L. A. R o ~ o
386
Discussion The data of Table I were analyzed by the IBM computer in order to determine the limiting conductances and other parameters, The program for associated electrolytes gave negative association constants for lithium and sodium tetraphenylborides; the data for these two salts therefore were analyzed to find the conskantp A3 and J for the equation = Ro
+
- SC"~ EC log c
+ JC
TABLE I CONDUCTANCE OF TETRAPHENYLBORIDES IN METHAKOI, 104,
14.935 11.517 7.896 3.932 19.650 15.640 12.807 8.540 5.082 17,682 13.977 9.133 4.882
10%
A
11.176 8.432 5.751 2.8791 12.405 10.291 7.865 5.857 3.5555 15.994 12.433 9.031 6.349 3.2519 14.902 12.053 8.622 6.226 3.3317
KBPh4 81.392 82.254 83.298 84.862 81.084 81.666 82.418 83.189 84.363 80.182 81.057 82.117 83.088 84.671 80.257 80.934 82.050 82.976 84.471
1 0 3 ~ ~
h
18.795 14.754 10.802 6.999 3.468
(1)
Potassium tetraphenylboride shows a small amount of association; for the four runs of Table I, these values of association constants K A were found: 24 f 6, 6 f 8, 35 f 15, 24 i 15. The limiting conductances (88.85 f 0.03. 88.83 f 0.06, 88.79 f 0.08, and 88.80 f 0.10) average to 88.82 f 0.07 for KB(CBH&. The conductance data of Gordon6 for lithium, sodium, and potassium chlorides in methanol also were analyzed in the same way in order to obtain the limiting conductances of the chlorides. (It would be inconsistent to use literature values for the limiting conductances of the chlorides, because the early extrapolations do not include the effect of the term Ec log c.) The conductances are summarized in Table 11. Usiiig Gordon's values5 of transference numbers of the chloride ion in methanol (0.4999 for KC1, 0.5366 for SaCl), and the limiting conductances of Table 11, Xo(Cl-) is found to be 52.37, whence Xo(Li+) = 36.69, Xo(Sa+) = 45.22, and Xo(K+) = 52.38. Combining these values with the limiting conductances of the tetraphenylborides, me find Xo(B(C6H6)4-) equal to 36.69, 36.54, and 36.44 from, respectively, the lithium. sodium, and potassium salts. The data for lithium chloride at the lowest concentrations (1 and 2 X lop4) show systematic deviations from the theoretical equation and were not used in computing Ao(LiC1); furthermore, the lithium tetraphenylboride was the least
Vol. 67
LiBPh4 67.893 68.706 69.647 70.789 72.287 NaBPhl 73.988 74.802 75.854 77.464 73.232 73.992 74.602 75.748 76.990 73.492 74.225 75.461 76.995
-3 5 1 -7 3 -1 4 -3 0 -2 6 -4 -1 1 1 -2 2 -1
1 0 3 ~ ~
- 2 5 - 4 1 -8 - 1 16 -12 5 1 -9 21 -18 4 16 -34 17 6 - 5
TABLEI1 LIXITINGCoNDrjCTANCES I N METH-4NOL AT 25" Salt
Ao
LiB(CGH& NaB(CGH& HB(CeH5)d
76.26 f 0.02 81.76 rt .02 88z82 f .07
Salt
LiCl NaCl KCl
AQ
91.94 f 0.02 97.59 f .01 104.75 f .01
stable of the three salts and experiment showed that the impurities due to oxidation rapidly raise the conductance. Consequently a weight of only '/8 was given to the lithium datum of Table 11. The three runs on the sodium salt average t o 36.54; the four on the potassium salt average to 36.44. The weighted average gives 36.50 f 0.05 for the limiting conductance of the tetraphenylboride ion in methanol a t 25'.
-
STABILITY OF KOX-AQUEOUS DISPERSIOXS BY L. A. RONIO~ The Pigments Department, E . I . du Pont de A7ernours 6 Company, Newport, Delauare Received April 28, 1962 Calculations based on the theories of Hamaker and Overbeek-Verwey lead to the conclusion that the stability of titanium dioxide suspensions in n-butyl alcohol and n-butylamine is due to electrostatic repulsion, whereas the stability of titanium dioxide suspensions in melamine and linseed oil thinned with xylene presumably is due to entropic repulsion of the interacting adsorbed polymeric molecules.
Introduction The stability of suspensions in polar and non-polar media can be explained quantitatively by combining the attractive van der Waals potential with the repulsive double layer potential. The investigation of this subject is of interest in organic media with lorn dielectric constants where the number of charges per unit of volume of suspension is low. Broadly, a suspension can be stabilized by either double layer electrostatic repulsion2-4 of by entropic (1) Director of Chemical Research, Laboratorios Life, Quito, Eouador. (2) ( a ) B. Derjaguin. Trans. Faraday Soc., 96, 730 (1940); (b) E. J. W. VPrwey, zhid., 36, 192 (1940). (3) H. Koelmans and J. Th. G. Overbeek, Dzscusstons Faraday Soc., 18,
repulsion of the interacting adsorbed m0lecules.5-~ This investigation was made vrith the purpose of determining which of these mechanisms is responsible for the stability of Ti02 dispersions made in organic liquids of various dielectric constants.
Experimental Materials.-Rutile Ti02 powders with (1) clean rutile surfaces (Sample DP-C) and (2) coated with 2% alumina (Sample DP-T) were used. The soluble salts from these samples were removed by washing until the filtrates had a resistivity of 1. 8 X Ioj ohm-cm. The titanium dioxide particles are roundish and have an average diameter of 0.22 f 0.05 p . The liquids used to make the dispersions were dry reagent grade n-butyl alcohol, nbutylamine, melamine (Cyme1 248-8), and bodied linseed oil.
52 (1954). (4) J. L. van der Minne and
(1953).
P. H. J. Hermanie, J . CoZZozd Scz., 8 , 88
(5) E. L. Mackor, {bid., 6 , 492 (1951).
(GI E. L. Maokor and J. H. van der Waals, ibzd., 7, 535 (1952).
STABILITY OF NOX-AQUEOUS DISPERE;IONS
Feb., 1963
The melamine and linseed oil were diluted with dry xylene to give solutions with viscosities of about 1 centipoise. Dispersions.-Samples of 0.50 g. of the powders, oven-dried a t 150’ for 48 hr., were transferred t o 30-ml. test tubes. Then, 25 ml. of the dry liquids was added. To each test tube 4 glass beads were added prior to shaking the suspensions for 15 min. in a Burrell wrist-action shaker. Following this, the rates of sedimentation a t 25 f 2’ were observed as a function of time. A summary of the relevant properties of the dispersing media is given in Table I. Electrophoretic Mobilities and Zeta Potentials.-To measure the electrophoretic mobilities of the Ti02 particles suspended in the various organic media, the suspensions which had been standing for 1 2 4 hr. were diluted further with the corresponding organic liquids to facilitate vision in the electrophoretic path. The microelectrophoretic cell, made of “Delrin’l7 acetal resin, has a flat glass path of 45 x 7 x 1 mm. The electric field was applied from a d.c. source with variable potentiah of 90 to 810 v. The polarity of the circuit was changed with a three-way switch. Platinum electrodes of 5 X 3 mm. were used. To eliminate any leakages of current in the electrophoretic path, the cell was insulated with a coating of silicone. No evidence of induced polarization was detected8 even when potential gradient of 150 v. em.-’ were applied. I n this cell, to observe the electrophoretic migrations, the microscope was focused a t a depth of 190 p from the top of the flat path which has a total depth of 1000 p . $ The errors in the times (seconds) of electrophoretic migration were kept below 3% by taking 6 to 10 pairs of time readings in both polar directions for the particles t o migrate 170 p . The viscosities of the liquids a t 25’ were determined by measuring their times of flow in calibrated Ostwald pipets. The densities a t 25’ were determined pycnometrically. The zeta potentials were calculated by the equation = 6 TVU,’~. The number of charges per unit of volume of suspension is very low and the thicknesses of the double layers exceed the particle size.10
Results The observations of suspension stability and the data on electrophoretic mobilities, charge, and zeta potentials are summarized in Table 11. To ascertain whether the stability of these dispersions is a result of double layer repulsion or entropic repulsion, the energies of electrostatic repulsion and van der Waals attraction were calculated as a function of separations between the particles. Electrostatic Energy of Repulsion.-The electrostatic energies of repulsionll mere calculated according to the equation e
-
7( 1 -
2)
ER = rry2 -S
Here { is the zeta potential, e.s.u.; r is the radius of the particles, cm.; E is the dielectric constant of the liquid; T is equal to r/6; and s is equal to R/r, where R is the center to center separation between particles. The use of .i+ instead of $o in the equation of E R to obtain a first approximation estimate of ER is valid because, in these non-aqueous systems with low dielectric constants, the potential decays very slowly with s in contrast to aqueous suspensions where the opposite is the case. I n our calculations, r/6 = 1. Values >> 1000 8. for the thickness of the double layer have but a very minor effect on the values of E R . van der Waals Energy of Attraction .-The energies (7) Registered Du Pont trademark. (8) J. L. van der Minne and P. H. J. Hermanie, J. Collozd Sci., 7 , 600 (1952). (9) (a) M. von Smoluchowski, “Hmdbuch der Elektrizitat,” Barth, Leipzig, 1921, p. 366; (b) M. Komagata, i3”lsctrochem. Res., Tokyo, No. 348 (1933). (10) H. R. Kruyt, “Colloid Science,” Elsevier, Amsterdam, 1952, p. 208. (11) E. J. W. Verwey and J. Th. G. Overbeek, “Theory of Stability of Lyophobic Colloids,” Elsevier, Amaterdam, 1948, pp. GO-152.
387
of attraction were calculated according to the formula derived by Hamaker.12
”[
EA = - ._ 6
~
82-4
++;nI!
2 s
- 41
82 S
I n the application of this equation there is some uncertainty about the correct value of the Hamaker constant A ,13,14 but considering that the value of this constant is dependent upon the polarizabilities of the interacting atoms, it appears to be reasonable in this case to use the value of A = 10-12 erg in our calculations. There is also a retardation correction15 to the Hamaker equation which becomes important as the distance of separation, H, between the particles exceeds the London wave length. This correction is usually necessary when H > 1000 8. because under this condition, EA decays proportionately to l / H 7 instead of 1/H6. Since the London wave length is related to the principal optical absorption band of the particles, which in the case of Ti02 is larger than 1000 8.,the retardation correction is not significant in our calculations. Stability of Dispersions.-The net electrostatic repulsion potential expressed in IcT units (4.1 X erg) of the particles in the dispersion at 25” corresponds to the maximum (E,) in the resultant curve obtained by plotting ER and -EA against the corresponding values of R/r. One should note that since the double layer repulsion potential falls off very slowly and the attraction potential very rapidly as a function of R/r, the magnitudes of Emare not too sensitive to changes in the value of the ‘Hamaker constant A used to calculate the attraction potentials. This is illustrated by Fig. 1, which shows the electrostatic repulsion potential curve obtained from values of ER calculated for the case where E = 18, [ = 50 mv., and r = cm. and two attraction potential curves, obtained from values of -EA calculated using values of A = erg and A = 3 X erg. Although there is a threefold variation of A , the value of the net electrostatic repulsion potential, Em,decreases only 6 kT units, namely from 38 to 32 kT units. The stability of the dispersions made with n-butyl alcohol and n-butylamine is the result of double layer electrostatic repulsion. Actually, the values of E , (Table 111) exceed the critical potential of 15 kT which is characteristic of stable dispersions.16 The dispersions made with melamine-xylene and bodied linseed oil-xylene are stable in spite of the fact that the net electrostatic repulsion potentials, E,, are negligible. The stability of these dispersions is attributed to entropic repulsion of the interacting adsdrbed polymeric chains on the surfaces of the particles. Discussion To ascertain the significance of the zeta potentials, it was essential to establish experimentally the extent of stability of the dispersions. One should note that! the dispersions DP-C and DP-T n-butyl alcohol and DP-T n-butylamine are stable and exhibit zeta potentials of +77.5, $84.0, and -79.0 mv., respectively, whereas (12) H. C. Hamaker, Phyezca, 4, 1058 (1937). (13) B. V. Deriaguin. A. S. Titijevskaia, I. Abucossova, and A. D. Malkina, ibad., 18, 24 (1954). (14) J. Th. G. Overbeek and M. J. Sprtrnaay, DzscussZons Faradmi SOL, 18, 12 (1954). (15) H. B. C. Casimir and D. Polder, Phys. Rev., 78, 360 (1948). (16) Reference 11, p. 171.
TABLE I1 ~ l ~ E C T I W P I i o R W l ! l C M O B I L I T I E S A N D Z E T A I’OTENTIALS
OF
NON-AQUEOUS DISPERSIONS U. cm.2 v.-l Ti02
DP-C DP-T DP-C DP-T DP-C DP-T DP-C DP-T
Ijispersion n-Butyl alcohol n-Butyl alcohol n-Butylamine n-Butylemine hlelamine-xylene
Melamine-xylene BQ-I. oil-xylene BQ-I. oil-xylene
800. - 1
+ 2 . 1 X 10-5 + 2 . 3 X 10-1 - 8 . 3 X 10-8 - 3 . 9 X 10-5 - 3 . 8 X lo-‘ -3.8 X 10-6
0 - 8 . 7 X 10-7
r, m v . +77.5 f84.0 -12.7 -79.0 -13.4
-12.0 0
- 5.2
Stability‘ Fairlystable Stable Unstable Stable
Stable Stable Stable Stable
“stable” indicates no evidence of phase separation after 24 hours, “fairly stable” indicates same but after only 12 hours, and “unstable” indicates phase separation after less than 3 hours. a
TABLE I11 KET ELECTROSTATIC REPULSIVE POTENTIALS, E,, OF Ti&NON-AQUEOU8 DISPERSIONS Fig. 1.-Combination of one repulsion potential curve, = 50 mv., r = 10-6 cm.) with two attraction potential curves: (a) E A ( A = IO-’* erg) and (b) EA (‘1 = 3 x 10-’2erg).
E R ( E = 17, r
the dispersion of DP-C n-butylamine is unstable (clear supernatant liquid is observed after three hours of standing) and has a acta potential of only -12.7 mv. This basic difference is attributed to differences in thc energetics of adsorption of thesc powders.17 The cvidence is that the stability of these dispersions is governed by double layer electrostatic repulsion (Table 111). Since the applied potentials were < 100 v. em.-’ in the determinations of mobilities, the corrections for e and 7 in the calculations of the zeta potentials are negligible and consequently do not alter this conel us ion. The dispersions made with melamine-xylene and bodied linsced oil-xylene contain the minimum amounts of these polymeric substances required to obtain stable dispersions. The negligible values of the zeta potentials and the net electrostatic repulsion potentials (Tables I1 and 111) indicate that it is impossible to stabilize these dispersions by double layer elcctrostatic repulsion. TABLE I PROPERTIES OF THE l’o~ der
Liquid
DISPERSINQ e
~ ~ E D IAT A pt
ohm-cm.
25’” 7, cp.
I)P-C
n-Butyl alcohol 17.1 1 . 1 X IO8 3.660 DP-T n-Dutyl alcohol 17.1 1.1 X lo8 3.660 TIP-C n-Butylamine 7.8 4 . 5 X 108 0.927 DP-T n-Butylamine 7 . 8 4 . 5 X IO8 .927 IIP-C Melamine, 0.20 g. 4.0 0 X lOla .829 Ill’-T hlelamine, 0.15 g. 4.0 =X .812 1)P-C RQ-1 oil, 1.00 g. 2.5 3 X IO1* .989 DP-T BQ-I oil, 0.20 g. 2.5 0 X IO“ .870 The dielectric constants and resistivities were taken from “Landolt Bernstem,” Vol. 7, Springer Verlag, Berlin, 1!)60, and “International Critical Tables,” McGraw-Hill Book Co , New York, N, Y .
To reduce the attractive potential to values approaching the thermal energy ( k T ) the thickness d of the adsorbed polymeric layer should be >60 A. (Table IV). Actually, the thickness of the bodied linseed oil and melamine adsorbed layers in TiOz surfaces, as estimated from adsorption experiments, is -25 A. Therefore, the stability of these dispersions may be attributcd to en(17) L. A. Ronio, J . Colloid Sct., 16, 139 (1961). (18) J. Lykloma and J. Th. G. Overbeek, ab& 16, 501 (19G1).
THE
Em.
kT
Dispersion
Ti02
DP-C
n-Butyl alcohol DP-T n-Butyl alcohol DP-C n-Butylamine UP-T n-Butylamine DP-C Melamine-xylcne 1)P-T Melamine-xylene DP-C BQ-linseed oil-xylene DP-T BQ-linseed oil-xylene
unitu
Stabilization
Electrost. repulsion Electrost. repulsion Unstable Electrost. repulsion
