J.
1270
Phys. Chem. 1982, 86, 1270-1277
the sign of APLs is of higher interest than ita accurate numerical value, this assumption ought to be acceptable. It is apparent that APLScan be positive as well as negative (the negative values of the Hamaker coefficients indicate repulsion). It is therefore clear that repulsive van der Waals interactions are by no means rare and unusual occurrences. It is also clear that there is a close relation between the AF,, data and the APLsvalues of Table I. It is seen from eq 1 and 2 that
AP* = mnet - YSL
Finally, the question needs to be answered under what circumstances the individual Hamaker coefficients Aij add up to repulsive or attractive van der Waals forces, i.e., negative or positive effective Hamaker coefficients A132. Calculations of AF132'* from contact angles and surface tensions reveal13 that A132 (20) for
'
(19)
As is proportional to APm, the essential difference between the two approaches centers around the solid/ liquid interfacial tension ysL. For most of the systems considered in this study ysL is very small, so that the predictions for the particle behavior on the basis of AFn, and A p u are virtually the same. The largest value of solid-liquid interfacial tension occur'^ for naphthalene' (ysL = 1.44 erg/cm2) which makes, in the case of naphthalene/Nylon-6,12, Apm > 0 in spite of the fact that Mnet > 0. The experimental observation is, suprisiily, "rejectionn, because mechanistically, if adhesion occurs, engulfing of the particle should ensue. As the particles are irregularly shaped, it is conceivable that adhesive contact is established only a t a few points and that, as the further steps of engulfment are not favored thermodynamically, convection in the liquid may be able to break the adhesive bonds, thus preventing engulfment. Although the observation is clear-cut, it nevertheless represents only one particular system. Clearly, an in depth study of this problem is required.
All > A33, A22 > A33
(21)
< A339 A22 < A33
(22)
< A33 < A22
(23)
< Y2V
(24)
as well as for All
For All
and hence for YN
73V
it follows that
