view of jet with focussed beam.
should be roughly m follows: At the center of the horizontal beam tpe discs would all lie horizontally, that is, the diffracted light would be a t a minimum and it should be distinctly less intense than in the sol a t rest. Where the beam impinges on the outer portion of the jet, the appearance will depend on its height above the center. In the central plane itself the light diffracted near the edge of the jet should be brighter than in the liquid a t rest and it should diminish as the plane of illumination moves upwards until, when the latter just grazes the jet, the intensity should be less than in the liquid a t rest. A considerable number of fractions of the clay minerals kaolinite, halloysite, beidellite, montmorillonite, and illite were examined in this apparatus, using a jet 1.5 111111. in diameter and flow rates up to 20 cc. in 8 sec., which corresponds to a mean linear speed of 140 cm. per second (near the critical velocity for a tube of this width). The orientation effects u-ere difficult to observe with fractions less than 100 mp in equivalent spherical diameter, but could just be detected a t the highest speed. The larger particles showed orientation much more easily, as anticipated. In all cases, however, the central portion, instead of decreasing in intensity, remained of
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85
approximately the same intensity as in the sol at rest. At the sides there was a well-marked increase in intensity. These observations suggest either that it is not possible to obtain a perfect alignment of platy particles tangential to the stream lines or else that the clay particles are ,distinctly lath-like in shape. The fact that different clay minerals and different fractions show exactly the same qualitative effect would tend to favor the former view. The Tyndall effects accompanying the electrical orientation of clay particles have also been investigated, but since they throw little direct light on particle shape they will not be considered here. 11. THE DETERMINATION OF AXIAL RATIOS
A . Thewy It is clear that in any attempt to determine quantitatively the mean shapes of clay particles we must rely on the results of qualitative experiments such as those described above, in order to make a reasonable choice of assumptions. Whatever these may be, the results will merely represent a nearer approximation to the truth than our customary descriptions in terms of equivalent spherical diameters. In what follows, we shall make the convenient assumption that the particles may be regarded &s flattened ellipsoids of rotation. For such particles Miiller (8) has worked out the hydrodynamic theory, and the author (6)in Part I of this series has shown how his equations may be used to develop a modified form of Stokes' law for the settling of such particles in random orientation. The equation takes the form: 2 ab(D -d)g
'=g
Fq
where v is the mean settling velocity for random orientation, a and b are the axial lengths of the ellipsoid, D aLld d are the respective densities of solid and liquid, g is the gravitational constant, q is the viscosity of the liquid, and F is a shape factor which has been shown to remain practically constant at 0.945 for all ratios of a: b between 1:2 and 1: rn . For movement in a centrifuge running at N revolutions per second, from a point z1 from the axis of the machine to the point 22 the corresponding equation will be Fqlog10
t=
52
3.81 abNZ(D-d)
t being the mean time taken by the particles in traversing the distance from 21 to 52. For small particles ( < 1 p ) the assumption of random
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orientation should hold reasonably accurately in the centrifugal fields employed for quantitative work. In order to evaluate a and b for particles of the same settling velocity it is necessary to use some other equation.connecting a and b. A convenient choice is that giving the volume ( V ) of the ellipsoid, V = nab2. The meali volume can easily be determined by ultramicroscopic count, provided the density of the solid and the weight concentration of the suspension are known. The combination of this equation with either of those preceding enables us to determine b and a. The accuracy of such a method c'epends largely on its application to fractions with a narrow range of settling velocity. Given an accurate mean settling velocity, the per cent errors in a and b will be sensibly ecpal to those of the ultramicroscopic counts.
+
B. The preparation of clay fractions The method which seems particularly well adapted to the preparation of comparatively monodisperse fractions of the clays is the two-layer method. As originally described for the tube centrifuge (6),it is possible to obtain quantitatively in a single operation a clean separation a t any chosen equivalent diameter from 1 p to 100 mp. For instance, starting with the total clay fraction 2 g, one such separation gives the fractions 2 p-500 mp and < 500 mg. Repetition of the procedure on this last fraction, using a higher centrifugal field, gives the 500-200 mp and
