On the modified Tabor parameter for the JKR–DMT transition in the presence of a liquid meniscus

Abstract

The JKR, DMT, Maugis models and Tabor parameter for contact under normal loading have been developed based mainly on solid-solid (van der Waals) interactions. In this case, the characteristic length scale for the adhesive forces in the Tabor parameter is the equilibrium interatomic spacing. However, for contact in humid environments, where a liquid meniscus may be present, capillary forces with a longer force range related to the Kelvin radius dominate. Fogden and White [J. Colloid Interface Sci. 138 (1990) 414] introduced a parameter that includes the Kelvin radius for the JKR-DMT transition. This topic was also addressed by Maugis and Gauthier-Manuel [J. Adhes. Sci. Technol. 8 (1994) 1311] who included capillary effects within the frame work that Maugis had previously established. The parameters introduced by Fogden and White and Maugis and Gauthier-Manuel can be viewed as a modified Tabor parameter for the JKR-DMT transition. In the present work, the Kelvin equation linking the Kelvin radius and the relative humidity was explicitly included in the modified Tabor parameter. This provided a quantitative description of the JKR-DMT transition in terms of the relative humidity. This parameter was examined via load and contact radius measurements, where the latter were obtained from Bowden and Tabor's assumption that the friction force f=tauA. The friction experiments were conducted at two different humidity levels using a newly-developed mesoscale friction tester (MFT), which provides a very wide range of contact radii. The modified Tabor parameter was used to reexamine data from pull-off experiments in water and cyclohexane vapor environments [L.R. Fisher, J.N. Israelachvili, Colloids Surf. 3 (1981) 303 and H.K. Christenson, J. Colloid Interface Sci. 121 (1988) 170]. Finally, guidelines are presented for the appropriate choice of contact mechanics models to be used in interpreting data from SFA and AFM experiments in humid environments.