11: Brownian Motion and the Stability of Colloids KAROL J. MYSELS University of Southern California, Los Angeles, California
THEfact that colloidal solutions are frequently quite stable and their particles do not sediment when kept in bottles under ordinary laboratory conditions, is frequently2 attributed to the incessant agitation of Brownian motion. This explanation has a small grain of tmth in it. Thermal agitation always tends to counteract the forces of gravity acting on a particle and when these forces are small, it may indeed give a practically uniform distribution. As the particle size increases,, however, and the gravitational forces grow proportionately, thermal agitation leads only to an equilibrium distribution in which the concentration decreases with height. Since this equilibrium is the result of a balance between the gravitational forces (which for a particle in water are proportional to its volume V , the gravitational constant g, and the difference of densities d - 1) and the kinetic energy of the particle (which is proportional to R T I N ) , the ratio of concentrations C1and Cs a t two levels differing by h, is givena by the modified barometric equation:
-For I ,
Gold Sulfur pmtein
P
CJC. = 2 at 15 em.-
MI
01,
cm./year
3 . 0 1 . 2 x 10' 1.2 7.8 2.8X10"0.43 12.0 5,6 0.33
For vr =
1 cm./hour
r2, P
M2
0.26 7 . 8 x 10" 1 .. 91 2.2 6 . X 1 ~ 1 10"1 0 ~ ~
shown in the table. Obviously these are toward the lower edge of the colloidal range. Hence, thermal agitation cannot account for the experimentally observed uniformity of these and much coarser suspensions. The correct explanation lies in the fact that the rate of sedimentation, v,, of these particles is incredibly slow, of the order of a year per centimeter, as shown in the table. By Stokes' law this rate increases with the square of the radius but does not become of the order of a centimeter per hour until particles reach the large sizes shown in the last columns of the table. Hence, not only is the rate of attainment of equilibrium very slow, but the slightest convection currents caused by In(C,/CJ = Vh(d - l)gN/RT least temperature differences are sufficient to stir the With the aid of this formula we can calculate the suspension to practical uniformity. Thermal convection currents are difficult to eliminate largest size of particle which would show less than a twofold difference of concentration at equilibrium be- completely, especially in large vessels. Elaborate tween the top and bottom of a bottle 15 cm. in height. thermostatting4 or enclosure by good insulators5.8 The corresponding radii rl and molecular weights MI, has been used to produce quiescent solutions in which for spherical particles of gold, sulfur, and protein, are equilibrium can be approached. Under these conditions sedimentation occurs unmistakably and the I Suggestions of material suitable for this column are eagerly sought and will be acknowledged. They should be sent with ss logarithmic distribution holds over a wide range,' showing conclusively that it is convection, and not many details as possible to K. 3. M. at the above address. Since the purpose of this column is to prevent the spread and Brownian motion which is responsible for the unicontinuation of errors and not the evaluation of individual texts, formity observed under usual laboratory conditions.
the source of the errors discuased will not be oited. The error must occur in at leaat two independent stmdard books to be presented. 8 E. g., SVEDBER~, T., "Colloid Chemistry," The Chemical Catalog Ca., New York, 1924, p. 97.
JOHNSTON, N.,
AND
L. G. HOWELL,Phy8. Rev., 35,274 (1930).
MCDOWELL, C. M., AND F. L. USHER,Prm. Roy. SOL,A138,
