THE ELECTROKINETIC POTENTIAL AND THE STABILITY OF COLLOIDS' HANS MUELLER Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts Received J u n e 14, 1934
Experimental evidence (6) shows that the stability of hydrophobic colloids is determined by the electrokinetic potential of the particles. In the case of hydrophilic colloids, however, the experiments indicate (1,4) that coagulation depends primarily on the amount of hydration, while the l-potential seems to be of much less importance. The question arises, therefore, whether the electric forces are sufficient to explain the stability of hydrophobic colloids. This problem has been investigated by A. March (3). He finds that the observed electrokinetic potentials are at least ten times too small to account for the existence of colloids with microscopic particles. March comes to the conclusion that the stability of colloids is essentially due to the existence of a protecting skin around every particle. This result is in agreement with the fact that colloidai particles do not grow or flow together during coagulation. Even liquid particles remain separated after coagulation. In view of the experimental facts, it seems natural to assume that in the case of hydrophilic colloids this protecting skin is formed by the hydrated water molecules. For hydrophobic colloids this explanation can obviously only be accepted if we can understand the origin and nature of this protecting skin. We must prove that the energy necessary to destroy this 'skin is largcr than the energy of the temperature motion of the partices. Finally its existence must be closely connected with the electrokinetic potential in such a way that its influence vanishes with small {-potentials. In a recent paper ( 5 ) I have proposed the following explanation of the origin of this protecting skin: The electric double layer creates a very strong inhomogeneous electric field around each particle. This field produces by electrostriction a large hydrostatic pressure in the range of the double layer. We find, therefore, around each particle a thin shell where the water is under considerable pressure. It is this shell which acts as the protecting skin. According to this theory the mechanism which produces 1 Presented before the Eleventh Colloid Symposium, held at Madison, Wieconsin, June 14-16, 1934. 743 THE JOURNAL OF PKYSICAL CHE4IISTRY, VOL.
39, NO. 6
744
HANS MUELLER
the stability of colloids is very similar for hydrophilic and hydrophobic sols. The difference lies in the fact that in hydrophilic colloids the water molecules are “attached” to the surface of the micelle by chemical (adsorption) forces and hence coagulation is to a large degree independent of the (-potential. In hydrophobic colloids the water molecules are only “attracted” to the surface by the electrostatic forces of the double layer, and hence their stabilizing infiuence diminishes as the l-potential gets smaller. The energy of this electrostatic effect can be calculated by means of the same considerations as given by Zwicky (7) for the electric field around ions. We consider a plane diffuse double layer. If the (-potential is not larger than 50 millivolts the electric potential cp at a distance x from the surface of the particle is given by cp =
(e-Kx
1 where - = X is the effective thickness of the double layer. The electric
K
field a t the distance z is E = Kle-KZ
and the dielectric polarization
P=- D - l E 4T
where D is the dielectric constant of water. We use the value D = 80. Dielectric saturation effects can be neglected. According to A. H. L0rent.z and Dallenbach (2) the force exerted on 1 cc. of the dielectric is then
F = 1 [ 1 + ( D - 1)(3D 4ir 5
+ 7)I E d-EZ
and hence the hydrostatic pressure p a t the distance x from the surface p =
lmc2 F dx = 155
K2e-2Kx
The maximum pressure exists along the surface z = 0 and reaches the value kg. per cm.2 po = 17K2p2 In this formula is the value of the potential in volts and has usually values smaller than 0.1. For a monovalent electrolyte K2 has, according to Debye and Huckel, the value
K 2 = v *1.07 X 10’’
ELECTROKINETIC POTENTIAL AND STABILITY OF COLLOIDS
745
where y is the molar concentration of the electrolyte. Using { = 0.1, y = 1/1000 we get therefore a maximum pressure of about 18 atmospheres. Five to ten times larger values of this pressure can be calculated if we take into account the curvature of the surface of small colloidal particles. In the case of a spherical particle the potential decrease is given by e-KP
v = A and since the pressure depends on E =
r
aV and aE 3% --= -one realizes ar ar ar2
that this more rapidly decreasing potential gives rise to a larger pressures2 It is intended to show here only that the proposed theory gives results of the correct order of magnitude. We shall, therefore, consider only the case of the plane double layer, keeping in mind, however, that for colloids the numerical values of all results will usually be considerably larger. This hydrostatic pressure will result in a volume contraction of the colloid and leads to the conclusion that agglutination produces an increase of the volume. This increase is given by AT' = 4aN
Lw
Kp(r)r2 dr
where x = 45. is the compressibility of water and N [the number of colloidal particles in one liter. The calculation gives, with the most favorable assumptions, an increase of 10-3 to 10-4 cc. for one liter of colloid. Linder and Picton (8) observed a n expansion of this order of magnitude for a sol of ferric hydroxide. While the work of compression JpdV is small and can be neglected, Zwicky has pointed out that this electrostrictive effect produces an appreciable change of the free energy of the water. According to measurements of Bridgman the specific heat of water a t room temperature decreases under the influence of pressure, and the free energy diminishes likewise. For small pressures the energy decrease is nearly linear and has the approximate value AU = 1.34.10-3 cal. per gram = 5.6.104 ergs per gram for a pressure of 1 kg. per em2. The layer of compressed water on the surface of a colloidal particle is 2The calculation of this case has been carried out, but since the result cannot be given in analytical form, it will not be given here. The above expressions for (a are only valid for small values of f . The solution for large values of f leads dv t o even larger values of - and hence to still larger pressures. dr
746
HANS MUELLER
therefore the seat of a negative free energy. The amount of energy necessary to destroy 1 cm.2 of this film is given by
U
=
la
Introducing again
5.6, 104pdz = 4.8. 10-6K{zergs per cmS2
= 0.1, y = 1/1000 gives
U
= 0.5 erg per cm.2
If we use the accurate solution for the plane double layer ( 5 ) for a Z-Z valent electrolyte the expression for U is
where
k = Boltzmann's constant, and e = 3, y = 1/1000, and = 0.1
U
=
=
electronic charge. This gives for 2
3 ergs per cmn2
Taking into account the curvature of the surface we can expect values of 10 ergs per cm2. This is almost of the same order of magnitude as the surface tensions of liquid-liquid interfaces, and we can readily understand that this surface layer of compressed water is able to stabilize the colloid. If we assume that coagulation can occur only if this surface layer is destroyed in the area of contact, and if we assume that for large particles this area of contact is larger than 10-14 cm.2, we see that the temperature motion of the particles is not large enough to destroy the protecting skin. Hence, the colloid is stable. A small reduction of the {-potential decreases the energy necessary to produce coagulation, and since U is proportional to t2the stability of a colloid is very sensitive to small changes of the' electrokinetic potential. Making allowance for the approximations used, the proposed theory is therefore able t o explain the dependence of the stability of hydrophobic colloids on the electrokinetic potential. It is interesting to note that the theory leads to the conclusion that the degree of stability of hydrophobic colloids should decrease rapidly for temperatures above 80°C. Bridgman's measurements show that above 80°C. the free energy of water decreases only slightly with pressure. For pressures larger than 1000 kg. per cm.2 the energy increases a t this tem-
ELECTROKINETIC POTENTIAL AND STABILITP OF COLLOIDS
747
perature. It seems possible that the coagulation produced by heating of certain hydrophobic colloids (Pt) is a consequence of this effect. The electrostrictive effect will also reduce the specific heat of colloids. This effect can be calculated with the method given by Zwicky (7) for electrolytes, but owing to the small number of colloidal particles this effect is too small to be measured. The magnitude of the electrostrictive effect depends on the type of electric double layer, but it will exist even for a Helmholtz double layer. REFERENCES (1) BRIGGS, D. R.:J.Phys. Chem. 84, 1326 (1930). (2) DALLENBACH, W.: Physik. Z. 27, 632 (1926). (3) MARCH,A.: Ann. Physik 84, 605 (1927). (4) MUDD,STUART: Cold Spring Harbor Symposia 1, 65 (1933). (5) MUELLER, H. : Cold Spring Harbor Symposia 1, 5, 60 (1933). (6) POWIS,F.: Z. physik. Chem. 89, 186 (1914). (7) ZWICKY, F.: Physik. Z. 27, 271 (1926).
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