ever, most of the data obtained from direct force measure-An atomic force microscope (AFM) was used to measure surface ments are for symmetric interactions, i.e., two macroscopic forces between a glass sphere and a silica plate. When the measurebodies of the same hydrophobicity interact with each other, ments were conducted between untreated surfaces, a ''shortwhile bubbles and particles may have very different hydrorange'' hydration force with decay lengths of 0.4 and 3.0 nm was phobicities. Therefore, it is difficult to estimate the magniobserved. When the surfaces were hydrophobized with octadecyltudes of the hydrophobic forces involved in bubble-particle trichlorosilane (OTS), on the other hand, long-range hydrophobic interactions based on the force data reported in the literature forces with decay lengths in the range of 2-32 nm were observed.
to date.
The force measurements were conducted between surfaces having
Surface forces measured experimentally are routinely similar and dissimilar hydrophobicities so that the results may be used for deriving an empirical combining rule. It was found that compared with those predicted from the DLVO theory, the power law force constants for asymmetric interactions are close to the geometric means of those for symmetric interactions. Thus,
hydrophobic force constants can be combined in the same manner as the Hamaker constants. A plot of the power law force constants in which F t is the total force between two surfaces in close versus water contact angles suggests that the hydrophobic force proximity, F e is the ion-electrostatic force between the overis uniquely determined by contact angle. These results will be lapping electrical double layers, and F d is the London-van useful in predicting hydrophobic forces for asymmetric interacder Waals dispersion force. When hydrophobic forces F h are tions and in estimating hydrophobic forces from contact angles.