DIELECTRIC COXSTANT AND STRUCTURE O F THIXOTROPIC SOLS* BY S . S. KISTLER
Introduction I t has been found in recent years, particularly by Freundlich and coworkersJi that rather a large variety of colloidal solutions may under suitable circumstances display the property of thixotropy. This phenomenon has been subject to rather careful investigation. The conditions under which it may be caused to appear are fairly well known, accompanying optical phenomena have been subject to careful scrutiny, the relations between time of setting, temperature, size of vessel, and concentrations of sol and electrolyte are thoroughly cataloged (at least in the case of Fe203),and empirical rules devised; yet not very much positive evidence has been accumulated supporting any one theory of the cause of the phenomenon. Even well-formed theories are scarce. It’ was with the idea in mind that any light whatever shed on the subject would eventually contribute to the solution of the problem that the present work was undertaken. That, thixotropy in hydrophobic sols, such as those of Fez03,A120sJor IT2O9,is closely connected with coagulation cannot be doubted. The same agencies which produce coagulation produce thixotropy. I t seems that when the repelling forces between the colloidal particles are reduced to a certain point, reversible gelation may occur. If these forces are still further reduced, coagulation occurs.2 The assembling of the particles into a semi-rigid framework, which, when disturbed, automatically reforms, has been explained by Haber3 as being due to the “ionic cloud” surrounding the particles. Cnder suitable conditions of charge on the micelles and ionic concentration in the dispersing medium, the electrical forces are such that the micelles tend to assume fixed positions with respect to each other. If the gel is agitated, they assume the randomness of a sol; but, immediately upon the restoration of quiet,, the orientating tendency exhibits itself again and gelation occurs, This conversion from sol to gel and vice-versa may be repeated an optional number of times without affect upon the cycle itself, unless the sol is sensitive to agitation and some disturbing effect arises such as coagulation. On the other hand, numerous workers4 have found the assumption of the existence of a hydration layer of considerable thickness surrounding the micelles, to be more satisfying. Upon approaching the conditions for thixo* Contribution from the Kaiser Wilhelm Institut fur physikalische Chemie und Elektrochemie, Berlin. 1 H.Freundlich: Kolloid-Z., 46,289 (1928). 2 W.Heller: KolIoid-Z., SO, 1 2 5 (1930). F. Haber: J. Franklin Inst., 199,437 (1925). + See for example E. A. Hauser: Kolloid-2. 48, 57 (1929); A. Paris: Sitaungsber. Xaturforsch. Gea. Univ. Tartu, 35, 135 (1929).
816
S. S. XISTLER
tropy, the amount of water held more or less firmly by rach particle in suspension increases until a point is reached where the particle no longer is frcc to move independently but becomes limited by its neighbors in such a m y that the aggregate displays elastic resistance t o deformation. Evidence for the electrical hypothesis is to be found in the conditions necessary to bring about solidification in the hydrophobic sols. IYhen electrolyte is added to the sol a little at a time, a point is finally reached whrrr the solidification will occur if given enough time and if the sol is in a small enough vesPel. Since one of the chief causes of precipitation in these sol? is assumed to be electrical and since thixotropy has been shown t o be so closelg connected with precipitation,. it is a small step to the asumption that thr forces producing the gel are electrical in origin. The addition of non-elecrrolytes, such as alcohol, produces thixotropy.5 1 his is attributed, howevcr, to the increased “efficiency” of the electrolyte present, produced bq- thc nonelectrolyte. Xone of the hydrophobic sols are stable without the p r c s n m of some electrolyte. I n the case of Bentonite the transition from the thixotropic to non-thisotropic condition can readily be brought about by dialysis, and the thixotropic condition again induced by addition of electrolyte. The affect of the individual ions also is such as would support thr rlectricnl hypothesis. The larger the charge of the anion the smaller the amount neccssary to produce thixotropy. For example, Freundlich’ lists the eoncentrations of various salts that have been found to have equal effects in inducing thixotropy in F e 2 0 3sols as shown in Table I. The charge on the cation dow not have so large an effect. TABLE I Electrolyte
SaCl KC1 KBr NaOH
Conc. Millimols/liter 45
45 62 I8
Electrolyte
Conc. Millimols/liter
Sa2901 Sa2CrO1 &Citrate
I2
9.5
7
Heat is also effective, at least in the case of Fe203sols, but here also it is not, excluded that the primary effect is not on the concentration of the electrolyte or on the amount of electrolyte adsorbed. On the other hand it has been assumed that the changes in electrolyte concentration effect changes in the amount of water held in the hydration shell surrounding the particles, and that the phenomenon of thixotropy is directly dependent upon hydration, which itself is dependent upon electrolyte concentration. Very strong evidence limiting the applicability of the purely electrical hypothesis is t o be found in the existence of thixotropy in hydrophilic sols such as gelatin6 that, are very insensitive to changes in electrolyte concentra5
8
E. Schalek and A. Saigvari: Kolloid-Z., 33, 326 (1923). Freundlich and Abrarnson: Z. physik. Chern., 131, 278 (1927).
DIELECTRIC CONSTANT O F THIXOTROPIC SOLS
8x7
tion, and in other sols where the presence of foreign electrolyte is entirely unnecessary, such as those of barium malonate and dibenzoylcystine.’ That aggregation of the particles of a so1 does not accompany the production of thixotropy was well shown by Hauser in the case of Bentonite sols.8 He observed dialyzed Bentonite sols under the ultramicroscope while the electrolyte concentration was gradually increased. .A small addition stops the translatory Brownian movement, while a little more stops also the rotatory movement. An excess of the salt produces coagulation, but with the concentrations to be found in the thixotropic gels the evidence is that the particles are no closer together than in the sols. Hauser considers that an increased hydration layer due to the presence of the salt accounts for the observed phenomena. General Considerations .Iccording to the Debye theory of the origin of dielectric constant in polar substances, it can readily be shown that an adsorbed layer should have a different and in general a lower dielectric constant than the free substance. It is well known that the measurements of dielectric constants in vapors and gases of large molecular weight are attended with difficulties on account of the adsorption on the electrodes with the consequent, uncertainty in both the actual mass of gas between the electrodes and the dielectric constant of the adsorbed part. Palmerg finds that it is necessary t o assume a dielectric constant of approximately 3. j for adsorbed water vapor on fine tungsten wire in order to explain his experiments on contact resistance. Kallmann and Dorsch’o carried out some very fine measurements on the dielectric constants of thin films of liquids in a n attempt to find an effect due to the adsorption or orientation of molecules on the electrodes, but in spite of the accuracy attained were not able to demonstrate any effect. Unfortunately, the number of molecules whose dielectric constants must be changed by proximity to the electrodes in order to give a measurable effect by this method is so large that a negative result is rather to be expected than to be surprising. Indeed, it would be astonishing if the sought effect were large enough to be so measured. Nnrinesco” has been active in determining the degree of hydration of hydrophilic colloids by measurement of their dielectric constants a t 6.5 meters wave-length. He has assumed that surrounding every particle of the disperse phase there is a layer of water that has been ”dielectrically saturated.” For example, he calculates the thickness of the water envelope surrounding a methemoglobin particle of radius z j X I O - ? cm. to be j o x IO-3 cm. He arrives a t the conclusion that crystalline hemoglobin “fixes” I j grams of water per gram of hemoglobin, gelatin 8-10 grams and egg albumin 11-r3 H. Zocher and W.Alhu: Kolloid-Z., 46,27 (1928).
8 E . A. Hauser: Kolloid-Z., 48, 57 (1929).
gW. G. Palmer: Proc. Roy. SOC.,106A,jj (1924). lo
H. Kallmann and K . E. Dorsch: Z. physik. Chem., 126, 30j (1927).
I’
S . hlarinesco: Compt. rend., 189,
I Z ; ~ (1929).
818
S. S. KISTLER
grams. By introducing degree of hydration he is able to calculate the dielectric constants of levulose solutions with fair agreement with the measurements. Although such calculations are undoubtedly of high value in indicating the direction in which to look in a search for a measure of the amount of hydration of colloidal particles, the assumptions made are perhaps a little too simple. If a shell of water is "fixed" around each particle so that it displays only the dielectric constant of ice, the mechanism of this fixation should a t least be placed on a plausible basis. Electrical saturation effects undoubtedly occur in solutions of electrolytes, where the field strength surrounding an ion is large. Sack'? has calculated the sphere of influence of an ion and arrived at the conclusion that the influence of the ion is practically independent of its radius and may be expressed by the equation e* = e (1-yYcI) where E * is the observed dielectric constant of a solution, e is the actual dielectric constant, C is the concentration in moles per liter and y is a constant for any one salt and varies from salt to salt directly with the number of ions produced and as the 3 1 2 power of the valences of the ions. I n the case of a colloidal solution, the concentration C is so small that even though there are numerous charges per micelle and the effect of the radius is included, the total measurable effect of the electric saturation on the dielectric constant is negligible unless y is of an entirely different order of magnitude than that found for electrolyt'es. The existence of a field of 70 A thickness surrounding a hemoglobin particle so strong as to greatly change the apparent dielectric constant of t'he water molecules within it through electric saturation is certainly not to be expected. On the other hand, it seems reasonable to assume that while the field does produce electrical saturation in a few molecules closest to the micelle it also has an effect upon the freedom of rotation of the molecules much farther removed, due to the orientation produced and their tendency to link up into chains.'s This linking tendency with its consequent interference with the freedom of rotation would presumably be most intense near the micelle and decrease with distance from it. I t would be observed as an increased relaxation time for the molecules affected. This predicted increased relaxation time would tend to give abnormally low dielectric constants, just as has been found to be the case with the solutions studied by Marinesco. The amount of this reduction of the measured dielectric constant will depend upon the frequency used in making the measurements, and it no longer is possible to make a simple calculation of the degree of hydration from measurements at one wave-length without the introduction of an arbitrary definition. l 2 H. Sack: Physik. Z., 27, 206 (1926). '3 J. W. McBain, [Kature, 120, 362 (I927)], considers the tendenry of molecules to orientate a t a surface and for transient chains to form extending from the orientated layer considerable distances, to be a very general tendency in liquids.
DIELECTRIC CONSTANTS O F THIXOTROPIC SOLS
819
The fact that values of the dielectric constant of non-conducting solutions may vary with wave-length has often been neglected. I t is well illustrated by measurements on sucrose. Table I1 and Fig. I show the measured values obtained by HarringtonI4 with a wave-length of approximately 300 meters, the author at 140 meters, Keller'j at 76 cm. and the a u t h o i a t 3 2 . 7 em.
FIG.I Sucrose Solutions
TABLE I1 Dielectric Constants of Sucrozr Solutions Author 140 m.
r;
wt.
0
.o
Keller* 76 em.
32.7 cm.
D. C. 81.5
D. C. 81.5
7Gwt.
D. C.
0 0
81 j
so j
80.2
IO
80
:.
i9.3
78.7
2 0 .
74 5
IO.I O
-.. 11.0
78.3
76.2. 71. I
30 ' 40.
2.6
5
I
19.4,;
.io
* Recalculated to a fiducial value for water of
,
0
67 5 60 4 19 3
8I.j.
The figure illustrates well the necessity of taking the wave-length into consideration in any theory devised to explain the slope of the solute concentration-dielectric constant curve. (It seems evident that the data of Keller's are not to be relied upon.) ' ( E . A. Harrington: Phys. Rev., ( 2 ) 8, j8I (1916) l5 R. Keller: Kolloid-Z., 29, 193 ( 1 9 2 1 ) .
S. 5. KISTLER
820
One might adopt as the degree of hydration that which is measured with such low frequency oscillations that only molecules very strongly bound will fail to rotate freely, but from the work of Kitchen and Mueller'6 on rosin and that of Errera" on ice, it appears that even molecules that might be thought of as being solidified on a surface, will have measurable relaxation times, and therefore a constant value for hydration a t long wave-lengths is not to be looked for. The function connecting the increase in the relaxation time of the solvent molecules with distance from the particle surface is entirely unknown; but one can safely assume that the effect decreases rapidly with distance, so that only molecules lying comparatively close are greatly affected. The nature of the function can be found by a study of the variation with varying frequency attribut'able to the solute of the dielectric constant. The nearer the frequency used lies to the frequency at which the uninfluenced solvent molecules no longer can freely follow the alternations in polarity of the field, the greater will be the influence of the solute on the measured dielectric constant. The greatest influence will occur where the curve connecting dielectric constant with frequency has a maximum slope. The lower limit of frequency available for studying solvation is probably in the region where the large molecule or particle, if polar, begins to follow the changes in the field and thus exhibits its own polarity. If the calculation of the degree of solvation is based upon measurements at one frequency only, one automatically introduces an arbitrariness into the results. Such results may have good value for comparison between several substances if the same wave-length is used throughout. The earlier objectiono to the electric field surrounding a hemoglobin particle extending for 7 0 A from the surface with such intensity as to produce electrical saturation applies also to some extent to the present argument. Rather than think of a hydrophile micelle as being surrounded by such a mass of strongly influenced water molecules, it is perhaps better to think of the particle as containing much water within its structure in such a may that very many molecules of water can come within a strong field of influence. In fact, that can well explain the fact that it has been difficult to demonstrate any hydration of hydrophobe colloids. The particles are compact and therefore a relatively much smaller mass of water is influenced. If there is a sufficiently large sphere of influenced water surrounding the hydrophobe particles in a thixotropic gel, such as that of Fe203,to account for the solid condition, it should have a measurably smaller dielectric constant a t very high frequencies than that of pure water. The present work is an attempt to measure this change in dielectric constant as a sol is brought to the thixotropic condition and then as it is allowed to solidify. Kallmann and Kreidl'* investigated the dielectric constant of VnOs sols and thixotropic gels at a wave-length of j o ni. and found that while that of l7
D. W. Kitchen and Hans Mueller: Phys. Rev., J. Errera: J. Phys., (6) 5 , 304 (1925). Not yet published.
( 2 ) 32, 9 j 9
(1928).
DIELECTRIC CONSTANT OF THIXOTROPIC SOLS
82 I
the gel was the same as that of water the sol had a dielectric constant of about 6% higher. No conclusions can be drawn from these results concerning the hydration of the particles or the condition of the water between the micelles in the gel except that the water is not solidified. The larger dielectric constant of the sol was undoubtedly due to some orientation of the smaller particles in the oscillating field, while this was prevented in the gel. In radio parlance a wave-length of 50 m. is considered very short, but it is still so far from the anomalous dispersion region for water that only very large changes in relaxation time of the molecules could be detected. In addition to the necessity for working at very high frequency, it has the very real advantage of eliminating t'he disturbing influence of small quantities of electrolyte. On the other hand, accurate measurement of dielectric constant with wave-lengths less than a meter becomes difficult due to the necessity of using one of the Drude m e t h o d P involving standing waves on parallel wires or an optical method such as that of Xichols and Tear.*O Of greatest difficulty is the generation of undamped oscillations sufficiently rapid, intense and constant.*' The most ideal wave-length with which to work with these sols would be less than I O cm. but due to the difficulties involved it was decided to work with somewhat longer wave-lengths a t first and eventually carry the measurements to this frequency. Owing to the constancy of wave-length and the satisfactory intensity obtained, it was decided to use the special high frequency tube modeled after the directions of K o h P made by the Telefon-, Apparat-, Kabel-, und Drahtwerke A. G., Nuernberg, Germany. The wavelength obtained was 32.; cm. and remained very satisfactorily constant during any one day although over a long period it showed some drift, probably due to reduction of the diameter of the filament due to evaporation. Jleasurements were made by the second Drude method as modified by Coolidgeg3and yielded an accuracy well within one per cent. The reproducibility of results depended largely on the character of the solution investigated, being excellent for sucrose solutions and rather disappointing for V 2 0 5sols, probably due to precipitation on the electrodes. With sucrose the deviations of single values from the average were within 0.2%. Although the method adopted is probably the best, it has the serious disadvantage for very sensitive colloidal solutions that any modification of the solution in the immediate neighborhood of the electrodes is much magnified in the results. When the frequency of alternation of the field becomes so great that the polar molecules lag behind, dielectric absorption occurs. In the study of the thixotropic solutions, it is evident that at frequencies where absorption oc~~
P. Drude: 2. physik. Chem., 23, 297 (1897). * O Nichols and Tear: Phys. Rev., (2) 21, j 8 7 (1923). For a ood summary of methods for generating high frequencies see W,H . Moore: J. FranuingInst., 209,473 (1930). 22 K. Kohl: Ann. Physik, (4)85, I (1928). 23 R. D. Coolidge: Ann. Physik, (3) 69, 125 (1899); see also G. Potopenko: 2. Physik, 20, Z I (I~zs), who has discussed the method and given equations. He has paid particular attention to absorption. Iy
S. S . KIBTLER
822
curs the greater relaxation time of molecules within the sphere of influence of the particles will pioduce enhanced absorption, unless the frequency used is greater than the frequency of the maximum absorption Measurement of absorption has the advantage that a small change in relaxation time can be detected at a greater wave-length than by measurement of dielectric constant if the percentage accuracy in the t n o cases is the same Absorption measurements %ere accordingly made on all the solutions investigated Unfortunately, the logarithmic damping decrement did not prove t o be constant over the whole resonance curve with the particular set-up used and consequently the absorption measurements do not carry the \?eight that they should otherwise h a \ e Also there occur5 an anomalous absorption band for water at the nave-length produced by the tube, and that reduced the accuracy of the measurement of the small effect sought Temperature as a factor viab ruled out by making all of the measurements in a constant tempwature room \\here the daily fluctuation amounts to o 2’ Three measuring condensers of different sizes were used, each calibrated against qolutions of acetone In water which Crude?j found to have practically a linear relationship b e h e e n per cent by aeight and dielectric constant As fiducial value for the dielectric constant of a a t e r at 17 so, the room temperature, that of (‘oolidgeZav,as taken, viz , 81 q The value of 2 1 3 for acetone -as taben from the measurements of Colle) ?6 Experimental Results A1203. Aluminum oxide sols made by Gann’s method (the hydrolysis of aluminum acetate) are quite Etable and are readily made thixotropic by the addition of electrolyte.?’ Upon shaking the gel it becomes a fluid of low viscosity which resets t o a gel again on standing. A well dialyzed sol was divided among eight well cleaned test-tubes with ground glass stoppers and solutions of KzS04added drop by drop with shaking until the concentration of the ii1203 was reduced t o 0.97%, while that of &SOI varied from tube to tube from 0.16 to 1.64 millimols per liter. The solutions containing 1.34 millimols per liter K2S04or more were thixotropic.
TABLE 111 Millimolar cone. KzSOl
Dielectric Constant
0.00
SI.I*
0.16 0.45
80. jj
Millimolar cone. KISOa 0.89
80.55*
.34 1.64 I
* Ave. of several measurements. 2a P. Drude: Z. physik. Chem., 23, 2 8 8 (1897). ?&W.D. Coolidge: Ann. Physik, (3) 69, 134 (1899).
26 ?i
R. Colley: Physik. Z., 11, 324 (1910). H . Freundlich and L. L. Bircumshaw: Kolloid-Z. 40, 19 (1926).
.4.
Dielectric Constant 80.4
80.I*
79.8*
DIELECTRIC CONSTANT O F THIXOTROPIC SOLS
823
Fig. z and Table I11 represent the results of the measurements of dielectric constants. It will be noted that the first small addition of electrolyte produces a much larger depression of the dielectric constant in proportion than additions thereafter. Although numerous measurements were made with the greatest possible care on the thixotropic sols before and after gelling, they showed the same dielectric constant within the experimental error. Absorption measurements indicated only that the absorptions in the sols and gels in water are the same within ~ - 3 ~ 2 .
.-
"rb",Y,F,ll#,,,s
s,,rg/c n r C r , 5 Y r c m c ? r h
v u
8
"i'L,nO'n,r
79
0
CONC n-,?SO*
I O
0 6
04
20
Frc. 2 .4luminum Oxide
Fig. 3 Ferric Oxide
To make sure that the above effects were not due to the &SO, in solution, 1.64 millimolar solution of KZSO? in pure water v a s measured, and showed a dielectric constant of 80.9 and an absorption of 6yc higher than water. R
The probabilities are that most of the &SO1 in the &03sols is adsorbed so that the disturbance due to that in solution is negligible. Pesos. The most completely studied of the thixotropic gels are those of Fe?Oast'. A commercial sample made by the hydrolysis of FeC13 x a s dialyzed through cellophane for 2 0 days and then made up into portions with different K . 3 0 , concentrations and an Fe2O8 content of 3 ' 3 . The longer dialysis of such a sol is pursued, the less electrolyte is required to give it thixotropic properties, and also the more readily it is precipitated. The ease of precipitation probably accounts for the relatively low accuracy of the results. Table I T and Fig. 3 show the results of measurements on one series of sols. The general decrease in dielectric constant with increasing quantities of &SO4 is quite plain. Sols with 0 . j millimols per liter of K2S04or more were thixotropic. TABLE IV Cone. K2S0, millimols/l
Dielectric constant
0.00
81.1
0.53
80.2
0.2j
80 o 80.4
0.6j
79,s
0.38
Cone. KISOl millimols;l
Dielectric constant
.Again numerous measurements were made on the same sols both before and after gelling. The results indicate that the gels may have constants 0.2 higher than the sols, but that is a smaller difference than the probable experimental error so cannot be relied upon.
824
S. S. KISTLER
The absorption was found to be the same as in water. Bentonite. Natural Bentonite forins a thixotropic gel when above 7-85; concentration.8 By dialysis it loses this thixotropy which can be revived by the addition of electrolyte. I n this case the most effective salts are those with polyvalent cations. The dielectric constant of a ;.IS; sol remained constant at 72.6 with increasing concentrations of CaC12 up to I.; millimolar. The absorption in the dialyzed sol was IOC; greater than in water and increased steadily with increasing CaCl? concentration to zcc; greater than water at I .; millimolar. Although the Bentonite had been dialyzed for two weeks in 0.03 nim. thick cellophane, the removal of electrolyte was not complete enough to completely destroy thixotropic properties, so no figure can be given on thc minimum concentration of CaC'12necessary t o bring it about. 7'205. The V205 sol was made according to the Biltz method'5 (th(1 treatment of ammonium vanadate with HC1, washing and peptizing with water). The sol was over 3 years old so that all ageing effects should h:ive already occurred. It was dialyzed I I days before using. -4s stated earlier, it was very difficult t o obtain concordant. r e d t s ( l i i ~ . no doubt, to precipitation on the electrodes. -1film of Y.?Oj we-; readily detectable over the electrodes after a measurement. The ayerage of riumerous measurements on a 0.9'-; dialyzed sol gave a dieleActric constant of 81.0, while the dielectric constant for a sol of equal coneeiitixtion made 2 . 2 millimolar in KC1 was 8 2 . 2 . This is the only sol showing high abaoiptim. Both the 0 . sol and sol containing the KC1 showed ioo( greater absorption than water. Gelatin. Since gelatin is a representative of the hydrophile colloids and represented by Keller15 as having a \-cry large affect upon the dielectric cnnstant at a wave length of 76 c n . : two solutions of Xgfa color fiiter grlat 0 . 5 5 and 1.107~ concentration respectively iTere meiisured. The reslllt compared with those of Keiler in dilutc solution in Tnble v.
Such a large difference in values is hard t o explain. It is to be noted that Keller, using the same apparatus, obtained the objectionable results for sucrose recorded earlier. RIarine~co's?~ figures at 6. j m. on the orher hnnd shotv a maxiniuni in the dielectric constant-concentration curve at 0 . 6 5 gelatin, w h c h he ascribes to 28 *@
H. Freundlich: Colloid Symposium Monograph. 2 , 46 (19zj). N. Marinesco: Compt. rend., 188: 1 1 6 3 (1929).
DIELECTRIC CONSTAST OF THIXOTROPIC SOLS
82j
large dipole moment in the single gelatin molecules. That a molecule of molecular weightso could display its dipole in a field of such rapid oscillations seems possible since the relaxation time varies directly as the volume of the molecule.31 If as a rough approximation it is assumed that the ratio of the relaxation times of gelatin and water is that of the molecular weights, gelatin should display anomalous dispersion at a wave length 500 times as great as for water. The region for water practically lies between 0.1-10 cm. which would place it roughly between j o - j o o o cm. for gelatin. Due to the highly hydrated character of the gelatin molecule, one would not expect its density t o be large and 6.5 meters should be on the high frequency side of its anomalous dispersion range. Sucrose. Although a study of sucrose does not properly belong with that of thixotropic gels, it seemed to be of sufficient interest to make measurements on its solutions since much attention has been given to its hydration.32 Table I1 and Fig. I give the results at two very different wave-lengths. The absorption increases with concentration of sugar and is SC’; greater than water in the 1 9 . 4 5 ~ ;solution. :I
10,000
Discussion The very definite slope t o thP curves for & 0 3 and F e z 0 3indicate that the previous assumption of increased hydration due to the addition of electrolyte to these sols is correct. The dielectric constants of the dialyzed sols are surprisingly near that of water. Little can be inferred fron this fact except that in the absence of all but a trace of electrolyte the fraction of the water molecules seriously hindered in their adaptation t o the impressed field is too small to be measured in the present experiments. The first small addition of electrolyte affects a larger relative change in hydration than subsequent additions, which might be expected from a consideration of the probable connection with adsorption of the ions on the micelles, One would also expect the curves to flatten out with larger quantities of electrolyte. I n the cases of & 0 3 and Fe20athis expectation would probably be realized if a suitahle correction were introduced for the electrolyte effect on the dielectric constant at the higher concentrations. With Bentonite where one can reasonably assume some electrolyte already present, the curve is found flat. Whether the increase in hydration and the decrease in stability of these sols are intimately connected or merely independent results of the same cause is uncertain but one is inclined to feel that the latter is more nearly correct. If the sol is considered to have two sources of stability affected by the addition of electrolyte, viz., the electrostatic repulsion between the charged particles and the cushioning effect of the hydration layer, the addition of electrolyte will serve on the one hand to decrease the stability due to the reduction of
30E. J. Cohn: J. Biol. Chem., 63, 7 2 1
(1925).
P. Debye: “Polar Molerules,” pp. 84-85 (1929). 32 J. W. McBain and S. S.Kistler: J. Phys. Chem., 33, 1806-12(1929).
826
S. J. KISTLER
charge on the particle and on the other hand to increase the stability by increasing the hydration layer. What the sum total effect will be with very m a l l additions of electrolyte cannot at present be predicted. n'ith large additions it is to destroy the stability. The course of the stability curve might very well go through a maximum. If the stability of the so1 is reduced by some other means than the addition of electrolyte, the decrease will probably be, in part at least, due to the reduction of charge.R3 The increase in hydration, if any, does not completely compensate for the decreax in charge. S o w when electrolyte is added the so1 is found very much more sensitive t o it because of the already diminished charge. One must assume that hydration alone cannot maintain the dispersion of hydrophobe particles. This prediction is very well confirmed by the behavior of Fez(>?sols. A sol that has been dialyzed a long time is several times as sensitive to the addition of electrolyte and the thixotropic gel formed is coagulated by much shaking, whereas a gel made from not too long dialyzed sol stands a great deal of shaking without effect. The hypothesis that the degree of hydration incrensrz with the decreasing total stability is borne out by the fact that the longer an l t 2 0 asol is dialyzed before the addition of necessary to produce electrolyte, the smaller is the concentration of the a thixotropic gel. (Dialysis and addition of electrolyte seem to be antagonistic treatments, but it must be borne in mind that the F e 2 0 3sols made by the hydrolysis of FeC13are really colloidal basic chloride with a certain tendency to decomposc irreversibly. Colloidal solutions of pure Fe203of the concentrations used cannot be produced.) One would look immediately to the absorption measurements for confirmation of the conclusion that addition of electrolyte to A 1 2 0 3 and F e 2 0 J sols increases hydration. X lack of an increase in absorption would not disprove the above findings since if the water molecules affected are altogether prevented from following the field, no absorption will occur; however, one would expect many of the molecules to be only partially hindered and consequently act as absorbers. It is unfortunate that the most convenient method of producing high frequency should have produced a wave-length lying in an absorption band of water, and also that the logarithmic damping decrement could not be exactly determined with the given set-up. Probably the most important conclusion t o be drawn from the measurements is that there is no measurable change in the degree of hydration as represented by dielectric constant and absorption measurements when a sol sets to a gel. This means that the internal viscosity of the gels is very little, if any, higher than that of the sols, since the measure of what we have chosen 33 B. PI'. Ghosh (J. Chem. Soc., 1929, 2693) finds that whether precipitation of an Fez03 sol is produced by the addition of univalent or divalent salts or by the addition of AmOH, at the point where rapid precipitation occurs the zeta potential has been reduced to practically the same value.
DIELECTRIC CO?ITST.INT O F THIXOTROPIC SOLS
827
to call the degree of hydration has been nothing more nor less than a measure of the change in the viscosity of the medium experienced by the water molecules t hem~elves.~' AIeasurements on the 1 . 1 ~ ;gelatin sol before and after gelling lead to the same conclusion. The fluidity of the solution in the interstices of the gelatin gel is very nearly the same as that between the micelles before setting, and not widely different from that of pure water. The behavior of VaOj sols was to be expected. Errera3' has found them extraordinarily polar at long wive-lengths, the polarity extending down to such short wave-lengths as to exclude any possibility of its arising from a fixed dipole in each colloidal particle. Szegvari and TVigneP have probably rightly placed this polarity as arising from surface Conductivity of the elongated particles greater than that of the surrounding medium so that ions can migrate along their lengths and produce charges on their ends. The calculations of Szegvari and JT-igner have been given a more acceptable mathematical foundation by bike^-mnn.3$ If one uses the assumptions of Rikernian's as to possible size of the particles and introduces surface conductivity of the order of magnitude of that found by 11cBain and Peaker3' for glass and fused silica in 0.001 S K('1, he can qualitatively duplicate the curve of dielectric constant against frequency found by Errera. The increase in dielectric constant of the T7?0:> sols with addition of electrolyte is readily explained on the ground of increased surface conductivity, while the large absorption is to be expected, both due to the surface conductivity of the particles and to the fact that the V?Oa is precipitated by the alternating charges and forms a film on the electrodes. .Iny hydration effects are completely obscured. I n order to set how great a change of relasation time the above figures would represent, two calculations were carried out using the equations of Debye relating dielectric constant, absorption and relaxation time.33 I n the first calculation an increased absorption of 10% was assumed, and it was further assumed that all of this increase in absorption is due to change of relaxation time. I n view of the fact that at the wave-length of 3 2 cm. there is more absorption than would be predicted from the Debye calculations, a large element of uncertainty enters since there is no way of predicting whether or not a change in relaxation time will be accompanied by a change in the other properties producing absorption. If, as above, the 10% increase in total absorption is ascribed solely to a change of relaxation time, it would represent an increase in this time of J , Errera: Kolloid-Z., 32, I j7 (1923). A. Szegvari and E. Wigner: Kolloid-Z., 33, 218 (1923). 36 J. J. Bikerman: Physik. Z., 27, 769 (1926). 37 McBain and Peaker: J. Am. Chem. Soc., SI, 3294 (1929). 3 8 P.Debye: loc. cit., p. 92. 34
35
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S. S. KISTLER
The second calculation showed that a five-fold increase in the relaxation time would decrease the dielectric constant measured a t 3 2 . 7 cm. wave-length by approximately one unit. From the measurements on the rZlZOsand Fe& sols it is safe to say that the reduction of dielectric constant ascribable to hydration is less than one unit so that the maximum effect, that the sol particles can have upon t,he relaxation time of the bulk of the water is a five-fold increase. Probably half t’hat value is more nearly correct. In other words, the viscosity of the water between the micelles in one of these thixotropic gels is of the order of three times that of pure jTater. Any change that may occur upon gelation must be a small one. Even though it has been shown that when a hydrcphobic so1 is brought t o the thixotropic rondition an increase in hydration occur>, it can be reasonably questioned whether this hydration is sufficient to account for gelation. If, however, chains of water molecules tend to extend out from the surfaces of the micelles, it is reasonable to suppose that’when sufficient of these chains exist and a solid support, such as the walls of the containing vessel, is suficiently close, the mass of micelles would tend to be linked into a complicated network that would possess some resistance to deformation. The network of chains of water molecules between the micelles would tend to draw them together, while electrical charge would resist this tendency and a state of equilibrium would be attained. l.-pon too large reduction of charge by addition of electrolyte, the repulsion could no longer balance the pull and coagulation ~ ~ ~ uoccur. ltl When one considers that the tensile strength of miter is of the order of thousands of kilograms per square centimeter, it is obvious that, only a very small fraction of the total water present need be connected in chains at any one instant. The observed phenomena in t,hixotropic gels are quite in harmony with this assumption of connecting chains. That, some sort of anisotropy exists in ordinary liquids is very strongly indicated by recent X-ray investigations. For example, Stewart33finds that if one assumes that the molecules group themselves into evanescent associations resembling crystallites the observed phenomena are most readily explained. Even in such a liquid as mercury where association is ordinarily assumed to be very small or absent Debye?” finds definite maxima in the molecularly scattered X-rays and is of the opinion that “the clarity of these maxima must be connected with a certain regularity of the arrangement of the molecules themselves in the liquid, a regularity which perhaps reminds one of the grating arrangement of atoms in solid crystals”. Whether the phenomena observed are due merely to rythmical density variations in the liquid with orientation of the molecules or possibly to linkage of niolecules into chains, it is perhaps too early to state, but the important fact for consideration here is that in all probability this anisotropy would a8
G. R. Stewart: Phys. Rev., 32, 558 (1928).
P. Dehye: Paper before the Deutsche Gesellschaft fur technische Roentgenkunde, Heidelberg, June z 3 , 1930,
DIELECTRIC COSST.4NT OF THIXOTROPIC SOLS
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tend to extend from an orientating surface, and under suitable circumstances could give rise to the phenomenon of thixotropy observed in gels. In this place I should like to express my gratitude to Professor H. Freundlich for permission to work in his laboratories and for kind advice and interest in the progress of the work, and also to H. Kallmann for the use of apparatus and for much friendly assistance. I am also indebted to the hmericanGerman Student Exchange for funds which greatly aided in the pursuit of the problem. summary Hypotheses of the origin of thixotropy in gels are reviewed, and the assumption that hydration is at least a contributory cause is favored. Calculation of degree of hydration from dielectric constant measurements is discussed and it is emphasized that the results obtained depend directly upon the frequency of oscillations in the measuring circuit. The influence of hydration on the dielectric constant is shown to be probably due to a direct influence on the relaxation time of the water molecules near a hydrated molecule or micelle due to their orientation and their tendency to link together. Electrical saturation effects are probably minor. S o quantitative values for the degree of hydration can be given without the introduction of some arbitrary definition or the arbitrary selection of conditions of measurement. The influence of hydration on dielectric constant will be greater the greater the frequency of the measuring circuit, reaching a maximum where the slope of the dielectric constant-frequency curve is a maximum. Measurements on dialyzed Fe203and &03 sols at 3 2 . 7 cm. wave-length show little, if any, hydration but give quite definite indications of hydration in the presence of small concentrations of electrolyte. In none of the cases studied is the viscosity of the intermicellar solution measurably higher in the gel than in the sol before gelling, nor is this viscosity widely different from that of water. Thixotropy is most readily explained by the assumption that some form of orientated anieotropy of the water, probably chains of water molecules, extends out from the surface of each colloidal particle and tends to link it with the neighboring particles. Kaiser Ti'ilhelm Inslitut f u r physikalische Chemie u n d Elektrochemie, Berlin. J u n e SO, 1950.
