Oct’., 1956
KINETICS OF SOLIDSOLID REACTIONS
1347
charge is taken as 0.38 A. This heat value should not be far from the actual value if the situation proposed exists; the contribution to the total adsorption energy from the non-polar van der Waals forces would be small. Lower values would of course result if impurity centers are pregrouped rather than isolated as ion pairs in the surface. Nevertheless, heats of adsorption near the heat of liquefaction, as found for the adsorption of water on Teflon, can be explained adequately by this type of impurity. An additional experiment was carried out to determine whether heat treatment would affect the nature of the surface. After activation a t 280” for 20 hr., the nitrogen area decreased only from 9.0 to 7.5 m2./g. but the water vapor adsorption was reduced to about one-third its former value. Pellets heated under the same conditions showed no change in the contact angle with water. The volatility of the hydrophilic sites points toward strongly adsorbed surfactants as the principal active centers. The lack of change in the contact angle supports the view that the angle is determined primarily by the nature of the non-polar surface. Acknowledgment.-The authors greatly appreciate the support provided by the Office of Ordnance Research, U. S. Army.
dominate in producing a greater hydrophobicity (a lower energy surface) compared to Graphon, although the number of polar sites per unit area and the adsorption energy of these sites are greater for Teflon. The limited polarizability of the surface fluorine atoms would account for the small interaction energy between water and Teflon. The higher polarizability of the surface atoms of Graphon, due to some double bond character of the C-C bonds, leads to a greater contribution to the total adsorption energy by non-polar van der Waals forces. This difference in polarizability is evident too from the much lower heat of wetting of Teflon in the organic liquids when the only important interaction is the non-polar van der Waals type. I n addition, the contribution resulting from the interaction of a water dipole and its image force accounts for the higher heat of wetting of Graphon in water compared to Teflon. It is interesting to speculate on the nature of the hydrophilic heterogeneities present on the surface of Teflon. This material was coagulated from an aqueous suspension and possible surface impurities are surface active agents and fluoride salts. A calculation of the coulomb interaction of a water dipole oriented parallel to an isolated KF ion pair impurity leads to a heat of adsorption of 10.2 kcal./ mole if a distance of separation of the water dipole
THE ENERGETICS AND STATISTICAL MECHANICS OF THE KINETICS OF SOLID SOLID REACTIONS --f
BY R. S. BRADLEY Department of Inorganic and Structural Chemistry, University of Leeds, England Received August .Wf 1966
The kinetics of reconstructive solid + solid transformations are developed in terms of a vapor transition state. The application to experimental data, especially those observed near the transition temperature, is discussed in the light of current theories of crystal growth. A critical discussion is given of the difficulties in interpreting the temperature independent factor of solid -t solid reactions in terms of transition state theory and also those theories which rely on crystal imperfections,
I. Energetics The simplest way of leading up to the complexities of solid + solid reactions is to imagine that the conversion is brought about via the vapor phase in an enclosure which contains the two separate solids, so that the rate depends on the “affinity.”l If a, and a p are the evaporation coefficients, and p a and pa the saturation vapor pressures of the two solids a and p, of which the latter is unstable a t temperature T , then for equality of loss and gain of vapor where p is the vapor pressure in the vessel, k is the Boltzmann constant, m the molecular mass, and it is assumed that the solids have equal surface area exposed t o the vapor. It follows that P = (“,Pa
+
+ “8)
(2)
(1) De Donder and Van Rysselberghe, “Thermodynamic Theory of Affinity,” Stanford University, Stanford, Cal., 1936.
The rate of the solid 4 solid reaction in molecules cm.-2 sec.-l is therefore v
aa(p
- pa)/(’*
m
‘
+
‘)‘I2 = “ a a ~ ( ~-a P a ) / l ( e a CY@) ( 2 T m k T ) ‘ h ] (3)
‘If d is the density of the a phase the linear rate for this phase is vmld cm.sec.-’. To a first, and often very good, approximation p g = B f i e - E @ / ( R T ) , and p a = Bae-Ed(RT) ‘
(4)
where the B’s are so-called temperature independent factors (and are related to entropies of vaporization) and the E’s are latent heats of sublimation. Hence the rate of the solid + solid reaction is given by (5)
since -AG = RT In (pa/pa)
(6)
assuming that the vapors are perfect gases. Equation 5 holds whether or not there is a transi-
R. S. BRADLEY
1348
tion point. For enantiotropes AG = 0 at the transition temperature To, in agreement with equation 5. If this equation is rewritten in the form
Vol. SO
ture coefficient of v is very large near to Tosince then
since To - T
