摘要:

CONTENTS vii PAGE IV. Viruses- Some Physicochemical Properties of Spontaneous Mouse Encephalomyelitis Virus, Strain Fa. By H. Leyon . . 217 By R. Markham . . 221 Physicochemical Studies of the Turnip Yellow Mosaic Virus. The Place of X-ray Diffraction Methods in the Estimation of the Size and Mutual Arrangements of Colloidal Particles. By J. D. Bernal and C. H. Carlisle . . 227 The Fine Structure of Protoplasm in Healthy and Virus-diseased Cells. By Ralph W. G. Wyckoff . . 230 Variations of the Size and of the Size Distribution of Tobacco Mosaic Virus Particles depending on the Method of Prep- aration. By J. Baudet, 0. Croissant, D. G. Dervichian, M. Joly and J. Moss& * 236 L GENERAL DIscuss1oN.-Dr. G. Oster, Dr. P. Johnson, Dr. R. Markham, Dr. D. D. Eley, Dr. C. E. Challice, Dr.R. D. Preston, Dr. H. Leyon, Dr. M. H. F. Wilkins, Dr. M. Joly . 247CONTENTS vii PAGE IV. Viruses- Some Physicochemical Properties of Spontaneous Mouse Encephalomyelitis Virus, Strain Fa. By H. Leyon . . 217 By R. Markham . . 221 Physicochemical Studies of the Turnip Yellow Mosaic Virus. The Place of X-ray Diffraction Methods in the Estimation of the Size and Mutual Arrangements of Colloidal Particles. By J. D. Bernal and C. H. Carlisle . . 227 The Fine Structure of Protoplasm in Healthy and Virus-diseased Cells. By Ralph W. G. Wyckoff . . 230 Variations of the Size and of the Size Distribution of Tobacco Mosaic Virus Particles depending on the Method of Prep- aration. By J. Baudet, 0. Croissant, D. G. Dervichian, M. Joly and J. Moss& * 236 L GENERAL DIscuss1oN.-Dr. G. Oster, Dr. P. Johnson, Dr. R. Markham, Dr. D. D. Eley, Dr. C. E. Challice, Dr. R. D. Preston, Dr. H. Leyon, Dr. M. H. F. Wilkins, Dr. M. Joly . 247

ISSN:0366-9033    

DOI:10.1039/DF95111FX001

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

GENERAL DISCUSSION Adam, N. K., 150. Alexander, A. E., 150. Bamford, C. H., 208. Barkas, W. W., 86, 210. Baudet, J., 236. Berg, Van den, 147 . Bernal, J. D., 227. Brindley, G. W., 75. Bruijn, H. de, 86. Butler, J. A. V., 153, 154. Carlisle, C. H., 227. Challice, C. E., 248. Cleverdon, D., 90, 94, 215. Cohen, M., 117. Croissant, O., 236. Dervichian. D. G.. 237. AUTHOR INDEX* Liische, A., 85. MacArthur, I., 148, 152, 207, 211, 217. Mardles, E. W. J., 43. Markham, R., 221, 247. Matalon, R., 117. Matthews, J. B., 91, 95. Moss&, J., 236. Neale, S. M., 89, 157. Nieuwenhuis, K. J., 212. Nissan, Alfred H., 15, 87. Olphen, H. Van, 82. Oster, G., 107, 152, 216, 247, 250. Park, G. S., 154, Philippoff, W., 96. Preston, R. D., 165, 209. 248. Dryden, I. 'G. C.,'28, 89, 91. Eirich, F., 135, 152.Eley, D. D., 247. Enoksson, B., 211. Eveson, G. F., 11. Fournet, G., 121. Fuoss, Raymond M., 125. Glueckauf, E., 154. Goring, D. A. I., 151. Hillier, James, 55. Howard, G. J., 153. Huxley, H. E., 148. Hyde, A. J., 150. Johnson, P., 151, 179, 216, 247. Joly, M., 214, 215, 216, 236, 250. Jordan, D. O., 153. Kamath, P., 135. Kitt, G. P., 154. Kratky, O., 171. Landolt, H. R., 179. Leyon, H., 217, 249. . - . Puddington, I.'E., 43. RBnby, B. G., 88, 89, 158, 208, 210, Rapson, H. D. C., 92, 94. Rideal, Sir Eric, 9. Riley, D. P., 95, 107. Rosen, B., 135. Schauenstein, E., 171. Schulman, J. H., 117, 147. Sikorski, J , , 209. Smith, P. G., 94. Stainsby, G., 150. Stevenson, Peter Cooper, 55. Szent-Gyargyi, A., 199, 213. Turkevich, John, 55. Ward, Stacey G., 11.Weibull, Claes, 195. Whitmore, R. L., 11, 94. Wilkins, M. H. F., 207. 214, 250. Williams, P. S., 47, 94. Winsor, P. A., 205. Wyckoff, Ralph W. G., 230. 211. * The references in heavy type indicate papers submitted for discussion.GENERAL DISCUSSION Adam, N. K., 150. Alexander, A. E., 150. Bamford, C. H., 208. Barkas, W. W., 86, 210. Baudet, J., 236. Berg, Van den, 147 . Bernal, J. D., 227. Brindley, G. W., 75. Bruijn, H. de, 86. Butler, J. A. V., 153, 154. Carlisle, C. H., 227. Challice, C. E., 248. Cleverdon, D., 90, 94, 215. Cohen, M., 117. Croissant, O., 236. Dervichian. D. G.. 237. AUTHOR INDEX* Liische, A., 85. MacArthur, I., 148, 152, 207, 211, 217. Mardles, E. W. J., 43. Markham, R., 221, 247. Matalon, R., 117. Matthews, J. B., 91, 95. Moss&, J., 236.Neale, S. M., 89, 157. Nieuwenhuis, K. J., 212. Nissan, Alfred H., 15, 87. Olphen, H. Van, 82. Oster, G., 107, 152, 216, 247, 250. Park, G. S., 154, Philippoff, W., 96. Preston, R. D., 165, 209. 248. Dryden, I. 'G. C.,'28, 89, 91. Eirich, F., 135, 152. Eley, D. D., 247. Enoksson, B., 211. Eveson, G. F., 11. Fournet, G., 121. Fuoss, Raymond M., 125. Glueckauf, E., 154. Goring, D. A. I., 151. Hillier, James, 55. Howard, G. J., 153. Huxley, H. E., 148. Hyde, A. J., 150. Johnson, P., 151, 179, 216, 247. Joly, M., 214, 215, 216, 236, 250. Jordan, D. O., 153. Kamath, P., 135. Kitt, G. P., 154. Kratky, O., 171. Landolt, H. R., 179. Leyon, H., 217, 249. . - . Puddington, I.'E., 43. RBnby, B. G., 88, 89, 158, 208, 210, Rapson, H. D. C., 92, 94. Rideal, Sir Eric, 9. Riley, D. P., 95, 107. Rosen, B., 135. Schauenstein, E., 171. Schulman, J. H., 117, 147. Sikorski, J , , 209. Smith, P. G., 94. Stainsby, G., 150. Stevenson, Peter Cooper, 55. Szent-Gyargyi, A., 199, 213. Turkevich, John, 55. Ward, Stacey G., 11. Weibull, Claes, 195. Whitmore, R. L., 11, 94. Wilkins, M. H. F., 207. 214, 250. Williams, P. S., 47, 94. Winsor, P. A., 205. Wyckoff, Ralph W. G., 230. 211. * The references in heavy type indicate papers submitted for discussion.

ISSN:0366-9033    

DOI:10.1039/DF95111BX003

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

SIZE AND SHAPE FACTOR IN COLLOIDAL SYSTEMS GENERAL INTRODUCTION BY SIR ERIC RIDEAL Received 18th July, 1951 Since many of the macro properties of colloidal systems are largely determined by the size and shape of the colloidal particles constituting the system, it is clearly important in attempting to establish the exact relationship to have precise knowledge of the size and shape of the ultim- ate particle. Indeed those who have read that intriguing work of the late Prof. D’Arcy Thomson may be persuaded that the secret of many biological forms may be determined to a great extent by the surface forces and thus can be elucidated by such an enquiry as we are proposing to hold in the next few days. Our enquiry is not simplified by the fact that there is a large variety of colloid systems each requiring its own method of analysis.In principle the simplest type consist of the suspensions which are not affected by the suspension medium, the hydrophobic colloids. Of these the uniform spherical particle system at infinite dilution is the prototype. Here the laws of Einstein for uncharged, and of Smoluchowski for charged, particles are rigorously true. If the particles are liquid and not solid the viscosity of both the suspension and dispersion medium as shown by Sir Geoffrey Taylor have to be considered. Very small par- ticles may well present their own problems, thus the relationship between crystal lattice energy and surface energy may be an important factor in determining this form. where A is the density, L the latent heat per gram and y the interfacial surface energy, the limiting radius r below which the particles of a crystall- izable solid may be spherical is evidently Y = 3y/AL.Inserting some approximate values y = 1000 ergs/cm.a, A = 3, L = 1010 ergsjg. we obtain r = 10 A. Nuclei in crystallization may be of this order of size. We shall be hearing a valuable contribution on the interactions and growth processes of colloidal gold during this session and one recollects that methods of measuring the size by metal plating in conjunction with the electron microscope permit us to get some idea of the shape and to determine the size of even very small nuclei or particles. Modification in the simple laws for the viscosity and rates of sedimentation arise both as the spherical particle concentration rises and also if the particles are non-uniform in size.One might mention the work of Wigner on the settling rates of particles non-uniform in size and the passage of liquids through packed particles studied by Carman. Both the viscosiw of concentrated suspensions and the problem of analysis by sedimentation are dealt with in this Discussion. The simplicity of the viscosity relation- ship found for the flow of a concentrated suspension of glass spheres is indeed remarkable. We attain the next stage in complexity when we come to deal with anisodimensional particles, the disc and the rod being the two forms most susceptible to analytical treatment. The viscosities, birefringence, Brownian agitation and rates of sedimentation are the usual experimental methods of attack.For more concentrated suspen- sions, methods involving light scattering, and for still more concentrated suspensions, X-ray and electron diffraction methods of examination have If we equate these free energies $ d A L = 47Nay, A 9I 0 GENERAL INTRODUCTION been employed. The extension of the axial ratio of the hypothetical ellipsoid for rod-like particles to large values, as given in the fibrous particles, involves at some point consideration of the extent of the con- tribution of the Brownian movement to orientation in a system under flow and of the flexibility under molecular bombardment of the rod-like or ribbon-like, or in many cases, helical particle. In highly concentrated solutions the stratified layers, like Schiller forms as found in goethite and the influence of charge and electrolyte on the layer separation are problems of some interest to the geologist whilst the biologist is frequently con- fronted with non-spherical forms where asymmetric particles are packed into a flexible membrane. The behaviour of the rod-like particle has of recent years received special attention due to the development of interest in the behaviour of polymers.Here it appears that the interaction of the solvent with the particle cannot be neglected since simple dispersions, at least for polymers of reasonable molecular weight, cannot be obtained except in what Mark has termed very good solvents, for in bad solvents, as defined by the interaction term p, the polymer-polymer contacts cannot be neglected even in very dilute solution and, as one of the contributors points out, are factors in the size distribution of virus.The interpretation of viscosity concentration curves in terms of polymer-polymer contacts, flexibility, and free or no draining through a coiled thread has each its own protagonists. Papers in this Discussion are devoted to the flexibility of polyelectrolytes, the extension of which is controlled to a large extent by the charge in the system. It seems probable that the size of the highly cross-linked systems such as the sols of the hydrous oxides must likewise vary as the charge on the particles is varied, since this factor is all important in the macro gel form where the ionic distribution follows the laws laid down by Donnan and the swelling is conditioned by the resulting osmotic pressure ; the surface extensions due to charge repulsion first postulated by Tolman seem to be a negligible factor.Finally’ we have to consider the methods for determining the size and shape of those particles which are formed as a result of association and dispersion equilibrium with simpler units in the environment. The ionic soap micelle is perhaps the system to which most attention has been given, both number of molecules, extent of charge and configuration dependence on molecular structure and temperature and salt content are all important variables. We have increasing evidence that systems other than the molecular amphipathic soap systems can undergo associ- ative equilibria, many of the proteins within their pH stability limits ma3’ consist of such systems both several varieties of virus and some streptococci appear to behave in a similar manner. In any discussion on size and shape of colloidal systems some attention should be paid to co-operative effects, the tactoids, Schiller layers, coacervate gels and thixotropic systems ; all represent forms definable in terms of colloidal equilibrium. It is in this field that closer analysis of the forces operative is highly desirable. The separation of a binary polymer-solvent solution into a two-phase system is not necessarily the result of the operation of long-range forces but the thermal and entropy terms are such that the two phases can be in true thermodynamic equilibrium. Evidence for this point of view is strengthened by’ the growing number of cases in which the interaction term generally symbolized as p has been determined in a variety of ways to yield identical values. Dept. of Chemistry, University of London King’s College, Strand, W.C.2.

ISSN:0366-9033    

DOI:10.1039/DF9511100009

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

I. CLASSICAL COLLOIDS THEORY OF SIZE DISTRIBUTION ; PAINTS, COALS, GREASES, ETC. ANOMALOUS VISCOSITY IN MODEL SUSPENSIONS BY G. I?. EVESON, STACEY G. WARD AND R. L. WHITMORE Received 6th April, 1951 An investigation has been made of the conditions in which the stress-strain relationship for stable suspensions of hard, discrete, non-interacting spherical particles in a Newtonian liquid is dependent upon the size distribution of the dispersed phase. Stable suspensions of spherical particles were found to behave as Newtonian fluids up to solid concentrations of a t least 20 yo by volume when the dispersed phase possessed a continuous size-distribution curve. In cir- cumstances where effects other than those due to physical interaction between particles were eliminated , stable suspensions of spherical material composed of varying proportions of two closely-sized fractions, the average diameters of which were widely different, behaved as anomalous fluids a t solid concentrations greater than 7.5 yo by volume over the range of shear rate investigated.At a given rate of shear they behaved similarly to suspensions of the large spherical particles in a liquid consisting of a suspension of the small particles. This non- Newtonian behaviour cannot at present be satisfactorily explained but i t ap- pears that the aggregate surface area and the degree of packing of the dispersed phase have no influence upon the relative viscosity. Detailed investigations of the rheological properties of suspensions have been made by’ a number of workers.Vand,l using glass spheres in an aqueous solution, and Ward and Whitmore, using methacrylate- polymer spheres in a different aqueous solution, found the viscosity to be independent of the rate of shear at all concentrations up to 45 yo by volume. Robinson, 3 however, found that with glass spheres suspended in certain dispersion media there was a tendency for the viscosity to decrease slightly with increasing shear rate. He attributed the variation to either the slow absorption of moisture by the liquid or an increase in its molecular weight due to mechanical stress at the high rates of shear employed (roo to 640 sec,-1). Broughton and Windebank * found that suspensions of glass spheres in organic liquids behaved as Newtonian liquids when the particle size exceeded about 30 microns. Below this value some anomalous behaviour was observed which they attributed to floccula- tion of the spheres in the suspending liquid.The general conclusion to be drawn from the work of these investigators and others 6,6 is that small par- ticles and organic liquids are most likely to produce anomalous effects, presumably due to flocculation effects. All workers have used spheres possessing a continuous size distribution and although it has been shown that the size ratio may affect the viscosity at a given concentrationJ2 size distribution has not been found to influence their stress-strain relationships. An investigation has now been made of conditions under which the relation- ship is dependent upon the size distribution of the suspended spheres.lVand, J . Physic. Chem., 1948, 52, 300. I&:ard and Whitmore, Brit. J , A+pl. Physics, 1950, I , 286, 326. Robinson, J . Physic. Chem., 1949, 53, 1042. Broughton and Windebank, Ind. Eng. Chem., 1938, 30, 407. Green and Weltman, Ind. Eng. Chem. (Anal.), 1943, 15, 201. Pryce-Jones, Proc. Phil. SOC. Durham, 1947, 10, 427. 11I 2 ANOMALOUS VISCOSITY Experimental Viscosities were measured in a modified Couette-type instrument designed to measure the rheological properties of fluids a t low rates oi shear. The visco- meter turntable was in the form of the frustum of a cone fitting into the base of a Perspex outer cylinder, 3-46 cm. int. diam. and 11-4 cm. deep. This material was selected in order to reduce heat transfer from the suspension to the visco- meter turntable and to facilitate the visual alignment of the inner cylinders.These were of Distrene and were hollow so that they could be loaded with suf- ficient mercury to give them a density slightly greater than that of the suspen- sion to be measured. This construction brought their centres of gravity near to their bases and simplified their vertical alignment in the viscometer. Their weights were sufficiently small for phosphor bronze galvanometer suspension wires to be used without exceeding the permissible tensile loads. Several cylinders were made to give three annular gaps and to enable the measurement of their end corrections. A full description of the viscometer, its characteristics and its calibration have been given elsewhere.' The instrument was set up in a room the air temperature of which could be controlled a t 25O f 1°C.Water from a thermostat was circulated through a jacket surrounding the outer cylinder at 25-2O C in order to maintain the sus- pension at 25' f 0-05OC. The viscometer was calibrated with each inner cylinder over a viscosity range of 1-4 to 18.6 centipoises and a shear-rate range within the limits of 0.04 and 1-2 sec.-l. The calibration liquids consisted of water-glycerol solutions the viscosities of which had been determined in N.P.L. calibrated B.S. Ostwald-tube viscometers. The suspensions consisted of methyl methacrylate polymer spheres in an aqueous lead nitrate + glycerol solution of density equal to that of the par- ticles and a viscosity of 8-5 centipoises, 0.01 yo of Dispersol OG being added to inhibit flocculation. The raw polymer powder (manufactured under the trade name of Kallodoc) was dry- and wet-sieved on B.S.screens and the finest sizes elutriated. Two closely-sized fractions, 72-100 mesh and finer than 300 mesh were then selected, the coarse fraction being also separated a t a definite density in order to remove all spheres likely to float or sink in the final suspensions. It possessed a flat-topped size-distribution curve with a ratio of largest to smallest sphere of 1.4/1 and an average sphere diameter of 182 microns. The fine sample had a similar size distribution with a ratio of largest to smallest sphere of 1.8/1 and an average sphere diameter of 38 microns. Viscosity determinations were first made on each of the samples a t intervaIs of 2-5 yo by volume up to a concentration of 20 yo.The rate of shear was varied by a t least 3/1 a t each concentration in three or four steps up to 1.0 sec.-1 at the surface of the inner cylinder. Only one inner cylinder, giving an annular gap of 2 mm. was used, since previous experimental work had shown that the measured viscosity was independent of the gap width. Six mixtures of the two samples, containing 10, 33&, 50, 66$, 90 and 95 yo by weight of the coarse material, were then prepared. Micrographs of the mix- tures containing 10 and 50 yo of coarse material are shown in Fig. I and z re- spectively. Viscosity determinations were then made on each mixture under the same conditions as for the two closely-sized samples. Results The measured viscosities were corrected for end effects in the viscometer, from the calibration curve for the particular inner cylinder used, giving the apparent viscosity, and the volume concentration adjusted to correct for the absence of sphere centres in a layer along the walls of the viscometer equal to the radius of the spheres by the method adopted by Vand.1 It was found that only the suspensions containing a single-sized fraction, and 95 % coarse fraction with 5 yo fine, behaved as Newtonian liquids over the whole range of concentration investigated.The remaining five suspensions exhibited anomalous effects, their apparent viscosities decreasing with increasing rate of shear a t all solid concentrations exceeding about 5 yo. Fig. 3 shows the variation, a t various volume concentrations, for a suspension of a mixture con- taining 10 yo of coarse and 90 yo of fine material.The rate of change of apparent viscosity with shear rate (which is a measure of the degree of anomaly present) Eveson, Ph.D. Thesis (University of Birmingham, 1950). Eveson, Whitmore and Ward, Nature, 1950, 166, 1074.FSG. I. E’lG. 2. [ T U fuce p a p 12.G. F. EVESON, S . G. WARD AND R. L. WHITMORE 13 a t any one rate of shear was almost constant, a t corresponding volume con- centrations, for mixtures containing from 35 t o 65 yo of the coarse material and rather higher for mixtures containing 10 yo and go yo of the coarse material. This is shown in Fig. 4 for a rate of shear of 0.5 sec.-l. The variation, a t one rate of shear, of the relative apparent viscosity of mixtures containing various proportions of the two closely-sized fractions is shown in Fig.5 a t various volume concentrations. FIG. 4. Discussion The experiments described above are of particular importance in that they illustrate the possibility of producing anomalies in a suspension of dispersed spheres solely through the physical interactions between the particles. By altering the size distribution of a mass of chemically identical spheres the magnitude of the viscosity anomaly can be changed at will or eliminated entirely, The properties of the suspending liquid are unimportant so long as they do not interact chemically with the spheres,I 4 ANOMALOUS VISCOSITY flocculate them, or permit electrostatic charges to develop on them (see ref.(2)). It is impossible at this stage to offer an adequate explanation of the phenomenon but the recognition that anomalous behaviour may, in some cases, be due solely to physical interactions between the suspended particles offers a new line of approach to the problem in which micro- scopic and cin6 techniques might play an important part. Fig. 5 indicates an appreciable and systematic variation in apparent viscosity with changes in the relative proportions cf coarse and fine spheres in the suspensions at a given rate of shear. This is unlikely to be due to the effect of packing amongst the spheres as the condition of closest packing (which is most likely to give a minimum viscosity) is obtained, FIG. 5. for the particular spheres employed, with I yo of fine and gg yo of coarse material. Fig. 5 shows that in fact the minimum was obtained with about equal proportions of the two sizes. There is also no doubt that the aggre- gate surface area is not a significant factor. It is possible, however, that they behaved as suspensions of the large particles in a liquid consisting of a suspension of the small particles. Calculated values based on this hypothesis are represented by the broken lines in Fig. 5 and show a marked similarity to the experimental curves. Further experiments designed to test this interesting possibility would be of considerable theoretical and practical value. The authors’ thanks are due to Mr. H. Stanley for assistance in the experimental work and to Imperial Chemical Industries (Plastics Division) for gifts of plastic materials. Department of Mining, The University, Edgbaston, Birmingham I 5.

ISSN:0366-9033    

DOI:10.1039/DF9511100011

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

PARTICLE SIZE ANALYSIS FROM SEDIMENTATION CURVES BY ALFRED H. NISSAN Received 26th April, 1951 It is assumed that an accurate sedimentation curve has been obtained experimentally and i t is required to derive from this the frequency of occurrence of particles of stated ranges in dimension. This means (i) calculating a charac- teristic dimension for the particles and (ii) deriving the frequency of their oc- currence. Both calculations involve approximations. The calculation of the characteristic dimension is complicated by the shape factor and by hydrodynamic and mechanical interference. It is recommended that sedimentation studies should always be accompanied by direct visual observations of the dimensions and shape of the particles. Examples from sedi- mentation of paper-making fibres illustrate how combining direct observations with sedimentation studies can produce useful or interesting results.The graphical tangent intercept method of calculating the frequency is compared with an algebraic method using a polynomial derived with the aid of tables prepared by Fisher and Yates and with another graphical method. Subjective errors influence the graphical methods. 1. Introduction.-There are several methods by which sedimentation curves are obtained in practice.’ In the different methods available, practical difficulties are encountered and solved in a manner specific to each of them ; the aim of all, however, is essentially the same. This is to provide data showing the concentration of the suspended particles in the liquid at, above, or below one plane in the suspension, either con- tinuonsly, or discontynuonsly as time proceeds.In this paper it will be assumed that a smooth curve has been obtained, indicating, accurately, say, on the ordinate, the total weight W which has settled through a height H, after time T and the corresponding values of T on the abscissa. It is then necessary t o deduce from this primary sedimentation curve an- other with the abscissa showing some characteristic dimension by which the particle size will be indicated, and the ordinate showing the weight or the percentage of the total particles with dimensions lying between the limits indicated on the abscissa. Thus the problem resolves itself into two : (i) to calculate from the time scale T a linear dimension Y, by which to characterize particle size ; and (ii) to deduce from the total weight sedimented W, that quantity of the material w with dimensions equal to or greater than Y.It would then be possible to plot either a cumulative curve of w against r, or a frequency curve (or a histogram) of (wj - wd) against (rj + vc)/2. Both conversions involve approximations which will be the specific study of this paper. 2. To Calculate a Linear Dimension of the Particle from the Time T.- In practice most methods of converting T into r rely on Stokes’ law. This states that a single rigid sphere of radius Y and density ps falling at slow speed (i.e. with Reynold’s number < I) in an infinitely extended viscous fluid of viscosity p and density p L will sediment through a height H in time T according to = [9PW2g(Ps - P L ) W .. (2.1) 1 Dallavalle, Micromeritics (Pitman and Sons Ltd., London, 1948). The Examination of Fragmental Rocks (Oxford University Press, 1939). wood, Tyans. Inst. Chem. Rng., rg47,25, (Suppl.), 14. Tickell, Hey- Oden, Soil Sci., 1925, 19, I . 1516 SEDIMENTATION CURVES Thus, in practice, each of the particles is assumed to follow Stokes' law and T is converted into r by means of (2.1). For smooth spheroids, or even polyhedra, suspended in very low concentrations in a wide vessel, eqn. (2.1) yields an excellent characteristic of the particle size as it gives the hydrodynamically equivalent sphere which is not very different from the sphere of the same volume and density as the particle.a For particles departing materially from the spherical shape and suspended in concentra- tions above certain limiting values, eqn. (2.1) still gives an " equivalent sphere ", in a certain hydrodqaamic sense, but the correlation of this sphere with the dimensions of the particles becomes somewhat problem- atical and, sometimes, even misleading.(a) THE SHAPE FACTOR.--When one of the principal dimensions of the particle is large compared with the others, eqn. (2.1) is not the ap- propriate one to use. gives explicit formulae and graphs to be used with ellipsoids of revolution and elliptical plates moving with their principal dimensions at different orientations with respect to the direction of the stream. For the derivation and limitations of these equations, either Lamb 8 mag be consulted for the usual authoritative and critical treatment of the subject or original papers4.g.Davies 4 or Gans 6- may be found instructive. An important point in the treatment of elongated bodies is that the resistance to motion of these bodies when they are moving at a uniform relative speed with respect to the fluid has been determined and, therefore, the radius of an equivalent sphere which has the same resistance as the body and not the same terminal speed is calculated. If the velocity HIT is determined experimentally and eqn. (2.1) is used, the value of Y so calculated is the radius of the sphere with the same terminal speed. To obtain the radius of the sphere with the same resistance as the particle, (2.2) should be used. Davies where R = radius of sphere of same resistance as the particle V = the volume of the particle as it sediments.= 3 Vl477e It is then possible to correlate R with the principal dimensions of the particle by the use of the curves and equations given by Davies, which are of the general form for each attitude the particle takes with respect to the direction of fall, where a, b and c are principal dimensions of the particle. Before illustrating the use of eqn. (2.1) and (2.2) another point should be emphasized. It is always advisable, and almost always necessary, to carry out microscopical or other direct methods of observations of the dimensions of particles in conjunction with the indirect methods of sedi- mentation if mistakes in interpretations are to be avoided. This prin- ciple is of particular significance when very elongated particles are being studied.As will be presently illustrated by the sedimentation of cellulose fibres in water, when the calculated values are compared with observed rates of sedimentation it is possible to draw reasonable conclusions re- garding the state of the particles only when detailed microscopical exam- inations are carried out. In order to study the influence of shape and size of paper-making fibres on their sedimentation velocities, it was decided to observe the rate of settling and the principal dimensions of single fibres, and then to 3 Lamb, Hydrodynamics (Cambridge University Press, 1932)~ 6th edn., Rla = f(b/a, cla) . ' (2.3) Davies, Trans. Inst. Chem. Eng., 1947, 25, (Suppl.), 25. Davies, R o c . Physic. SOC., 1950, 43, 288.Gans, Ann. Physik, 1928, 86, 654. pp. 604-6.17.ALFRED H. NISSAN I 7 correlate the observations with theoretical predictions, as summarized and extended by Davies.* Accordingly a sample of kraft pulp was stained in an aqueous solution of Congo Red, suspended in distilled water, boiled for I hr,, and finally subjected in a desiccator to the vacuum produced by the water pump for a further hour. In this way, it was believed, and later proved, that the fibres were freed from air occlusions. The water suspension was then brought to 15" C. A few drops of the suspension were transferred by means of a dropping tube to a glass plate placed under a Greenough microscope. A teasing needle was used to extract one fibre by carrying a small drop of water at its tip in which the fibre was suspended, and the fibre was immediately transferred to the glass sedimentation cell.This was a rectangular parallelopiped, 3 in. x 3 in. x Q in. in dimensions, with a centimetre graticule fixed on one of its vertical 3 in. x 3 in. faces. The cell was full of boiled and cooled distilled water at 15" C. The fibre was allowed to fall z cm. and then its passage over the succeeding 4 cm. timed, and its mode of sedimentation noted. A large number of determinations has shown that approximately 95 yo of the fibres sediment vertically, with no oscillation, and with their length in a horizontal plane. One in 20 fibres, on average, fell with their length in an inclined attitude, making an angle of some 30' with the horizontal, though the sedimentation itself was still vertical and without oscillation.After the fibre had passed the timing marks it was extracted by means of a dropping tube and placed on a slide for microscopical examination. The length was measured, in the wet state, by means of a 16 mm. objective and a filar micrometer eyepiece giving a magnification of x 120. The width was similarly measured in the wet state with a 4 mm. objective and a filar eyepiece giving a magnification of x 480. To determine the thickness of the fibre, the wet fibre was taken off the slide and washed three times in industrial absolute alcohol on a spotting dish. The fibre was removed from the alcohol and dipped in paraffin wax kept just above its melting point. The diminutive candle so formed, still at the tip of the needle, was next embedded into a small amount of melted wax which was then rapidly cooled by immersing its container in cold water.The solid wax was mounted in a microtome and 5 micron sections made. These sections, mounted in liquid paraffin, were exam- ined under the microscope and the angle of the object holder adjusted until a true cross-section was obtained. The thickness was finally measured, using a 4 mm. objective, under a magnification of x 480. Fig. I shows a typical appearance of a fibre under the microscope ; the cross-section shown is at a higher magnification than the outside view. There were two obvious corrections to be made in this series of ob- servations : (i) for the wall effect on sedimentation velocity and (ii) for the effects of shrinkage of the cellulose fibre, caused by the alcohol treat- ment and wax solidification, on the measurement of the thickness.To determine the wall effect a number of single fibres, after preparation and treatment which were identical with those described above, were timed as they were allowed to sediment in the cell, then transferred to a 400 ml. beaker and their rate of fall timed again. The ratio of times was a direct measure of the wall effect as all other factors were the same. The fibres were subject to convection influences to a far greater extent in the wide beaker than in the cell but after a great many observations a mean was obtained for the ratio of the two velocities which is believed to be reasonably accurate. The magnitude of the wall effect was sur- prisingly high, considering that the fibre averaged only 0.2545 x 0.0046 xo-0012 cm., and the fact that very great care was always taken to place them in the middle of the sedimentation cell with the long axis of the fibre parallel to the face of the cell.The mean ratio of the rate of fall in the wide beaker to that in the cell was 1.65/1. All sedimentation rates in the cell were accordingly corrected by multiplying them by this factor.18 SEDIMENTATION CURVES Measurement of a number of fibres in the wet state and after washing them with alcohol showed that alcohol-dried fibre was 0.84 of the width of the wet fibre. Actually, the width of the fibre (b) as reported here was that of the water-wet fibre, and i t was only the thickness of the fibre (c) which was affected by the dehydration step of alcohol washing.However, assuming that the thickness of the fibre would exhibit the same proportion of shrinkage as was observed with the width, and taking into account the shrinkage of the wax on solidification, it was estimated that the thickness measurements is probably underestimating the thickness of the fibres by about 2 microns or 20 yo and accordingly the measured value was cor- rected by this amount. The density of the fibres was determined by suspending a mass of the same haft fibres in water and measuring their density by a weighing bottle method. The values obtained were 1.624, 1.614 and 1.633 giving a mean of 1.62. This value agrees with results obtained by Hermans6 after taking extreme precautions t o expel the air from the fibres. It was concluded, therefore, that the fibres were completely saturated with water. Table I gives the mean values for the measured and calculated dimen- sions of 20 fibres which survived the sectioning operation ; the means for the sedimentation velocity and for a and b apply to about 140 observations.,Ria '1' from Davies It will be noticed that 7, calculated by means of (2.1) is a very small fraction of the length Z of the fibre. It should perhaps be added that it is not a measure of the width of the fibre as a statistical analysis of the results showed a negative correlation coefficient between Y and b and that of only 0.236. Thus, the near equality between 2; and b must be ruled as fortuitous. and of 211b are, as expected, more reasonable than those of 7 and 2TlZ for such a long particle as a fibre.bTonetheless, the actual ratio of 2xb is nearly twice the predicted value and it becomes necessary to look for the reasons for this significant difference. The wall effect has already been discussed. Although, it is large, observations on about IOO fibres falling freely in a 400 ml. beaker full of water confirmed that the average value for the speed of fall of a fibre of average dimension given by Table I is of the order of 0.08 cm./sec., and this was nearly the corrected value used in Table I (i.e. 0.0517 x 1-65 = 0.085 cm,/sec.). Similarly, observations on several scores of the same fibres falling freely in N/IOO salt solutions in wide beakers confirmed these values as the fall in the salt solutions was of the order of 0.8 of the rate of fall in distilled water and this reduction could almost entirely be correlated with the observed shrinkage in the width b and the thickness c of the fibre. Thus it was concluded that HIT used in eqn.(2.2) for calculating was most probably of the right order of magnitude, The density of the fibre as measured gives a fictitious value. Dry cellulose gives a a Hermans, Physics and Chemistry of Celldose Fihres (Elsevier Publishing Co. Inc. 1949), p. 197 et seq. The values of It became necessary to look into the density of the fibre.FIG. I. [To face page 18.FIG. I. [To face page 18.ALFRED H. NISSAN density As it sorbs water there is an apparent shrinkage in total volume until a density of 1-62-1.63 is reached when further sorption of water results in a decrease in the density again.When the fibre density is measured by weighing it saturated with water and then when it is dry, it is the maximum density that is determined ; the effective density of the fibre when it is actually suspended in water, or falling through it, must of necessity be less. There are two ways in which water is held by the fibre (i) water in the lumen or canal of the fibre and (ii) water held within the cellulose wall of the fibre. It should, therefore, be possible either to determine the rate of fall of the fibre if the true effective density of the fibre is known or conversely to determine from the rate of fall, the true effective density and thence the amount of water sorbed in the wall. It is quite difficult to determine experimentally the amount of water in the fibre wall when it is fully saturated with water and, therefore, it was decided to use the sedimentation technique as a tool for this purpose. Obviously, from eqn.(2.2) and Table I, the effective density p8* bears a relationship to the measured density ps, given by Thus pa* comes out as 1-35 g./ml. The cellulose fibre reaches 1-62 g./ml. when it has sorbed water to the extent of 12-15 yo of its own weight or 0.20 of its own volume. After that the volume increases on sorption very nearly additively. Thus if x is the volume of water associated with I volume of dry cellulose, then : in helium equal to 1.53. (p8* - p L ) / ( p 8 - PL) = 0'24/0*42. 1.62 ( X - 0*2)/[I + ( X - 0*2)] = 1-35, X = 0.97.To determine the amount held in the fibre wall, it is necessary to subtract the quantity held in the lumen. Therefore, it became necessay to deter- mine the ratio of the volume of the lumen to that of the cellulosic wall. To do this it was essential to section the fibre in the wet state. The opera- tion of waxing the fibre without first drying it with alcohol, results in high rate of fibre losses, but after several attempts 20 sections were ob- tained. These were not truly cross-sections, as the control over the fibre was very poor, but they could still be used to evaluate, at least approxim- ately, the ratio of the volume of the lumen to that of the cellulosic wall. It was not possible to obtain photomicrographs as with dried sections ; instead they were projected on a white board and the outlines of the fibre were drawn around the projected image.A mm. grid was then used to measure the areas of the lumen and the walls. Fig. 2 gives the appearance of the 20 sections used, whilst Table I1 gives the data on the lumen and the wall areas and their ratios to one another. It follows that the volume of water held in the lumen per volume of dry cellulose is 1-97(0.2/1.2) = 0.33. Thus it may be concluded that the kraft fibre studied consists of I volume of cellulose associated with 0.33 volumes of water held in the lumen and 0.64 volumes of water sorbed in its wall, giving an effective density of 1.35 g./ml. These values are in accord with observations on water sorp- tion by cellulose made by other methods 7 and contradict any suggestion that paper-making fibres hold large amounts of water as " bound water " on their external surfaces.As the fibres were not beaten, consequently these conclusions must be limited to unbeaten kraft pulp. pact shapes of inert particles the effects of hydrodynamical interaction between the particles themselves and between the particles and the wall is to render the value of r in eqn. (2.1) in error by variable amounts (b) HYDRODYNAMICAL AND MECHANICAL INTERACTION.-with COm- Gallay, PuIjh Paper Mag. Can., 1950, 51, 115.2 0 SEDIMENTATION CURVES depending on the time T. The rea.son is that the concentration of the suspension starts at its maximum at the beginning of the experiment and decreases continuously with time until it reaches zero. (Brownian motion and diffusion are assumed to be negligible.For sedimentation of very small particles where these phenomena are significant, see Davies.8) Thus, the effect can be visualized either by imagining the viscosity to be decreasing with time, so that the larger particles settle in an effectively more viscous liquid than that in which the smaller particles are observed to settle, or alternatively to consider the viscosity as constant and imagine the larger particles to be settling with average speeds lower than that required by eqn. (2.1). Burghers,* Simha,l0 Vand l1 and others have succeeded in their attempts to evaluate the effects of the hydrodynamic TABLE I1 Fibre No. I 2 3 4 5 6 7 8 9 I0 I1 I 2 I 3 I 4 I5 16 I7 18 I 9 20 Area of Lumen (P2) 36'53 54'7 54'7 42.2 28-15 75'0 17-18 20.3 14-06 46-8 46.8 61.0 79'7 53'1 50.0 3 7'5 45'3 117.8 125.0 65.6 Area of Cellulose Wall ( P I 275'47 388-3 145'3 234.05 128.1 259'2 174'32 196.95 187.44 289.2 307'7 341'0 245'3 535'9 2 64-2 434'0 390'7 492'7 340'5 156.2 Total Area (P2) 3 I 2-0 443'0 276.25 156-25 334'2 191'5 217.25 201-5 3 36.0 354'5 402.0 325.0 589.0 314.2 471'5 436.0 610.5 465'5 221.8 200'0 I Mean - Ratio of Area of Lumen to Area of Wall 0.1 3 0.14 0.38 0-1 8 0.29 0.08 0-16 0.15 0.18 0-32 0.19 0.09 0.24 0'3 7 0.42 0'22 0'10 0'10 0'10 0'12 0'20 interaction of the particles with each other and with the walls on the motion of particles of simple geometric shape.The results are not in complete agreement with each other but it is apparent from these analyses that there is a significant effect on the rate of sedimentation when the total volume of the particles approaches 0.5 yo of the volume of the sus- pension.At this concentration spherical particles would sediment with a speed of the order of 0.967 to 0.987 l1 of that given by Stokes' law. Experimental results with simple systems coniirm the order of mag- nitude of these values. The large effect of the wall has already been demonstrated ; however, provided very wide tubes are used, or empirically determined corrections are introduced, the effects can be nullified. If accurate conversion of T into Y is required, the simplest procedure is to * Davies, Proc. Boy. Soc. A , 1949, 200, 100. Q Burghers, 2nd Report on Viscosity and Plasticity (Noord-Hollandsche Uitgeversmaatschappij, Amsterdam, 1938).p. 128 ; Nederl. Akad. Weten- schap$en P Y O C . , 19411.44, 1045 ; lo Simha, J . Colload Sca., 1950, 5, 386 ; J. Res. Nat. BUY. Stand., 1949, 42, 409, and several previous papers. 1941. 4.4, 1177 ; 1942, 45, 9 ; 1942, 45, 126- Vand, J . Physic. Chem., 1948, 52, 277.ALFRED H. NISSAN 21 limit, wherever possible, the concentration by volume of the suspended particles to a maximum of 0.1 yo. The effect of the hydrodynamic inter- action at this concentration is probably very much less than I yo reduction in sedimentation speed with most systems and the value obtained for Y would be in error, due to this cause by less than 0-5 yo. (It is assumed that the liquid chosen would not interact with the particle to produce solvation phenomena.) If the density of the solid material is of the order of D times the density of the liquid, i.e.p J p L = D, this limiting of the volumetric concentration to 0.1 yo would correspond to an upper limit of (0.1 x D) yo by weight. Where it is desirable to use higher concentra- tions and it is very often necessary to do so, eqn. (2.1) would have to be modified slightly. For concentrations less than I yo, probably the simplest procedure is to calculate the mean concentration from the beginning of the experiment to time T and to multiply Y by a factor in accordance with the following. Mean volumetric concentration of Factor to be used for correcting Y as particles from start to time T in yo I 0.5 0'1 calculated by (2.1) . . 1-03 1-01 1'00 The third significant figures of the correction factors given here are in some doubt and therefore it is not, as yet, possible to justify advocating a more elaborate and rigorous method of correction.For concentrations exceeding I yo, it is suggested that an empirical determination of the correction is first made and then applied. For particles which sediment completely-i.e. leaving a clear fluid-all that is necessary is to make two or three suspensions of the particles at various concentrations, but in- cluding one at a concentration less than 0-2 yo, and t o observe the initial rate with which the surface of the clear fluid travels. Assuming the concentration effect is independent of particle size the ratio of the retes in the low to the high concentration suspensions will be the reciprocal of the ratio of their effective viscosities.Thus the correction factor with which to multiply Y will be equal to the square root of this ratio. When long particles, such as paper-making fibres, are sedimenting, these purely hydrodynamic interactions may be completely masked by the effects of mechanical entanglements even at very low concentrations unless special precautions are taken to keep the fibres apart. The result of entanglement is, at first, to cause the fibres to sediment at a higher speed than they would have done singly, but with increased entanglement the whole mass may set solid ; cellulose fibres suspended in concentrations exceeding 0.5 yo will not normally sediment in a 2-1. measuring cylinder. Hydrodynamic interaction would cause the fibres to sediment at slower rates than they would do singly.Thus the results of mechanical and hydrodynamic interactions may be confusing, unless visual or other direct observations are made on the state of the suspensions and their mode of settling. To illustrate these points, the following observations might be found of some interest. Having established the behaviour of single fibres, it was decided to study their behaviour as they sedimented in the form of a swarm of very dilute suspension in a large amount of water. Accordingly, a kraft pulp was first divided into four fractions by wet sieving in a standard manner. Each of the four fractions was then examined microscopically in order that an average fibre length and average fibre width might be assigned to it. An average thickness for the fibre was then assumed to be equal to 1/2.6 of the width as was observed in the previous series of experiments.A dilute suspension of the fibre was then made as before by boiling and evacuating, and dispersion of the fibres was encouraged by adjusting the pH of the water to 5 by means of aluminium sulphate. About 0.5 ml. of the suspension, which held about 60 fibres on average, was transferred2 2 SEDIMENTATION CURVES to a 2-1. measuring cylinder filled with boiled and cooled distilled water at 15°C. The rate of sedimentation of the centre of the swarm of particles was observed. This procedure was repeated in triplicate and the mean taken as the average rate of sedimentation for the particular fraction. To illustrate the method of obtaining the average fibre length and width, Table 111 gives details of measurements on one of the fractions- that of kraft pulp passing through an approximately 80-mesh screen.45'45 27-27 7.66 6.70 5'74 7-18 IOO'OO -_II_ --- - (1 1 Intervals IIM. -~ 0'0-0'1 0'1 -0'2 0'2-0.3 0.3 -0.4 0.4-0.5 0-5-1.0 Totals Means 0.05 0.15 0.25 0.35 0.45 0.75 - - (4 No. of Fibres 95 57 16 I4 15 209 I2 -- - Average TABLE I11 2-272 j 4'0905 1-91 50 2'3450 2-5830 5'3850 -- 18.5910 0-19 132930 1012 I -- 92116 5 2 I 3 - 2 2 6 2 2 2 - - 1 1 2 2 6 - 1 1 - 2 4 2- 3 I- - I 1 5 4 1 2 1 (7) Average Width mm. o-01gr 0.0187 o.oz1g 090275 0.02 54 0.0297 0.8681 0.5099 0.1678 0.1843 0.2 I 32 2.089 I 0.1458 -- 0*0209 To obtain this table, a representative sample of some 500 fibres was taken, a dilute suspension made, and four slides each containing 70 to 80 fibres were mounted in an iodine stain after drying in air at 65' C.A Leitz microprojector was used to project the field on to the bench with a mag- nification of x roo. The length and width of 200 fibres were measured and then corrected for magnification. In Table IV are given the calculated and observed characteristics of the fibre swarms. These swarms were at a constant concentration of 0.0818 g. oven dry fibres per IOO g. of water just before they were dropped into the 2-1. cylinder of water. gives the radius of the sphere which would offer the same resistance as the average It will be remembered that TABLE IV ___ Characteristics bl (PL) . c (assumed = 5/26 as for Table I), (i) . Sedimentation speed (cm./sec.) .Density (assumed same as for single fibres) - (g. /ml. 1 - R:(E) - K/G . zR/a . 8 0 190 20.8 8.0 0.189 1'35 3-06 0.032 0'1 I Fractions 42 930 28.8 11'1 0.185 1-35 0.063 0.03 I 29.4 24 I 270 30'4 I 1-7 0.278 1-35 0.047 0.024 29-6 ~ + 24 2350 33'3 12.8 0'322 1'35 0.04s 0.014 56-6ALFRED H. NISSAN 23 fibre constituting the swarm. The calculated values of H come out very low for the particular values of for all the swarms. (Similar experi- ments with other types of fibres, i.e. sulphite and groundwood fibres, yield the same results.) A tentative explanation of this fact offered here is that the fibres are flocculating even in these extremely dilute suspensions and thus the resistance encountered is effectively reduced. Eqn. (2.2) obviously fails as knowledge of the effective volume V of the floc is necessary for its application.Extra work is needed but if tentatively the ratio of the width of the floc to its length is assumed to be 0.05 then the average volume of the floc to that of the fibre comes out approximately as (0.3/0.05)~/2 or 15/1 that is, on average each of the dimensions of the floc is 2.5 that of the average fibre. The experiments with the fibres are quoted to illustrate : (i) The necessity for extreme caution in the treatment of sedimentation results when elongated shapes are under study. (ii) The necessity for combining the indirect method of sedimentation analysis with some direct observation as a calibrating procedure for the sedimentation method. (iii) Some of the difficulties of applying sedimentation analysis to suspensions of elongated particles even in low concentrations.(iv) The often useful results obtainable when sedimentation analysis is coupled with a direct observation of the dimensions of the particles even when the sedimentation results on their own appear to be most confusing. 3. Determining the Frequency of Particles of a Size Range.-The second problem in analyzing the sedimentation curve is to deduce from it the frequency of particles between, say, ~j and rk equivalent radii. Here the complication is that “ fines ”, which are originally suspended at lower levels than the top datum surface, will settle, and contribute their quota to the total number or weight of particles observed to have sedimented to the bottom datum surface. Oden’s methods 1~ l2 are usually followed and of these the most popular, and the simplest, is the tangent intercept method.In this method, tangents are drawn to the sedimentation curves a t points the abscissae of which are ~ j , Yk, etc., to intercept the ordinate at wi, wkr etc. wj, wk, etc., then give the quantities in the units used for plotting the ordinates of particles with radii equal to or exceeding ~ j , Y ~ , etc. Thus (wj - wk) give the quantities of par- ticles with radii between ~j and yk. This method is normally all that is required but occasionally a little difficulty is experienced : in the initial stages where the curve is usually steep and also in the final stages where the slope does not change rapidly, the graphical determination of the tangent to the curve is occasionally problematical. Oden himself ap- preciated this difficulty for in a paper by Werner l3 which was com- municated by Oden, the undesirability of having to draw tangents is emphasized to the extent that an alternative experimental procedure, by which the particles are fractionated by size, is proposed in place of the ordinary sedimentation methods.However, the alternative procedure itself is not free from certain sources of errors. It was, therefore, decided to investigate the sort of errors encountered by using the tangent intercept method and also the possibility of eliminat- ing them. Such an investigation presupposes a standard by which the results of the tangent intercept method is to be judged and consequently a method of deriving w without serions error had to be established. The basis of the tangent intercept method is that for each point on the curve, w = ~ + T .d W l d T , . * (3.1) l2 Oden, Proc. Roy. Soc., Edin., 1916, 36, 219. l3 Werner, Trans. Faraday Sot., 1925, 21, 381.24 SEDIMENTATION CURVES where W is the total quantity sedimented at time T , and w that portion of the material with radii equal to or greater than the radius of the equi- valent sphere which would have sedimented through the experimental height H in time T. Therefore, the most accurate evaluation of w can be obtained by first obtaining an explicit numerical formula for the most accurate form of W = f ( T ) and then calculating w according to (3.2), w = f ( T ) - Tf’(T). . (3.2) As this problem essentially deals with the practically observed data on W and T, it resolves itself into a method of curve fitting so that the curve -and its equation-shall, on the one hand utilize all, or most, of the data and on the other shall give a minimum for the average error.I f f ( T ) is assumed to be a polynomial of ascending powers of T Fisher and Yates l4 provide a method and tables for its solution with three outstanding advantages: (i) the whole of the data, up to 75 observations can be utilized in an equation with a maximum number of terms of 6-i.e. up to a power of 5. (Anderson and Housemann l5 extend these tables to utilize 104 observations to the same number of terms.) (ii) The number of terms, up to a maximum of 6, to be taken in the polynomial is statis- tically determined, so that succeeding terms do not contribute signifi- cantly to the accuracy of evaluation of f ( T ) from T .(iii) The use of the tables gives the coefficients of a standard form of the equation which can be readily transformed to whatever form is necessary. On the other hand the method demands that (i) the variance of the dependent variate is the same for all values of the independent variate: (ii) the values of the dependent variate must all be of equal weight ; and (iii) the simplification that the ordinates shall be at equally spaced intervals. The first two requirements could be assumed and the third could be arranged by solving the equations in the form W = f(logl, T ) instead of f ( T ) and then obtain- ing (3.2) by the appropriate steps. This transformation is necessary because in sedimentation experiments it is necessary to take a larger number of readings per unit of time at the beginning of the experiment- when settling is rapid-than at the end.Therefore, a geometrical pro- gression in time is a useful way of meeting the requirements of experi- mental accuracy and precision and, simultaneously, the demands of solving the polynomial by using Fisher and Yates’ tables for an equally spaced set of abscissa values. It was, therefore, decided to use this method to provide a standard by which to judge the accuracy of the tangent intercept method. The errors of the tangent intercept method can arise from two causes where subjective judgment is exercised: (i) the original drawing of the sedi- mentation curve to pass smoothly through or between the experimental points, and (ii) the actual tangent drawing operation.It was decided, at the same time, to investigate which of these two was the greater source of variation in evaluating w from a given set of W and T values. There- fore, a method was evolved which still required a curve to be drawn, but which eliminated the step of tangent drawing by a system of suc- cessive approximation of the intercept arithmetically. This method which will be called the successive approximation method, will be de- scribed next so that results by all three methods can be studied together. The successive approximation method takes twice as long as the tangent intercept method to evaluate, say, 10 values for w from a curve and thus is not recommended as a substitute for it.Supposing from a curve showing W against T it is desired to evaluate wj at time T,. The procedure in the successive approximation method is to read off from the curve the value of Wi at T, and also 3 or 4 more pairs 1 4 Fisher and Yates, Statistical Tables for Biological, Medical and Agriculturn I 15 Andersson and Housemann, Res. Bull. No. 292 (Ames, Iowa, 1942). Research Workers (Oliver and Boyd, 1948), 3rd. edn.ALFRED H. NISSAN 25 Wk at Tk, W, at T,, etc. Now let Tk = nT5 and T , - T j = AT = (n - I)T,, W, = wj + T,(dW/dT),, (3.3) Wk = ~j + (dwj/dT)j AT + nTj[(dW/dT), + (d2W/dT2)5ATJ (3.4) From these two equations, w5 = (nW5 - W,>/(n - I) + AT[(d.rer,/dT), + nT,(d2W/dT2),l/(n - I ) (3.5) Now let w’, = (nWj - W,)/(n - I), . - (3.6) dWj/dT - T,(d’W/dT’),, .- (3.7) w’j 2 ~j + (TZ - I)Tj2(d2W/dT2),. . (3.8) lim w’, = wj. - (3.9) and noting from ( 3 . 3 ) that it follows that This means that, since in practice (d2W/dT2) is always finite, ?l+l Therefore, the method consists of (i) calculating several values for dj by applying eqn. (3.6) to pairs of W, and wk, (ii) plotting w‘, against n and (iii) extrapolating to n = I and reading off w,. To test the accuracy of the methods, cellulose fibres were not con- sidered suitable as they provided too many unknowns and another in- gredient of paper, kaolin clay suspension, was tested instead. Conse- quently, an experiment in which clay was suspended in water and the amounts settled were determined at times arranged in geometrical pro- gression beginning with a first determination at * hr.and using a factor of 2 , was subjected to an analysis. by all 3 methods. The orthogonal polynomial method using Fisher and Yates’ tables as aids in its solution showed that terms beyond the quadratic were insignificant and gave the equation where from which Table V gives the results, obtained by the three methods, for w at different times. W = 2.389 + g-227X - 0.1322X2, 2X = 8 T , or X = log,ST, w = - 10.923 + 9 - 6 0 8 X - 0.1322X2. It will be seen that : (i) The graphical methods give reasonably good results for ordinary routine analysis ; however, where the accuracy required is high, and especially where the proportion of a particular fraction is required to be known precisely, the graphical methods are not sufficiently precise.The polynomial method is simply limited in accuracy by the experimental precision and accuracy. (ii) There is not much to choose between the two graphical methods except that the tangent intercept method is quicker than the successive approximation method. This means that the chief source of error in the graphical methods is the original curve drawing rather than the tangent drawing operation. (iii) The graphical methods can be used to gloss over experimental errors by drawing the curves to pass smoothly, when they are expected to do so, through a region where observation does not strictly meet expecta- tion. Thus in this experiment, apparently conditions were not uniform for a little time-giving a curve which should have yielded a negative tangent intercept at 2-hr.period if strict adherence to the results were enforced-but the graphical methods which are partly subjective auto- matically adjusted the results to yield a more rational and acceptable value.26 SEDIMENTATION CURVES To test further the subjective influence it was decided to choose a sedimentation curve from the literature and to compare the results obtained by the original authors using the tangent intercept method with (a) results obtained by worker A who did not know the results of the original authors and who used the orthogonal polynomial method, (b) results obtained by worker B and who knew neither the original authors' results nor those of morker A but who used the successive approximation method, and (c) the same as (b) but using the tangent intercept method on the same curve which was analyzed by the successive approximation method.TABLE V T h e (hr.) * Q I 2 4 8 16 32 64 Orthogonal Polynomial -1.447 7'764 16.711 25'394 33-812 41-966 49.855 57'480 64.841 w % obtained by Successive Approximation 7'5 I 1-7 I 6.5 23-0 32-0 42'9 50'4 54'5 - Tangent Intercept 7'3 I 6.0 23'9 33'5 43'6 52-2 57'4 10'0 - Accordingly the original table of sedimentation times and amounts settled obtained by Jacobsen and Sullivan 16 on the sedimentation of quartz was given to A and B who were asked to analyze for w. The first worker plotted the results, as they were not in geometrical progression of time, and then read off the curve the amount settled for times arranged in geometrical progression. (This procedure introduces a subjective influence in the otherwise purely objective statistical analysis.) The orthogonal polynomial method gave W = 0.8098 - 0.1385X + 0-1843X2 - o.o188Xs + 0~0006X4, where zx = 4T, or X = log24T, from which The results for w are shown in the second column of Table VI.The second worker similarly plotted the curve and obtained from it the third and fourth columns by the successive approximation and the tangent intercept methods. The original results are in the fifth column. It will be seen that the previous conclusions still remain-that whilst the two graphical methods are of about the same accuracy, when judged by the polynomial method as a standard, the tangent intercept method must be judged superior to the successive approximation method as it is much quicker.The errors can be a few per cent. However, the most significant point is again the subjective influence. The fourth column, although using the graphical tangent intercept method, agrees as much or more with column 3 which was based on a different method, than with column 5 obtained by the same graphical tangent intercept method. This is apparently because both columns 3 and 4 are based on the curve drawn by one worker from the original sedimentation data, whilst that of column 5 was based on a curve drawn by another worker. I* Jacobsen and Sullivan, Ind. Eng. Clzenz. (Anal.), 1947, 19, 855. w = 1.0096 - 0.6703X + 0~2656x2 - 0.0224Xa + 0-0006X4.ALFRED H. NISSAN 27 It is, therefore, concluded that (i) To attain the highest accuracy in estimating w froin W and T a method, such as the orthogonal polynomial method, which does not require either the plotting of the original points for reading of particular values nor the reading of intercepts by extrapolation or tangent drawing, should be used.For such methods to be completely effective, when Fisher and Yates' or similar tables are to be used, readings should be taken at equal intervals of T or of log,, T. Otherwise, statistical analysis of the results, at unequal intervals of T, would be extremely laborious. The limits on the accuracy of this method are those of the experimental technique employed as the statistical approach insures getting the utmost out of the experimental results. TABLE VI Time (min.) w % obtained by I I Orthogonal Polynomial by Analyst A 1'2 2'2 5'0 8.8 19'9 40.6 79'6 221'0 497'0 10.63 = 5'45 25'74 34-15 46-80 57'32 66.14 76'72 82.62 Successive Approximation by Analyst B 9'3 1 14-25 27-62 35'43 48.05 59'45 69.5 80.1 - Tangent Intercept by Analyst B 8-66 15-39 28-79 35'78 46-4 58.1 67'55 80.7 - Tangent Intercept by Original Authors 10.j I 6-0 2 6.5 34'0 49'0 58.5 65'5 79'5 89.0 (ii) Subjective influences are introduced as much in plotting the original sedimentation curve as in the later stages of graphical analysis. (iii) Graphical methods can be a few per cent. in error in evaluating 2p1 from W. This fact can be of serious proportions if interest is centred on a particular narrow fraction. In such a circumstance the only safe procedure is to replicate the experiments and to analyze the results by a rigorous curve-fitting procedure such as solving the equation by the orthogonal polynomial method discussed here. (iv) Where the facilities of a rapid calculating machine are not avail- able the tangent intercept method remains the most convenient, reason- ably accurate method for evaluating w from W for most industrial control purposes. Mr. B. H. Browning of the Central Research Laboratories of &waters Development and Research Limited carried out the tedious microscopical work reported here and I cordially acknowledge my indebtedness to him. Several members of the staff of the Laboratories co-operated with and helped the author and to them too are due sincere thanks. Bowaters Development and Research Limited, Ce.Pz€ral Research Laboratories, Northfleet, Kent.

ISSN:0366-9033    

DOI:10.1039/DF9511100015

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

THE APPARENT SOLUBILITY OF COLLOIDAL MATERIALS COMPRISING A CONTINUOUS DISTRIBUTION OF MICELLAR SIZE, WITH SPECIAL REFERENCE TO COALS BY I. G. C. DRYDEN Received 10th May, 1951 Attempts to obtain a fundamental understanding of the fractionation of coals by solvent methods have resulted in a re-examination of the factors con- trolling the solubility behaviour of colloids, with emphasis on unfractionated mixtures, and of the relationship of the equations of Bransted, Schulz and Gee to the experimental conditions employed ; the problem of defining solution strength in a polydisperse material undergoing precipitation is raised. An endeavour is made in this paper to determine the conditions under which this type of approach may be extended to more complex systems, in which the laws of regular solution are not obeyed and the shape of molecular units is not known.A method of fractionation based on the extraction ofsolvents with solid samples a t a series of temperatures is considered to have certain advantages over those employing precipitation from solution ; this method is generally applicable whatever the form of the curve obtained, but with coal i t appears to lead to a simple algebraic expression defining a reasonable size distribution (with constant modal size) of molecules or micelles, whereas precipitation bv non-solvent does not. Incomplete thermodynamic function against compositidn curves for the coal + ethylene diamine system, of unusual iorm, are presented. There is evidence that a certain degree of equilibrium imbibition must be reached before equili- brium solubility can control.In order to account for earlier discrepancies between molecular weights of coal extract determined by various methods, it would seem that the presence of a small proportion of much smaller molecuIes, independent of the above, must be postulated. Many features of the dissolution of coals in solvents at moderate tem- peratures recall the behaviour of colloids and high polymers.1, 2~ The search for and explanation of the variation of yield of extract with changing temperature led to a theorethl treatment of the extraction of materials comprising a continuous distribution of micellar (or molecular) size, thought to be of general interest, and to a clarification of ideas on this and related subjects. Although the coal-solvent system proved far from convenient for verifying these conceptions experimentally, and the ex- perimental material itself was not yet adequate for a precise test, it was felt worth while to present at this time the first results of an investigation still in progress and stimulate discussion of the principles involved.In- clusion in this paper of a note on current conceptions of coal structure and a careful re-examination of the theory of polymer solubility has been found unavoidable. Coals, particularly bright coals, have long been understood to possess a colloidal structure. Studies of heat of wetting,* microporosity and the sizes of pore constrictions 5 have been interpreted with some success in terms of a model in which near-spherical and physically undissociable Dryden, Fuel, 1951, 30, 39.Dryden, Part IV. (in press). Griffith and Hirst, The Ultrafne Structure of Coals and Cokes (B.C.U.R.A., Dryden, Fuel, 1951, 30, 145. '944)J p* ' O . Franklin, Trans. Faraday SOL, 1949, 45, 274. * Bangham, Franklin, Hirst and Maggs, Fuel, 1949, 28, 231. 28I. G. C . DRYDEN 29 colloidal units (termed by Bangham micelles but herein treated as mole- cules), impenetrable to helium and to the wetting liquids, are assembled in a system showing increasing compaction (flattening of contact areas and decrease in pore size) as the rank (carbon content) of the coal increases. The average size of unit necessary to yield a model consistent with experi- ment (about 180 A) is independent of rank up to about go %carbon content, above which the concept of an assembly of individual units is more use- fully replaced by that of a continuous solid phase containing pores.Several lines of evidence 3s 7 , * have indicated that the bulk of the soluble material obtained when coals are extracted with solvents a t lower temperatures is similar in nature to the parent coal. Solutions have been shown 9 to consist largely of colloidal particles ; the larger of these are of the order of magnitude required by the model just described. The low viscosity 10 of solutions of coal extract in solvents confirms that the soluble colloidal units are not far from spherical in shape. Attempts to apply chromatography and electrophoresis to the separation of coal extracts 3 have modified the above model to the extent that a wide and fairly continuous distribution of micellar sizes around the average is indicated ; in this form it remains a useful working hypothesis and will be assumed in this paper to be substantially correct.On this hypothesis, coal may be regarded as a colloid with molecular (micellar) weights distributed around an average of 106-106. In contrast,? molecular weights of coal extracts determined cryo- scopically (usually in such solvents as catechol) lie commonly between 300 and 1000. by the author on material as nearly as possible identical with that in which Kann 9 observed the colloidal units ; and there is evidence 3 that catechol does not dis- sociate the larger units. Two factors-a fairly wide range of molecular or micellar size and deviations from ideal behaviour in solutions at the concentrations, exceeding I g./Ioo ml., necessary in order to obtain measurable freezing point depressions-would lead to a discrepancy of this kind.How far these factors can account quantitatively for the difference experiment must decide. of Riley 11 would have ‘ I molecular ” weights of the order of I O ~ . In the present state of knowledge the evidence for these is no stronger than for the colloidal micelles, and the general be- haviour of solutions favours the larger units. The process of solution of the coal substance, which does not approach completion unless the temperature is raised to a level (above 25oOC) where pyrolysis must be suspected, appears to require prior imbibition of solvent by the coal particles. The author has interpreted a mechanism of solution proposed by Agde and Hubertus la in terms of Bangham’s micellar model : briefly, it is supposed that when the coal substance is swollen by solvents some of the intermicellar contacts are loosened or completely broken, allowing the freed micelles, if small enough, to diffuse out through the swollen pore system leaving behind a residual matrix consisting of micelles not completely freed or of size sufficient to render them insoluble.Further consideration of this idea, in relation to Brransted’s empirical equation 13 for colloidal solubility as interpreted by Gee,14 suggested that the results might be used to determine the size distribution of those units that could be dissolved between room The discrepancy has been confirmed The “ crystallites Dryden, Fuel, 1950, 29, 197, 221.Biggs, J . Amer. Chem. SOC., 1936, 58, 484, 1020. Kann, Fuel, 1951, 30, 47. lo Boas-Traube and Dryden, Fuel, 1950, 29, 260. l1 Blayden, Gibson and Riley, l2 Agde and Hubertus, Braunkohlenarchiv, 1936, No. 46, 3. l3 Brensted, 2. physik. Chem. (Bodenstein Festband), 1931, 257. l4 Gee, Ann. Reports, 1942, 39, 29, The Ultrafine Structure of Coals and Cokes (B.C.U.R.A., I944), p. 176.30 APPARENT SOLUBILITY OF COLLOIDAL MATERIALS temperature and the onset of pyrolysis. Use of amine solvents was dictated by practical considerations ; in spite of disadvantages, ethylene diamine in particular gave more reproducible results and larger yields of extract at the lower temperatures than other solvents. Solubility of Colloids.-The equations of classical thermodynamics can be applied to the solubility of colloids and polymers irrespective of whether it is possible to set up a statistical model of the system.In this Section it will be convenient to refer frequently to the work on the solu- bility of chain polymers with which the available literature is mostly concerned ; since the larger size (rather than shape) of the molecule is t9e cause of characteristic colloidal solubility phenomena, the connection between physical processes and thermodynamic equations can thus be clarified without prejudice to the considerable differences of details which exist between these and coal-amine systems. It is also necessary to examine the conditions under which various approximate relationships can be applied in practice, and to show that temperature change may be used to determine molecular size distribution.The Brransted colloid solubility equation is so widely useful in illustrat- ing how the peculiar characteristics of colloid solubility develop as a direct consequence of molecular weight increase that it is desirable to generalize Gee’s derivation 14 and to translate the relationship into physical terms. The basic equations determining equilibrium when two phases coexist are Aglc = Agla, . 6 (1) Ag2c = Agzd , - - (2) where Ag refers to the increment of the partial Gibbs function when I g. of one component is mixed with a very large quantity of the given mixture. The subscripts I and 2 are used for solvent and solute respectively, and the superscripts c and d refer to concentrated and dilute phases.It is common practice to use a weight basis, and volume fraction instead of mole fraction, for colloidal systems in which the molecular weight of one component is unknown or indefinite. Above a critical temperature T,,15 the Gibbs function increments in a system showing solubility are negative ; they increase or decrease con- tinuously as the composition of the mixture varies from 0-100 yo of solid, and the components are thus miscible in all proportions. But below the critical temperature a minimum and maximum appear (these two coin- ciding at the critical temperature and then forming a horizontal inflection in the curve), and since it is then possible to have two phases with the same Gibbs function, separation into swollen solid and solution takes place unless the overall composition approaches one or other pure com- ponent.Curves of the type shown in Fig. I are then found to represent the variation of phase composition with temperature. Ag is related to the corresponding heat function and entropy by the usual equation Ag = Ah - TAs. The mean molar entropy of mixing for ideal mixtures of molecules equal in size is given by - R[nl In (I - x,) + n, In x,] = - R[nl In ( I - v2) + n, In v2]. Flory l6 deduced from a segment and reference lattice model that for linear high polymers in normal liquids the expression in terms of volume fraction (vz) was correct ; v 2 in this case is not equal to x,, but for dilute solutions (In v, - In x,) is effectively constant ; and Hildebrand 17 ob- tained a similar expression, without recourse to the lattice model, by making the assumption that the free volumes of the components were proportional l6 Alexander and Johnson, Colloid Science (O.U.P., London), 1949, p.794. I 6 Flory, J . Chem. Physics, 1941, 9, 660 ; 1942, 10, 5 r . l7 Hildebrand. J . Chcm. Phjrsics, 1947, 15, 225.I. G. C. DRYDEN to their molecular volumes (if assumed independent of these, the equation reduced to the ideal form). Differentiation to obtain the partial entropies and conversion to a weight basis leads, for example, to which reduces to the equation for ideal solutions if M , = MI. The use of volume fractions is a practical necessity in dealing with polymers of unknown molecular weight, and in view of this and the above consider- ations it is proposed to write R Ml Asl = - -In (I - v,) + al, R As, = - -In v, + 8,.M2 FIG. 1.-Typical phase com- positions for polymer solutions below the critical temperature. v 2 The 8 terms take care of departure from ideal behaviour, whether due to molecular size difference or to association structures giving rise to preferred orientation. Eqn. ( I ) and (2) can now be expressed in the form where the a's and b's are functions of the phase compositions and there- fore, in general, of temperature and the properties of the components. b , is commonly a function of M,/Ml also. Eqn.. (4) is similar in form to that which represents the solubility of a crystalline solid, for which v2c = I, a , = - AhZa/R and b, = - S,d/R become effectively constant.Both a, and b , in eqn. (4) become zero at T,, since the two phases then become identical. But when the temper- ature is sufficiently below the critical to ensure that the dilute phase con- tains very little of the solid component, a , and b, can attain quite large values ; in the special case of systems composed of chain polymers and liquids with which they form regular solutions, it can be shown that the values of a, and a , approach constancy (Ah,%=l/R and - Ah,"r=o/R re- spectively), whilst b, and b, approach corresponding limiting values (almost independent of M , if > 104). This is because the composition of the concentrated phase varies but little with temperature and is frequently32 APPARENT SOLUBILITY OF COLLOIDAL MATERIALS almost independent of M,.As the temperature falls below the critical, therefore, the analogy in simple systems between eqn. (3) and (4) and the solubility equation for a crystalline solid rapidly becomes more complete. Gee l4 has shown that eqn. (4) then becomes the complete expression of Br~nsted’s relationship and accounts for its comparative success, although Rrsnsted neglected the important entropy term b,. For polymer solutions in which the partial heat of mixing varies with concentration as in regular solutions, the value of the (unique) critical solution temperature’ obtained by equating the first and second differ- entials of the expression for either Agl or Ag, to zero, is found to be pro- portional to the total heat of mixing and dependent on M2/M1, tending to constancy when M , =- 104.From the general Ag against composition curves, phase compositions are derived by finding two values of v a which correspond to the same Agl and the same Ag,. I O ~ - Z O ~ C below the critical temperature the equilibrium eqn. (I) and (2) are represented conveniently by (3) and (4) ; eqn. (3) or (4) alone will fix the concentration ratio of the two phases but both are required to solve the problem completely. Taking advantage of the approximate constancy of the a’s and b’s well below the critical temperature and the fact that In ( v , ~ / u , c ) is then much larger numerically than In (v1d/v1c), an approximate solution of the simultaneous equations can be obtained analytically, namely, RT In vlc = - M(Ahlc - TS,c), which shows that the low temperature coefficient of imbibition is directly due to the low molecular weight (and hence molar heat function) of the solvent, and RT In uZd = RT In (I - ulc) - M,(Ah,d - T B , d ) , which together with the first shows that the high temperature coefficient of solubility is determined almost entirely’ by the high molecular weight and molar heat function of the solute.For the ensuing discussion on the application of eqn. (4) to fractionation, it may thus be approximated by putting v , ~ = I and writing In v , d a, - = - - Ma T bz* ‘ Schulz 18 extended Br~nsted’s relationship to the precipitation of polymer solutions by non-solvents, and his simple assumption that the heat term a, is a linear function ( X + $6) of the percentage of non-solvent (6) has been found adequate in a number of systerns.l% ~ Q s 2 o The validity of Schulz’s relationship depends also upon that of eqn.(5)’ on the assump- tions that a , and b, are independent of MB,* and on the constancy of v , ~ . It takes the form where T a=- Tba - ’ and /3 = -lnv,d * + are constants. If b,, instead of being substantially independent of .$ as for linear polymers in regular solution, is related linearly to it, values of u and will be different but still constant, but with any other relationship between 5 and b,, eqn. (6) will not hold. Schulz 18 and Gee 21 have shown that for efficient Schulz, 2. physik. Chem. A , 1937, 179,321. lo Blease and Tuckett, Trans. Faraday SOC., 1941, 37, 571. 2o Gee, Trans. Faraday SOC., 1942, 38, 276. * For linear polymers the M,-dependent portion of b, can be transferred to the left side as an addition to In v2d ; the equation is then valid below as well as above M , = IO*.21 Gee, ref. (14), p. 30.I. G. C. DRYDEN 33 fractionation the solution from which precipitation takes place must be very dilute, but the above method of derivation makes it clear that the Schulz relation is itself only applicable to dilute solutions. In fact it would be possible so to choose the proportion of solute, solvent and non- solvent that turbidity would begin at the true critical composition, the critical temperature simultaneously becoming equal to that of the experi- ment ; in this case all the terms in eqn. (4) would be zero and the derived Schulz equation would be meaningless. At ’a given (low) concentration level, a definite size of molecule will be in equilibrium ; apart from a small transition range, larger molecules will be effectively insoluble, smaller soluble.Since the critical solution temperature is related to the heat of mixing, Schulz’s method of precipitation is in effect to increase T, and so cause the curve in Fig. I to move upward. Alter- natively, according to eqn. (5), T may be reduced ; a convenient modifi- cation of this, for a solute of broad molecular weight range, is to extract solid samples in a Soxhlet apparatus at various temperatures. Ad- vantages are : (i) no question arises of different proportions of solvent to non- solvent occurring in the two phases-a weakness of the Schulz method ; (ii) the possibility of the entropy term b , being different in the solvent and non-solvent does not arise ; (iii) the meaning of In v 2 d is clearer and its value can be measured ; it is thus easier to establish an absolute value of fi in eqn.(6). The practical application of these conceptions must now be considered. A common method making use of Schulz’s equation is to titrate a fairly homogeneous fraction in solution, against a non-solvent, to the point of turbidity. The value of v , d in eqn. (6) is then, presumably, the total concentration present at the end point. Turbidity does not necessarily occur when the unique temperature T, equals T ; reference to Fig. I will show that in very dilute solutions the end point will correspond to T, > T, and in fact unless this is so, eqn. (6) does not apply. It has been customary 1% 10 to work at ql,d = 0-01-0-02 which may be rather high. Another method is to add a definite amount of non-solvent to a solution of polymer with a molecular weight distribution.Conditions here are more complex, but it is generally assumed that a cumulative weight distribution curve of reciprocal molecular weight may be derived from the curve of weight precipitated against non-solvent added. Treatment of the precipitation of unfractionated colloids requires some general knowledge of the rate at which solubility ( v , d ) decreases with increasing molecular weight and other changes. Curves given by Alex- ander and Johnson 22 and Gee 2 o are helpful in establishing general prin- ciples. It may be deduced from these that solubility becomes very low (and the temperature coefficient very high) about 20° K below T,.Once precipitation starts in dilute solution the solubility of a given molecular size may fall by a factor of IOO (i.e. g g yo may be precipitated) over about 5” C, or on addition of about I yo of non-solvent ; but by’ then molecules of only 40-50 yo of the weight of this species may have started to pre- cipitate. These statements apply’ to molecules with M , > 50,000. Thus the fraction precipitated will be less than the true fraction above M,, and to correct for this when translating the 6 scale into a scale of M,-1 according to eqn. (6) a value of u 2 d less than the initial must be used. This can be estimated as follows. When the species M , starts to precipitate, the total weight precipitated will correspond to a larger value M,’ on the true distribution curve.Now In general, solubility decreases as M , increases. 22 Alexander and Johnson, ref. (15), p. 794, Fig. 27.11.34 remembering that b in eqn. (6) is proportional to lnv,, the solubility of M,’ will be given by v,’, and APPARENT SOLUBILITY OF COLLOIDAL MATERIALS B B’ a + - = a + - p‘ In 21,’ M2’ fi In v2 M , . M2 M,’ ’ -=- =.- Of the species M,’, only a proportion M i 1 - v ’ 2 = 1 - &G 4 V2 will have been precipitated. If t$ is the weight frequency factor for M,, 00 4 (I - v , ( z - ’)) dM, = f,, 00 (2-1) dM2 = If:’ +dM,. 5’ Since v, g 0.01, v , ( M 2 - ’) will equal 0.1 when M,’ = 1-5 M,, so that the decrease in this factor is rapid ; the integration in effect will extend over a small range only, and regarding t$ as constant over this interval we have - 1 = 2 - I M2’ - -- - - In’’ I and v 2 ’ = 2 .. In v, M, In 21, (7) Thus 63 yo of species M,’ is precipitated. v,’ should be used in eqn. (6) instead of v2. If the distribution is continuous, solubility or concentra- tion can only be conceived as an average, and it would seem that the total vg for all species remaining unprecipitated, and allowing for dilution by’ non-solvent, is the correct quantity from which to calculate 0,’ at any point. The same considerations hold for Soxhlet extraction, but since in this method the smaller molecules are removed first the correction to be made is in the opposite direction (v,’ > v,). If the equilibrium solubility is measured, the incompletely-removed smaller molecules will contribute to and thus increase v,, so that further correction may not be required ; the same holds for successive extraction at room temperature.In theory, however, these methods only approximate to equilibrium, because when vZd becomes very small extraction is correspondingly slow ; in infinite time all would be expected to dissolve, and in fact marked changes in rate but no absolute end points are observed. When the extraction rate has fallen, for example, to I yo per 24 hr., the yield in periods of the order allowed experimentally would obviously be negligibly effected if the solubility were only one-tenth as great, although 1nvzd in eqn. (5) would increase by 2-3 and the value of M , in equilibrium with this lower concentration would be measurably larger.This probably explains why tube and Soxhlet methods (see later), in spite of the different degrees of washing with fresh solvent involved, agreed so well in the yields attainable in reasonable periods at the same temperatures, and may account for certain unusual characteristics of the coal extraction mechanism. 2 Finally, it is important to note that owing to the dependence of 8, on M l / M , at lower values of M,, eqn. ( 5 ) is unlikely to apply at all accurately below M , N 104, although when the Flory expression holds, a slight modification will be more widely valid. Application to Coal-Amine Systems.-The interaction of coals with amines is complex, and had not the regular variation of extraction yield with temperature, the behaviour of solutions with precipitants, and the accumulated evidence 3~ 6, * that extracts differed from residues in molecularI. G.C. DRYDEN :-: 5 t O * 35 size or state of aggregation rather than in fundamental nature appeared to call for an interpretation of the kind outlined above, this approach would not have been contemplated. Support for the general principle is forthcoming from Kann's 0 observation that the size of colloidal coal units in a given solution increased with time and temperature of extraction. The thermodynamic functions of the system are incompletely known, and have been determined on the whole coal. So long as the fraction with M , < 104 is not great' i t is unlikely that the characteristics of the Ag against composition curves will be smoothed out by the range of sizes present, since the critical temperature will not be greatly different for all components ; evidence suggests that this is the case.The solubility of coal in liquid ammonia is extremely small at - 33" C but quite appreci- able at 20" C ; this may indicate that in this solvent T, for the smaller units lies within that range. Fig. 2 shows the thermodynamic data avail- able on mixtures of coal and ethylene diamine. The most reliable results, 65 % 55 v2 FIG. 2.-Thermodynamic functions of coal D3-ethylene diamine system a t 25' C. A. - Ah1 B. - Ah2 C. - TAs, D. - Ag, E. - TAs1 F. - Ag,. a t higher values of u2, were determined from measurements of the sorption isotherm 23 and of partial heats of wetting.24 At lower values of v, data are sparse, but there can be little doubt on two points : (a) the existence of a swelling equilibrium requires that Agl and Ag, must pass through maxima or minima in this region, and (b) since the yield of extract in- creases with temperature the difference of Ah2 appropriate to eqn.(4) must be positive, so that the Ah, curve should pass through inflections between v, = 0.2 and zero. No experiment of sufficient accuracy to confirm these points has yet been made. Uncertainty as to partial pressures during the adsorption of the first few percent of solvent (involv- ing a transition from chemisorbed layer to more normal sorption) renders the absolute scale of Ag2 uncertain to within perhaps I cal./g. ; this will not affect the differentials required for the present purpose.A fuller account 25 will appear elsewhere. The curves in Fig. z are of unusual shape, and suggest that above v 2 N 0.5 coal-solvent interaction is the predominant factor whereas below this the much smaller changes are related increasingly to mutual separ- ation of the coal units in the colloidal structure, for which energy is 23 Dresel, Dryden and Farenden, Research, 1951, 4. *' Dresel and Pritchard, Reseawh, 1951, 4. 26 Dryden (in course of publication).36 presumably required. In the interaction portion of the curve, both energies and entropies are high and negative, the negative entropies in- dicating an ordering effect of the interaction (sorption) greatly exceeding the normal positive entropy of mixing, The almost constant values of As, as low values of v, are approached support the view that M , is large, since the positive term - -In u, becomes of appreciable importance at u, = 0.1 when M , = 103 but only at v 2 = 1 0 - l ~ when M , = 104.Over Ah are both approxim- the range u, = 0.5 - 1.0, the ratios 1 and -2 TAs, T A s , ately constant at I -2. For the swollen phase of those coals to which the earlier concepts are considered applicable, v,C = 0.4-0.5 (0.4 for the coal represented in Fig. 2) ; u,d in the experimental work reported was about z x I O - ~ . The therrno- dynamic functions required lie therefore wholly in the range considered to represent colloidal disaggregation, and in this range it is possible that the conditions necessary for the application of eqn. (5) and (6)-namely, (Ah," - Ah,d) and (6,c - a2d) substantially independent of M , and vari- ation of phase composition-may be met.This assumption has been made in order to test whether the experimental results then lead to reason- able conclusions. In view of the incompleteness of the data, values of a, and b , in eqn. (4) cannot be estimated. Ah,c - Ah,d = - I cal./g. would correspond to a2 =- 0 . 5 ~ K. Experimental and Results APPARENT SOLUBILITY OF COLLOIDAL MATERIALS R M2 Ah (u) Dried coal ground to pass a 72 B.S. mesh sieve was extracted with " pure " ethylene diamine containing not more than 0.5 % water (and in one or two cases with commercial " pure " diethylene triamine). For most of the measure- ments of extraction yield a small Soxhlet apparatus with vapour-jacketed extraction compartment was used.This was vented to nitrogen and could also be run a t low pressures maintained by a manostat. Another method used was to extract coal in successive stages at room temperature ; a coal-solvent mixture was shaken mechanically in a tube containing a sintered-glass filter near the base, and the solution filtered off. These techniques, and the method of correc- tion to an ash-free and adsorbed-solvent-free basis, have already been described ; certain features of the extraction processes, demonstrated in the same paper, are important for the understanding of the results here reported and the argu- ments later advanced : (i) Extraction was at first rapid, and then became very slow but never zero within any reasonable period. A compromise was struck by regarding 48 hr.in the Soxhlet, 8 stages in the tube, as standard. The yields thus obtained were only slightly dependent on time or stage number. (ii) The extraction yield in the tube method, for the open-structured coal Dg, amounted in a single treatment to about Q of the standard yield approached by 8 successive treatments (for the purpose of this paper a similar comparison was made using the coal of low porosity Dg, and the same relationship was found to hold). (iii) Standard tube extraction yields were closely in line with yields obtained in the Soxhlet apparatus operating (under vacuum) a t similar tempera- tures, or obtained (more rapidly) when a mixture was exposed to ultra- sonic vibration during extraction ; the standard yield from a given coal thus appeared to depend on the solvent and temperature only.At room temperature results in Table I have been calculated from the yields in a single stage tube extraction, using the factor 1.5 (see note (ii)). (iv) The amount of extract obtained at room temperature was an ap- proximately linear function2* (when both coal and solvent, within a defined group of amines, were varied) of the equilibrium amount of solvent imbibed by the residue. (v) The equilibrium imbibition varied little with temperature. z6 Dryden, Fuel, 1951, 30,217.I. G. C. DRYDEN 37 Table I suminarizes the extraction yields from a number of briglit coals of increasing rank a t various temperatures and values of the equilibrium imbibition N a t room temperature. N is equal to the ratio between volume increase on swelling and (true) volume of the unswollen coal substance.(b) Piecipitation of coal extract from solution in ethylene diamine by non- solvent was effected by slowly adding a chosen proportion of benzene to the solution with vigorous stirring, followed by warming, shaking and storage in a thermostat a t 25" C for 48 hr. ; the precipitate was then filtered off, dried, washed with water to remove any entrained amine, dried again in cacuo a t 105' C , and weighed. TABLE EXTRACTION YIELDS AND IMBIBITION RATIOS (BASIS : MOISTURE, ASH AND SOLVENT-FREE COAL AND PRODUCTS) Solvent Diethylene triamine . @-Hydroxy e t hylamine % Carbon (dry mineral- .ree basis) Tube (zoo C.) >hen- ionless mbibi- t ion ( N ) Soxhlet Temp. 'C I I0 I I0 I I 0 I I0 95 95 65 50 40 40 35 30 I I0 I I0 I I0 I I 0 I I0 95 65 35 I I0 I I0 I I0 I I 0 I I0 a.160 60 a. 160 80 40 a. 160 uncertain (atni. press.) a. 113 & Yield tract) (EX- 47'2 37'3 33'8 38.8 34'7 32-1 27'5 2 6 9 24'7 24'5 23'9 21'0 28.8 31'2 25'3 34'2 25.8 21.7 I 6.0 I 0.8 33'3 I 6.6 28.2 I 8-2 19.6 65 28.9 58.4 38.3 31.6 25'5 39.7 39'0 % Total Products 100.3 98.5 98.4 97.8 94'4 94'7 95-4 (tube) 98.3 (tube) 95-6 (tube) 97'3 87.6 98.0 97'7 94'5 93.1 94'5 92.8 94'1 97'0 92'3 98-4 I00 I00 94'5 96.4 96.3 97'2 9 6 2 90'7 100'0 Ratio of Yield at Vormal 1.p. and zoo c 2'0 1'7 1-85 1'9 - - - - - - -- - 2'0 2'3.5 2-05 2.05 2.8 - - - 2.85 2.85 5-05 4'3 1-95 3-15 - 2-95 -- - - 2 - 5 2-3538 APPARENT SOLUBILITY OF COLLOIDAL MATERIALS The upper portion of Fig. 3 shows some earlier results, on the precipitation by chloroform of a solution prepared a t room temperature, which indicated that the position of the curves obtained approached a limiting value as the con- centration of the original solution before precipitation was reduced, finally reach- ing constancy below 0-5 g./Ioo ml.Similar curves were obtained with a solu- tion prepared a t higher temperature, but precipitation was then greater at a given percentage of non-solvent, as would be expected since such solutions contained some additional material with a lower solubility (even in pure ethylene diamine) a t room temperature. The lower curve in Fig. 3 was determined on a room-temperature extract (precipitated by acid and dried, portions redissolved as required) which was tested also by the method described in the next para- graph ; this extract represented 10 yo by weight of the raw coal (D3) extracted. FIG.3 .-Precipitation of coal extract from solution in ethylene diamine a t 25' C. Top : Chloroform . x 3.75 g./Ioo ml. Bottom : Benzene . 0 0.53 g./Ioo ml. 0.10 g./Ioo ml. Mo/e percenkuye of non-solvenr (c) Aniline is a rather poor solvent for raw coal a t room temperature and a considerably better one a t its normal boiling point (184" C ) ; i t was found to dissolve a portion only of the dried extract (see ( b ) ) originally prepared with ethylene diamine. Aniline was therefore used in order to make a direct com- parison cn the same sample between the curves obtained by Soxhlet extraction at various temperatures and by precipitation with non-solvent respectively.As explained earlier, these two curves should be related. The yields of extract were : zoo C, 66 % ; 75" C, 79 "/o ; 127" C , go % ; 184" C, 97 %. ( d ) Solutions prepared a t higher temperature were found to throw down sludge on standing at room temperature, whereas those prepared a t room tem- perature did not. In order to examine the nature of this sludge its extraction (aiter filtering off) by excess solvent was examined. It was found to be virtually insoluble a t room temperature in ethylene diamine, only partly soluble in boiling ethylene diamine (solvent/extract ratio > IOO ml./g.), but almost completely soluble in ethylene diamine after Soxhlet extraction for 48 hr. This is the be- haviour to be expected from a polydisperse colloidal material.(e) Some of the residues from the Soxhlet extractions reported in Table I, after drying, were treated with ethylene diamine at the normal boiling point and also at zoo C until equilibrium was reached, and the concentration of the solutions, filtered off a t these temperatures, were then measured by comparison with standard solutions in a light absorption comparator. It was found by inter- polation that the concentrations during the final stages of extraction must have been within the range 0.1 to 0.4 g./roo ml. The average concentration required to account for the increase in yield between 48 and 96 hr. respectively was lowerI. G. C. DRYDEN 39 than this ; as would k expected, equilibriurn was not reached owing to the barrier imposed by the extraction thimble.It was considered that 0-2 g./ioo ml., i.e. zlzd = 0.0015, should be used in eqn. ( 5 ) . Discussion Interpretation of the Experimental Results .-It is evident from Table I that when the imbibition and extraction yield a t room temperature are small the temperature coefficient is abnormally high. In Fig. 4 are plotted ratios of the yields at boiling point and room temperature against the im- bibition number. It will be seen that when the imbibition exceeds unity the temperature coefficient is approximately constant. When the jm- bibition is unity, and provided that swelling is entirely due to mutual separation of the micelles, the swollen pores should on the average equal in diameter these solid units. It is reasonable to suppose that above this point mechanical hindrance to the diffusion of micelles into solution I I I I 1 I FIG.+-Relation of temperature Coefficient of extraction yield to imbibition : becomes negligible, SO that equilibrium solubility' alone controls and the temperature coefficient then reaches its natural value which depends upon this and the micellar or molecular size distribution. Yield ratios for &ethylene triamine are somewhat higher because of the higher boiling temperature. In Fig. 5, the constancy of the coefficient at imbibition numbers ex- ceeding unity is illustrated in another way, by plotting the logarithm of the yield of extract against the reciprocal of the absolute temperature of extraction. The lines for different coals are approximately parallel and undoubtedly straight; straightness is not due to the small range of values, for the direct plot of yield shows distinct curvature.Moreover, to the first order of approximation, the extraction yield a t a given temper- ature depends on the coal med but not on the particular solvent. There is no obvious reason why the curves on this graph should be straight lines, since the extraction yield is not a reversible equilibrium property like solubility. But accepting the experimental evidence, and comparing the empirical equation thus derived with eqn. ( 5 ) , i t is seen that the results can be explained if the cumulative weight distribution of molecular or micellar size is given by the expression ethylene diamine. B I n y = A -- Mi where y is the quantity of coal below size M2, and is identified with the extraction yield.A size distribution of this general character, but with40 diameter instead of volume as the index of size, has been derived theoret- ically by Griffith 2' from a Maxwellian surface energy distribution. The slope of the curves in Fig. 5 is then equal to - Ba,/ln v,d, and the intercept ( T = a) to ( A + Zd). ed will equal IOO if no completely insoluble material of different character is present. The slope is thus proportional to the mean molar or micellar heat of solution, just as i t would be if equi- librium solubility were the variable, since /? is proportional to the mean size; the intercept has no physical meaning in terms of yield, because when T, is approached the theory no longer applies. APPARENT SOLUBILITY OF COLLOIDAL MATERIALS /.y I I I I I FIG.5.-Va,riation of extraction yield with temperature. Do-D7 and D24, N > I ; Dg, N < I. 0 Ethylene diamine. Diethylene triamine. Even when the value of a2 is unknown, considerable information can be obtained from this expression. Its differentiation leads to a size frequency distribution with modal size equal to B / z , and when molecular sizes are expressed as a ratio (m) to this modal size the equation for weight frequency factor becomes dr = 2ede-2,,. d m m, Fig. 6 shows the corresponding dimensionless weight frequency and cumulative distribution curves, and the number frequency curve derived from them, all calculated on the assumption that e* = roo. For the whole coal, in terms of the weight distribution modal size as unity, the number modal size is 2/3, the number average is 2-0 and the average on a basis of specific surface (assuming spherical units) is 1.30 ; for the curve up to 20 yo cumulative yield (e.g.a room temperature extract) the cor- responding averages on the same scale are 0-77 (number), 0.74 (surface). These figures are in the right direction to reduce the gap between surface and cryoscopic determinations, but by no means eliminate i t ; if the 27 Griffith, Can. J . Res. A , 1943, 21, 57.I. G. C. DRYDEN 41 present findings are correct i t is necessary to postulate independent much smaller groups of molecules making the size distribution bi- or poly-modal. The extract used in the precipitation and aniline extraction experi- ments should correspond to the portion of the curve (Fig. 6) up to 10 % cumulative yield.Assuming that the Schulz expression applies, a weight distribution curve for this extract has been plotted in Fig. 7 ; the yields from aniline extraction at different temperatures, which owing to the small range give straight lines against I / T whether plotted directly or as logarithms, have been added. The precipitation curves were obtained from Fig. 3 by converting mole percentage to volume percentage I, assuming o! = 25 %, corresponding to the commencement of precipitation and to M , = 00, and thus obtaining according to eqn. (6) and (7) a quantity -(( - a)/(ln v, - I) proportional to I/M, (curve A). V Z Was 0 re1oh.w m;ce/~ar size w- 1 FIG. &-Derived size distribution curves, A. Cumulative weight distribution.B. Differential weight distribution. C. Differential number distribution. taken at each point to be the actual concentration remaining in solution, The shape of the curve was not sensitive to changes in the exact value of By plotting directly against [, on a scale such that the ends coincided, curve B was obtained. The aniline extraction results covered a smaller range, and in this case yield was plotted directly against I / T according to eqn. (5) (curves C and D), the scales again being adjusted to bring the ends into agreement with curves A and B since no other method of establishing correspondence was available. This method of course is applicable even when the results do not lead to a simple equa- tion such as that derived from Fig. 5.Finally, the corresponding portion of the cumulative curve in Fig. 6, after conversion of nz to ~ / m , was added with similar scale adjustment (curve E). It will be seen from Fig. 7 that whereas with scale adjustment the aniline extraction curve for the extract and the ethylene diamine extrac- tion curve for the whole coal, both derived from eqn. ( 5 ) , can be brought into close correspondence, the precipitation curves take different forms ; the direct plot against (curve B), theoretically less correct than curve A, is closer to the temperature curves. It seems probable that the pre- cipitation method is in this case the less sound of the two, since the number of conditions to be met before the theory is applicable is greater. within small limits. B42 APPARENT SOLUBILITY OF COLLOIDAL MATERIALS Since all the lines in Fig. 5 are parallel, and their slope, if eqn. ( 5 ) (which requires that a , is constant) applies, should be proportional only to the modal size, i t may be deduced that the modal size is independent of the rank of the coal over the range cons:dered. Bangham et aZ.6 came to a similar conclusion. The greatest interest attaches to the actual value of the modal size. The average slope of the lines (Fig. 5 ) for all coals in Table I with imbibition exceeding unity is - 850" K, and us.ng the estimate v , ~ = 0.0015 a modal " micellar weight " of 2,8oo/a, is obtained. Unfortunately it has so far proved impossible to establish the value of a,, a!though this must be small ; thus if 0.5" K is used (see earlier Section), the modal value would be about 6,000. FIG. ./.-Size distribution of coal extract (10 % of coal) according to benzene precipitation, aniline extraction and Fig. 6. A. Pptn., Abscissa - (4 - a) /In v,d. B. F'ptn., Abscissa 4. C, D. Extraction, Abscissa T-l. E. Fig. 6, Abscissa m-I. Conclusion.-This work arose from the necessity of explaining some unusual results obtained with the rather complex system of coals and amine solvents, b u t since knowledge of this system is still far from com- plete i t has not been possible to demonstrate rigidly the correctness of the interpretations advanced. A simple method of fractionating coals and their solutions quantitatively is urgently required, and i t is hoped that during the discussion suggestions may arise which will lead to a more satkfactory development along the lines indicated. In particular, the definition of solubility in unfractionated colloidal materials needs clarifying. The method of temperature variation would seem to have advantages over that of Schulz when dealing with unfractionated colloids, and to be worthy of application to systems for which more of the basic data are known. The author wishes to thank Mrs. I. Helledie, Mr. R. H. J. Fitch and Mr. I. B. P. Fitch for experimental assistance and the British Coal Utilization Research Association for permission to publish this paper. Chemistry De#artment, B.C. U.R.A., Randalls Road, Leatherhead, Suwey.

ISSN:0366-9033    

DOI:10.1039/DF9511100028

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

SOLID PHASE STRUCTURE IN LUBRICATING GREASE BY E. W. J. MARDLES* AND I. E. PUDDING TON^ Received 5th April, 1951 In order that a system may have desirable properties as a lubricating grease, the ultimate solid phase particles should be highly anisometric. In addition, i t is important that the solid phase surface should promote aggregation of the individual particles to produce sufficient structure to give the system a yield value. This structure should be capable of reversible breakdown under con- ditions of shear and show little hysteresis in recovery. Conventional lubricating greases are dispersions of metallic soaps in lubricating oil. The most common forms are soft solids and contain about 10 yo of soap by volume. The usefulness of greases depends on a unique property ; at low stresses, the viscosity is very high-approaching infinity under the influence of gravity alone-but as the rate of shear is increased, the viscosity falls and finally reaches a value only slightly higher than that of the contained oil, so imposing low loads on the power supply, when the bearings operate at high speeds.It is desirable that the rheo- logical properties of grease remain relatively constant over the range of operating conditions encountered in use. The different behaviour of individual soap dispersions in this connection has led to a number of classes of lubricants for special purposes, with no one variety having sufficiently suitable properties to be classed as an all-purpose grease. Dispersions of materials, other than soaps that are now appearing for use as lubricants include carbon black, bentonite and silica.While practical considera,tions limit the choice of ingredients that may be used industrially, many combinations may be produced experimentally that have the de- sired properties. The similarity in refractive index of soap and oil makes optical micro- scopy of greases difficult. Dark field illumination and removal of the oil by selective solvents have been useful in some cases.l, Electron microscopy along with metal shadow casting 8, 4 have extended the range of examination considerably. These techniques show that the ultimate soap particles in soda, lime and lithium base greases are unbranched, flexible fibres with mean axial ratios in the vicinity of 20 to 30. The particles in aluminium soap greases do not appear to have been resolved.While the shape and size of the ultimate particles have a considerable influence on the flow properties of the dispersion, these are governed to a greater extent by the actual solid phase structure, and the ease with which this may be broken down and reformed under alternate conditions of strain and rest (thixotropy). This, in turn, is controlled by particle- particle interaction or flocculation in the particular liquid medium used. The most useful information on these systems is therefore, obtained from an examination of the flow properties. Rheological measurements on greases are complicated by the strong tendency of these systems to show plug flow. This is apparently due to * Royal Aircraft Establishment, Farnborough.t National Research Council, Ottawa, Canada. Farrington and Davis, Ind. Eng. Chem., 1936, 28, 414. Gallay, Puddington and Tapp, Can. J . Res. B., 1944, 22, 66. Birdsall and Farrington, J . Physic. Chem., 1948, 52, 1415. 4 Ellis, Can. J . Res. A , 1947. 25, 119. 4344 PHASE STRUCTURE IN LUBRICATING GREASE the combination of strong interparticle attraction and the relatively low viscosity of the liquid phase. In such cases the use of rotational visco- meters is limited to dispersions of low solid content, and most measurements have been made with capillaries having a large length to diameter ratio. A useful method when only a small amount of material is available involves the measurement of the variation of the distance between two parallel plates, with time, when a known volume of substrate is contained between them.This can be done with simple equipment and the viscosity calculated from the approximate equation where F is the force in dynes, d the distance between the plates, t the time elapsed, and G = 3v2q/8r, where ZI is the volume of liquid and the viscosity. From rate of shear against shearing stress curves, the yield value and mobility of the system can be found, The yield value may also be deter- mined separately by a rapid test involving the depth of penetration of a plate of known weight into the grease. This is actually a measurement of the structure of the grease and indicates its ability to " stay put " but tells little of the load that will be imposed on the bearings when it is used as a lubricant.Some light may be thrown on the process of flocculation by the follow- ing simple experiment. If equal amounts of dry talc are dispersed in two samples of toluene and about I yo of water, based on the talc, added to one, and an equal amount of oleic acid to the other, visible flocculation will be seen at once in the sample containing the water, while the particles in the second portion remain well dispersed. The aggregates will settle rapidly, leaving a clear supernatant liquid, to an equilibrium volume of about twice that occupied by the second sample. The unflocculated sample is comparatively slow in reaching its final condition. Shear, imposed by shaking or stirring reverses the process, causing temporary deflocculation. Aggregates form again in the sample containing the water, as soon as stirring is stopped.This same process occurs with many other two phase systems and it is of interest that the flocculation and sedimentation are much more rapid when the liquid medium is non- viscous. Removal of the supernatant liquid from the flocculated sample after sedimentation will give a solid with properties very similar to those of grease. Greases are thus composed of a minimal quantity of a solid material suspended in a liquid to give a scaffolding type of structure that enmeshes large quantities of the second phase, The effect of varying degrees of interparticle reaction on the viscosity of some suspensions is shown quantitatively in Tables I and I1 where the Einstein coefficients (theoretical 2-5 to 5 depending on particle shape) for various suspensions are compared.5 It is clear from these data that only with those liquids that are strongly absorbed by the solid is the predicted value of the Einstein coefficient approached.In the other cases the apparent overall particle geometry is radically changed. At higher concentrations this coefficient loses its usual significance, but the data in Table I1 show that the dispersion medium has a marked effect on the apparent particle shape. Experiments using a moving plate (edge-on) viscometer at unit rate of shear to determine the effect of the ultimate particle size were carried out by measuring the viscosity of 54 yo, by volume, suspensions of grain aluminium in kerosine. The suspension containing 300 mesh aluminium gave a viscosity of 150 poises compared to 10 poises for the 120 mesh particles.This indicates a higher degree of inter1 article reaction with increase in the specific surface. When suspensions axe sufficiently highly concentrated, interesting effects, such as apparent stress hardening, occur. These effects are due d4 = ct-lF-1, Mardles, Trans. Faraday SOC., 1940, 36, 1007, I 189.E. W. J. MARDLES AND I. E. PUDDINGTON 45 to interparticle friction and they can usually be eliminated or radically reduced by altering the liquid medium, so reducing the coefficient of friction between the particles, or by changing the shape of a portion of the suspended solid. Such behaviour is usually peculiar to substantially spherical particles and the addition of a small percentage of fibres has a large modifying effect.In more dilute dispersions, however, interparticle adhesion can take place by at least three mechanisms : (i) mechanical entanglement of long fibres ; (ii) adhesion on contact due to particle-liquid interfacial surface tension. This phenomenon is greatly enhanced by the presence of a second liquid phase that preferentially wets the solid. The sedimentation of talc in toluene, already described, is a typical example ; (iii) adhesion of the particles due to incipient surface swelling. TABLE I.-THE EINSTEIN COEFFICIENTS FOR SUSPENSIONS Liquid Medium n-Hexane . Oleic acid . Ethylene dibromide . Water . Lubricating oil . Boiled linseed oil . Silica (Irregular Grains) 4 9 5 6 I1 I2 Mica (Irregular Plates) 7 6 7 9 I0 - Aluminium (Flakes) Graphite (Plates) TABLE II.-THE RELATIVE VISCOSITY OF SUSPENSIONS OF 7.5 yo VOL.KAOLIN IN VARIOUS LIQUIDS Relative Einstein Viscosity Liquid Medium Light mineral oil . Benzyl alcohol . nz-Cresol . Diamyl phthalate . Aniline . Oleic acid rllrlo 4'8 1'9 1.7 1-6 1'5 2'2 51 16 9 8 7 I2 The first and third of these mechanisms would not be expected to be operative in the systems discussed so far, where the solids have been in- organic and the particles reasonably isometric. With the soap greases, however, they may assume considerable importance. Mechanism (iii) is a factor with all these greases at elevated temperatures and mechanical entanglement has a strong influence with long-fibred soda-soap greases. With these greases fibre length and toughness is increased by using a larger portion of oleate in the soap stock.The amount of grease that can be made from a given quantity of soap is considerably increased by this procedure, but so, too, is the difference in yield value when this is determined before and after the grease has been sheared. Indeed it is only with those soda greases where the fibres are kept purposely short that this difference is kept to a minimum, and this is accomplished at the expense of reduced consistency. If this procedure is not used, however, the useful properties of the grease soon deteriorate during service. Al- though individual greases vary a good deal, the data presented in Table I11 are illustrative. In contrast to soda soap greases, lime soap fibres are much tougher and smaller, though they also have a high axial ratio.High shear has46 None . Passed 3 times through a capillary at a mean shear rate of 2000 sec.-l Passed twice through a colloid mill at a mean shear rate 700.000 sec.-l . . PHASE STRUCTURE IN LUBRICATING GREASE 45,000 20,000 13,000 little effect on the individual particles and recovery in consistency after agitation is very rapid. These greases almost invariably contain small quantities of free water and it seems likely that the second mechanism of flocculation predominates in this case. TABLE III.-CHANGES IN YIELD VALUE OF 15 yo SODA BASE GREASE AFTER SHEARING Yield Value dynes/cmP Treatment I The importance of solid phase structure becomes very apparent with some greases containing no soap. Using silica aeragel,* for example, as little as 3 yo by volume dispersed in oil produces a grease of approximately the same consistency as 10 yo of soap and further additions of silica increase the yield value markedly with little effect on the mobility.Like the calcium soap greases, this dispersion shows almost no hysteresis after shearing and the worked and unworked penetrations are virtually identical. Dispersion of finely divided cellulose in oil behave similarly. If, however, the disperse phase is finely-divided carbon, a relatively large volume concentration is required and the solid phase structure appears to break down irreversibly with shear, at least recovery is slight and extremely slow. Increased concentrations of the carbon influence the yield value only slightly but decrease the mobility considerably and hence bearings lubricated with such dispersions are unduly loaded at high speeds.With both of these solid phases interparticle adhesion would not be influenced by mechanical entanglement or surface swelling. Illustrative data are pre- sented in Table IV. Values in Table IV were obtained from capillary flow measurements . TABLE IV.-YIELD VALUES OF SUSPENSIONS IN LUBRICATING OIL CONTAINING 10 yo SOLIDS CONCEN- TRATION BY VOLUME Solid Phase 1 Yield Value, dyneslcm2 Carbon black . Barium sulphate . Sodium stearate . Calcium soaps . Silica aeragel . 400 5,000 25,000 I 2 7,000 5,000 The variation of the yield value of a suspension with concentration of the solid phase is a most useful indication of the value of the solid in preparing greases with good rheological properties. Those solids that are efficient in contributing to the solid phase structure do not substantially decrease the mobility or increase the high shear viscosity. The reverse is true for those dispersions where a high solids concentration is required * From the method of preparation the ultimate particles in silica aeragel probably have a high length to breadth ratio.They are too small, however, t o be readily resolved microscopically. Kistler, J. Physic. Chem., 1932, 36, 52.E. W. J. MARDLES AND I. E. PUDDINGTON 47 to give a high yield value. A plot of yield value against volume concentra- tion of solids using petroleum jelly as a dispersion medium is shown in Fig. I. This gives a good indication of the variability of solids, when used as thickening agents. The aluminium grains used here would I A A 0 / I' 2 ' a / FIG. I.-The relation between log u (yield value g./sq. cm.) and volume addition of particles to B.P. petroleum jelly. I. Cotton fibres to z mm. length. 2, Hair fibres to z mm. length. 3. Glass fibres to 3 mm. length. 4. Glass fibres to z mm. length. 5. Graphite. 6. Aluminium grains (spheroidal). almost certainly have a surface coating of soap, making them hydrocarbon rather than metallic in their behaviour. The similarity of aluminium and graphite is obvious from the curves. The advantage of using solid par- ticles with a polar surface in the hydrocarbon medium when a high yield value is desired is also apparent. Royal Aircraft EstabEishment, Farnborough . National Research Council, Ottawa, Canada.

ISSN:0366-9033    

DOI:10.1039/DF9511100043

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

E. W. J. MARDLES AND I. E. PUDDINGTON 47 SOME EFFECTS ON THE FLOW OF CONCENTRATED SUSPENSIONS OF VARIATIONS IN PARTICLE SIZE AND SHAPE BY P. S. WILLIAMS Received 24th May, 1951 Classical colloids used in industry involve suspensions of particles with a wide range of size, shape and surface state. One of the most marked departures in behaviour from the laws of solution is observed in the viscosity or consistency of liquid paint. Flocculation of pigment, the strength of interparticle forces giving rise to thixotropy and false-body paints are but little understood, and the paper briefly reviews the present stage of knowledge on these matters. Studies have been made of the rheological properties of glass spheres, of pigment48 FLOW OF CONCENTRATED SUSPENSIONS size range, dispersed in stand-oil + paraffin, or glycerine.Such systems can be regarded as idealized paints in which some of the usually uncontrolled factors, e.g. surface condition and shape are known. The method of preparation and particle size analysis of these spheres is given. It is shown that the viscosity of a suspension of hard spherical particles, over the size range examined, is (a) Newtonian up to 50 yo by volume concentration, for particles > rp diam., (b) dependent on particle size, increasing as particle size decreases, and becoming non-Newtonian for particles > ~p diam. A co-axial cylinder viscometer, de- signed to enable a detailed study of stress-rate of shear-time relationships of materials exhibiting such viscosity anomalies as thixotropy, is described. From the physical point of view, paint, before application, is essentially a suspension of finely divided solid in a viscous liquid.We can at once justify the inclusion of paints in the classification of a colloid, when we consider the particle sizes of pigments. These sizes range from greater than 10 microns in diameter for the earth oxides to less than 0.01 microns for fine Prussian Blue and Carbon Blacks. It is only recently-since the application of the electron microscope to industrial problems-that the size and shapes of most pigments has been capable of resolution. The shapes of pigments may vary from nearly spherical to extremely acicular, while the size range may be very narrow or extremely wide. Illustrative of these variations are electron photomicrographs of Lemon Chrome, Prussian Blue, white lead, zinc oxide (Fig.I). It is well known that the f l ~ w properties of a suspension of small particles will depend to a first order on the viscosity of the suspending medium, and the concentration of the solid phase. Einstein 1 derived the relation where qs is the viscosity of the suspension, qo the viscosity of the sus- pending medium, v the volume concentration of the disperse phase, and k is a constant, equal to 2-5 for spheres. The conditions for the validity of this relationship are that the particles be uncharged, hard and non- interacting. Smoluchowski e has considered the case when particles are charged, and numerous investigators have proposed relationships covering the case when the concentration of the suspended phase increases so that there is interaction between the particles.In general, the viscosity of a concentrated suspension of small particles does not obey Newton’s law which states that for a liquid in laminar flow, the force per unit area required to maintain the flow, is proportional to the velocity gradient. On plotting rate of shear D against applied shear stress per unit area T a curve will be obtained and the ratio 7/0 varies with rate of shear. The differential d.r/dD may vary continuously with rate of shear, or may become constant beyond some limiting value of D. In many cases this ratio is not constant with respect to time of application of shear, but decreases, more or less slowly, to an equilibrium value. On leaving the suspension unsheared for some time, i t will be found that its viscosity will have regained its former value, only to de- crease again on being sheared.Freundlich 3 made extensive studies of such systems which he called thixotropic. Originally referring only to systems undergoing a reversible sol-gel-sol transformation, the term thixotropy now covers a wider range of phenomena, but all have the common feature of a decrease in viscosity with increasing rate of shear and a subsequent regain in viscosity when the material is left at rest. Several mechanisms have been postulated to account for the phe- nomenon of thixotropy 4, but as yet, little progress has been made in 7s = VO(I + kv), 1 Einstein, Ann. Physik, 1906, 19, 280. Smoluchowski, Kolloid-Z., 1916, 18, 194. Freundlich, Thixotropy (Hermann and Cie, Paris, 1935).Langmuir, J . Chern. Physics, 1938, 6, 873. Goodeve, Trans. Faraday SOC., 1939, 35, 342.P. S. WILLIAMS 49 deriving any quantitative theories, Recent theoretical work by Hamaker 6 and others present possible explanations for the thixotropic nature of various suspensions a t low concentrations. These authors derive curves of potential energy for spherical particles in suspension against distance of separation between them, for various ionic conditions. It is shown that, as a result of attractive and repulsive forces acting on the particles, it is possible that the particles will fall into a weak potential trough at some distance from that of closest approach. Such an occurrence could account for observed thixotropic phenomena, The difficulties of investigating the flow behaviour of suspensions of fine particles are not entirely theoretical. The greatest difficulty is en- countered in collecting quantitative data on D - 7- t (time) relationships of concentrated suspensions of fine particles. It would seem that as a result of particle-particle, and particle-medium forces, a dispersed suspension may in time, arrange itself in a state of minimum energy.This may result in a flocculated strmture of the dis- persed phase in the suspending medium. The formation of this structure will be a t a certain rate when the system is unsheared, but may be a t a very different rate under shearing. Any experimental work must take into account the fact that the rheological properties of the material under investigation may be dependent on the previous history of that material.In order to obtain quantitative data relating to the rheological be- haviour of concentrated suspensions in general, and to derive theoretical relationships governing this behaviour, experimental determination of shear stress, rate of shear, time curves must be obtained. It must be emphasized that the rheological behaviour of concentrated suspensions of colloidal particles can seldom be deduced from results obtained on suspensions containing much larger particles. It is only when particles are of the order of I micron or less in diameter that the inter-particle forces, which play so great a part in determining rheological properties, become effective. The author is engaged in work on the effect of particle size and shape on the flow properties of concentrated suspensions of the kind encountered in the paint industry. This paper will present some results obtained on suspensions of glass and silica spheres of various diameters, which were chosen as representing ideal systems of a more simple nature than en- countered in practice.Experimental The method of production of glass and silica spheres is not new* but the method of collection differs from previous attempts, and results in the retention of the finest particles. Glass (Pyrex or other hard glass) is ground to a fine powder in a rubber-lined mill. This powder is then placed in a container connected in the oxygen supply of an oxy-hydrogen torch. The torch is fastened through the lid of a 5 gallon steel drum, and when the oxy- hydrogen supplies are correctly adjusted, the " bush " flame is thrust into the drum and the lid is fitted.This 5 gallon drum has a depth of I or z in. of water in the bottom and is surrounded by a water jacket. The glass powder reaching the flame zone melts ; surface tension forms i t into spheres and these are col- lected in the layer of water in the bottom of the drum. There are, therefore, no effluent gases to be led away which would normally carry off a high propor- tion of the smallest spheres. The spheres are centrifuged out of the water, cleaned, washed and dried. A gravity sedimentation method is used to obtain various sized spheres down to about I micron. The glass spheres are well dispersed by ball-milling in a small quantity of a solution of sodium hexametaphosphate.This suspension is added to a further quantity of water Verwey and Overbeck, Theory of the Stability of Lyophobic Collozds (Elsevier The spheres must now be fractionated. 0 Hamaker, Bet. trav. chim., 1936, 55, 1015 ; 1937, 56, 727 ; 1938, 57, 61. Publishing Co., New York, 1948). * Sollner, Ind. Eng. Chem. (Anal.), 1939, 1 1 , 48.50 FLOW OF CONCENTRATED SUSPENSIONS so that there results a suspension of glass spheres I yo by volume concentration, in 0.1 yo sodium hexametaphosphate solution. This suspension is contained in a 10-gallon drum 200 cm. high. A float resting on the surface of the suspension supports one limb of a syphon, and the syphon rate is adjusted so that the float falls a t the same rate as that of a par- ticular size of sphere.The syphoned suspension then contains all spheres less than this size, By repeating this process, for different syphoning rates, the spheres may be fractionated. The advantages of this method over collecting materid, which has settled after various periods of time, is that the spheres collected have never been at a higher concentration than that originally put in the drum, therefore there has been no deviation from Stokes' law daring the settling period. The use of an anti-flocculating agent is essentia.1 when suspending fine particles, or there will be a possibility of flocculation upsetting the size fractionation, The 10 gallons of dilute suspension are then put through a laboratory cofltinuous centri- fuge, and are collected, washed and dried.Pig. ;1 is electron photomicrographs of spheres produced and fractionated by the above dethod. Fig. 3 is of soheres The spheres are allowed to settle. produced from very &&silica pGwder, instead of Pyrex glass. As can be seen from these photo- FLOW micrographs, the size range and distribution of these spheres is very wide and any attempt a t connecting rheological behaviour with size de- mands some method for particle size analysis to within closer limits of accuracy than are readily obtainable by counting from photomicrographs. A method described by Loukom- sky and O'Brien has been adapted to deal with a wide range of particle L,Qu,o F,LM sizes. The method depends on obtaining a sediment " spectrum " along the length of a Sharples laboratory centrifuge bowl (Fig.4). The heavier particles are deposited NER in the first few centimetres after entry into the bowl, while the finer particles are deposited a t the top of RCMOVABLE the bowl. From an analysis of the weight of the deposit in each centi- meter interval, a particle size dis- tribution may be obtained. The merits of such a method are that -h(o'lOR cDupl1~6 ,ltWO EXIT --FEED NOZZLE SUSPENSION A' the limits of accuracy are due to experimental errors, and not due to FEED 4w oF ROiAiiON C r c A -Ch?rnlnc 1 o h n r Q t n r x r oz=ntrifiina c t o t i c t i r i l nrvnrc nf , - n i r n t ; m n C n n q n x x r * 1". 4. "Ilu.IyIu.3 'U""'C"L"'J u u I I c I I & u ~ u d * U * I U * I " W * b L I " I i . "I u"Uuc1116 C"" lu.. particles. Fig.5 shows particle size - .-. bowl. analyses on glass and silica spheres. The experimental data on the D-r-t relationships of materials described in this paper, were obtained using a co-axial cylinder viscometer designed and constructed at I.C.I. Paints Division. This viscometer (to be described in detail elsewhere) consists of a rotating outer cylinder, with a rigidly held co-axial inner cylinder. The material to be studied is placed in the annular gap between these two cylinders. The rotational speed of the outer cylinder can be varied over a wide range by means of an infinitely variable gear box. The torque on the inner cylinder is measured by a strain gauge torque unit, the output from the strain gauges being amplified and used to drive a D.C. recording milliammeter.By altering the gain of the amplifier, a full-scale deflection on the recwder can be obtained over a stress range of 5 to 50,000 dynes per sq. cm. Plate I is a photograph of the apparatus. The main features of interest in this viscometer are that the shearing stress may be recorded continuously during an experiment, the rate of shear is very nearly uniform throughout the sample and that both the sensitivity of the stress recording and the rate of shear may be altered without introducing any discontinuity in the experiment. Loukomsky and O'Brien, Proc. A.S.T.M., 1946, 1437.FIG. I .--Electron photomicrograph of typical pigments. FIG. 2.-Electron photomicro- FIG. 3.-Electron photomicro- graph of glass spheres, of dia- meter 4p and under. [To face $age 50.graph of silica spheres.PLATE I.-Co-axial cylinder viscometer and recording equipment.P. S. WILLIAMS 5 1 Results and Discussion Experiments were carried out in order to determine the effect of vari- ation of particle size on the viscosity of suspensions of fine particles at various concentrations. Shear stress, rate of shear curves are shown in Fig. 6 for suspensions of glass spheres in the size range 2-10 microns diameter, a t concentrations ranging from 26 % to 50 yo by volume, in a mixture of zinc iodide, glycerine and water, of viscosity 0.63 poises. i \ FIG. 5.-Particle size analyses of (u) silica spheres, (b) glass spheres. FIG. 6.--0-7 curves of glass spheres, Z - I O ~ diam. in ZnI, + glycerine + water mixture of r) = 0.63 poise. ( a ) 5 0 yo ; ( b ) 46.4 Yo ; (c) 40.4 "/b ; (d) 35-6 yo.This suspending medium was chosen since easy variation of density and viscosity may be obtained. Work reported by Vand 10 on the flow be- haviour of suspensions of glass spheres up to 50 Yo by volume concentra- tion in a similar medium, states that the suspensions exhibit a time thixo- tropy in the reverse sense to that which might be expected. On stirring the suspensions, an increase in viscosity was observed for suspensions of concentration above 40 yo by volume. The viscosity after stirring was greater than normal, but decreased exponentially to its normal value, lo Vand, J . Physic. Chem., 1948, 52, 277.52 FLOW OF CONCENTRATED SUSPENSIONS Over the range of rates of shear used in the present experiments (up to 50 sec.-l) the behaviour of the suspensions was Newtonian] with no evidence of variation of shear stress with time of application of the shear.Table I gives values of 7,. (experimental) and q,. calculated from Vand's equation, Agreement between the two values is not obtained. qr = I + 2 . 5 ~ + 7'349ca* qsp = kV* If, in Einstein's equation] the volume concentration V is replaced by the value V / ( I - S V ) , where S is the volume the sediment of a suspension would occupy, whose par- ticles themselves occupy unit volume, then on plotting V / T ~ ~ against V, a straight line would be obtained. Values of Y and V/qep obtained in the present experiment are given in Table I and pIotted in Fig. 7. The - 4 5 Volume uoncentration V FIG. '/.-Plot of V against V/qaD for glass spheres, 2 - 1 0 ~ &am.in ZnI, + glycerine + water mixture of r) = 0.63 poise. value of S obtained from the graph is 1-9, in close agreement with values obtained by Robinson l1 using spheres between 10 and 30 p diam. TABLE I Volume Concentration V 50.0 46-6 40'4 35'6 31.6 26.0 rlf (Obs.) 50.0 25.0 9'3 6.0 4'7 3'3 tlf (Calc.) 4'1 3'7 3'2 2.8 2'5 2.15 V h p 0'0 I 0'02 0.05 0.07 0.09 0'12 The void space for ideal 6-fold packing is 0.4764 cm.-a per cm.-*, so that the value of S for such a sediment would be 1-91. There is obviously very close agreement between this value of S for 6-fold packing, and the value obtained experimentally. For a concentrated suspension showing Newtonian flow properties] the most likely spatial arrangement of the particles would be close to that of the 6-fold arrangement of a packed sediment.l1 Robinson, J . Physic. Chem., 1949, 53, 104.P. S. WILLIAMS 53 In order to test the above theory, namely, that on plotting V against V / T ~ ~ , a straight line should be obtained, with intercept on the V axis equal to r/S, an attempt was made to repeat the initial experiment, but using spheres of silica with diameters I to 0.1 p and 0.025 p. It was found very difficult to disperse these smaller spheres at concentrations approaching 40 yo by volume, or over. Fig. 8 and g show D-r-t curves for a suspension of 44 yo by volume silica spheres in a glycerine + water mixture of viscosity 0.35 poise. This suspension was observed to set to a gel after a period of about 24 hr. at rest. It was therefore decided to investigate the flow properties of suspensions of these spheres at a con- centration of about 10 yo by volume, in a linseed stand oil+paraffin mixture.This medium was chosen because of the excellent dispersing power of stand-oil, while the viscosiv of the mixture may be varied by alteration of the paraffin concentration. FIG. 8.-D-r curve for 44 yo silica spheres < ~p diam. in glycerine + watei mixture of 7 = 0.35 poise. FIG. g.--D-~-t curves for 44 yo silica spheres < I,U &am. in glycerine + water mixture of 7) = 0.35 poise. (a) immediately after stirring ; ( b ) after 12 hr. a t rest ; (c) after 24 hr. at rest. Fig. 10 and 11 show the 0--7 and D-T-~ relationships for these suspensions. The suspensions containing spheres down to O - I ~ diam.are Newtonian, but the finest spheres, of diameter 0-025p are thixotropic in flow behaviour, giving suspensions with a yield value even a t low con- centrations. The following conclusions may be drawn from the above results. The viscosity of a suspension of hard spherical particles over the size range examined is : (I) Newtonian up to 50% by volume concentration, for particles greater than about ~p diam.54 FLOW OF CONCENTRATED SUSPENSIONS (2) Dependent on particle size, increasing as particle size decreases, and becoming non-Newtonian for particles less than about ~p diam . (3) For suspensions exhibiting Newtonian flow behaviour, the vis- cosity against concentration relationship may be represented by the equation V / q s p = I l k - SV/k. This equation does not apply to thixotropic suspensions.The results presented in this paper indicate the complexity of the flow behaviour of concentrated suspensions of spherical particles in the colloidal size range. FIG. ~o.--D-r curves for (a) silica spheres, 0-025p diam. ; < ~p diam. ; (b). silica spheres (c) glass spheres 2-10p diam., at 11 % concentration in stand-oil + paraffin mixture of 9 = 11 poise. FIG. II.-D--~ curves for silica spheres, o'oz5p diam. in stand-oil + paraffin mixture. (a) 8-65 %, qmix 7-4 poisf ; (b) 8-17 %. qmix 5.3 poise ; (c) 7.7 %, Tmix 3'4 poise ; (a) 7'3 %, Vmix 2.6 poise ; (e) 6'7 %, qmix, 1-35 poise ; ( f ) 6.1 %, Attempts have been made to measure quantitative thixotropic char- acteristics of a system. Green and Weltman,f* and Moonep19 derive various coefficients, which are correlated to the observed flow behaviour of thixotropic systems. These authors have attempted to fit mathe- matical equations to the results they have obtained. In the present l2 Green and Weltman, I n d . Eng. Chem. (Anal.), 1943, 15, 201 ; 1946, 18, 167. l3 Mooney, J . Colloid Sci., 1946, I , 195. qmix 0.6 poise.P. S. WILLIAMS 55 author’s opinion, the factors to be considered in formulating any theory attempting to explain the rheological properties of concentrated sus- pensions of fine particles should consider (a) the force between the particles of a flocculate, tending to hold (b) the stability of a flocculate to the forces imposed upon it during It is not until a sound theory on these two important factors governing the flow behaviour of concentrated suspensions of colloidal particles has been derived, that a close understanding of this behaviour will be made. On the other hand, the gaining of quantitative data on these suspensions may well help the theoretician on his way. Mr. N. D. P. Smith, of I.C.I. Paints Division, Slough. Imperial Chemical Industries Limihd, them together, and shear. The author wishes to acknowledge with.thanks the helpful advice of Paints Division Research Laboratories.

ISSN:0366-9033    

DOI:10.1039/DF9511100047

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

P. S. WILLIAMS 55 A STUDY OF THE NUCLEATION AND GROWTH PROCESSES IN THE SYNTHESIS OF COLLOIDAL GOLD BY JOHN TURKEVICH PETER COOPER STEVENSON AND JAMES HILLIER Received 18th May 1951 After a preliminary survey with the electron microscope of various prepara- tions of colloidal gold a study was made of the process of nucleation and growth in gold colloids. It was shown that nucleating agents may be identified with reducing agents which form a mixed polymer with chlorauric ion before the reduction to the nucleus takes place. It was also shown that the law of growth is exponential. The average size the deviation from the average size and the character of the particle size distribution curve are determined by the amount of gold the nucleation process and the law of growth.Colloidal gold may be considered as a typical hydrophobic colloid with particle size falling below the resolution limit of the optical micro- scope. With the development of the electron microscope which has s resolution permitting the examination of the individual colloidal particles 1 it was natural to make an extensive study of the shape mean size and size distribution of the various preparations of colloidal gold and determine the factors that govern these properties. Previous work on the subject was limited to one or two preparations.4 Experimental Electron Microscopic Examination of Various Preparations of Colloidal Gold.-In order to gain an insight into the colloidal gold system a systematic survey was made of all standard preparations of colloidal gold.Due precautions were taken to ensure cleanliness of the distilled water reagents 1 Turkevich and Hillier Anal. Chem. 1949 21 475. (a) Beischer and Krause 2. angew. Chem. 1938 51 331 ; (b) Ardenne 2. physik. Chem. A 1940 187 I ; (c) Koch 2. Elektrochem. 1941 47 717 ; (d) Feitknecht Signer and Bergern Kolloid-Z. 1942 101 12; (e) Roginski Shekhter and Sacharova Compt. rend. U.R.S.S. 1946 52 687; (f) Borries and Kausche Kolloid-Z. 1947 90 132 ; (g) Harris Jeffries and Siegel J . A+pZ. Physics 1948 791. SYNTHESIS O F COLLOIDAL GOLD 56 and the glass vessels used. The water was distilled water purified from nuclei by ultrafiltration. The glass vessels used were not only cleaned with aqua regia to remove traces of colloidal gold which might subsequently serve as nuclei but were also treated with chromic acid and steamed for 20 min.to remove any grease film. Contact with rubber tubing or rubber stoppers was scrupulously avoided. The colloidal gold preparations were examined in an RCA electron to evaporate. The resolution of the microscope was about 10-20 A. microscope by placing a drop of the colloid on a collodion screen and allowing it BREDIG SOL^ was prepared by striking an arc from two gold wires under very dilute sodium hydroxide solution with a 115 V 60-cycle potential. The gap between the electrodes was about 5 mm. and the electrodes were agitated to keep them from fusing. A purple cloud was observed t o drift away from the arc gradually darkening the entire solution. The process was continued until a fairly intense purple colour had developed and the colloid so obtained was examined with the electron microscope.The particles ranged in diameter from 30-100 A but due to their small size and extensive clumping no precise measure- ments of size distribution could be made. FARADAY SOL* was prepared in the following way. A saturated solution of white phosphorus in freshly distilled diethyl ether was diluted with three times its volume of diethyl ether. 50 ml. of chlorauric acid solution (50 mg. of Au) was diluted with 45 ml. of distilled water and with 5 ml. of 0.1 N KOH. This solution was treated using good mechanical stirring in one case with 2-0 ml. of the phosphorus-ether solution and in the other case with 1-0 ml. of the same solution.The solution turned first brown then grey purple and red finally giving a deep-red product. The sol was then heated to boiling and a stream of filtered air was drawn through it in order to oxidize any remaining phosphorus. Electron microscopic examination revealed that both sols con- tained extremely fine particles more or less clumped. The sol reduced with 2 ml. root-mean-square deviation of 30 yo. This preparation was grown to double of phosphorus solution consisted of particles of mean diameter of 50 A with a quadruple and eight-fold of the original diameter by means of the hydroxyl- amine development technique (described below) in an attempt to deduce the smallest particle size in the original Faraday preparation. An electron micro- scopic examination of these developed preparations showed that the smallest particle in the original Faraday sol was about 30 A diam.This is interpreted to mean either that particles smaller than 30 A are not formed by the Faraday method or if they are formed they do not serve as nuclei in the hydroxylamine + gold chloride growth medium. The size distribution of the Faraday sol particles is not symmetrical having a gradual rise on the small diameter size passing through a sharp maximum to a rapid drop on the large diameter size and showing a small tail of larger particles. The significance of this distribution curve characteristic of many gold sols will be discussed later. The sol made by the reduction with I ml. of phosphorus diethyl ether solution consisted of par- ticles of mean diameter of 70 with a root-mean-square deviation of about 25 yo.Rinde studied Faraday sols by growing them in a hydrogen peroxide + gold chloride medium and determined the particle size distribution by gravity and ultracentrifugal sedimentation. His curves have a similar general appear- ance to those found in the present investigation. Rinde however deduced the average particle diameter to be 19 A. ACETONE SOL.* 98 ml. of chlorauric acid solution (containing 12 mg. of Au) were heated to boiling and treated with I ml. of acetone purified by dis- tillation from alkaline permanganate. On boiling a faint coloration appeared in the solution after about go sec. darkening gradually to deep red. Under the electron microscopic investigation the particles appeared in clusters of about 50.The individual particles were non-spherical with a probable diameter of about 200 A and a root-mean-square deviation 13 %. TANNIN GOLD SOL.'-IO ml. of chlorauric acid (containing 10 mg. of Au) was added to IOO ml. of water the solution was made neutral to litmus with Bredig 2. angew. Chem. 1898 I I 951. Faraday Phil. Trans. 1857 147 145. 6 Rinde The Distribution of Sizes of Colloidal Gold Sols prepared according to the Nuclear Method (Uppsala 1928). 6 Davies J . Physic. Chem. 1929 33? 276. 7 ( a ) Wieser Inorganic Collozd Chemzstry I (John Wiley and Sons New York 1g33) p. 40 ; (P) Garbowski Ber. 1903 36 1215 ; (c) Ostwald Kleiner Prak- tzkum der Kollozdchernie 2nd edn. (1920). J. TURKEVICH P.C. STEVENSON AND J. HILLIER 57 sodium carbonate and heated to boiling. A fresh I yo tannin solution was added dropwise until no colour change was observed on further addition. The the sol consisted of small spherical particles of 120 A mean particle diameter sol was pink and had a slight opalescence. Electron micrographs showed that and a root-mean-square deviation of 28 yo. The particles occurred singly or in small clusters. It is of interest to note that the particles making up the clusters were not in contact but were separated by a space of not less than 40 A. This may be interpreted to indicate that the particles are surrounded by a skin of protective colloid (tannin) of too low a contrast to be visible in the electron microscope. OXALIC ACID S0~.-38 ml.of chlorauric acid solution (containing 20 mg. Au) was treated at the boiling point with z ml. of I yo oxalic acid. Turbidity ap- peared in about 5 sec. and the reaction seemed complete in 20 sec. The sol was light blue in colour while the scattered light was yellow. The particles were about 2000 A diam. irregular in shape and the size distribution was rather broad. HYDROXYLAMINE SoL.s-Hydroxylamine hydrochloride in slightly acid solution has been described by a number of investigators as an inhibitor for the nucleating agent. 20 ml. of ow27 yo hydroxylamine hydrochloride solution nucleation of colloidal gold. In neutral or basic solution however i t is a was added to 20 ml. of chlorauric acid solution (containing 2 mg. of Au) pre- viously neutralized with potassium carbonate.A dark blue colloid formed instantaneously. Unlike the ordinary unstable blue colloidal gold this colloid was stable. The blue colour had been ascribed to this preparation by Thiessen 9 as due to the presence of aurous oxide. The sol was found to consist of small non-spherical particles aggregated into clusters. The distribution curve was broad with a maximum at about 150 A and a root-mean-square deviation of 44 %. DONAU SoL.lo-Carbon monoxide gas was bubbled through a chlorauric acid solution (containing 0.001 yo Au) at room temperature. The solution highly irregular particles of about 200 A diam. and 400-800 A long. Their darkened assuming finally a purple colour. The sol was found to consist of appearance suggested that the particles were formed by the deposition of gold on straight or bent chains of smaller particles and that the growth took place during coagulation (Fig.I). ACETYLENE SOL.-IS ml. of chlorauric acid solution (containing 10 mg. of Au) were treated with 2 ml. of water saturated with acetylene gas. A pink colour appeared in 20 sec. and in 2 min. the sol became dark ruby-red. Electron microscope examination of this sol revealed small particles mostly spherical in shape with a mean diameter of 285 A and a root-mean-square deviation of 22 %. The size distribution curve was definitely skewed the slope on the large diameter side of the maximum being markedly steeper than on the smaller diameter side. An unusual feature of the separation was the presence of a few particles in the form of triangular plates.Since the acetylene sol was definitely acidic the effect of the hydrogen ion concentration was investigated. Solution of pH 10.4 and 8.0 gave no sol formation. Solution with a pH of 5.8 obtained by adding an appropriate amount of sodium carbonate to the original reagents produced a sol slowly taking 5-7 min. to develop full colour while the non-neutralized acetylene + chlorauric acid solution required 2-3 min. The particles in the neutralized medium were smaller having a mean diameter of 170 with a root-mean-square deviation of 16 yo. The size distribution curve was again skew-shaped. No plates were found. If the starting reagents were of lower pH value containing 20 and 64 mequiv. of added HC1 the sols formed had a definite blue tint and contained a large number of irregularly-shaped flat plates and bipyramids.The distribution in size was very broad. CITRIC ACID GOLD So~.-g5 ml. of chlorauric acid solution (containing 5 mg. of Au) were heated to the boiling point and 5 ml. of I yo citric acid solution was added to the boiling solution with vigorous mechanical stirring. The solution remained clear for about 15 sec. and then suddenly a dark blue-purple sol was formed. There was no further change of colour on prolonged boiling. When examined in the electron microscope this sol proved to be identical in appear- ance to the one prepared in acidified acetylene solution. Large numbers of flat triangles and hexagons were seen. There were also some bipyramidal forms.The particle ‘‘ diameter ” ranged from IOO to 500 A. Because of the extensive variability in shape no size distribution curve was determined (Fig. 2). * (a) Rinde ref. (15) ; (b) Thiessen 2. anorg. Chew. 1929 180 5 7 ; (c) Thiessen Kolloidckem. Beihefte 1929 29 122. sThiessen 2. anorg. Chem. 134 1924 393. lo (a) Donau Monatsh. 1905 25 525 ; (b) n7eiser ref. (7a) p. 41. SYNTHESIS OF COLLOIDAL GOLD 58 SODIUM CITRATE SOLS.-This Preparation of great importance in our in- vestigation is a modification of the one described by Hauser and Lynn.ll The following is a description of a preparation which we shall term the " standard " sodium citrate sol 95 ml. of chlorauric acid solution (containing 5 mg. Au) were heated to the boiling point and 5 ml.of I yo sodium citrate solution was added to the boiling solution with good mechanical stirring. After about a minute a very faint greyish-pink or greyish-blue tone appeared gradually darkening over a period of about 5 min. The final colour was deep wine red. Electron microscopic examination of a number of preparations showed that this colloid is highly reproducible and gives spherical particles (Fig. 3) with a mean diameter of about zoo 15 A and a root-mean-square deviation of 12.5 %. The size distribution curve based on a count of 1046 particles is not symmetrical but shows a distinct " tail " on the small diameter side (Fig. 4). The effect of % Deviation Temp. "C IOO (standard) 80 Mean Particle Size in A 2 00 165 Approximate Time for the Completion of Reaction in min.5 25 45 12.5 8.1 8-6 I80 70 effect of decreasing the amount of sodium citrate (Fig. 5 ) in the preparation on the properties of the gold sol are given in Table 11. The colour changes ac- companying the reaction show marked variation as the amount of the citrate is decreased. The early stages become more definitely blue and the transition from the blue to the red becomes more sharply defined. The overall reaction appears to take place more rapidly a t the lower citrate concentration. Using I/Ioth the standard amount of citrate the reaction could be divided sharply l1 Hauser and Lynn Ex9eriments in Colloid Chemistry (McGraw Hill 1g40) p. 18. FIG. I.-Electron micrograph of a gold sol reduced with carbon monoxide magnification of 50,000 diameters.FIG. 2.-Electron micrograph of a gold sol reduced with citric acid magnification of 50,000 diameters. [To face page 58. FIG. n.-Electron micrograph of a gold sol reduced with sodium citrate (standard citrate sol) magnification 50,000 diameters. FIG 12 -Electron micrograph of nuclei for colloidal gold isolated by the ion eschange resin method magnification 43,600 diani. [See page G 5 . J. TURKEVICH P. C. STEVENSON AND J. HILLIER 59 into three stages. The reaction mixture was colourless for 12 sec. after the addition of the citrate then i t turned bliie within a fraction of a second. After a total reaction time of 72 sec. it suddenly turned clear red. The colour changes accompanying this reaction were very striking.Size distribution curves were obtained for all preparations but the one using 1/2oth of the amount of citrate used in the standard preparation. This Iattersol was highly turbid and coagu- lated very rapidly. Decreasing the amount of citrate caused the mean particle % 25 n 20 /5 25 20 k 0-005 ZAu. % ! AIL ~ ZOO 100 FIG. 5.-Size distributions of sols reduced with varying amounts of sodium citrate. Upper curve one-tenth the standard amount of citrate ; middle curve one- fifth the standard amount of citrate ; lower curve half the standard amount of citrate. Approximate Time for the Completion of Reaction in min. Citrate (mg.) 50 (standard) Mean Particle Size in A LOO 5-0 300 400 500 FIG.6.-Size distribution of sols reduced with sodium citrate a t different dilutions. Upper curve twice standard dilution ; middle curve standard dilution ; lower curve half standard dilution. diameter to increase somewhat and the size distribution curve showed a definite " hump " on the large diameter side of the average diameter. The effect of dilution of reagents on the properties is given in Table I11 and Fig. 6. Sols made in the more concentrated solutions had a smaller particle diameter but were somewhat contaminated. Further detailed studies on the sodium citrate TABLE II.-'rHE EFFECT OF CITRATE CONCENTRATION ON THE SODIUM CITRATE SOL yo Deviation 12'5 9'4 11.8 12'1 5'0 25 2.0 1.2 I0 5 240 3'75 I45 15.5 dirty and clumped dirty and clumped 2.0 2'0 2'5 SYNTHESIS OF COLLOIDAL GOLD 60 sol will be considered in connection with the process of nucleation and growth of colloidal gold.TABLE 111.-THE EFFECT OF DILUTION ON THE SODIUM CITRATE SOL PREPARATION Dilution Time for the Completion of Reaction in min. 1 Mean Parti& inA Size % Deviation 1 /2 I74 200 I (standard) 5 2 6 2 10.4 12-5 I 2.6 235 electron microscopic survey of the methods of preparation of gold colloids has shown that the nature of the product formed was highly dependent on the reagent used and on the conditions. The particle shape the particle size and the nature of the size distribution curve have been shown to vary within quite large limits.The Nucleation Process .-An The shape of the size distribution curve will be shown to depend largely on the relative rates of two separate processes nucleation and growth. Nucleation will be defined as the process whereby a discrete particle of a new phase forms in a previously single-phase system in our case a homogeneous solution. Growth will be defined as a process in which addi- tional material deposits on this particle causing i t to increase in size. It has been shown that these two processes are indeed separable. Zsigmondg and Thiessen la have studied the nucleation using several reducing agents. This section will deal with sodium citrate and hydroxyl- mine hydrochloride as reducing agents of auric ion the former acting as both a nucleating agent and a growth agent while the latter functioning only as a growth agent.Nucleation in the formation of gold sols is a difficult phenomenon to investigate directly. Preliminary evidence indicated that the nuclei are very small of the order of 50 k or less in diameter and consequently not susceptible of effective direct examination with the electron microscope. Furthermore these nuclei have only a transitory existence in the reaction mixture during the ordinary methods of gold sol preparation. The experi- mental criterion for the presence of nuclei that was used was the following the solution suspected of containing nuclei is added to the growth medium consisting of a solution of 12 x I O - ~ parts of hydroxylamine hydrochloride and 10 x 10-4 parts of chlorauric acid.If the nuclei are present in the solution tested reduction takes place either to colloidal gold a coagulated gold sol or to large particles of gold depending on whether the number of nuclei is large or small. Each particle produced in this growth medium is presumed to have formed from the nucleus present in the solution tested at the time of its addition to the growth medium of chlorauric acid and hydroxylamine hydrochloride. In the absence of nuclei and in a dust-free atmosphere the growth medium undergoes no reduction of the auric ion for several hours. This test for the existence of nuclei may be adapted for the growth of nuclei to a size convenient for observation by the choice of a proper amount of the growth medium (development technique).It was decided to study the nucleation process in the production of colloidal gold by the sodium citrate reduction taking advantage of this develop- ment technique to bring the nuclei formed at various times into a range of size capable of ready evaluation. The number of particles in the sols so developed and consequently the number of nuclei were determined either by counting in the slit ultramicroscope or deduced from the optical properties of the developed sol. In addition a method was developed l2 (a) Zsigmondy 2. physik. Chew. 1906 56 65 ; ( b ) Thiessen ref. (8b) and (8c). J. TURKEVICH P. C. STEVENSON AND J. HILLIER 61 for determining the rate of nucleation from the ultimate particle size distribution curve as revealed by the electron microscope.Furthermore a study was made of the disappearance of the auric ion as a function of time and this was correlated with the nucleation rate. In addition a method was found for removing the auric ion from solution after nucleation was essentially complete and examining the isolated nuclei with an electron microscope. Finally an oxidation product of sodium citrate was studied as a nucleating agent Slit-Ultramicroscopic Examination.-Since nuclei are difficult to see in slit-ultramicroscope the following procedure due to Zsigmondy l3 was adapted to the study of the rate of formation of nuclei from gold chloride by sodium citrate. Reagents necessary for the production of the standard sodium citrate sol were mixed in clean glass-stoppered Erlenmeyer flasks and kept in a thermo- stat.At fixed intervals samples were drawn from the nucleating solution and were added to a volume of the growth medium so chosen empirically as to give developed particles of a size chosen to minimize coagulation during the counting operation. The samples so obtained were diluted to standard volume and ali- quots were introduced into a cell of a Bausch and Lomb slit-ultramicroscope for counting. Nucleation curves for the formation of gold sol were measured FIG. 7.-Nucleation curve at 58.5" C measured with the slit ultra-microscope. in the sodium citrate 3- chlorauric acid solutions a t 23.0' C and at 58.5O C and are presented in Fig. 7. Examination of the data shows that it takes about 40 min. to complete nucleation a t 23O C and 4 min.a t 58.5" C indicating a high temperature coefficient foi- the nucleation process. Furthermore the curves indicate that the rate a t the start is reasonably constant and then drops off suddenly a t the end. The nuclei formation is complete long before the process of colloidal gold formation ends because the colour of the solution deepens a t 23' C for 12 hr. and at 58.5' C for 2 hr. Previous investigations of the rate of nucleus formation were carried out by Thiessen l4 who used the same technique for the study of the nucleation of gold by potassium oxalate hydrogen peroxide sodium citrate potassium thiocyanate and ultra-violet light. The experiments with sodium citrate were carried out a t one temperature. The general character of his sodium citrate nucleation curve is similar to the one reported in this investigation.It is felt that the method of counting particles in the slit-ultra- microscope has definite disadvantages. In the first place the method is subjective and involves errors arising from dark adaptation and subsequent fatigue of the eyes. Secondly the time of count is often comparable to the time of stability of the developed colloids. Thirdly there is always an error arising from defining the depth of the liquid examined. Finally the question arises as to whether very small particles can be detected with as much assurance as the larger ones. For this reason it was thdught that other methods should be developed to deter- mine the rate of nucleation.l4 Thiessen ref. (84. l3 Zsigmondy ref. (124. SYNTHESIS OF COLLOIDAL GOLD FIG. 8.-Nucleation curve a t 49' C measured with a nephelo- meter. Ordinate particles per unit volume ; abscissa time (sec.). 6 2 Nephelometric Method.-In this method sodium citrate + chloraurate mixture was allowed to nucleate and aliquot portions were developed by addition to a constant amount of the hydroxylamine growth medium. A series of de- veloped gold sols were obtained having the same total gold content but differing among themselves in the number and consequently size of the gold particles. The number was determined by nephelometric comparison with an appropriate standard set of colloids of the same gold concentration but different known particle concentration.This graded set of standards was obtained in the follow- ing way. A gold sol was prepared by allowing a nucleating mixture identical to the one under investigation to go to completion. This sol contained the maximum number of particles which could be determined experimentally. This number corresponded to the final number of nuclei formed. The particles in this completed sol were of minimum size compared to the other members of the graded set. Other members of the standard series were prepared by taking known volumes of this final solution (containing known number of particles) and developing them in a hydroxylamine hydrochloride + chlorauric acid solu- tion of such a strength in gold that the total gold concentration was the same as in the developed samples from the sodium citrate run under investigation.The particle concentration of the developed aliquot sample from the run was ob- tained by comparison with an appropriate standard in a nephelometer. Using this procedure i t was not difficult to prepare a curve for each run showing the fraction of nuclei formed as a function of time. The number of nuclei per ml. in the completely nucleated sol could be easily determined either by a nephelo- metric comparison based on the zoo A standard sol or by an electron microscopic investigation of their particle size. A typical nucleation curve obtained in this way is shown in Fig. 8. The curve is similar in nature to the one obtained with the slit-ultramicroscope. It is more convenient to determine and its ac- curacy and reproducibility are much greater An assumption is made that the total scattering observed is determined primarily by the mean particle volume and is independent of small variations in the particle size distribution curve.Electron Microscopic Methods.-There are two methods that can be used to determine the nucleation curve using the electron microscope. The first method consists of stopping the nucleation process a t various times and develop- ing the samples. Each individual developed sample is examined in the electron microscope and a size distribution curve is obtained. The mean particle volume of each sample is determined from these curves. Since the total gold content is known one can determine the number of particles per unit volume present in the nucleating mixture at the time of development of each sample.This pro- cedure however is rather time-consuming and tedious. J. TURKEVICH P. C. STEVENSON AND J. HILLIER curve ordinate N ( t ) ; abscissa time. 03 N ( t ) = n(D)dD. - dD/dt = K(C T)D . 63 The second method consists of determining the nucleation curve from the particle size distribution curve of the completed preparation of the gold sol. The metbod is based on the assumption that the principal cause of the spread in particle size of a gold colloid is the spread in time in the nuclei formation. Particles formed early in the nucleation process begin to grow immediately so that in the final sol the particles that first form and hence have the longest time to grow attain the largest size.Nuclei which form later attain smaller and smaller sizes corresponding to shorter and sborter growing times. The size distribution of a sol can be considered as a regularly distorted mirror image of the nucleation curve. In Fig. 8 are shown schematically a size distribution curve (upper curve) and a nucleation curve (lower curve) of the same colloid. The marked diameter D in the size distribution curve was chosen to be the diameter finally attained by those particles formed during nucleation a t the time f marked FIG. 9.-Schematic diagrams to illustrate the calculation of nucleation curves from size distributions. Upper curve schematic size distribution ; ordinate yo total particles ; abscissa diameter D(t) ; lower curve schematic nucleation on the nucleation curve.The ordinate of the nucleation curve at t represents the total number of particles present in the unit volume of the solution a t time t i.e. all those particles which have formed up to and including time t . It is con- venient to express this number as the fraction of the number of particles that are going to be eventually formed a t infinite time N ( t ) . The total number of particles formed up to time t is simply the total number of particles with diameter greater than D(1) or - (1) The value of this definite integral is the shaded area under the distribution curve and this can be determined as a fraction of the total area. In the section on growth it will be shown that a gold particle grows according to the law - (2) where D is the diameter of the particle and k is the velocity constant dependent on the temperature and reagent concentrations.In the integrated form i t - (3) where a is a function of time a t which an arbitrarily-selected reference particle forms and of the rate constant k while b is proportional to k. If one obtains becomes 1 = (a - log D)/b . SYNTHESIS O F COLLOIDAL GOLD 64 from independent observations the values of a and b one can derive a nucleation curve from a particle size distribution curve by means of the equations above. Since knowledge of these constants was incomplete a t the time of the in- vestigation i t was decided to modify the procedure by taking at least three samples from a nucleating sol and developing them.These three developed samples taken a t three definite times and the completed sol were examined in the electron microscope. (Actually two samples taken a t two times during nucleation are sufficient but the third was taken to obtain check values.) Dis- tribution curves were taken of these four sols. Three incompletely nucleated sols were used to determine the mean diameter and thus the number of nuclei present in the reaction mixture at the three definite times when the nucleation was stopped by development. One therefore obtains three points on the nucle- ation curve and these points will be used later to convert the time size scale into a time scale. One then examines the size distribution of the completed sol. The area lying to the right of a particular D value is determined from the experi- mental distribution curve for a number of arbitrarily chosen D values.The values of these areas the fraction of particles having a diameter greater than D are plotted against log D. We thus have a plot of the number of nuclei against log D. In order to convert this to a time scale one uses the relation t = (a - logD)/b the constants a and b being determined from the three values of the number of nuclei at three different times previously obtained by the study of the distribution curves of the three partially nucleated sols. The size distribution curve has been converted into a nucleation curve. Several implicit assumptions were made in this treatment In the first place all nuclei were assumed to form with the same original diameter secondly the law of growth was assumed to hold for nuclei as for the larger particles and finally i t was assumed that the addition of hydroxyl amine hydrochloride in the development process stopped the nucleation instantly.Thiessen l5 has stated that in nucleation with citrate the nucleation process is stopped im- mediately by the hydroxylamine. His statement is based however on his failure to observe ar? induction period. As will be shown below our experiments indicate that there is a definite induction period in the nucleation with sodium citrate. Finally before leaving the subject of the relation of the size distribution curves as determined by the electron microscope to the nucleation curve i t was of interest to see how the partial nucleation curve (obtained from the samples for which the nucleation was stopped a t definite times by development) fit into the complete nucleation curve.The nucleation curves were determined for the three samples from their distribution curves using the method described above. The constant b was the same for all the three developed samples and was taken as that of the final sol since prior to development these partially nucleated samples were mere undifferentiated portions of the nucleating solutions. The curves so obtained were translated along the time axis to obtain for their lower parts the best fit with the complete nucleation curve (Fig. 10). A study of the curve so obtained shows an excellent fit for the lower portions of the nucleating curve of each developed sol.The upper portions of the curve however show marked deviations. Instead of a sharp break from the overall curve the three partially developed sols approach t3eir final nucleus numb2r gradually. Part of this rounding-off of the expected sharp break is undoubtedly due to the imperfect resolution of the electron microscope and to errors in the measurement of the smaller particles. It is thus seen that a good insight can be obtained into the kinetics of nucleation of gold sols by the study of the particle size distribution curves by means of the electron microscope. Thiessen ref. (8c). 1@ Scotts Standard Methods of Chemical Analysis (ed. N. H. Furman) (D. van The Rate of Disappearance of the Auric Ion.-A study was made of the rate of disappearance of the auric ion during the formation of a gold sol in a sodium citrate + chloraurate system by withdrawing a t definite times aliquot portions running them into concentrated potassium iodide solution reducing the iodine liberated by a measured excess of standard thiosulphate solution and titrating the remaining thiosulphate with standard iodine solution.lG The results of a typical experiment are given in Fig.I I. It will be observed that the nucleation process is essentially complete before as much as 5 yo of the auric ion has been reduced. The statement of Thiessen l7 that nucleation stops due l7 Cf. ref. (8b). Nostrand Co.) 5th edn. I p. 437. J. TURKOVICH P. C. STEVENSON AND J. HILLIER sodium citrate a t 49' C. 65 to the exhaustion of the ionic gold is therefore not applicable to our system.The rate of disappearance of the auric ion is proportional to the concentration of the nuclei and an indication of the size of the nuclei may be obtained in the following way. About one-twentieth of the auric gold has disappeared by the end of nucleation. The ratio of diameters is the cube root of this fraction or 0.36. Since the final diameter of the sol is about 170 the mean nuclear size a t the end of the nucleation is about 60 A. From the size distribution curve the smallest particle has a diameter between one-half to two-thirds of the mean the smallest nucleus should have a diameter of about 30-40 A. FIG. I I .-Concentration of auric ion as a function of time during reduction with Ordinate concentration of [Au+++] x 10 ; abscissa time (min.).- 100 50 FIG. 10.-Nucleation curves calculated from particle size distribution for a com- pleted sol and three samples developed during nucleation. Ordinate number of particles per unit volume ; abscissa time (min.). Isolation of the Nuclei.-An attempt was made to isolate the nuclei for direct examination and the use of ion exchange resins suggested itself for the removal of the auric ion. Four ion exchange resins were used the cation ex- change resins being charged with sodium ion and the anion exchange resins with hydroxyl ions (sodium carbonate). They were well washed with distilled water. A nuclear solution was prepared by incubating the standard sodium citrate + chloraurate system for 19 min.at 30-5' C. The colour of the solution a t this time was pale grey. Dowex-go cation exchange resin had no appreciable effect on the reaction mixture and both nuclei and auric gold passed through the column. Amberlite IRC-roo cation exchange resin proved to be a rapid reducing agent for the nuclear solution ; a clear red colloid came from the bottom of the column. This resin did not however reduce pure solution of chlorauric acid. Amberlite IR-4 and IR+ both anion exchange resins produced no visible effect on the colour. The emergent solution did not liberate iodine from potassium iodide and was therefore substantially free of auric ions. Furthermore i t was stable toward boiling and produced a colloid when introduced into growth medium.Electron microscopic examination showed that the particles were surprisingly large and diffuse. Their irregular shape did not permit the deter- mination of a size distribution curve (Fig. 12). Their form and lack of opaque- ness suggests that they may contain organic material because irregular bodies such as were seen often result from the decomposition of organic material by the electron beam. The ionic gold could not be eluted from the column by SYNTHESIS OF COLLOIDAL GOLD CH,COOH (+ CO;+H,O) CHz-CooH HO C-COOH -0 [Ol I I I CH,COOH 66 solutions of sodium carbonate sodium hydroxide sodium chloride sodium sulphate hydrochloric acid sulphuric acid or nitric acid. The latter attacked the resin vigorously. It is therefore believed that the auric ion was reduced to gold on the surface of the resin.Role of the Sodium Citrate.-An investigation was made of the chemistry of the process and particularly the role of the citrate ion. The final products and the intermediates if any occur of the citrate + chloraurate reaction have not been reported in the literature. However in the oxidation of citric acid by various reagents acetone dicarboxylic acid has been described as the first intermediate step.** This substance can be prepared from citric acid either by intensive dehydration or by mild oxidation the reactions being CHzCOOH + CO + H,. It was proposed to study the action of acetone dicarboxylic acid on chlorauric acid. Acetone dicarboxylic acid was prepared in the following way.lg 25 g.citric acid were treated in an Erlenmeyer flask with 50 g. fuming sulphuric acid (15 yo ture for 4 hr. and 25 g. of crushed ice were added. Crystals of acetone dicar- excess SO,). After standing for 15 min. the flask was cooled in an ice-salt mix- H&SO + SO - - I boxylic acid were filtered off this viscous mixture washed with ethyl acetate and dried in air. A solution of 0.05 M of the sodium salt was made by dissolving the acid in 0.1 N NaOH. 10 ml. of chlorauric acid (containing I mg. of Au) was diluted with g ml. of water and treated at the boiling point with I ml. of the sodium acetone di- carboxylate solution. A clear red colloid formed with great rapidity passing swiftly through the blue state similar to that observed during the synthesis using the citrate ion.A faint but definite odour was observed similar to that noted during the synthesis with the citrate ion and resembling the odour of formalde- hyde. Kuyper 20 reports that the oxidation products of acetone dicarboxylic acid are formic acid formaldehyde and CO,. An identical reaction mixture prepared a t room temperature (23' C) showed the first detectable colour of faint pink in I min. growing darker over a period of several hours. The reaction was believed to be complete in 4 hr. The synthesis with acetone dicarboxylate ex- hibits little or no induction period and this is verified from the nucleation curve (Fig. 13) obtained from the size distribution curve (Fig. 14). examination of the nucleation curve (Fig.15 16) shows that i t has in general four regions an induction period followed by a rapid rise at the beginning of the nucleation a " linear " portion and finally a decay portion. The general nature of the curve is characteristic of an autocatalytic reaction. The Character of the Nucleation Curves .-An The induction period can best be examined by the nephelometric techniques. Its exact duration is difficult to determine for i t involves extrapolation to zero of a curve of rapidly changing curvature. One can say however that its duration decreases with increase in temperature as the approximate induction times of 26 min. at 15'C 5 min. at 3ooC 3 min. at 39' C and z min. at 49" C indicate. One can use these values to calculate an approximate activation energy of about 10 kcal./mole. The process responsible for the induction might be interpreted as the removal of an inhibitor of the nucleation process. However the fact that when one uses acetone dicarboxylate an oxidation product of the citrate ion there is an induction period of less than I min. indicates that the induction period is the time necessary to form an amount of acetone carboxylate ion necessary for nucleation. Examination of the effect of dilution on the induction period at IOOO C with the citrate ion as the re- ducing agent shows that it increases with dilution. Varying the citrate 19338 55 1722. l8 Bruce I n d . Eng. Chem. (Anal.) 1943,6,283 ; Kuyper. J . Amer. Chem. SOC. 19 Organic Synthesis (Ed. Marvel) (John Wiley and Sons Inc.) 5 p.5. 2 0 See ref. (IS). J. TURKEVICH P. C. STEVENSON AND J. HILLIER ion does not affect the induction time. Finally the decrease in the auric ion concentration during the induction period is less than I yo. Since the production of acetone dicarboxylate ion involves the reduction of auric ion this indicates that only a small number of acetone dicarboxylate ions can have been produced during this time. 67 r / 2 3 4 5 6 7 FIG. 13.-Nucleation curve of a gold sol produced by acetone dicarboxylic acid. Ordinate yo total number of particles per unit volume ; abscissa time (min.). FIG. 15.-Nucleation curves a t 49*5O 3g.0° 30.0~ and 15.4' C (nephelometric method). Ordinate particles per unit volume ; abscissa time (min.). FIG.~q.-Size distribution of a sol reduced with acetone dicarboxylic acid. Ordinate % particles ; abscissa diam. (A). 68 SYNTHESIS OF COLLOIDAL GOLD The second portion of the nucleation curve is one of rapid increase in the number of nuclei with the rate of increase increasing with time. On increasing the temperature this autocatalytic character becomes more pronounced in that d2n/dt2 is greater the higher the temperature (n is the number of nuclei and t is the time). Dilution markedly decreases the autocatalytic character indicating a high order dependence of this rate on the total concentration of the reactants. Decrease in the citrate ion concentration produces a similar effect. It should be noted that this autocatalytic character is absent from the nucleation curve produced by the acetone dicarboxylate.The rate of nucleus formation is a maximum at the start of nucleation and falls off exponentially indicating a first-order mechanism. One is therefore led to the conclusion that the autocatalytic nature of the nucleation reaction is due to the autocatalytic nature of the formation of the acetone dicarboxylic acid from the citric acid or some complicated phenomenon involving acetone dicarboxylate. 10 FIG. I 7.-Nucleation curves a t various dilutions (size distribution method) ; ordinate and abscissa same as Fig. 16. I FIG. 16.-Nucleation curves at various citrate concentrations a t 100' C (size distribution method). Ordinate particles per unit volume ; abscissa time (min.). The third portion of the curve the " linear " portion is most pro- nounced for experiments at high concentration or high temperatures.- It is significant to note that under these conditions i t resembles the nucleation curve observed with acetone dicarboxylate.We are again inclined to ascribe to the acetone dicarboxylate an important role in this region of the nucleation curve. If one plots the logarithm of (N - Nt) against time for the nucleation by acetone dicarboxylate at 100' C one obtains a curve given in Fig. 18. The straight-line character of the relationship shows that we have a kinetic expression of the type * Nt = N,(I - e-kt) (4) . and this suggests that the rate-determining step in the nucleation process is the unimolecular decomposition of a complex of gold and acetone dicarboxylate.The kinetics of this decomposition will be a subject of further study. J. TURKEVICH P. C. STEVENSON AND J. HILLIER 69 The slope of the last portion of the nucleation curve decreases rapidly with time as if one of the reagents is being exhausted. The explanation of this phenomenon is just as important as the explanation of why nuclei form. It is a region most difficult to examine experimentally because one is dealing with a system undergoing small changes in large absolute values of the observables. One cause contributing to the decrease in the rate of formation of the nuclei is the competition of the growth process. For as the particles grow larger and are present in greater number they grow more rapidly and begin to exhaust the " active " species of the nucleation process.This active species cannot be the auric ion for i t has been pre- viously established that about 95 yo of the original auric ion is present a t the time when the nucleation process has ceased. The active species cannot be the citrate ion because it is present in three to tenfold excess over the auric ion. One is thus led to the conclusion that the active species that is exhausted must be closely identified with acetone dicarboxylate. It is this compound that creates the nuclei and i t is quite possible that when there is a sufficient number of nuclei present they adsorb the acetone dicarboxylate on their surface and either utilize it as a reducing agent for the growth process or merely decompose i t catalytically.In support of this idea we wish to cite from an experiment on the growth process which will be presented in more detail in the section on the growth process. A solution of sodium citrate and chloraurate was allowed to interact at 70OC. A few minutes after mixing these reagents a known amount of zoo A gold sol was added. Examina- tion of the product in the electron microscope revealed but one maximum in the distribution curve. If however the 200 sol was added to the sodium FIG. 18.-Demonstration that nu- citrate dicarboxylic cleation + chloraurate system several acid resembles with acetone a first order reaction. abscissa time (min.). minutes after the completion of the Ordinate log [N(oo)-N(t)] ; nucleation the sol obtained had two maxima one due to the growth of the added 200 A particles and one due to the growth on the nuclei already formed.The absence of a second maxima in the first case is taken as evidence that a large number of nuclei artificially introduced inhibit the nucleation process. Thus we are inclined to ascribe the slowing-down of the nucleation process to the removal of the acetone dicarboxylate by the increasing number of gold particles. Further evidence that a gold-contain- ing species is strongly adsorbed on the growing particles during the growth stage of the citrate reaction will be presented in the following section. The total number of nuclei per unit volume increases with the con- centration of the gold and citric ions and appears to reach a maximum a t some temperature between 40° and 70' C .This unusual temperature dependence may be associated with the observation that dilute aqueous solutions of acetone d.carboxylic acid begin to decomposed a t about 60' C. Hence above this temperature the tendency of increased temperature to produce a greater number of nuclei is more than compensated by the lower concentration of the acetone dicarboxylate ions due to its decomposition. This point will be the subject of further study. SYNTHESIS OF COLLOIDAL GOLD 28 Bruce ref. (18). 70 Mechanism of Nucleation.-No completely satisfactory theory con- cerning the precise mechanism of the formation of nuclei in dilute solution has yet been worked out.One possible theory is that nuclei are artificially introduced. This " impurity " theory in its various forms reduces simply to the hypothesis that the nuclei are introduced into the system as dust particles bacteria spores bits of glass or sharp points on the inside of glass containers. There is no doubt that very often such substances pro- duce nucleation and lack of cleanliness and flagrant disregard of certain common-sense precautions such as cleaning vessels from nuclei of previous preparations can explain the varying success of many previous workers in the field of colloidal gold. Again it should be pointed out that a few nuclei accidentally introduced do not produce colloidal gold but a coagulum of metallic gold. Because of the consistent behaviour obtained in this investigation under different conditions of concentration temperature time of the year starting materials and glass apparatus we have come to the conclusion that impurities were not a variable in our investigation.The fluctuation theory is one of great tradition. It postulates the formation of a supersaturated solution of atoms of metallic gold some of which coalesce into a nucleus only when the statistical fluctuation of their concentration brings a sufficiently large number of them together to form a particle of a size that is thermodynamically stable. Thiessen 2 0 has stated that this number is about a hundred. This theory has been shown by LaMer and KenyonS1 to apply to the formation of colloidal sulphur. It is possible that i t might apply to our case but it is difficult to understand the marked temperature dependence of the rate of nucle- ation from the fluctuation point of view.Furthermore our investigation indicates that the nuclei are about 30 diam. and this would involve a fluctuation of the order of a million of gold atoms. We wish to advance the following " organizer " mechanism for the formation of a nucleus. The fundamental difficulty in building up a nucleus is the accumulation of a large local concentration of atoms to produce a particle whose size is greater than that just demanded by the stability of the particle. The fluctuation theory describes such an event as being rare but significant and due primarily to the statistical nature of physical events.One may attain the same result by postulating that the nucleating agent gradually builds up a complex between the gold ions thereby chemically binding a large number of both gold ions and reducing agent molecules into large macromolecules which at some stage or other will undergo a molecular rearrangement to produce m e W c gold particle of sufficiently large size. This event will be accompanied by the production of oxidation products of the reducing agent. This precursor of the nucleus may be considered as a copolymer of the gold ion and the organizer-a reducing agent which is polydentate and thus capable of forming cross-links between gold ions. This hypothesis finds some support in the nature of the reducing agents capable of causing nucleation.All of these are polydentate containing in the same molecule more than one group capable of forming a bond with the gold ion. Acetone dicarboxylic acid is known to form a stable complex with mercury 48 and is functiondy related to acetoacetic acid a well-known complex-former. Citric acid is known to form complexes with copper and iron 2s and is tetradentate in these complexes. Carbon monoxide forms carbonyls24 which are stated to be polymeric for elements of odd atomic number such as gold. Acetylene forms complexes with silver and copper acting as a dibasic acid. * o See ref. (8b). LaMer and Kenyon J. Colloid Sci. 1947 2 257. Kenney Inorganic Quantitative Analysis (The Century Company New York '939)J p* 345' 2s Lanford and Quinan J . Amer.Chem. SOC. 1948 70 zgoo ; Fales and 24 Wells Structural Inorganic Chemistry (Clarendon Press Oxford 1945) P. 453. J. TURKEVICH P. C. STEVENSON AND J. HILLIER 71 An ether solution of phosphorus has been suggested by Faraday as a reducing agent for the production of colloidal gold. In our point of view it is the fine emulsion of phosphorus in water produced by the mixing of the ether solution with the gold chloride solution that acts as an organizer. The gold ions are adsorbed on the surface of the phosphorus droplets are reduced there to metallic gold and migrate on the surface to form a particle of sufficient size to exist as a nucleus. It is the binding on the surface in this case just as the binding of the gold atoms by the polydentate reducing agents in the macromolecule that ensures the con- tinued high concentration of gold atoms on the surface of the phosphorus droplet thereby permitting the gold particle to reach a size great enough for an independent existence as a nucleus.Growth Process .-In order to complete the experimental study of the process of the formation of colloidal gold in solution i t was thought desir- able to study the process of growth. Most reagents used for the preparation of gold colloids by reduction cause both nucleation and growth. Fortun- ately two substances hydrogen peroxide and hydroxylamine hydrochloride have been found by' previous workers to act under certain conditions as solely growth reagents. The study of the growth reaction differs markedly from that of nucleation in that in the latter one studies the number of particles as a function of time while in the former the size of the individual particle is examined.Was GROWTH IN HYDROXYLAMINE HYDROCHLORIDE REAGENT.-It shown in the previous section that particles of gold prepared by the re- duction of gold chloride with sodium citrate at 100' C are very uniform in size at about zoo A diam. It was thought desirable to use the method of Zsigmondy 25 to prepare a graded series of gold sols of different but predetermined particle size. Accurately measured amount of the growth medium (equal volumes of chlorauric acid (0.01 yo Au) and hydroxylamine hydrochloride (0.027 yo by weight) were added to various amounts of sodium citrate gold sol containing a known concentration of 200 A particles.Reduction commenced immediately on mixing and proceeded rapidly and smoothly the gold sol developing completely within a few minutes of the mixing. In cases where the preparation of sols of a very large diameter was desirable i t was felt advantageous to carry out the reaction in steps using sols grown from the zoo particles for the in- oculation of the growth medium. In this method advantage is taken of the fact that a slightly acid solution of chlorauric acid and hydroxyl- amine hydrochloride (growth medium) in a scrupulously clean closed vessel will not produce colloidal gold until a sufficient number of nuclei are introduced. When the growth medium is inoculated with nuclei the chlorauric acid is reduced by the hydroxylamine and the metallic gold so formed is deposited only on the nuclei so that they increase in size but not in number.The mean diameter of the resulting particles can easily be shown to be where Df is the mean diameter of the final colloidal particle Do is the mean diameter of the nuclei used Mi and M are the respective masses of the ionic gold in the growth medium and the metallic gold of the gold nuclei used in the growth medium. The results are presented in Table IV. The observed mean particle size compare very favourably with those predicted on the basis of the above formula. In addition to this con- firmation of the formula i t was noted that the percentage root-mean-square deviation changed but relatively little with quite large changes in the particle size.A definite trend in this change was observed however in 25 Zsigmondy and Thiessen Das KGZZoide Gold (Leipzig 1925) and ref. 8(b) ; and Rinde ref. ( 5 ) . SYNTHESIS OF COLLOIDAL GOLD 72 that the percentage root-mean-square deviation decreased from 13 yo for the zoo A nuclear sol to about 8.5 % for the 1000 A sol. This decrease is believed to be more apparent than real for the following reasons. In the first place the average experimental error in the particle size measure- ment due to imperfect resolution of the electron microscope and to personal errors in the image measurement was approximately constant in amount from sample to sample and hence contributed more to the percentage deviation of the distribution of the smaller particles.In the second place a study of the small angle X-ray scattering 26 of the 200 A sol has revealed that the root-mean-square deviation of particle diameters is not 13 yo but may be about 8.5 Yo. We are thus led to the conclusion that the percentage root-mean-square deviation does not change with growth in particle size in the range size investigated. Our observations con- firm the experiments of Rinde2' on the particle size determinations by sedimentation studies. It can be easily seen that the law of growth consistent with the observation that the root-mean-square deviation does not change is dD/dt = kD . where D is the diameter of the particle t is the time and k is a constant whose magnitude depends on the temperature and reagent concentration but not on particle size.A further insight into the law of growth was obtained from the following experiment. From a standard 200 A mean diameter sol a (6) of 300 A 27 ml. of this sol were mixed with 8 ml. of the 200 A sol and the sol was prepared by the method described above with a mean diameter size distribution curve of the mixed sol was measured. The mean diameter of the mixed sol was then increased by a factor of two by growth in a hydroxylamine + auric chloride solution. The size distribution of the particles of the resulting sol was also measured. In both cases two maxima were observed. In the first sol the maxima were at 200 A and 300 while in the second case they were 400 A and 600 A (Fig. 19). Integrating the law of growth leads to the conclusion that during growth the ratio of the particle sizes is In D' - = c(t - t') D remains constant and not the difference in particle sizes.The above experiment clearly confirms this deduction. A chemical study was also made of the growth reaction using hpdroxyl- amine hydrochloride. Observations with the glass electrode indicated that the pH dropped during the growth reaction. It was not found possible to study the rate of formation of the hydrogen ions. The iodometric method of Gooch and Morley 28 was applied to the study of the kinetics of the disappearance of the auric ion. Runs were made at four tem- peratures at several nuclear concentrations with nuclei of different sizes and several hydroxylamine concentrations. The reaction was found to be first order with respect to the auric ion hydroxylamine added metallic gold nuclei and hydroxyl ion concentrations indicating that none of these reagents is strongly adsorbed.The first-order dependence on the added nuclei is stated on the basis of added gold atoms i.e. the rate observed when a large nuclei were added was the same as observed when the smaller nuclei were added provided that the total concentration of metallic gold was the same (more smaller particles). This is equivalent to the law of growth stated above. The experimental activation energy was found to be 9-1 f 0.6 kcal./mole for two sizes of nuclei. 26 Turkevich and Hubbell J . Amer. Chem. SOC. 1951 73. 27 Rinde ref. ( 5 ) . 28 Kolthoff and Furman Volumetric Analysis (John Wiley and Sons) 2 p.469 ; Kurtenacker and Wagner 2. anorg. Chem. 1922 120 26. J. TURKEI'IC'IT P. C. STEVENSON AND J. HIL1,IER 73 The stoichiometry of the reaction was also investigated. The gold ion solution used was standardized iodometrically as described above while the hydroxylamine hydrochloride was oxidized in strong hydro- chloric acid solution by the method of Kurtenacker and Wagner.29 The metallic gold colloid must be removed by adsorption on TiO previous to titration since acid bromate solutions readily oxidize metallic gold and give false readings. It was found that 1-00 mmole of HAuCl oxidizes 1.0 -I- 0.5 mmoles of hydroxylamine. The reaction is probably - 12 /o D L % -/2 % ;I 2 il A n 5 -/o HAuC1 + NH,OH .HC1+ Au + 5HCl + NO. GROWTH IN SODIUM CITRATE REAGENT.-It is quite possible that the exponential law of growth obtained for the hydroxylamine hydrochloride reagent mav be peculiar to reduction by the hydroxylamine hydrochloride. It >as thkrefoie decided to investigate the law of growth in the sodium citrate system. In a subsequent communica- tion on the optical properties of monodisperse gold sols of different diameters i t will be shown that the absorption spec- trum of uncoagulated colloidal gold has a single absorption maximum in the visible region which varies in a regular way with the particle size after 300A and that the optical density of the sol per particle for the absorption maximum follows the law d = const.nD2'8 . (7) -8 6 FIG. 19.-Demonstration of the law of growth using the electron microscope. where n is the number of colloidal particles per ml. and D is the mean particle diameter. Since we have shown in the preceding section that the number of particles per unit volume becomes constant very soon after the mixing of the reagents at the higher tem- perature this relationship can be used to obtain the particle size as a function of time from the equation the final diameter D( co ) being determined by the electron microscope. Three runs were made on the standard sodium citrate preparation at 70" C using a Beckmann spectrophotometer to measure d. The readings were found to be reproducible the points for the three runs falling close to the same smooth curve.Points obtained for very short reaction times were not considered reliable as the number of particles was not constant. A plot of log D against t gives a straight line up to times until almost all of the gold is reduced indicating that the growth reaction follows the growth law given above but is zero order in the reagents used (Fig. 20). This zero-order behaviour is consistent with a surface reaction in a strongly adsorbed layer of reactants. It may be recalled that the cessation of the nucleation process was ascribed by us to the strong adsorption of the C SYNTHESIS OF coI,r,oimu ~ o r m 1 FIG. 2o.-Growth in the citrate sol. Ordinate log relative diameter ; abscissa time (min.). 74 active species by the gold particles formed.Extrapolation of the straight line to zero time gives a value of 48 f 5 A for the diameter of the nucleus a value consistent with estimates given in the section on nucleation. Some further evidence was desired to show that the exponential law of growth did indeed hold for the growth process using sodium citrate. It was shown above that when the law of growth was exponential the ratio of the diameters of two particles growing in the same reaction medium does not change with time. Experiments were devised in which particles of known large size were added to the growing colloid a t several times during the growth process. It was expected that the size distribution curve of the resulting sol on completion of the reaction would show two maxima one due to the added particles and one due to those present when the particles were added.The ratio of the diameters a t which these maxima occurred should be the ratio of the mean particle size in the growing sol to the mean diameter of the added particles at the instant of mixing. Since the latter is known the former can be easily evaluated. Several samples were prepared using sodium citrate as the nucleating and growth agent a t 70’ C. The first of these was allowed to go to com- pletion. At definite times the other samples were diluted with equal volume of the completed sol. Size histograms were obtained with the electron microscope for these sols after the reaction was completed. In most cases two maxima were observed in the size distribution curve.When these occurred the ratio between the diameters at which these peaks occurred were used to calculate the diameter of the growing colloid at the time of the addition of the completed sol. The points so obtained agree with those derived by the optical method (Fig. 21). In the sample prepared by adding the completed gold colloid immediately after mixing of the sodium citrate and the chlorauric acid solutions only a single maxi- mum in the size distribution curve was produced. This was interpreted to mean that a large number of gold particles in solution inhibits nucleation by successful competition for the active species. Mechanism of Particle Growth.-Consideration of the law of growth of a particle in a solution which deposits material on the surface by a typical heterogeneous reaction leads to a formula of the following type where K is the specific rate constant for unit area for the surface reaction D is the diameter of the particle A is the diffusion coefficient of the active J.'I'URKEVICH P. C. STEVENSON AND J. HILTJER 75 species V is the molal volume of the metallic gold and coo is the con- centration of the active species at large distances from the particle. It is seen that if the diffusion is the rate-determining quantity then the rate of change of diameter is inversely proportional to the diameter; while if the process is limited by the surface reaction then the rate of change of the diameter with time is independent of the diameter. The observed law is neither and demands that the rate of change of diameter with time be proportional to the diameter.A mechanism of this exponential law of growth must await further experimental studies of the growth reaction. I f i m e in Minukes I 10 30 > I~ P. S. WILLIAMS 55 A STUDY OF THE NUCLEATION AND GROWTH PROCESSES IN THE SYNTHESIS OF COLLOIDAL GOLD BY JOHN TURKEVICH PETER COOPER STEVENSON AND JAMES HILLIER Received 18th May 1951 After a preliminary survey with the electron microscope of various prepara-tions of colloidal gold a study was made of the process of nucleation and growth in gold colloids. It was shown that nucleating agents may be identified with reducing agents which form a mixed polymer with chlorauric ion before the reduction to the nucleus takes place. It was also shown that the law of growth is exponential.The average size the deviation from the average size and the character of the particle size distribution curve are determined by the amount of gold the nucleation process and the law of growth. Colloidal gold may be considered as a typical hydrophobic colloid with particle size falling below the resolution limit of the optical micro-scope. With the development of the electron microscope which has s resolution permitting the examination of the individual colloidal particles 1 it was natural to make an extensive study of the shape mean size and size distribution of the various preparations of colloidal gold and determine the factors that govern these properties. Previous work on the subject was limited to one or two preparations.4 Experimental Electron Microscopic Examination of Various Preparations of Colloidal Gold.-In order to gain an insight into the colloidal gold system, a systematic survey was made of all standard preparations of colloidal gold.Due precautions were taken to ensure cleanliness of the distilled water reagents (a) Beischer and Krause 2. angew. Chem. 1938 51 331 ; (b) Ardenne, 2. physik. Chem. A 1940 187 I ; (c) Koch 2. Elektrochem. 1941 47 717 ; (d) Feitknecht Signer and Bergern Kolloid-Z. 1942 101 12; (e) Roginski, Shekhter and Sacharova Compt. rend. U.R.S.S. 1946 52 687; (f) Borries and Kausche Kolloid-Z. 1947 90 132 ; (g) Harris Jeffries and Siegel J . A+pZ. Physics 1948 791. 1 Turkevich and Hillier Anal. Chem. 1949 21 475 56 SYNTHESIS O F COLLOIDAL GOLD and the glass vessels used.The water was distilled water purified from nuclei by ultrafiltration. The glass vessels used were not only cleaned with aqua regia to remove traces of colloidal gold which might subsequently serve as nuclei but were also treated with chromic acid and steamed for 20 min. to remove any grease film. Contact with rubber tubing or rubber stoppers was scrupulously avoided. The colloidal gold preparations were examined in an RCA electron microscope by placing a drop of the colloid on a collodion screen and allowing it to evaporate. The resolution of the microscope was about 10-20 A. BREDIG SOL^ was prepared by striking an arc from two gold wires under very dilute sodium hydroxide solution with a 115 V 60-cycle potential. The gap between the electrodes was about 5 mm.and the electrodes were agitated to keep them from fusing. A purple cloud was observed t o drift away from the arc gradually darkening the entire solution. The process was continued until a fairly intense purple colour had developed and the colloid so obtained was examined with the electron microscope. The particles ranged in diameter from 30-100 A but due to their small size and extensive clumping no precise measure-ments of size distribution could be made. A saturated solution of white phosphorus in freshly distilled diethyl ether was diluted with three times its volume of diethyl ether. 50 ml. of chlorauric acid solution (50 mg. of Au) was diluted with 45 ml. of distilled water and with 5 ml. of 0.1 N KOH. This solution was treated using good mechanical stirring in one case with 2-0 ml.of the phosphorus-ether solution and in the other case with 1-0 ml. of the same solution. The solution turned first brown then grey purple and red, finally giving a deep-red product. The sol was then heated to boiling and a stream of filtered air was drawn through it in order to oxidize any remaining phosphorus. Electron microscopic examination revealed that both sols con-tained extremely fine particles more or less clumped. The sol reduced with 2 ml. of phosphorus solution consisted of particles of mean diameter of 50 A with a root-mean-square deviation of 30 yo. This preparation was grown to double, quadruple and eight-fold of the original diameter by means of the hydroxyl-amine development technique (described below) in an attempt to deduce the smallest particle size in the original Faraday preparation.An electron micro-scopic examination of these developed preparations showed that the smallest particle in the original Faraday sol was about 30 A diam. This is interpreted to mean either that particles smaller than 30 A are not formed by the Faraday method or if they are formed they do not serve as nuclei in the hydroxylamine + gold chloride growth medium. The size distribution of the Faraday sol particles is not symmetrical having a gradual rise on the small diameter size passing through a sharp maximum to a rapid drop on the large diameter size and showing a small tail of larger particles. The significance of this distribution curve characteristic of many gold sols will be discussed later.The sol made by the reduction with I ml. of phosphorus diethyl ether solution consisted of par-ticles of mean diameter of 70 with a root-mean-square deviation of about 25 yo. studied Faraday sols by growing them in a hydrogen peroxide + gold chloride medium and determined the particle size distribution by gravity and ultracentrifugal sedimentation. His curves have a similar general appear-ance to those found in the present investigation. Rinde however deduced the average particle diameter to be 19 A. ACETONE SOL.* 98 ml. of chlorauric acid solution (containing 12 mg. of Au) were heated to boiling and treated with I ml. of acetone purified by dis-tillation from alkaline permanganate. On boiling a faint coloration appeared in the solution after about go sec.darkening gradually to deep red. Under the electron microscopic investigation the particles appeared in clusters of about 50. The individual particles were non-spherical with a probable diameter of about 200 A and a root-mean-square deviation 13 %. TANNIN GOLD SOL.'-IO ml. of chlorauric acid (containing 10 mg. of Au) was added to IOO ml. of water the solution was made neutral to litmus with FARADAY SOL* was prepared in the following way. Rinde Bredig 2. angew. Chem. 1898 I I 951. Faraday Phil. Trans. 1857 147 145. 6 Rinde The Distribution of Sizes of Colloidal Gold Sols prepared according 6 Davies J . Physic. Chem. 1929 33? 276. 7 ( a ) Wieser Inorganic Collozd Chemzstry I (John Wiley and Sons New York, 1g33) p. 40 ; (P) Garbowski Ber.1903 36 1215 ; (c) Ostwald Kleiner Prak-tzkum der Kollozdchernie 2nd edn. (1920). to the Nuclear Method (Uppsala 1928) J. TURKEVICH P. C. STEVENSON AND J. HILLIER 57 sodium carbonate and heated to boiling. A fresh I yo tannin solution was added dropwise until no colour change was observed on further addition. The sol was pink and had a slight opalescence. Electron micrographs showed that the sol consisted of small spherical particles of 120 A mean particle diameter and a root-mean-square deviation of 28 yo. The particles occurred singly or in small clusters. It is of interest to note that the particles making up the clusters were not in contact but were separated by a space of not less than 40 A. This may be interpreted to indicate that the particles are surrounded by a skin of protective colloid (tannin) of too low a contrast to be visible in the electron microscope.OXALIC ACID S0~.-38 ml. of chlorauric acid solution (containing 20 mg. Au) was treated at the boiling point with z ml. of I yo oxalic acid. Turbidity ap-peared in about 5 sec. and the reaction seemed complete in 20 sec. The sol was light blue in colour while the scattered light was yellow. The particles were about 2000 A diam. irregular in shape and the size distribution was rather broad. HYDROXYLAMINE SoL.s-Hydroxylamine hydrochloride in slightly acid solution has been described by a number of investigators as an inhibitor for the nucleation of colloidal gold. In neutral or basic solution however i t is a nucleating agent. 20 ml.of ow27 yo hydroxylamine hydrochloride solution was added to 20 ml. of chlorauric acid solution (containing 2 mg. of Au) pre-viously neutralized with potassium carbonate. A dark blue colloid formed instantaneously. Unlike the ordinary unstable blue colloidal gold this colloid was stable. The blue colour had been ascribed to this preparation by Thiessen 9 as due to the presence of aurous oxide. The sol was found to consist of small non-spherical particles aggregated into clusters. The distribution curve was broad with a maximum at about 150 A and a root-mean-square deviation of 44 %. DONAU SoL.lo-Carbon monoxide gas was bubbled through a chlorauric acid solution (containing 0.001 yo Au) at room temperature. The solution darkened assuming finally a purple colour. The sol was found to consist of highly irregular particles of about 200 A diam.and 400-800 A long. Their appearance suggested that the particles were formed by the deposition of gold on straight or bent chains of smaller particles and that the growth took place during coagulation (Fig. I). ACETYLENE SOL.-IS ml. of chlorauric acid solution (containing 10 mg. of Au) were treated with 2 ml. of water saturated with acetylene gas. A pink colour appeared in 20 sec. and in 2 min. the sol became dark ruby-red. Electron microscope examination of this sol revealed small particles mostly spherical in shape with a mean diameter of 285 A and a root-mean-square deviation of 22 %. The size distribution curve was definitely skewed the slope on the large diameter side of the maximum being markedly steeper than on the smaller diameter side.An unusual feature of the separation was the presence of a few particles in the form of triangular plates. Since the acetylene sol was definitely acidic the effect of the hydrogen ion concentration was investigated. Solution of pH 10.4 and 8.0 gave no sol formation. Solution with a pH of 5.8 obtained by adding an appropriate amount of sodium carbonate to the original reagents produced a sol slowly taking 5-7 min. to develop full colour while the non-neutralized acetylene + chlorauric acid solution required 2-3 min. The particles in the neutralized medium were smaller having a mean diameter of 170 with a root-mean-square deviation of 16 yo. The size distribution curve was again skew-shaped. No plates were found.If the starting reagents were of lower pH value containing 20 and 64 mequiv. of added HC1 the sols formed had a definite blue tint and contained a large number of irregularly-shaped flat plates and bipyramids. CITRIC ACID GOLD So~.-g5 ml. of chlorauric acid solution (containing 5 mg. of Au) were heated to the boiling point and 5 ml. of I yo citric acid solution was added to the boiling solution with vigorous mechanical stirring. The solution remained clear for about 15 sec. and then suddenly a dark blue-purple sol was formed. When examined in the electron microscope this sol proved to be identical in appear-ance to the one prepared in acidified acetylene solution. Large numbers of flat triangles and hexagons were seen. There were also some bipyramidal forms.The particle ‘‘ diameter ” ranged from IOO to 500 A. Because of the extensive variability in shape no size distribution curve was determined (Fig. 2). * (a) Rinde ref. (15) ; (b) Thiessen 2. anorg. Chew. 1929 180 5 7 ; (c) Thiessen Kolloidckem. Beihefte 1929 29 122. sThiessen 2. anorg. Chem. 134 1924 393. lo (a) Donau Monatsh. 1905 25 525 ; (b) n7eiser ref. (7a) p. 41. The distribution in size was very broad. There was no further change of colour on prolonged boiling 58 SYNTHESIS OF COLLOIDAL GOLD SODIUM CITRATE SOLS.-This Preparation of great importance in our in-vestigation is a modification of the one described by Hauser and Lynn.ll The following is a description of a preparation which we shall term the " standard " sodium citrate sol 95 ml. of chlorauric acid solution (containing 5 mg.Au) were heated to the boiling point and 5 ml. of I yo sodium citrate solution was added to the boiling solution with good mechanical stirring. After about a minute a very faint greyish-pink or greyish-blue tone appeared gradually darkening over a period of about 5 min. The final colour was deep wine red. Electron microscopic examination of a number of preparations showed that this colloid is highly reproducible and gives spherical particles (Fig. 3) with a mean diameter of about zoo 15 A and a root-mean-square deviation of 12.5 %. The size distribution curve based on a count of 1046 particles is not symmetrical but shows a distinct " tail " on the small diameter side (Fig. 4). The effect of Approximate Time for Temp."C the Completion of Reaction in min. IOO (standard) 5 70 45 80 25 Mean Particle Size in A % Deviation 2 00 12.5 I80 8-6 165 8.1 effect of decreasing the amount of sodium citrate (Fig. 5 ) in the preparation on the properties of the gold sol are given in Table 11. The colour changes ac-companying the reaction show marked variation as the amount of the citrate is decreased. The early stages become more definitely blue and the transition from the blue to the red becomes more sharply defined. The overall reaction appears to take place more rapidly a t the lower citrate concentration. Using I/Ioth the standard amount of citrate the reaction could be divided sharply l1 Hauser and Lynn Ex9eriments in Colloid Chemistry (McGraw Hill 1g40), p. 18 FIG.I.-Electron micrograph of a gold sol reduced with carbon monoxide, magnification of 50,000 diameters. FIG. 2.-Electron micrograph of a gold sol reduced with citric acid, magnification of 50,000 diameters. [To face page 58 FIG. n.-Electron micrograph of a gold sol reduced with sodium citrate (standard citrate sol) magnification 50,000 diameters. FIG 12 -Electron micrograph of nuclei for colloidal gold isolated by the ion eschange resin method magnification 43,600 diani. [See page G 5 J. TURKEVICH P. C. STEVENSON AND J. HILLIER 59 into three stages. The reaction mixture was colourless for 12 sec. after the addition of the citrate then i t turned bliie within a fraction of a second. After a total reaction time of 72 sec. it suddenly turned clear red. The colour changes accompanying this reaction were very striking.Size distribution curves were obtained for all preparations but the one using 1/2oth of the amount of citrate used in the standard preparation. This Iattersol was highly turbid and coagu-lated very rapidly. Decreasing the amount of citrate caused the mean particle FIG. 5.-Size distributions of sols reduced with varying amounts of sodium citrate. Upper curve one-tenth the standard amount of citrate ; middle curve one-fifth the standard amount of citrate ; lower curve half the standard amount of citrate. % 0-005 ZAu. 25 20 /5 n % 25 20 k ! AIL ~ , 100 ZOO 300 400 500 FIG. 6.-Size distribution of sols reduced with sodium citrate a t different dilutions. Upper curve twice standard dilution ; middle curve standard dilution ; lower curve half standard dilution.diameter to increase somewhat and the size distribution curve showed a definite " hump " on the large diameter side of the average diameter. The effect of dilution of reagents on the properties is given in Table I11 and Fig. 6. Sols made in the more concentrated solutions had a smaller particle diameter but were somewhat contaminated. Further detailed studies on the sodium citrate TABLE II.-'rHE EFFECT OF CITRATE CONCENTRATION ON THE SODIUM CITRATE SOL Citrate (mg.) 50 (standard) 25 5 3'75 2'5 I0 Approximate Time for the Completion of Reaction in min. 5-0 5'0 2.0 1.2 2.0 2'0 Mean Particle Size in A yo Deviation LOO I45 15.5 240 dirty and clumped dirty and clumped 12'5 9'4 11.8 12' 60 2 5 6 SYNTHESIS OF COLLOIDAL GOLD I74 235 200 sol will be considered in connection with the process of nucleation and growth of colloidal gold.TABLE 111.-THE EFFECT OF DILUTION ON THE SODIUM CITRATE SOL PREPARATION Dilution 1 /2 I (standard) 2 Time for Mean Parti& Size 1 inA the Completion of Reaction in min. % Deviation 10.4 12-5 I 2.6 The Nucleation Process .-An electron microscopic survey of the methods of preparation of gold colloids has shown that the nature of the product formed was highly dependent on the reagent used and on the conditions. The particle shape the particle size and the nature of the size distribution curve have been shown to vary within quite large limits.The shape of the size distribution curve will be shown to depend largely on the relative rates of two separate processes nucleation and growth. Nucleation will be defined as the process whereby a discrete particle of a new phase forms in a previously single-phase system in our case a homogeneous solution. Growth will be defined as a process in which addi-tional material deposits on this particle causing i t to increase in size. It has been shown that these two processes are indeed separable. Zsigmondg and Thiessen la have studied the nucleation using several reducing agents. This section will deal with sodium citrate and hydroxyl-mine hydrochloride as reducing agents of auric ion the former acting as both a nucleating agent and a growth agent while the latter functioning only as a growth agent.Nucleation in the formation of gold sols is a difficult phenomenon to investigate directly. Preliminary evidence indicated that the nuclei are very small of the order of 50 k or less in diameter and consequently not susceptible of effective direct examination with the electron microscope. Furthermore these nuclei have only a transitory existence in the reaction mixture during the ordinary methods of gold sol preparation. The experi-mental criterion for the presence of nuclei that was used was the following : the solution suspected of containing nuclei is added to the growth medium consisting of a solution of 12 x I O - ~ parts of hydroxylamine hydrochloride and 10 x 10-4 parts of chlorauric acid. If the nuclei are present in the solution tested reduction takes place either to colloidal gold a coagulated gold sol or to large particles of gold depending on whether the number of nuclei is large or small.Each particle produced in this growth medium is presumed to have formed from the nucleus present in the solution tested, at the time of its addition to the growth medium of chlorauric acid and hydroxylamine hydrochloride. In the absence of nuclei and in a dust-free atmosphere the growth medium undergoes no reduction of the auric ion for several hours. This test for the existence of nuclei may be adapted for the growth of nuclei to a size convenient for observation by the choice of a proper amount of the growth medium (development technique). It was decided to study the nucleation process in the production of colloidal gold by the sodium citrate reduction taking advantage of this develop-ment technique to bring the nuclei formed at various times into a range of size capable of ready evaluation.The number of particles in the sols so developed and consequently the number of nuclei were determined either by counting in the slit ultramicroscope or deduced from the optical properties of the developed sol. In addition a method was developed l2 (a) Zsigmondy 2. physik. Chew. 1906 56 65 ; ( b ) Thiessen ref. (8b) and (8c) J. TURKEVICH P. C. STEVENSON AND J. HILLIER 61 for determining the rate of nucleation from the ultimate particle size distribution curve as revealed by the electron microscope. Furthermore a study was made of the disappearance of the auric ion as a function of time and this was correlated with the nucleation rate.In addition a method was found for removing the auric ion from solution after nucleation was essentially complete and examining the isolated nuclei with an electron microscope. Finally an oxidation product of sodium citrate was studied as a nucleating agent, Slit-Ultramicroscopic Examination.-Since nuclei are difficult to see in slit-ultramicroscope the following procedure due to Zsigmondy l3 was adapted to the study of the rate of formation of nuclei from gold chloride by sodium citrate. Reagents necessary for the production of the standard sodium citrate sol were mixed in clean glass-stoppered Erlenmeyer flasks and kept in a thermo-stat. At fixed intervals samples were drawn from the nucleating solution and were added to a volume of the growth medium so chosen empirically as to give developed particles of a size chosen to minimize coagulation during the counting operation.The samples so obtained were diluted to standard volume and ali-quots were introduced into a cell of a Bausch and Lomb slit-ultramicroscope for counting. Nucleation curves for the formation of gold sol were measured FIG. 7.-Nucleation curve at 58.5" C measured with the slit ultra-microscope. in the sodium citrate 3- chlorauric acid solutions a t 23.0' C and at 58.5O C and are presented in Fig. 7. Examination of the data shows that it takes about 40 min. to complete nucleation a t 23O C and 4 min. a t 58.5" C indicating a high temperature coefficient foi- the nucleation process.Furthermore the curves indicate that the rate a t the start is reasonably constant and then drops off suddenly a t the end. The nuclei formation is complete long before the process of colloidal gold formation ends because the colour of the solution deepens a t 23' C for 12 hr. and at 58.5' C for 2 hr. Previous investigations of the rate of nucleus formation were carried out by Thiessen l4 who used the same technique for the study of the nucleation of gold by potassium oxalate hydrogen peroxide, sodium citrate potassium thiocyanate and ultra-violet light. The experiments with sodium citrate were carried out a t one temperature. The general character of his sodium citrate nucleation curve is similar to the one reported in this investigation.It is felt that the method of counting particles in the slit-ultra-microscope has definite disadvantages. In the first place the method is subjective and involves errors arising from dark adaptation and subsequent fatigue of the eyes. Secondly the time of count is often comparable to the time of stability of the developed colloids. Thirdly there is always an error arising from defining the depth of the liquid examined. Finally the question arises as to whether very small particles can be detected with as much assurance as the larger ones. For this reason it was thdught that other methods should be developed to deter-mine the rate of nucleation. l3 Zsigmondy ref. (124. l4 Thiessen ref. (84 6 2 SYNTHESIS OF COLLOIDAL GOLD Nephelometric Method.-In this method sodium citrate + chloraurate mixture was allowed to nucleate and aliquot portions were developed by addition to a constant amount of the hydroxylamine growth medium.A series of de-veloped gold sols were obtained having the same total gold content but differing among themselves in the number and consequently size of the gold particles. The number was determined by nephelometric comparison with an appropriate standard set of colloids of the same gold concentration but different known particle concentration. This graded set of standards was obtained in the follow-ing way. A gold sol was prepared by allowing a nucleating mixture identical to the one under investigation to go to completion. This sol contained the maximum number of particles which could be determined experimentally.This number corresponded to the final number of nuclei formed. The particles in this completed sol were of minimum size compared to the other members of the graded set. Other members of the standard series were prepared by taking known volumes of this final solution (containing known number of particles) FIG. 8.-Nucleation curve a t 49' C measured with a nephelo-meter. Ordinate particles per unit abscissa time (sec.). volume ; and developing them in a hydroxylamine hydrochloride + chlorauric acid solu-tion of such a strength in gold that the total gold concentration was the same as in the developed samples from the sodium citrate run under investigation. The particle concentration of the developed aliquot sample from the run was ob-tained by comparison with an appropriate standard in a nephelometer.Using this procedure i t was not difficult to prepare a curve for each run showing the fraction of nuclei formed as a function of time. The number of nuclei per ml. in the completely nucleated sol could be easily determined either by a nephelo-metric comparison based on the zoo A standard sol or by an electron microscopic investigation of their particle size. A typical nucleation curve obtained in this way is shown in Fig. 8. The curve is similar in nature to the one obtained with the slit-ultramicroscope. It is more convenient to determine and its ac-curacy and reproducibility are much greater An assumption is made that the total scattering observed is determined primarily by the mean particle volume and is independent of small variations in the particle size distribution curve.Electron Microscopic Methods.-There are two methods that can be used to determine the nucleation curve using the electron microscope. The first method consists of stopping the nucleation process a t various times and develop-ing the samples. Each individual developed sample is examined in the electron microscope and a size distribution curve is obtained. The mean particle volume of each sample is determined from these curves. Since the total gold content is known one can determine the number of particles per unit volume present in the nucleating mixture at the time of development of each sample. This pro-cedure however is rather time-consuming and tedious J. TURKEVICH P. C. STEVENSON AND J.HILLIER 63 The second method consists of determining the nucleation curve from the particle size distribution curve of the completed preparation of the gold sol. The metbod is based on the assumption that the principal cause of the spread in particle size of a gold colloid is the spread in time in the nuclei formation. Particles formed early in the nucleation process begin to grow immediately so that in the final sol the particles that first form and hence have the longest time to grow attain the largest size. Nuclei which form later attain smaller and smaller sizes corresponding to shorter and sborter growing times. The size distribution of a sol can be considered as a regularly distorted mirror image of the nucleation curve. In Fig. 8 are shown schematically a size distribution curve (upper curve) and a nucleation curve (lower curve) of the same colloid.The marked diameter D in the size distribution curve was chosen to be the diameter finally attained by those particles formed during nucleation a t the time f marked FIG. 9.-Schematic diagrams to illustrate the calculation of nucleation curves from size distributions. Upper curve schematic size distribution ; ordinate yo total particles ; abscissa diameter D(t) ; lower curve schematic nucleation curve ordinate N ( t ) ; abscissa time. on the nucleation curve. The ordinate of the nucleation curve at t represents the total number of particles present in the unit volume of the solution a t time t , i.e. all those particles which have formed up to and including time t .It is con-venient to express this number as the fraction of the number of particles that are going to be eventually formed a t infinite time N ( t ) . The total number of particles formed up to time t is simply the total number of particles with diameter greater than D(1) or 03 N ( t ) = n(D)dD. - - (1) The value of this definite integral is the shaded area under the distribution curve and this can be determined as a fraction of the total area. In the section on growth it will be shown that a gold particle grows according to the law where D is the diameter of the particle and k is the velocity constant dependent on the temperature and reagent concentrations. In the integrated form i t becomes where a is a function of time a t which an arbitrarily-selected reference particle forms and of the rate constant k while b is proportional to k.If one obtains dD/dt = K(C T)D . - (2) 1 = (a - log D)/b . - (3 64 SYNTHESIS O F COLLOIDAL GOLD from independent observations the values of a and b one can derive a nucleation curve from a particle size distribution curve by means of the equations above. Since knowledge of these constants was incomplete a t the time of the in-vestigation i t was decided to modify the procedure by taking at least three samples from a nucleating sol and developing them. These three developed samples taken a t three definite times and the completed sol were examined in the electron microscope. (Actually two samples taken a t two times during nucleation are sufficient but the third was taken to obtain check values.) Dis-tribution curves were taken of these four sols.Three incompletely nucleated sols were used to determine the mean diameter and thus the number of nuclei present in the reaction mixture at the three definite times when the nucleation was stopped by development. One therefore obtains three points on the nucle-ation curve and these points will be used later to convert the time size scale into a time scale. One then examines the size distribution of the completed sol. The area lying to the right of a particular D value is determined from the experi-mental distribution curve for a number of arbitrarily chosen D values. The values of these areas the fraction of particles having a diameter greater than D, are plotted against log D. We thus have a plot of the number of nuclei against log D.In order to convert this to a time scale one uses the relation the constants a and b being determined from the three values of the number of nuclei at three different times previously obtained by the study of the distribution curves of the three partially nucleated sols. The size distribution curve has been converted into a nucleation curve. In the first place all nuclei were assumed to form with the same original diameter secondly the law of growth was assumed to hold for nuclei as for the larger particles and finally i t was assumed that the addition of hydroxyl amine hydrochloride in the development process stopped the nucleation instantly. Thiessen l5 has stated that in nucleation with citrate the nucleation process is stopped im-mediately by the hydroxylamine.His statement is based however on his failure to observe ar? induction period. As will be shown below our experiments indicate that there is a definite induction period in the nucleation with sodium citrate. Finally before leaving the subject of the relation of the size distribution curves as determined by the electron microscope to the nucleation curve i t was of interest to see how the partial nucleation curve (obtained from the samples for which the nucleation was stopped a t definite times by development) fit into the complete nucleation curve. The nucleation curves were determined for the three samples from their distribution curves using the method described above. The constant b was the same for all the three developed samples and was taken as that of the final sol since prior to development these partially nucleated samples were mere undifferentiated portions of the nucleating solutions.The curves so obtained were translated along the time axis to obtain for their lower parts the best fit with the complete nucleation curve (Fig. 10). A study of the curve so obtained shows an excellent fit for the lower portions of the nucleating curve of each developed sol. The upper portions of the curve however show marked deviations. Instead of a sharp break from the overall curve the three partially developed sols approach t3eir final nucleus numb2r gradually. Part of this rounding-off of the expected sharp break is undoubtedly due to the imperfect resolution of the electron microscope and to errors in the measurement of the smaller particles.It is thus seen that a good insight can be obtained into the kinetics of nucleation of gold sols by the study of the particle size distribution curves by means of the electron microscope. The Rate of Disappearance of the Auric Ion.-A study was made of the rate of disappearance of the auric ion during the formation of a gold sol in a sodium citrate + chloraurate system by withdrawing a t definite times aliquot portions running them into concentrated potassium iodide solution reducing the iodine liberated by a measured excess of standard thiosulphate solution and titrating the remaining thiosulphate with standard iodine solution.lG The results of a typical experiment are given in Fig. I I.It will be observed that the nucleation process is essentially complete before as much as 5 yo of the auric ion has been reduced. The statement of Thiessen l7 that nucleation stops due 1@ Scotts Standard Methods of Chemical Analysis (ed. N. H. Furman) (D. van t = (a - logD)/b, Several implicit assumptions were made in this treatment, Thiessen ref. (8c). Nostrand Co.) 5th edn. I p. 437. l7 Cf. ref. (8b) J. TURKOVICH P. C. STEVENSON AND J. HILLIER 65 to the exhaustion of the ionic gold is therefore not applicable to our system. The rate of disappearance of the auric ion is proportional to the concentration of the nuclei and an indication of the size of the nuclei may be obtained in the following way. About one-twentieth of the auric gold has disappeared by the end of nucleation.The ratio of diameters is the cube root of this fraction or 0.36. Since the final diameter of the sol is about 170 the mean nuclear size a t the end of the nucleation is about 60 A. From the size distribution curve the smallest particle has a diameter between one-half to two-thirds of the mean, the smallest nucleus should have a diameter of about 30-40 A. - 100 50 FIG. 10.-Nucleation curves calculated from particle size distribution for a com-pleted sol and three samples developed during nucleation. Ordinate number of particles per unit volume ; abscissa time (min.). FIG. I I .-Concentration of auric ion as a function of time during reduction with sodium citrate a t 49' C. Ordinate : concentration of [Au+++] x 10 ; abscissa time (min.).Isolation of the Nuclei.-An attempt was made to isolate the nuclei for direct examination and the use of ion exchange resins suggested itself for the removal of the auric ion. Four ion exchange resins were used the cation ex-change resins being charged with sodium ion and the anion exchange resins with hydroxyl ions (sodium carbonate). They were well washed with distilled water. A nuclear solution was prepared by incubating the standard sodium citrate + chloraurate system for 19 min. at 30-5' C. The colour of the solution a t this time was pale grey. Dowex-go cation exchange resin had no appreciable effect on the reaction mixture and both nuclei and auric gold passed through the column. Amberlite IRC-roo cation exchange resin proved to be a rapid reducing agent for the nuclear solution ; a clear red colloid came from the bottom of the column.This resin did not however reduce pure solution of chlorauric acid. Amberlite IR-4 and IR+ both anion exchange resins produced no visible effect on the colour. The emergent solution did not liberate iodine from potassium iodide and was therefore substantially free of auric ions. Furthermore i t was stable toward boiling and produced a colloid when introduced into growth medium. Electron microscopic examination showed that the particles were surprisingly large and diffuse. Their irregular shape did not permit the deter-mination of a size distribution curve (Fig. 12). Their form and lack of opaque-ness suggests that they may contain organic material because irregular bodies such as were seen often result from the decomposition of organic material by the electron beam.The ionic gold could not be eluted from the column b 66 SYNTHESIS OF COLLOIDAL GOLD solutions of sodium carbonate sodium hydroxide sodium chloride sodium sulphate hydrochloric acid sulphuric acid or nitric acid. The latter attacked the resin vigorously. It is therefore believed that the auric ion was reduced to gold on the surface of the resin. Role of the Sodium Citrate.-An investigation was made of the chemistry of the process and particularly the role of the citrate ion. The final products and the intermediates if any occur of the citrate + chloraurate reaction have not been reported in the literature. However in the oxidation of citric acid by various reagents acetone dicarboxylic acid has been described as the first intermediate step.** This substance can be prepared from citric acid either by intensive dehydration or by mild oxidation the reactions being CH,COOH (+ CO;+H,O) -0 CHzCOOH + CO + H,.CHz-CooH H&SO + SO - I I I I - HO C-COOH [Ol CH,COOH It was proposed to study the action of acetone dicarboxylic acid on chlorauric acid. 25 g. citric acid were treated in an Erlenmeyer flask with 50 g. fuming sulphuric acid (15 yo excess SO,). After standing for 15 min. the flask was cooled in an ice-salt mix-ture for 4 hr. and 25 g. of crushed ice were added. Crystals of acetone dicar-boxylic acid were filtered off this viscous mixture washed with ethyl acetate and dried in air. A solution of 0.05 M of the sodium salt was made by dissolving the acid in 0.1 N NaOH.10 ml. of chlorauric acid (containing I mg. of Au) was diluted with g ml. of water and treated at the boiling point with I ml. of the sodium acetone di-carboxylate solution. A clear red colloid formed with great rapidity passing swiftly through the blue state similar to that observed during the synthesis using the citrate ion. A faint but definite odour was observed similar to that noted during the synthesis with the citrate ion and resembling the odour of formalde-hyde. Kuyper 20 reports that the oxidation products of acetone dicarboxylic acid are formic acid formaldehyde and CO,. An identical reaction mixture prepared a t room temperature (23' C) showed the first detectable colour of faint pink in I min.growing darker over a period of several hours. The reaction was believed to be complete in 4 hr. The synthesis with acetone dicarboxylate ex-hibits little or no induction period and this is verified from the nucleation curve (Fig. 13) obtained from the size distribution curve (Fig. 14). The Character of the Nucleation Curves .-An examination of the nucleation curve (Fig. 15 16) shows that i t has in general four regions : an induction period followed by a rapid rise at the beginning of the nucleation a " linear " portion and finally a decay portion. The general nature of the curve is characteristic of an autocatalytic reaction. The induction period can best be examined by the nephelometric techniques. Its exact duration is difficult to determine for i t involves extrapolation to zero of a curve of rapidly changing curvature.One can say however that its duration decreases with increase in temperature as the approximate induction times of 26 min. at 15'C 5 min. at 3ooC, 3 min. at 39' C and z min. at 49" C indicate. One can use these values to calculate an approximate activation energy of about 10 kcal. /mole. The process responsible for the induction might be interpreted as the removal of an inhibitor of the nucleation process. However the fact that when one uses acetone dicarboxylate an oxidation product of the citrate ion there is an induction period of less than I min. indicates that the induction period is the time necessary to form an amount of acetone carboxylate ion necessary for nucleation. Examination of the effect of dilution on the induction period at IOOO C with the citrate ion as the re-ducing agent shows that it increases with dilution.Varying the citrate l8 Bruce I n d . Eng. Chem. (Anal.) 1943,6,283 ; Kuyper. J . Amer. Chem. SOC., Acetone dicarboxylic acid was prepared in the following way.lg 19338 55 1722. 19 Organic Synthesis (Ed. Marvel) (John Wiley and Sons Inc.) 5 p. 5. 2 0 See ref. (IS) J. TURKEVICH P. C. STEVENSON AND J. HILLIER 67 ion does not affect the induction time. Finally the decrease in the auric ion concentration during the induction period is less than I yo. Since the production of acetone dicarboxylate ion involves the reduction of auric ion this indicates that only a small number of acetone dicarboxylate ions can have been produced during this time.r / 2 3 4 5 6 7 FIG. 13.-Nucleation curve of a gold sol produced by acetone dicarboxylic acid. Ordinate yo total number of particles per unit volume ; abscissa time (min.). FIG. ~q.-Size distribution of a sol reduced with acetone dicarboxylic acid. Ordinate % particles ; abscissa diam. (A). FIG. 15.-Nucleation curves a t 49*5O 3g.0° 30.0~ and 15.4' C (nephelometric method). Ordinate particles per unit volume ; abscissa time (min.) 68 SYNTHESIS OF COLLOIDAL GOLD The second portion of the nucleation curve is one of rapid increase in the number of nuclei with the rate of increase increasing with time. On increasing the temperature this autocatalytic character becomes more pronounced in that d2n/dt2 is greater the higher the temperature (n is the number of nuclei and t is the time).Dilution markedly decreases the autocatalytic character indicating a high order dependence of this rate on the total concentration of the reactants. Decrease in the citrate ion concentration produces a similar effect. It should be noted that this autocatalytic character is absent from the nucleation curve produced by the acetone dicarboxylate. The rate of nucleus formation is a maximum at the start of nucleation and falls off exponentially indicating a first-order mechanism. One is therefore led to the conclusion that the autocatalytic nature of the nucleation reaction is due to the autocatalytic nature of the formation of the acetone dicarboxylic acid from the citric acid or some complicated phenomenon involving acetone dicarboxylate.I FIG. 16.-Nucleation curves at various citrate concentrations a t 100' C (size distribution method). Ordinate particles per unit volume ; abscissa time (min.). The third portion of the curve, 10 FIG. I 7.-Nucleation curves a t various dilutions (size distribution method) ; ordinate and abscissa same as Fig. 16. the " linear " portion is most pro-nounced for experiments at high concentration or high temperatures.- It is significant to note that under these conditions i t resembles the nucleation curve observed with acetone dicarboxylate. We are again inclined to ascribe to the acetone dicarboxylate an important role in this region of the nucleation curve. If one plots the logarithm of (N - Nt) against time for the nucleation by acetone dicarboxylate at 100' C one obtains a curve given in Fig.18. The straight-line character of the relationship shows that we have a kinetic expression of the type and this suggests that the rate-determining step in the nucleation process is the unimolecular decomposition of a complex of gold and acetone dicarboxylate. The kinetics of this decomposition will be a subject of further study. Nt = N,(I - e-kt) . * (4 J. TURKEVICH P. C. STEVENSON AND J. HILLIER 69 The slope of the last portion of the nucleation curve decreases rapidly with time as if one of the reagents is being exhausted. The explanation of this phenomenon is just as important as the explanation of why nuclei form. It is a region most difficult to examine experimentally because one is dealing with a system undergoing small changes in large absolute values of the observables.One cause contributing to the decrease in the rate of formation of the nuclei is the competition of the growth process. For as the particles grow larger and are present in greater number they grow more rapidly and begin to exhaust the " active " species of the nucleation process. This active species cannot be the auric ion for i t has been pre-viously established that about 95 yo of the original auric ion is present a t the time when the nucleation process has ceased. The active species cannot be the citrate ion because it is present in three to tenfold excess over the auric ion. One is thus led to the conclusion that the active species that is exhausted must be closely identified with acetone dicarboxylate.It is this compound that creates the nuclei and i t is quite possible that when there is a sufficient number of nuclei present they adsorb the acetone dicarboxylate on their surface and either utilize it as a reducing agent for the growth process or merely decompose i t catalytically. In support of this idea we wish to cite from an experiment on the growth process which will be presented in more detail in the section on the growth process. A solution of sodium citrate and chloraurate was allowed to interact at 70OC. A few minutes after mixing these reagents a known amount of zoo A gold sol was added. Examina-tion of the product in the electron microscope revealed but one maximum in the distribution curve.If however, the 200 sol was added to the sodium citrate + chloraurate system several minutes after the completion of the nucleation the sol obtained had two maxima one due to the growth of the FIG. 18.-Demonstration that nu-cleation with acetone dicarboxylic acid resembles a first order reaction. Ordinate log [N(oo)-N(t)] ; abscissa time (min.). added 200 A particles and one due to the growth on the nuclei already formed. The absence of a second maxima in the first case is taken as evidence that a large number of nuclei artificially introduced inhibit the nucleation process. Thus we are inclined to ascribe the slowing-down of the nucleation process to the removal of the acetone dicarboxylate by the increasing number of gold particles.Further evidence that a gold-contain-ing species is strongly adsorbed on the growing particles during the growth stage of the citrate reaction will be presented in the following section. The total number of nuclei per unit volume increases with the con-centration of the gold and citric ions and appears to reach a maximum a t some temperature between 40° and 70' C . This unusual temperature dependence may be associated with the observation that dilute aqueous solutions of acetone d.carboxylic acid begin to decomposed a t about 60' C. Hence above this temperature the tendency of increased temperature to produce a greater number of nuclei is more than compensated by the lower concentration of the acetone dicarboxylate ions due to its decomposition. This point will be the subject of further study 70 SYNTHESIS OF COLLOIDAL GOLD Mechanism of Nucleation.-No completely satisfactory theory con-cerning the precise mechanism of the formation of nuclei in dilute solution has yet been worked out.One possible theory is that nuclei are artificially introduced. This " impurity " theory in its various forms reduces simply to the hypothesis that the nuclei are introduced into the system as dust particles bacteria spores bits of glass or sharp points on the inside of glass containers. There is no doubt that very often such substances pro-duce nucleation and lack of cleanliness and flagrant disregard of certain common-sense precautions such as cleaning vessels from nuclei of previous preparations can explain the varying success of many previous workers in the field of colloidal gold.Again it should be pointed out that a few nuclei accidentally introduced do not produce colloidal gold but a coagulum of metallic gold. Because of the consistent behaviour obtained in this investigation under different conditions of concentration temperature, time of the year starting materials and glass apparatus we have come to the conclusion that impurities were not a variable in our investigation. It postulates the formation of a supersaturated solution of atoms of metallic gold some of which coalesce into a nucleus only when the statistical fluctuation of their concentration brings a sufficiently large number of them together to form a particle of a size that is thermodynamically stable. Thiessen 2 0 has stated that this number is about a hundred.This theory has been shown by LaMer and KenyonS1 to apply to the formation of colloidal sulphur. It is possible that i t might apply to our case but it is difficult to understand the marked temperature dependence of the rate of nucle-ation from the fluctuation point of view. Furthermore our investigation indicates that the nuclei are about 30 diam. and this would involve a fluctuation of the order of a million of gold atoms. We wish to advance the following " organizer " mechanism for the formation of a nucleus. The fundamental difficulty in building up a nucleus is the accumulation of a large local concentration of atoms to produce a particle whose size is greater than that just demanded by the stability of the particle.The fluctuation theory describes such an event as being rare but significant and due primarily to the statistical nature of physical events. One may attain the same result by postulating that the nucleating agent gradually builds up a complex between the gold ions thereby chemically binding a large number of both gold ions and reducing agent molecules into large macromolecules which at some stage or other will undergo a molecular rearrangement to produce m e W c gold particle of sufficiently large size. This event will be accompanied by the production of oxidation products of the reducing agent. This precursor of the nucleus may be considered as a copolymer of the gold ion and the organizer-a reducing agent which is polydentate and thus capable of forming cross-links between gold ions.This hypothesis finds some support in the nature of the reducing agents capable of causing nucleation. All of these are polydentate containing in the same molecule more than one group capable of forming a bond with the gold ion. Acetone dicarboxylic acid is known to form a stable complex with mercury 48 and is functiondy related to acetoacetic acid a well-known complex-former. Citric acid is known to form complexes with copper and iron 2s and is tetradentate in these complexes. Carbon monoxide forms carbonyls24 which are stated to be polymeric for elements of odd atomic number such as gold. Acetylene forms complexes with silver and copper acting as a dibasic acid. The fluctuation theory is one of great tradition. * o See ref.(8b). 2s Lanford and Quinan J . Amer. Chem. SOC. 1948 70 zgoo ; Fales and Kenney Inorganic Quantitative Analysis (The Century Company New York, 24 Wells Structural Inorganic Chemistry (Clarendon Press Oxford 1945) , LaMer and Kenyon J. Colloid Sci. 1947 2 257. 28 Bruce ref. (18). '939)J p* 345' P. 453 J. TURKEVICH P. C. STEVENSON AND J. HILLIER 71 An ether solution of phosphorus has been suggested by Faraday as a reducing agent for the production of colloidal gold. In our point of view it is the fine emulsion of phosphorus in water produced by the mixing of the ether solution with the gold chloride solution that acts as an organizer. The gold ions are adsorbed on the surface of the phosphorus droplets are reduced there to metallic gold and migrate on the surface to form a particle of sufficient size to exist as a nucleus.It is the binding on the surface in this case just as the binding of the gold atoms by the polydentate reducing agents in the macromolecule that ensures the con-tinued high concentration of gold atoms on the surface of the phosphorus droplet thereby permitting the gold particle to reach a size great enough for an independent existence as a nucleus. Growth Process .-In order to complete the experimental study of the process of the formation of colloidal gold in solution i t was thought desir-able to study the process of growth. Most reagents used for the preparation of gold colloids by reduction cause both nucleation and growth. Fortun-ately two substances hydrogen peroxide and hydroxylamine hydrochloride have been found by' previous workers to act under certain conditions as solely growth reagents.The study of the growth reaction differs markedly from that of nucleation in that in the latter one studies the number of particles as a function of time while in the former the size of the individual particle is examined. shown in the previous section that particles of gold prepared by the re-duction of gold chloride with sodium citrate at 100' C are very uniform in size at about zoo A diam. It was thought desirable to use the method of Zsigmondy 25 to prepare a graded series of gold sols of different but predetermined particle size. Accurately measured amount of the growth medium (equal volumes of chlorauric acid (0.01 yo Au) and hydroxylamine hydrochloride (0.027 yo by weight) were added to various amounts of sodium citrate gold sol containing a known concentration of 200 A particles.Reduction commenced immediately on mixing and proceeded rapidly and smoothly the gold sol developing completely within a few minutes of the mixing. In cases where the preparation of sols of a very large diameter was desirable i t was felt advantageous to carry out the reaction in steps using sols grown from the zoo particles for the in-oculation of the growth medium. In this method advantage is taken of the fact that a slightly acid solution of chlorauric acid and hydroxyl-amine hydrochloride (growth medium) in a scrupulously clean closed vessel will not produce colloidal gold until a sufficient number of nuclei are introduced.When the growth medium is inoculated with nuclei, the chlorauric acid is reduced by the hydroxylamine and the metallic gold so formed is deposited only on the nuclei so that they increase in size but not in number. The mean diameter of the resulting particles can easily be shown to be GROWTH IN HYDROXYLAMINE HYDROCHLORIDE REAGENT.-It Was where Df is the mean diameter of the final colloidal particle Do is the mean diameter of the nuclei used Mi and M are the respective masses of the ionic gold in the growth medium and the metallic gold of the gold nuclei used in the growth medium. The results are presented in Table IV. The observed mean particle size compare very favourably with those predicted on the basis of the above formula. In addition to this con-firmation of the formula i t was noted that the percentage root-mean-square deviation changed but relatively little with quite large changes in the particle size.A definite trend in this change was observed however in 25 Zsigmondy and Thiessen Das KGZZoide Gold (Leipzig 1925) and ref. 8(b) ; and Rinde ref. ( 5 ) 72 SYNTHESIS OF COLLOIDAL GOLD that the percentage root-mean-square deviation decreased from 13 yo for the zoo A nuclear sol to about 8.5 % for the 1000 A sol. This decrease is believed to be more apparent than real for the following reasons. In the first place the average experimental error in the particle size measure-ment due to imperfect resolution of the electron microscope and to personal errors in the image measurement was approximately constant in amount from sample to sample and hence contributed more to the percentage deviation of the distribution of the smaller particles.In the second place a study of the small angle X-ray scattering 26 of the 200 A sol has revealed that the root-mean-square deviation of particle diameters is not 13 yo but may be about 8.5 Yo. We are thus led to the conclusion that the percentage root-mean-square deviation does not change with growth in particle size in the range size investigated. Our observations con-firm the experiments of Rinde2' on the particle size determinations by sedimentation studies. It can be easily seen that the law of growth consistent with the observation that the root-mean-square deviation does not change is where D is the diameter of the particle t is the time and k is a constant whose magnitude depends on the temperature and reagent concentration but not on particle size.A further insight into the law of growth was obtained from the following experiment. From a standard 200 A mean diameter sol a sol was prepared by the method described above with a mean diameter of 300 A 27 ml. of this sol were mixed with 8 ml. of the 200 A sol and the size distribution curve of the mixed sol was measured. The mean diameter of the mixed sol was then increased by a factor of two by growth in a hydroxylamine + auric chloride solution. The size distribution of the particles of the resulting sol was also measured. In both cases two maxima were observed. In the first sol the maxima were at 200 A and 300 while in the second case they were 400 A and 600 A (Fig.19). Integrating the law of growth leads to the conclusion that during growth the ratio of the particle sizes is In - = c(t - t') dD/dt = kD . (6) D' D remains constant and not the difference in particle sizes. The above experiment clearly confirms this deduction. A chemical study was also made of the growth reaction using hpdroxyl-amine hydrochloride. Observations with the glass electrode indicated that the pH dropped during the growth reaction. It was not found possible to study the rate of formation of the hydrogen ions. The iodometric method of Gooch and Morley 28 was applied to the study of the kinetics of the disappearance of the auric ion. Runs were made at four tem-peratures at several nuclear concentrations with nuclei of different sizes and several hydroxylamine concentrations.The reaction was found to be first order with respect to the auric ion hydroxylamine added metallic gold nuclei and hydroxyl ion concentrations indicating that none of these reagents is strongly adsorbed. The first-order dependence on the added nuclei is stated on the basis of added gold atoms i.e. the rate observed when a large nuclei were added was the same as observed when the smaller nuclei were added provided that the total concentration of metallic gold was the same (more smaller particles). This is equivalent to the law of growth stated above. The experimental activation energy was found to be 9-1 f 0.6 kcal./mole for two sizes of nuclei. 26 Turkevich and Hubbell J . Amer. Chem.SOC. 1951 73. 27 Rinde ref. ( 5 ) . 28 Kolthoff and Furman Volumetric Analysis (John Wiley and Sons) 2, p. 469 ; Kurtenacker and Wagner 2. anorg. Chem. 1922 120 26 J. TURKEI'IC'IT P. C. STEVENSON AND J. HIL1,IER 73 The gold ion solution used was standardized iodometrically as described above while the hydroxylamine hydrochloride was oxidized in strong hydro-chloric acid solution by the method of Kurtenacker and Wagner.29 The metallic gold colloid must be removed by adsorption on TiO previous to titration since acid bromate solutions readily oxidize metallic gold and give false readings. It was found that 1-00 mmole of HAuCl oxidizes 1.0 -I- 0.5 mmoles of hydroxylamine. The stoichiometry of the reaction was also investigated. The reaction is probably HAuC1 + NH,OH .HC1+ Au + 5HCl + NO. GROWTH IN SODIUM CITRATE REAGENT.-It is quite possible that the exponential law of growth obtained for the hydroxylamine hydrochloride reagent mav be peculiar to reduction by the hydroxylamine hydrochloride. It >as thkrefoie decided to investigate the law of growth in the sodium citrate system. In a subsequent communica-tion on the optical properties of monodisperse gold sols of different diameters i t will be shown that the absorption spec-trum of uncoagulated colloidal gold has a single absorption maximum in the visible region which varies in a regular way with the particle size after 300A and that the optical density of the sol per particle for the absorption maximum follows the law d = const. nD2'8 .(7) where n is the number of colloidal particles per ml. and D is the mean particle diameter. Since we have shown in the preceding section that the number of particles per unit volume becomes constant very soon after the mixing of the reagents at the higher tem-perature this relationship can be used to obtain the particle % - 12 /o ;I 2 D % -/2 -/o -8 6 il A L n 5 FIG. 19.-Demonstration of the law of growth using the electron microscope. size as a function of time from the equation the final diameter D( co ) being determined by the electron microscope. Three runs were made on the standard sodium citrate preparation at 70" C using a Beckmann spectrophotometer to measure d. The readings were found to be reproducible the points for the three runs falling close to the same smooth curve.Points obtained for very short reaction times were not considered reliable as the number of particles was not constant. A plot of log D against t gives a straight line up to times until almost all of the gold is reduced indicating that the growth reaction follows the growth law given above but is zero order in the reagents used (Fig. 20). This zero-order behaviour is consistent with a surface reaction in a strongly adsorbed layer of reactants. It may be recalled that the cessation of the nucleation process was ascribed by us to the strong adsorption of the 74 SYNTHESIS OF coI,r,oimu ~ o r m active species by the gold particles formed. Extrapolation of the straight line to zero time gives a value of 48 f 5 A for the diameter of the nucleus, a value consistent with estimates given in the section on nucleation. Some further evidence was desired to show that the exponential law of growth did indeed hold for the growth process using sodium citrate. It was shown above that when the law of growth was exponential the ratio of the diameters of two particles growing in the same reaction medium does not change with time. Experiments were devised in which particles of known large size were added to the growing colloid a t several times during the growth process. It was expected that the size distribution curve of the resulting sol on completion of the reaction would show two maxima one due to the added particles and one due to those present when the particles were added. The ratio of the diameters a t which these maxima occurred should be the ratio of the mean particle size in the growing sol to the mean diameter of the added particles at the instant of mixing. Since the latter is known the former can be easily evaluated. Several samples were prepared using sodium citrate as the nucleating 1 FIG. 2o.-Growth in the citrate sol. Ordinate log relative diameter ; abscissa time (min.). and growth agent a t 70’ C. The first of these was allowed to go to com-pletion. At definite times the other samples were diluted with equal volume of the completed sol. Size histograms were obtained with the electron microscope for these sols after the reaction was completed. In most cases two maxima were observed in the size distribution curve. When these occurred the ratio between the diameters at which these peaks occurred were used to calculate the diameter of the growing colloid at the time of the addition of the completed sol. The points so obtained agree with those derived by the optical method (Fig. 21). In the sample prepared by adding the completed gold colloid immediately after mixing of the sodium citrate and the chlorauric acid solutions only a single maxi-mum in the size distribution curve was produced. This was interpreted to mean that a large number of gold particles in solution inhibits nucleation by successful competition for the active species. Mechanism of Particle Growth.-Consideration of the law of growth of a particle in a solution which deposits material on the surface by a typical heterogeneous reaction leads to a formula of the following type where K is the specific rate constant for unit area for the surface reaction, D is the diameter of the particle A is the diffusion coefficient of the activ J. 'I'URKEVICH P. C. STEVENSON AND J. HILTJER 75 species V is the molal volume of the metallic gold and coo is the con-centration of the active species at large distances from the particle. It is seen that if the diffusion is the rate-determining quantity then the rate of change of diameter is inversely proportional to the diameter; while if the process is limited by the surface reaction then the rate of change of the diameter with time is independent of the diameter. The observed law is neither and demands that the rate of change of diameter with time be proportional to the diameter. A mechanism of this exponential law of growth must await further experimental studies of the growth reaction. > I f i m e in Minukes 10 30 I I

ISSN:0366-9033    

DOI:10.1039/DF9511100055

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

J. 'I'URKEVICH, P. C. STEVENSON AND J. HILT,IER 75 THE INTERPRETATION OF BROADENED X-RAY REFLECTIONS WITH SPECIAL REFERENCE TO CLAY MINERALS BY G. W. BRINDLEY Received 24th May, 1951 The problems arising in the determination of colloidal sizes from the broaden- ing of X-ray reflections are surveyed. Instrumental broadening can be taken fully into account. Diffraction broadening may be produced by lattice strain, lattice mistakes or small crystal size separately or in combination. In the domain of clay minerals, the two latter commonly occur together and this is the main complication in using X-rays for size determinations of clay colloids. In addition, the diffraction process is often 2- rather than 3-dimensional in character76 BROADENED X-RAY REFLECTIONS so that experimental studies have been concerned as much with the difiraction process as with crystal size determinations.Electron microscope data on clay particle sizes are summarized. Crystal sizes of balloysite and montmorillonite from X-ray data are of the order of 0~01-0~02p which is comparable with the smallest observed particle dimensions. Investigations of the thickness of kaolinite and dickite crystals could be usefully undertaken but similar studies of other clays are rendered difficult by the occurrence of interstratified mixed- layer structures. 1. 1ntroduction.-This contribution to the Discussion on the size and (I) a survey of the interpretation of broadened X-ray reflections, and As regards (I), the subject can be discussed broadly since comprehensive treatments of the subject up to about 1947 have been given by James and by Wilson ; 2 the latter has also summarized some of the more recent developments.8 X-ray diffraction by clay minerals has also been recently reviewed.4 Since colloidal sizes are measured with X-rays by determining the breadths of reflections, the questions involved are concerned with the interpretation of line breadths.* The observed breadth B of a re- flection arises partly from instrumental effects for which a correction must be made before the true diffraction breadth /3 can be obtained.Since diffraction broadening of lines can arise in a number of ways, i t is important to be able to distinguish them experimentally. Failure to do so may result in quite false results for the size and shape of particles. 2.Corrections for Instrumental Broadening .-Instrumental broaden- ing arises from factors such as slit widths defining the X-ray beam, size and form of powder specimen, type of X-ray camera, doublet character of the Kci radiation usually employed. The instrumental breadth b of a line is found by using a well-crystallized material such as quartz or an annealed metal wire with a crystal size N 10-4 cm. which gives negligible diffraction broadening. To obtain the diffraction breadth ,!l of a broadened line from the observed breadths B and b, various procedures axe possible, for example shape of colloidal particles aims at (11) a summary of results obtained with clay minerals. P = B - b , . ' (1) B'=Ba--bS . ' (2) Eqn. (I) was given by Scherrer,6 and recently Wood and Rachinger have shown that i t is generally valid if the line profile takes the form I / ( I + cZxS), (G, a constant and x, distance along the film).Eqn. (2) given by Warren and Biscoe was shown by Taylor * to be valid for a Gaussian intensity distribution. Graphical methods involving line pro- files have been described by Jones and widely applied. Rachinger lo and Pease 11 have described direct methods for correcting for Koc,a, separation. 1 James, The Crystalline State, Vol. 2 ; The Optical Principles of the Daflrac- tion of X-rays (Bell, London, 1948). 2 Wilson, X-ray Optics (Methuen, London, 1949). Wilson, Research, 1950, 3, 394. 4 Brindley, X-ray Identificataon and Crystal Structures of Clay Minerals (The Mineralogical Society, London, 195 I).* The breadth may be taken either as the angular width of a line a t half its maximum intensity (the so-called half width) or as the integrated intensity divided by the maximum intensity (the integral width) ; the latter is almost invariably used in theoretical treatments of the subject. 6 Scherrer, Nachr. Gottingen Gesell., 1918, 98. Zsigmondy's Kolloidchemie (3rd edn.) , p. 387. Wood and Rachinger, J . Inst. Metals, 1949, 75, 571. 7 Warren and Biscoe, J . Amer. Ceramic SOC., 1938, 21, 49. Taylor, Phil. Mag., 1941, 31, 339. Jones, Proc. Roy. SOC. A , 1938, 166, 16. lo Rachinger, J . Sci. Instr., 1948, 25, 253, 353. l1 Pease, J . Sci. Instr., 1948, 25, 353.G. W. BRINDLEY 77 Stokes la has made a notable contribution by developing a Fourier method giving the true diffraction profile of a line corrected for all forms of instrumental broadening.The profile enables more information to be obtained than can be obtained singly from the width of a line, and the form in which Stokes' results are obtained is particularly suitable for these further developments (see 3 6 ) . 3. Diffraction Broadening Due to Crystal Size .-Measurable broadening, distinguishable from instrumental effects, is obtained only with crystals of colloidal and near-colloidal size. ( A .= wavelength, L = crystal size, and K is a constant of the order of unity) gives correctly the order of magnitude of L if K is made equal to unity. The value of K depends on the relation of the reflecting planes to the shape of the crystal, and can only be calculated explicitly for relatively simple shapes.The theoretical calculation of K has been the subject of many investigations too numerous to list here. Reference may be made to the books by James 1 and by Wilson and to recent papers by Stokes and Wilson.18 The latter show that for a general reflection hkZ from a crystal of any shape whatever, The Scherrer e q ~ a t i o n , ~ j? = KA/LCOS e . (3) j? = A/L cos e, where L = V-lST(hkZ)dV, . (4) or L is the " volume average of the thickness of the crystal measured perpendicular to the reflecting planes ", T(hkZ). Only for spherical crystals will L be a constant for all reflections. In other cases, the variation of L with (hkl) will enable the crystal shape to be determined. 4. Broadening of X-Ray Reflections Due to Strain.-X-ray reflections are broadened by any departure of a crystalline structure from strict regularity.Crystal size broadening may be included in this statement if the boundary of a crystal is regarded as a discontinuity in its regularity. Strain broadening arises (a) if the strain 7 is uniform in a crystal but varies from crystal to crystal in a powder,ld (b) if the distortion in a crystal is non-uniform, so that 9 varies with direction, hkl.15 This type of broaden- ing has been investigated chiefly in relation to cold-worked metals 16 and is probably not likely to be important for free colloidal particles. Briefly, in case (a) the strain breadth & is proportional to tan 8 and in- dependent of A (19 = Bragg angle), and in case (b) Comparison of eqns. (4) and (5) suggests that strain broadening may be distinguished from crystal size broadening by (i) the variation of with sec 8 or tan 0 ; (ii) the variation of p for a particular reflection hkl with A.Of these possibilities, (i) tends to be insensitive and is likely to be com- plicated by the dependence of L or 7 on hkl ; (ii) is the more satisfactory method but is inconvenient experimentally. 5. Broadening of X-Ray Reflections Due to Lattice Mistakes.-This type of broadening is less easily summarized because i t can arise in a variety of ways. Among clay minerals and layer silicates generally, lattice mis- takes of several kinds are common (Brindley,4 especially Chap. XI and XII), and i t is principally for this reason that the X-ray determination of the size and shape of clay colloids is rendered difficult.l3 Stokes and Wilson, Proc. Carnb. PhiE. Soc., 1942, 38, 313 ; 1944, 40, 197. l4 Brindley and Ridley, Proc. Physic. Soc., 1938, 50, 501. Brindley, Proc. Physic. Soc., 1940, 52, 117. l6 Stokes and Wilson, Proc. Physic. Soc., 1944, 56, 174. 16 Smith and Stickley, Physic. Rev., 1943, 64, 191. Wood, Nature, 1943, 151, 585. Lipson and Stokes, Nature, 1943, 152, 20. Hall, PYOC. Physic. j?, oc q m . tan 8. - ( 5 ) Stokes, Proc. Physic. Soc., 1948, 61, 382. sot., 1949,162, 741.78 BROADENED X-RAY REFLECTIONS The diffraction patterns of such structures are characterized by a mixture of relatively sharp and diffuse reflections, a general account of which is given by Wilson.8 Crystal size broadening gives lines in powder diagrams having a symmetrical or largely symmetrical profile whereas lines broadened by certain types of mistakes may appear as markedly asymmetric bands.", 1% 19,20 Thus, if in layer lattices the displacements of the layers are so frequent that the structure may be treated as a random stacking of two-dimensional lattices, characteristic bands are obtained having relatively sharp low-angle terminations and spreading towards high angles ; the band profile can show considerable variation from one band to another depending on the variation of the structure factor F with angle of diffraction.% 89 When F is constant or largely constant over the range of diffraction, then a formula developed by Warren18 analogous to the Scherrer formula is applicable for the determination of the layer size : A slight modification of this procedure is required if L is very small, -20 A, as Miss Franklin 23 has recently' indicated.Other bands are largely insensitive to crystal size, so that considerable care is required in utilizing data of this kind for the determination of crystal dimensions. The theory of diffraction by two-dimensional lattices has been treated by Laue,l7 Wa,rren,lB Wilson, l 9 Brindley and MBring.20, 22 An alternative method of estimating crystal sizes from two-dimensional diffraction bands rests on the fact that the peaks are displaced from the positions of the corresponding normal reflections which can be calculated from the lattice parameters. The method is feasible only when the structure factor F is largely' constant and for low-order bands.Warren Is has given, in effect, the following approximate formula, (Ad = apparent error in lattice spacing, d = spacing calculated from the lattice parameters). Another type of lattice mistake which is also common among clay minerals arises from the interstratification of layers of different kinds, having different thicknesses and/or scattering factors. With layers of different thickness, a non-integral series of reflections is obtained of very varying widths. Hendricks and Teller 24 first treated problems of this kind theoretically assuming the crystal size to be large (effectively in- finite) and M6ring 2 5 has more recently developed the theory in a form applicable to a specified number of layers. Brown and MacEwan (see BrindleyJ4 Chap. XI) have given numerous curves illustrating these effects for mixed layer clays of several kinds. 6 .Range of Crystal Sizes in a Powder Specimen.-In any powder specimen a range of crystal sizes and shapes will be present so that L determined from the diffraction breadth /3 will represent an average value, This average is expressed by eqn. (4) for a single crystal or an assemblage of crystals. Bertaut 26 and independently Warren and Averbach 27 have @ = 1e84X/L cos 9. . - (6) Ad = o-32d2/L, . (7) 17 Laue, 2. Krist., 1932, 82, 127. l8 Warren , Physic. Rev., 1941 , 59, 693. lS Wilson, Acta Cryst., 1949, 2, 245 ; also Nature, 1948, 161. 2o Brindley and Mbring, Nature, 1948, 161, 774. 21 Brindley and Robinson, Min. Mag., 1948, 28, 393. 22 Brindley and Mering, Acta Cryst., 1951 (in press) 22a Brindley and Mering, paper in course of preparation ; a continuation of 24 Hendricks and Teller, J.Chem, Physics, 1942, KO, 147. 2sM6ring, Acta Cryst., 1949, 2, 371 ; see also Fourth Int. Cong. Soil Sci., 26 Rertaut, Acta Cryst., 1950, 3, 14 ; also Conzpt. rend., 1949, 228, 187, 492, 27 Warren and Averbach, J. Appl. Physics, 1g50,21, 595. ref. (22). Amsterdam, 1950, 3, 21. 1597- Franklin, Acta Cryst., 1950, 3, 107.G. W. BRINDLEY 79 shown that by a Fourier analysis of the profile of a diffraction-broadened line, the distribution of the particle sizes may be found. In Warren's notation, if A , is the nth Fourier coefficient, then (un/dn)n,o = - I I N , and (d2A,/dn2f = (r/N)$(n), where IN is the average number of unit cells in a crystal normal to the reflecting planes, N is the total numbers of cells and p(n) is the number of columns containing n cells.7. Combination of X-Rays and Other Techniques.-In the study of clay mineral colloids, the writer believes that the most useful results will be obtained by a combination of techniques and in particular by combining electron microscope studies with X-ray analysis and perhaps also electron diffraction analysis. A pure X-ray approach to the deter- mination of clay mineral dimensions is beset with very great difficulties on account of the frequency with which these minerals exhibit lattice imperfections. The electron microscope, by showing directly the indi- vidual particles of a clay colloid, is of very great value, but i t will not replace entirely the X-ray method of examination, since the latter is con- cerned essentially with crystal dimensions.With well crystallized clays such as many kaolinites which show clear hexagonal forms in the micro- scope there is little doubt that the individual particles are single crystals, but with poorly crystalline clays, such as the montmorillonites, the par- ticles will often be crystal aggregates. An important contribution to this question has been made by Mdring and co-workers 28 who have shown that montmorillonite crystals tend to adhere along edges and faces in a manner depending on the number and kind of exchangeable cations. Experiments such as those of Birks and Friedman29 have clearly shown that crystal sizes determined by X-rays and with the electron microscope are in close agreement ( f 10 yo) over a wide range of crystal sizes when the conditions are favourable for both methods. Electron diffraction has so far been applied very little to clay minerals, but by combining the diffraction technique with the electron microscope i t may be possible to obtain useful results for single crystals of clay colloids.Experiments of this kind on kaolinite and montmorillonite have been described by Forslind 30 while MacEwan and Finch 81 have reported diffraction experiments on montmorillonite. The accompanying table summarizes data obtained with the electron microscope and is based largely on a recent report of the American Petroleum Institute s2 which contains a valuable bibliography and an extensive series of electron micrographs (see also the book by Marshall 9.The numerical data are to be regarded as indicating orders of magnitude only. The majority of clays form thin hexagonal or pseudo-hexagonal plates but a number exist as thin laths, rods or tubes. In the former group, the plane of the flake corresponds to the plane of the Si-0 network in the crystal structure, and is the basal (001) plane. In the latter group, i t is of great interest to determine the relation of the crystal habit to the structure. Clays having flaky crystals tend to form well-ordered ag- gregates when sedimented and these can be used to obtain clear basal (ool) reflections. One would expect to be able to determine the thickness 2* MBring, Mathieu-Sicaud and Perrin-Bonnet, Fourth Int. Cong. Soil Sci., 29 Birks and Friedman, J .Appl. Physics. 1946, 17, 687. 3O Forslind, Svenska Forskningsinst. f& Cement, (1948), Bull. No. 11. 31 MacEwan and Finch, to appear in Clay Minerals Bulletin. 33 American Petroleum Institute (Project 49, Clay Mineral Standards), (Col- 33 Marshall, The Colloid Chemistry of the Silicate Minerals (Academic Press, Amsterdam, 1950, 3, 29. umbia Univ., N.Y., 1950). N.Y., 1949).SO BROADENED X-RAY REFLECTIONS of the flakes from the (004 reflections and the layer dimensions from the (hko) reflections, or from the (hk) bands when the crystalline layers are randomly disordered. SURVEY OF SIZES OF CLAY MINERAL PARTICLES FROM ELECTRON MICROGRAPHS 28, 32, 35, 34, 95 Mineral Dickite . . Kaolinite . . Kaolin mineral in many fireclays Halloysite . Montmorillonites Nontronite .Hectorite . c Hydrous mica, illite Palygorskite or Sepiolite . Attapulgite Habit I Partidesize Well-defined hexagonal plates. Hexagonal plates, often well-developed. Thick- ness, variable. Some- times elongated. Hexagonal plates, often poorly developed. Elongated forms having the appearance of rods or tube.s.85 Split and partly unrolled tubes are observed. Usually very poorly de- fined, occasionally show- ing hexagonal forms. Tendency to aggregate.28 Poorly crystallized. Lath- like or ribbon-like ap- pearance. Thin laths. Poorly defined, thin hexa- Ribbon-like particles. gonal flakes. Fibres. Rod-like and flaky forms observed. Commonly - r-rop, Plates usually 0.1-3 p. occasionally larger. Plates usually much less than ~ p . Outer diameters N 0-05-0.2~.Length - 0-1-1 p. Wall thickness N o*ozp. than ~ p . Plates much less Length N rp. Width N 0 . 1 ~ . Width - ~ p . Length +- ~ p . Length - 0-I-5p. Width N O - O I - O . I ~ . Length of rods N 0-I-5p. Flakes N 0-1-0-5p. 8. Difficulties of Determining the Thickness of Clay Mineral Particles with X-Rays .-In the montmorillonite clays, the non-integral orders of basal reflections ordinarily obtained and the marked variations in their breadths arise from the occurrence of randomly interstratified water layers or hydrated layers.24 Organic-montmorillonite complexes 8% a7 (especially with glycerol and glycol) give clearer reflections and a series of integral orders which are much less influenced by random effects. They have not been critically considered as yet from the standpoint of the thickness of the flakes.I n the mica clays also the line profiles in- dicate random interstratifications. The lines are considerably sharpened by heat treatment, but they have not been considered in relation to particle size measurements. 34 CaiUbre, Mathieu-Sicaud and Henin, Bull. SOC. Frmnq. Min. Crist., 1950, 35 Bates, Hildebrand and Swineford, Amer. Min., rgjo, 35, 463. 38 MacEwan, Nature, 1944, 154, 577 ; J . SOC. Chem. Id., 1946, 65, 298 ; 37 Bradley, J . Amer. Chem. SOG., 1945, 67, 975 ; Amev. Man., 194.5, 30, 704. 73, 193. 7’wm.s. Faraday SOC., 1948, 4, 349,G. W. BRINDLEY 81 The situation is less complex among the kaolin group of clays, apart from halloysite which must be considered separately. Kaolinite and dickite could be usefully examined from this standpoint, but no measure- ments have so far been reported.The less well-defined kaolin clays found in many fireclay deposits must be considered more cautiously. They commonly give broader basal lines than the well-crystallized kaolinites, suggesting thinner flakes, but there is evidence (admittedly rather slender a t present) that they may contain some hydrated layers.4 The electron micrographs were first interpreted as showing lath-like crystals but with improved techniques it has become apparent that at least some halloysite crystals are tube-like.ss It was inferred from the non-orientation of halloysite sedimented in water that the particles were probably not plate-like. Halloysite exists in a variety of hydrated forms. Fully hydrated halloysite, Al,Si,0,(OH)4 .2H,O, with alternate silicate and water layers, may be a regular layer structure suitable for an X-ray study of crystal thickness, but some water is lost very readily and the regularity of the layer sequence is not very certain. Fully dehydrated halloysite is difficult to obtain and seems to require heat-treatment to the point of decomposition.38, 39 Naturally occurring metahalloysite is largely but not wholly dehydrated and this applies also to the mineral heated at temperatures up to about 3ooOC. The possibility that the incompletely dehydrated mineral may contain randomly interstratified water layers requires careful consideration in any study of X-ray line breadths. The fact that some crystals are curved, even tubular, is a further complication, and Wilson’s analysis 40 of diffraction by curved layers may find an important application in this connection.To summarize : to the writer’s knowledge, no detailed measurements have been made to obtain the thickness of clay mineral particles from the broadening of basal X-ray reflections. Kaolinite and dickite axe suitable for such measurements, but with all other clay minerals serious difficulties arise from the irregularity of the layer sequences. 9. Layer Dimensions of Clay Mineral Particles .-Detailed studies have been made to interpret quantitatively the broad diffraction bands given by the clay minerals halloysite 21 and montmorillonite.22 Although the centre of interest in this work has been the process of diffraction by single silicate sheets acting as two-dimensional gratings, the determin- ation of the size of the layers is implicit in the work.The procedure adopted was to estimate L by applying eqns. (6) and (7) to suitable bands and then to calculate the distribution of intensity in the diffracted bands for a range of crystal sizes of the estimated order of magnitude. In this way the approximations involved in arriving at eqns. (6) and (7) do not enter into the final results which rest directly on comparisons of observed and calculated intensity distributions. The results obtained for halloysite ar although broadly satisfactory in that they furnish ample evidence that the mineral consists essentially of two-dimensional diffracting units and that the theory of diffraction developed by Warren l8 is essentially correct, do not give more than the order of magnitude of the crystal size, namely about 100-200 A, i.e.0~01-0~02p. The crystal size therefore appears to be of the same order of magnitude as the smallest particle dimensions seen in the electron microscope. Since the electron micrographs of halloysite show elongated forms (laths, rods or tubes) some variation of L with direction hR in the crystal lattice may exist, i.e. if the diffracting units (crystals) are similar in shape to the observed particles. While some of the anomalies may be explainable in this way, other difficulties remain, notably for the bands Halloysite presents a particularly complex problem. 38Brindley and Goodyear, Man. Mag., 1958, 28, 407. 39 Brindley, Robinson and Goodyear, Mdn.Mag., 1948, 28, 423. 4 0 Wilson, Acta Cryst., 1949, 2, 220.82 RHEOLOGICAL PHENOMENA OF CLAY SOLS hk = 02, 11 and 06, 33. These, being different orders of reflection from the same planes, should at least give the same L value, in fact they give about zoo A and 85 respectively ; this difference may be due to a small but appreciable separation of the 06 and 33 reflections, but this explana- tion is not yet fully established. Halloysite, however, is not ideal for testing the theory of diffraction by random layer structures in view of the probable curvature of the layers and for this reason no further attempt has yet been made to analyse the data in detail. Montmorillonite appeared to offer a better chance of obtaining quanti- tatively satisfactory results.The theory' of the diffraction process has been re-examined and certain approximations in the purely algebraic treatment involving the assumption of a constant or slowly varying F factor have been removed by developing a method involving partly algebraic, partly numerical integration.22 The results obtained by the more detailed calculations do not differ very greatly from those obtained from the Warren formulae and it seems probable that the anomalies in the L values obtained for halloysite cannot be attributed entirely if at all to approximations in the Warren theory. In the application of the Warren theory 18 or the more detailed analysis of Brindley and MQing 22 to the diffraction bands from montmorillonite, a further complication has arisen. In order to carry through these ana- lyses for two-dimensional diffracting units, i t is necessary to know the angular variation of F within a diBraction band, i.e., to know the struc- tural arrangement in the layer. Now with montmorillonite not only is the structure of the silicate layer still a matter of discussion (see, for example, MacEwan, in ref. (4), Chap. IV) but also the exchangeable cations and water molecules between the layers must be considered. The shape of the bands has been found to be dependent on the particular saturating cations and on the degree of hydration. The problem is still not yet fully solved, but the prospects of obtaining quantitative agreement be- tween observed and calculated intensity distributions and therefore of reliable L values from the X-ray data appear to be good. At the time of writing, the most probable value for the layer dimensions of montmorillon- ite appears to be about 250 A.aaa and this agrees with the electron micro- graphs of the same material. 28 Physics Laboratories, University of Leeds.

ISSN:0366-9033    

DOI:10.1039/DF9511100075

出版商:RSC    

年代:1951

数据来源: RSC