O X THE XATURE O F COAGULATION VISCOSITY9 AND THIXOTROPY I N COLLOIDAL SYSTEMS BY S. S. KISTLER
Introduction The most prominent, division of colloids into classes is that into lyophilic and lyophobic. Many phenomena have been more or less satisfactorily explained on the basis of the differences in the relationship of the colloidal particle to the dispersion medium in t,hese two groups. I t has been assumed with considerable justification that, the lyophilic particle is closely associated with a comparatively large quantity of the dispersion medium, and numerous investigations have had as their goal the measurement of the amount of “bound” solvent. Although the results unquestionably lead to the conclusion that’ there are large differences in this relationship of dispersed to dispersing medium, quantitatively there has been little agreement between the various methods used. The conception of “bound” solvent has led to the general conclusion that a cert,ain amount of the solvent is held in more or less of a rigid condition within or surrounding the micelle. The author’ ha,s shown quite conclusively, however, that, at least in the case of certain of the hydrated sols and gels, the amount of water that can be held in anyt,hing like a rigid condition niust be very small. The fluidity of the water in these cases investigated was found to be not widely different from that of pure wa,ter. Also, Brig@ in a recent very illuminating article has clearly pointed out that “bound” water in its usually accepted meaning is purely a fiction. In spite of these objections, nevertheless, qualitatively t’hereis no question of the large differences between the lyophilic and lyophobic colloids and the concept of solvation will undoubtedly continue to be useful although its exact meaning remains unknown. The Existence of Cvbotactic Complexes i n Liquids. I n recent years considerable progress has been macle in our understanding of the struct’ure of liquids, and I feel that the time has come when these findings can be applied to our knowledge of colloidal systems with much clarification of mooted subjects. X-ray investigations3 apparently indicate conclusively that within liquids the molecules are constantly associating into evanescent complexes of crystal-like arrangement. Even in the case of liquid mercury Debye4 has demonstrated the existence of these complexes. That these corriplexes must
..____ ~. Kistler: J. Phys. Chem., 35, 81j (1931).
J. Phys. Chem., 34,367 (1932). Stewart and Morrow: Phys. Rev., 30, 2 3 2 (1927); St,ewart: Rev. Modern Phys., 2, n16-22 (1930). Debye and Menke: Physik. Z., 31, 797 (1930). 3
COAGULATION VISCOSITY AND THIXOTROPY
2949
be widely different from true crystal nuclei seems certain from the fact that, although Stewart estimates that a t any one instant a large fraction of the molecules in a liquid are thus associated, numerous liquids may be undercooled for long periods of time without crystallization. Richards and Harris5 conclude from their observations on the scattering of light that in undercooled liquids there are evanescent amorphous complexes. Whether these amorphous complexes of Richards and Harris are the same as the crystal-like complexes of Stewart, Debye, and others, it is impossible to decide. It may be that they are the same but only upon undercooling of the liquid do the densities of the liquid and complex differ enough to scatter light appreciably. Stewart has applied the term cybotactic complexes to those that show evidence of crystal-like structure with X-rays. His definition is sufficiently broad and vague, however, so that for lack of a better term, I shall refer to all associations of molecules into transitory groups as cybotactic complexes and for convenience shall refer to them as cybomas. Whatever the nature of the cybomas, their existence can scarcely be questioned. Within a liquid the molecules must be constantly associating into cybomas, remaining thus associated for a brief moment and dissociating again only to reassociate with other neighbors. How rigid these associations may be remains a t present unknown, but it seems very reasonable to assume that for the brief period of its existence, a cyboma will behave as a single particle and go through Brownian movements. I n fact, it seems a perfectly reasonable assumption that any one complex may not disappear in entirety but rather that it is experiencing growth and decay a t the same instant. I n other words, the probability for the existence of any small group of molecules within the larger complex in a rigid framework is independent of the probability for the complex as a whole, so that while new molecules are adding to the surface of the complex, older portions are a t the same time liquefying. A single cyboma, therefore, may progress through the liquid by growth on one side and decay on the other. It may branch and the branches quickly split off or it may liquefy as a whole. If there is some sort of orientation of the molecules within the complex, growth by orientation of liquid molecules a t the surface may be more probable than the sudden association of a group of neighboring molecules into a coherent mass. Regardless of how these cybomas arise, it is to be expected that they will on the average consist of relatively few molecules and, therefore, will diffuse rapidly compared to the velocity of a moderate sized colloidal micelle.
Influence of the Surface of a Colloidal Particle on Cyboma Formation If we consider an imaginary boundary in the undisturbed liquid, an equal number of cybomas will cross from each side in unit time due to Brownian motion. Suppose, however, that this boundary is replaced by the surface of a colloidal particle; there will now come to the surface in unit time the same number of cybomas as would have crossed the imaginary boundary. But the J. Am.Chem. SOC.,54, 3799 (1932).
S. S. KISTLER
2950
surface may materially influence the number that progress outward from it. I n other words, the substitution of a solid surface for the imaginary boundary may materially affect the equilibrium conditions at this boundary. Three possibilities exist: ( I ) The cybomas coming to the surface are reflected from it so that the same number will be leaving as approaching, or in other words, the equilibrium will be undisturbed. ( 2 ) The cybomas in contact with the surface disappear more rapidly on the average than those in the center of the liquid. Under these circumstances there will be fewer cybomas leaving the surface than approaching it, and when an equilibrium is established the concentration of the cybomas in the neighborhood of the colloidal
FIQ.I Schematic arrangement of cybotactic complexes around a lyophobe and a lyophile particle
particle will be less than in the center of the liquid. (3) At the surface of the particles, the probability that neighboring liquid molecules will associate into a more or less rigid framework will be greater than the average for the liquid. I n other words, more cybomas will leave the surface than will approach it, and when the steady state is reached there will be a concentration gradient established diminishing with distance from the particle. The second and third possibilities are represented by a and b respectively of Fig. I. It seems probable that deviations from case ( I ) will be greater with (3) than with ( 2 ) since the concentration gradient built up in (2) depends on the number of cybomas in contact with the particle surface, whereas in case (3) it is independent of the number of cybomas present and depends only on the interrelationship between the surface and the liquid molecules. The number of cybomas in contact with unit area of a surface at any one instant must be small compared to the number of liquid molecules in contact at the same instant. If we assume that there are a cybomas per second formed per unit volume and that there are kn, cybomas vanishing, where no is the number present per unit volume, in the steady state
a = kn,
or
no = a/k
COAGULATION VISCOSITY AND THIXOTROPY
2951
Assuming case (3), that is, a concentration of cybomas at the surface greater than no,and considering the surface to be plane it can be shown6 that nf = Ple-dkTDx where D is the diffusion coefficient, n’ is the difference between the concentration a t the distance x from the surface and norand P‘ = n’ when x = 0. The expression for variation in concentration with distance fron the surface of a sphere is7 n f = 5p t e - d m (r - ro) r where r. is the radius of the sphere. Since we are totally in the dark as to the average size and average life of these eybomas, the best we can do is to make some reasonable assumptions and see where they lead us. Assuming that the average cyboma in water contains I O molecules, that its density is the same as water and that its average life is IO-^ seconds, the curves of Fig. 2 were obtained for variation in n’ with distance from a flat surface, a spherical particle 400 A in diameter, and a spherical particle 100 d in diameter.* The concentration a t the surface, 6 In the stationary state, the number of com lexes crossing one cm2 of a plane parallel with the surface at a distance x will be -D(dnrdx) per second, and this must be equal to the number of complexes in excess of novanishing er second in a column of one cm2 crosssymbolic form, section extending from the plane outward to infinity.
%
-D differentiating
=
kn’dx
d2n’ D= kn’ dx2
which gives on integration, x = CZ’ - -In (n’+ v G ~ ) Now when x = m, n’ = o and therefore CI= o. Postulating that when x = 0 , n’ = P’ we get n‘ p ’ e - d m
’
Starting with the same assumptions as in note 6, the number of complexes radiating from a particle and crossing concentric spherical envelope of radius r is dn’ 4 d D -, dr therefore - 4 d D dn’ = kn’dv = 4rkLmn’fidr. Differentiating d s 1 dz’ - k dr2 r dr Dn’ = ” The general solution is n ’ = -C! e f l D r + p e - m r . +
Now introducing the conditions that n’ = o when r = m and that n‘ = P’ when r = r,,, n’ = ! ? p t e - d k z ( r - r o ) . r The radius of a cyboma containing IO water molecules will be about 4.2 X IO-^ cm. Now from Stokes’ law and kinetic theory. where 9 is the viscosity of water (o.oI), r the radius of the cyboma and N the number of molecules in one gram mole. From the assumption that the average life is 10-8, k = 106, and d/ki~= 4.4 X 101 cm-1 = 4.4 x 1 0 - 8 AO-1.
2952
S. S. KISTLER
FIG. 2
Vnrintion in concentration of cybomas with distance from flat and spherical lyophilic surfaces
P', is taken as unity. This value will undoubtedly be widely different for different surfaces. What its magnitude is can only be guessed, but it can easily be such that the diffusion pressure is that of a half molal solution. The influence of a surface a t relatively large distances out into the liquid is strikingly shown by this figure. Coagulation A colloidal solution in which. the micellar surfaces either decrease or do not affect the number of cybomas in t,heir immediate neighborhood will be essentially unstable and will flocculate rapidly unless it can depend upon electric charge or some other means of keeping the particles from coming together and adhering. This is the case with the lyophobic colloids. If the concentration of the cybomas decreases with decreasing distance from the surface there will actually be a difference in the diffusion pressures due to the cybomas on the adjacent and far sides of two micelles near together, which will manifest itself as though there were an attractive force drawing the particles together. Fig. 3 represents this situation. That means that in such a sol the particles must have high electric charges in order to. remain permanently dispersed. The addition of a small amount of precipitating ion, while not sufficient to neutralize the charge, may reduce it, to the point where a particle of higher than average energy can penetrate through the electric atmosphere of another particle and adhere. This situation is strikingly parallel with that found in the typical lyophobic sols. The sols become unstable at Zeta potentials rather widely removed from zero. Also SmoluchowskiOin the derivation of his familiar equation for rat,e of flocculation found it necessary to postulate the existence of an attractive force extending beyond the surface of a colloidal particle, although there has never been a satisfactory explanation of the nature of this force. 9
Physik. Z., 17, 557, 583 (1916);Z. physik. Chem., 92, 129 (1917).
COAGULATION VISCOSITY AND THIXOTROPY
2953
FIG.3 Conditions surrounding two adjacent lyophobic particles, showing how they are forced together in the absence of electric charges.
Not only may an adsorbed substance affect the Zeta potential but it is highly probable that i t also affects the relationship of the surface to the cyboma concentration. Thus it is possible that a sol that fits case ( I ) or even case ( 3 ) above may be so changed by the addition of an electrolyte or other substance that this attractive force will be brought into play and the sol will behave as a typical lyophobic sol. Such cases are rather common. For example, although aluminum oxide and vanadium pentoxide sols are classed among the hydrophilic sols, they are readily sensitized by various means so that very small quantities of electrolytes will precipitate them. The opposite may also be true and an added substance can very much increase the stability of a sol such as, for example, the addition of a protective colloid or the protective action of polyhydric alcohols on certain sols. In the case where the concentration of cybomas in the immediate neighborhood of a micelle is considerably larger than that in the mass of the dispersing
Conditions surrounding two adjacent lyophilic particles, showing how cyboma pressure is built up between them.
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8. S. KISTLER
phase, when two particles approach each other the conditions set up will be similar t o that depicted in Fig. 4. There will be a decided increase in concentration of the cybomas in the region between the micelles which will have the effect of increasing the cyboma pressure on the particles and forcing them apart. The exact mathematical treatment of the rise in pressure on a micelle as it approaches another is very difficult, but it can be approximated by assuming that this rise in pressure will be proportional to the rise that would be produced if the micelle were surrounded by an envelope] of radius equal to half the distance between micelles] that is impervious to cybomas. I n other
b
I
too
I
300
ZOO
r-6 ,Angstroms
FIQ.j The variation of n' with distance from the surface of a spherical particle of radius IOO A" when the cybomas are prevented from diffusing beyond an envelope of radius R.
words, all the cybomas produced by the surface would have to remain within this spherical envelope. Fig. 5 represents the effect of this envelope radius, R upon n', the concentration of cybomas. I n this figure z (R-rJ represents the distance separating the micelle surfaces and II' the pressure at the surface when R = m i.e., when there is no interference with the outward diffusion of the complexes.1o Differentiating the general solution given in note 7, one gets dn'ldr = K / r (cle+Kr - c2e-Kr) - n'/r, where^ = dK/D. Now where r = R, dn'/dr = o 10
where
and
P' = _
n'
Kro
I
- K"K
+
I
1Kx KR-
eK(ro-zR) - e-m.
I
I'
2955
COAGULATION VISCOSITY AND THIXOTROPY
Fig. 6 shows the change of the ratio P’/U with changing values of R. Here P’/II’ represents qualitatively the repulsive force acting upon the side of the particle adjacent to another particle as compared to the normal pressure on the side discharging its complexes into free liquid. Here the existence of the equivalent of a repulsive force at large distances is illustrated. In Figs. 5 and 6 i t is assumed that the rate of formation of cybomas a t a surface is independent of P’/II’, which seems reasonable within limits. As one can readily see, .this pressure tending to force particles apart will give the sol stability without electric charge and this is the case with the typi-
FIG.6 The variation of the cyboma preasure on the surface of a particle of duced by variation of the radius of an impermeable envelope.
IOO
radius pro-
cal lyophilic colloids such as gelatin or agar. With this type of colloid it can readily be seen from our picture that small concentrations of electrolytes will be relatively ineffectual in causing precipitation. From what has been said so far, i t would be expected that lyophobic oolloids would normally require some special means for dispersing them, while Iyophilic colloids would tend to disperse themselves spontaneously, a difference which is one of the most characteristic of these two groups. Again, the same picture that we have drawn would indicate that when rate of diffusion is measured by the diffusion of a sol along a concentration gradient, such as into pure water, the lyophilic particles should diffuse more rapidly than lyophobic of the same diameter due to this repulsion between the micelles with surfaces of type (3). This difference has been observed by Bruins,” who found that hydrophobic particles diffuse at the expected rate, while hydrophilic diffuse faster. Addition of electrolyte in the latter case decreased the rate, a fact easily explained on the basis of a decrease in the rate of complex formation a t the surface. He also noted a parallel decrease in viscosity which is in complete harmony with this view, as will appear later. At first thought it Kolloid-Z., 54,265;57,152(1931).
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8. 6. KISTLER
might appear that the electric field surrounding the lyophobic particles would produce the same repulsion at a distance as the cyboma cloud, but this is not the case due to the electric double layer, which although diffuse will reduce the repulsion between the particles to a negligible value at a relatively small distance. The identification of lyophobic and lyophilic sols with types ( 2 ) and (3) respectively seems particularly logical since it would be expected that if there is an influence on the formation of cybotactic complexes by a surface, the surface more nearly chemically related to the solvent would be more apt to stimulate growth. In all cases of highly solvated colloids, the solvent and the colloid surface can be shown to be very similar in character. It may be that on solvated surfaces there is a distinct orientation of molecules that induces the orientation and addition of other neighboring liquid molecules upon it. Complexes grow outward from the surface, split off and others appear. Such a particle would appear like a large permanent cyboma seeding the surrounding liquid with its offspring. Another prediction that comes directly from the interrelationship of the cybomas with a surface concerns the lyotropic series of monovalent cations. I t is a common fact that with the more or less hydrophilic colloids such as aluminum oxide the precipitating power of these ions increases in the order Li++ Na++ K++ " I + , while there is practically no difference in their precipitating values with lyophobic sols. One of the most outstanding differences between these ions is the degree of hydration which decreases in the order given. The lithium ion is surrounded by a larger sphere of water molecules and perhaps by a larger number of cybomas than the other ions. The repulsion, therefore, between a lyophilic micelle and a lithium ion will be greater than between the same micelle and any of the other ions and, therefore, when equilibrium is established with a solution of definite concentration the amount of these ions adsorbed will be greater the lower the degree of hydration of the ion. In the case of the lyophobic particle, the establishment of equilibrium will be so much more dependent upon the charges than upon the hydration of the ions that this difference will have a negligible effect. As two colloidal particles with lyophilic surfaces approach each other, there will be no repulsive force experienced by either as the cyboma clouds interpenetrate until sufficient time has elapsed for the new conditions between the particles to effect a rise in the concentration of the cybomas a t the surface of the particle. This time lag means that the faster moving particles will be able to come much closer together before repulsion is experienced and therefore will have much better opportunities to come together and adhere. Since all particles on the average possess the same kinetic energy, the smaller micelles will move faster and have greater opportunities to attach themselves to others. This effect of size will be further accentuated by the fact that the smaller particles have less dense clouds of cybomas surrounding them as is shown by Fig. 2 . This means that very small or very large particles in lyophilic sols will not be as common as some intermediate size, or in other words,
2957
COAGULATION VISCOSITY AND THIXOTROPY
the lyophilic sols will tend t o have uniform particle size. It is possible that the pronounce? uniformity of certain proteins may be thus explained. The action of a protective colloid is readily understood in the present light. The particles of highly lyophilic colloid surround the lyophobic particle giving it a lyophilic character. Adsorption of the protective colloid can occur even though adhesive forces are negligible, due to the fact that when once the particle with its cyboma cloud has come into contact with the lyophobic particle, there will be a decided difference in diffusion pressure of the cybomas between the particles and on the outside, which will tend to hold them together.
. .
.
*
.
. . . FIG.7 Distribution of cybomaa around an irregular lyophilic body, showing the much decreased density where the radius of curvature is small. Micelles can therefore most readily attach to edges and corners.
FIG.
a
Conditions surrounding a colloidal particle settling in a gravitational field illustrating the buoyant effect of the cyboma cloud.
The fact that the concentration of cybomas at a given distance from a solvated surface is smaller the smaller the radius of curvature of the surface leads one immediately t o the conclusion that under circumstances in which agglomeration may occur, i t will be easier for micelles to penetrate the cyboma cloud and attach themselves on edges and corners of a mass already coagulated. One, therefore, would anticipate that the agglomeration of such micelles would lead t o the formation of chains, plates, or irregular fibrous or membranous structures rather than solid masses. The conditions surrounding an irregular mass would be somewhat as shown in Fig. 7 . This type of structure would tend to surround and occlude large quantities of the dispersing medium and form a semi-solid spongy mass of practically the same volume as the original sol. Such a coagulated colloid we term a gel, and gel formation is one of the most characteristic manifestations of the lyophilic colloids. The strength of such a gel would depend upon forces of cohesion between micelles, as well as upon their shape and the structure of the agglomerated mass. Probably the stronger the character (3) the stronger will be the gel, due to the more fibrillar structure. Notable exceptions occur to this rule-such as silica
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8. 8. KISTLER
ge1,in which the structure is probably not that of agglomerated colloidal particles but is, a t least in part, due to what one might term dendritic crystallization, An interesting possibility is that cyboma clouds surrounding large hydrated molecules such as those of sucrose may have a real influence in preventing crystal nuclei from forming in supersaturated solutions. I t is logical that if they are present they will tend to hinder the proper orientation and close approach of sufficient molecules to form a stable crystal nucleus. It is clear that a cloud of these evanescent molecular complexes surrounding a colloid particle will have a very decided influence upon its rate of sedimentation. As the particle settles through the liquid the complexes diffusing out from the lower side will be continually swept back toward the particle by the counter current of liquid, so that there will build up in the layer immediately in contact with the particle a higher concentration on the lower side and a proportionately lower concentration on the upper than normal. The conditions will be somewhat as represented in Fig. 8. The total effect will be as though a rigid sphere of liquid surrounding the particle were carried along with it. The particle will experience greater resistance than would be predicted by Stokes’ Law. Not only will this effect occur with particles falling in class (3) but it should manifest itself as well in case ( 2 ) because in this instance, the approach of cybomae to the lower side of the particle will be aided, while that to the upper side will be hindered and again a differential pressure on the two surfaces will be produced. Viscosity One of the most prominent features of colloidal solutions is their viscosity, which has been the subject of numberless investigations, but which as yet has received no adequate treatment. I n view of the fact that viscosity of pure liquids itself has not been understood the failure to make marked progress with colloids is not surprising. Recently, however, AndradeI2 and Edwards and Stewartla have indicated the very close connection between the cybotactic complexes and viscosity, which intimates strongly that in this direction also lie large possibilities of application to the colloid field. Accepting these authors’ point of view, which is the most reasonable so far presented, it is evident that the fluid in a colloidal solution of the third type, that is, in which the number of complexes is increased due to the influence of the particle surfaces, will have a greater viscosity. This change of viscosity of the liquid will depend upon the surface character of the suspended particles. Its magnitude cannot a t present be predicted, but will probably be small. Since it is a function of the total surface of the colloid, in sols of the same concentration but different particle size, it will be greater the smaller that size, which is one possible explanation of the variations that have been observed. An influence of larger magnitude than that above will be that of the interaction of the cyboma cloud with the micelle. The same effect as that del2 13
Nature, 125, 580 (1930). Phys. Rev., (2) 38, 1575 (1931);Stewart: Nature, 128, 727 (1931):
COAGULATION VISCOSITY AND THIXOTROPY
2959
picted in Fig. 8 will come into play but in this case there will be two regions of increased pressure on opposite sides of the particle under shearing stress, as shown in Figs. 9, a and b. Fig 9, a, shows the effect of a low rate of shear in the liquid upon the cloud surrounding the micelle. Here the cloud is distorted and the resultant concentration on opposite sides of the particle will praduce equal and opposite forces upon it directed at an angle with the plane of shear, the angle increasing with the rate of shear. These compressive forces will have resultants opposing the motion of the fluid so that the viscous drag of the particle will be greater than would be the case in the absence of the cloud. Fig.
..
. . . . '.. . .
:
9
. .. .
*
. .. .. .. . . . . \
FIGg A lyophilic partic!e under low and high shear ahowing how the cyboma cloud opposes the motion of the fluld. 9, b, shows the effect of a high rate of shear. It is hardly to be expected that the opposing force due to the distortion of the cloud will be a linear function of the rate of shear, but it seems probable that it will go through a maximum at high shearing rates. Compliance of a colloidal solution of type ( 2 ) or (3) with Newton's Law of the constancy of viscosity with rate of shear can, therefore, not be expected. The deviations will most likely be much greater with colloids of the third type. Again in this case the effect will be more pronounced with small particles than with large. The influence on viscosity just described will be independent of the existence of other particles in the solution. There is yet another influence on viscosity due to the proximity of the micelles and which will doubtless have the greatest effect in concentrated sols. As two particles pass each other in a sol under shear, the clouds surrounding each will interpenetrate and produce repulsions which can greatly increase the viscous drag, both due t o the parallel components of the forces and to the fact that the particles will describe lengthened paths around each other. Fig. IO, a, represents schematically the interactions of two particles as they approach a t low rate of shear. It will be re-
2960
9 . S. KISTLER
membered, from what has been said earlier, that the repelling force will depend upon disturbance of the equilibrium at the surface of a particle and, therefore, there will be a lapse of time between the penetration of the outer parts of the clouds and the development of the repulsion. The work required to move one particle past the other a t a given distance will, therefore, diminish with increasing velocity of the particle. In addition, the extent of the cloud in the direction of the other particle will be reduced by rate of shear as shown in Fig. IO, b, so that at high rates of shear, the particles can approach much closer to each other, and they will be more nearly opposite before experiencing
*
L
F I G . IO
a b Two lyophilic particles passing at low and high shearing rates. The effect of rate of shear upon the mutual interference of the particles is clearly seen.
repulsion, so that the viscous drag will be much less at high shearing rates than at low. This difference in affect of rate of shear can be easily seen by comparing Figs. IO, a and b. It might be assumed that as the particles pass each other a t high shear and the distorted clouds intermingle there will be a repulsive force which will contribute to their progress and thus tend to decrease the viscous drag. Fig. I I shows such a case. However, upon more careful consideration of the conditions existing in Fig. 11, it is evident that these distorted sections of the clouds intermingling are being swept away from the particles so that, although there will be a region of greater density of the cybomas between the micelles, the time lag previously mentioned will prevent any appreciable concentration effect at the micelle surfaces before they are swept out of range. As would be gathered from examination of Figs. 5 and 6, this viscous effect depending on the proximity of the particles should increase rapidly with increasing concentration, and also at constant concentration should increase with decreasing particle size. The latter effect being due to the much smaller average distances between the small particles.
2961
COAGULATION VISCOSITY AND THIXOTROPY
From what has gone before it is to be concluded that a decrease in particle size will inevitably lead to an increase in viscosity in all solutions of type (3), and probably also of type ( 2 ) since the interactions of the particles will probably play a more important rBle than the effect on the total number of cybomas in the liquid. Experimental results such as those of OdBn14 on sulphur sols lend support to this prediction. Double Refraction of Non-Spherical Particles From general considerations it would be predicted that the optical axis of non-spherical particles suspended in a liquid under shear would coincide
. - .. . . * . . ... .: * . . 3
,..* . .. .. .
. . . * . . ..
.
*
. *. ,
. .
. . . .. . . . I
.
.
FIG.1 1 Conditions existing after two particles under shear have passed.
I
.
.
.
I
’
FIG.12 Illustration of the unbalanced forces acting on an elon ated particle lying in the plane of shear. #he necessity for rotation of the axie out of the plane of shear is shown.
with the plane of shear, but this has been found to be the case only with coarse dispersions. In most cases that have been investigated the axis lies a t an angle between o and 45’ with the plane. With elastic solids and jellies the angle is 45’.. There has been no adequate explanation of the failure of the particlee to orientate themselves completely in the plane of shear and statements such as the following from KraemeF have received widespread if tentative acceptance. “The particles in the sols mentioned seem to be united in some way, forming a more or less tenuous, elastic structure that undergoes deformation as well as orientation.” An orientation of non-spherical particles a t an angle with the plane of shear arises out of necessity from our hypothesis of the conditions surrounding 2.physik. Chem., 80,709 (1912). Kraemer: “Treatise on Physical Chemistry,” Edited by Hugh S. Taylor, 2, 1609 (1931). (The first person to ostulate this connection between orientation and elastic deformation seems to have been 8ontremoli: Atti Accad. Lincei, 30 11,216(1921).). l4
16
a
2962
S. S. KISTLER
a particle of type ( 2 ) or (3). Referring to Fig. 9, a or b, one will immediately see that in case the particle is elongated, the forces acting upon it from opposite sides will no longer be balanced and there will be a rotation of the particle to a new position at an angle with the stream. This unbalanced condition can more readily be visualized by reference to Fig. I 2 . The particle will rotate in a direction away from the approaching current and the extent of rotation will be less the more elongated the particle is. With increasing rate of shear the angle of deviation should be reduced since the viscous drag on the surface is in such a direction as to oppose the orientating forces. Freundlich, Neukircher, and Zocher16 have carefully measured the optic axis of several non-spherical sols and their results confirm completely the predictions made above. For example, the angle is found to decrease with age of a vanadium pentoxide sol, while the length of the particle increases. The angle decreases with increasing rate of shear and its direction with respect to the motion of the liquid is what has been predicted. While their offered explanation based on the existence of swarms of micelles can in no way be said to be invalidated, certainly the explanation based on the influence of the cybomas seems to involve less artificiality. It does not longer seem to be necessary to postulate the existence of elastic forces acting a t relatively great distances throughout the sols.
Thixotropy In sols of type (3), ibis evident that particles will tend to take up positions at maximum distances from each other, which means that barring other disturbances, a quiet sol will assume a definite structure. Any small force tending to destroy this structure will be met by a quasi-elastic resistance, and if the disturbing force is quickly enough withdrawn, there will be elastic recovery from the deformation. Such elastic resistance must be met due to the fact that when the micelles are in the configuration of maximum distance from each other, any small deformation must reduce this distance, thus increasing the forces between certain of the micelles in a direction which would oppose the disturbance. Even in the absence of Brownian movement, the opposing force, induced by a small deformation, would gradually sink to zero due to the migration of the particles to new optimum positions, a phenomenon which resembles closely in external aspects relaxation under stress in elastic solids. The presence of Brownian movement will naturally hinder the complete orientation of the micelles into optimum positions, so that the higher the temperature, other things being equal, the less distinctly will the elastic properties manifest themselves. Since the repelling forces between particles rise rapidly with increase in concentration, a concentrated sol may show a definite yield point, whereas a more dilute sol may be sufficiently disturbed by Brownian movement so that no yield value can be obtained even at very low rates of shear. In the more concentrated sol, the shearing stress will approach a conKolloid-Z., 38, 43, 48 (1926).
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stant value with decreasing rate of shear as shown by Curve I, Fig. 13,while in the dilute sol, due to the rapid relaxing affect of the Brownian motion, no limiting value of shearing stress will be approached but as the rate of shear becomes very small, the shearing stress will drop off in the manner of Curve 2 , Fig. 13. These two curves will be recognized to be very typical of lyophilic colloidal solutions. Again decrease in particle size will manifest itself in a direction similar to increase in concentration, since, although Brownian disturbances will increase with decreasing particle size, the intermicellar forces will increase more rapidly. The influence of concentration upon the yield point cannot be exactly $ given, but in the simplified case where ;; Brownian movement is assumed to be p negligible, it seems justifiable to assume $ that each particle is surrounded by * practically a sphere of other particles, Le., it is circumscribed by a spherical envelope where dn‘/dr = 0, the conRate of Shear ditions assumed for Figs. 5 and 6. The yield point of the sol should therefore FIG.r3 be approximately proportional to Typical stress-rate of shear curves for Sols. Curve I shows a definite yield dP’/dR, since the restoring forces after point while 2 shows none. a disturbance will be proportional to the same quantity. Taking R as proportional to the cube root of the volume, the variation of yield point wiih volume of sol should be somewhat as shown in Fig. 14for particles of IOO A radius. From this figure one would certainly anticipate evidence of yield point in sols of small particle size when the volume of colloid is greater than 10% of the total volume. Due to the time required for the forces to produce optimum orientation, a lyophilic sol that has been thoroughly mixed will show a rise in viscosity with time. On the other hand, if the sol is allowed to stand quiescent in a viscometer and then its viscosity is measured a t constant rate of shear, it will be found to decrease with time and extent of working to some constant value which, however, will be smaller the greater the rate of shear, due to the smaller opportunity for the repelling forces to set up the ordered arrangement. This rise in viscosity with quiescence and return again upon working, particularly when the sol develops a definite yield value upon standing, has been termed thixotropy. Several tentative explanations have been proposed for it but none have been found satisfactory, and it was in a search for a satisfactory explanation that the author was led to a consideration of the influence of cybotactic complexes.l7 Although the explanation as given seems to account successfully for numerous observations, it does not seem to me that the yield value described above Kistler: J. Phys. Chem., 35, 828 (1931).
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can have the magnitude of that found in certain thixotropic gels, such as those of Fez03and Ai&. In these cases, probably reversible coagulation plays a part. These gels belong to the class in which a decided Zeta potential is necessary for stability] and it may be that upon the addition of the small amount of electrolyte necessary to bring about the thixotropic condition] the surface is changed to type ( 2 ) in which there is a definite attraction between particles. Since this attractive force undoubtedly extends farther than the electric repulsion there will be a tendency for the particles to take up positions with respect to each other at a smaller distance than the average distance of separa-
FIQ.14 Curve illustrating the probable influence of the dilution of a lyophilic sol upon the yield point.
tion of the particle in the sol. Under such circumstances the particles in a quiescent sol will tend to collect into flocks which may be irregular and tenuous. Within each swarm of micelles the particles would tend to assume very definite positions with respect to each other in which the attractive forces would be counter balanced by the electric repulsions. Since the average distance separating the particles in any one swarm would probably be small due to the limited extent of the electric fields, the swarm could possess considerable rigidity. Since the micelles forming any swarm must be drawn from the liquid in the immediate neighborhood, the swarms must necessarily be small in cross section but may be inter-connected so that they form in effect an anastamosing sponge-like structure extending throughout the whole volume of the sol. Such a structure when completely formed could give the sol a rigidity much greater than it could possess if the particles remained dispersed at maximum distances. This two-phase sol would assume the aspects of a gel but would again become a mobile liquid upon mechanical agitation and dispersion of the swarms. If the above explanation of this particular type of thixotropic sols is correct, one would expect that the thixotropic condition would occur only in a very limited range of electrolyte concentration. Occurring as a balanced condition between electric charge and attractive force one should expect that only cer-
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tain sols would be capable of attaining this balance. In general, the sols of type (2) would coagulate rather than halt on this metastable plateau. These expectations have been realized and although it may become possible to induce thixotropy in many more sols, a t present the number of electrolyte-sensitive sols that have been brought into this condition is relatively small. Such swarms of particles as have been postulated above have beendemonstrated to exist in aged V20, and Fez03 sols.1s Zocher has applied the term “tacto-solsJ’ to these swarms. Those that he has studied have shown a definite optic axis which indicates that the particles are non-spherical and orientated. The orientation, there observed, would be a natural consequence of formation as above postulated. Although the theory of the influence of cybotactic complexes upon colloidal systems as presented above, offers, in itself, an explanation of a large number of phenomena, I do not wish to imply that it is the sole cause of these phenomena, but that it is a general background upon which may be superimposed other effects which have been given credence in the current literature. It is a pleasure to acknowledge my indebtedness to Dr. David G. Bourgin, Mathematic Department, University of Illinois, for his assistance in deriving and checking the formulas used, and to Professor H. Freundlich, Berlin, for carefully reviewing the manuscript before its presentation. summary
The existence of cybotactic complexes in liquids is discussed and it is shown that colloids may be divided roughly into two classes, corresponding to lyophobes and lyophiles, depending upon whether the surfaces tend to depress or stimulate the formation of cybotactic complexes, called here “cybomas.” 2. The stability of a lyophilic sol is shown to depend mainly upon a concentration gradient of cybomas decreasing with distance from each colloid particle, while the tendency to coagulate and the previously postulated force of unknown origin tending to draw particles a t a distance together in lyophobic sols are connected with a gradient of opposite sign. 3 . Reasonable assumptions are made in regard to the average size and average life of cybomas, and equations derived showing the relatively great distance into a liquid a t which a surface may have influence. 4. The differences between ease of dispersion of lyophile and lyophobe colloids, and the unexpectedly large rate of diffusion of the former are explained. 5 . An explanation of the lyotropic series Li+-+Na++K+-+NH4+ is given. 6. The fact that lyophilic sols tend to possess very uniform particle size is predicted from the interactions with cybomas. 7. The tendency shown by lyophiles to precipitate in fibriles, plates or “brush heaps” enclosing much liquid is shown to be a necessary consequence of the assumptions made. I.
Zocher: 2. anor . Chem., 147, 91 (1925); Zocher and Jacobson: Kolloid-Z., 41, (1927); Kolloidchem. %eihefte,28, I 6 7 (1929).
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8. A probable influence of cybomas on the tendency of large hydrated molecules such as sucrose to supersaturate is indicated. 9. The influence of a colloid on the viscosity of a liquid is ascribed to three separate affects, (a) the influence on the total number of cybotactic complexes, (b) the interaction between these complexes and a particle under shear, tending to increase the resistance offered by the particle to viscous flow, and (c) the interactions between two particles while passing, due to intermingling of their attendant cyboma swarms. It is pointed out that the particle size of lyophiles must have a large influence on viscosity, the smaller the particles the greater the viscosity. IO. The fact that nonspherical particles do not orient themselves in the plane of shear is shown to arise of necessity from the adopted assumptions, and the direction of rotation as well as the influence of rate of shear and particle size are predicted. 11. The failure of a lyophilic sol to show constant viscosity with different rates of shear, the rise in viscosity with decrease in shearing rate, the decrease of viscosity with time a t constant rate of shear, and the existence of a yield point are predicted. I n other words, thixotropy is given a rational explanation. 12. A reasonable explanation is offered for Zocher’s “tacto-sols.” University of Illinow, Urbana, Illinois.
