Determination of solid surface tension at the nano-scale using atomic force microscopy

Engineered surfaces, such as thin inorganic or organic films, self-assembled organic monolayers and chemically-modified polymeric surfaces, cannot be melted, dissolved, or fractured; therefore, their surface/interfacial tension (gamma) cannot be determined using conventional surface tension measurement techniques. New surface tension characterization methods need to be developed. Atomic force microscopy (AFM) is capable of solid surface characterization at the microscopic and sub-microscopic scales. As demonstrated in several laboratories in recent years, and reviewed in this paper, it can also be used for the determination of surface tension of solids from pull-off force measurements. Although a majority of the literature gamma results were obtained using either Johnson-Kendall-Roberts (JKR) or Derjaguin-Muller-Toporov (DMT) models, a re-analysis of the published experimental data presented in this paper indicates that these models are often misused and/or should be replaced with the Maugis-Dugdale (MD) model. Additionally, surface imperfections in terms of roughness and heterogeneity that influence the pull-off force are analyzed based on contact mechanics models. Simple correlations are proposed that could guide in the selection and preparation of AFM probes and substrates for gamma determination. Finally, the possibility of AFM measurements of solid surface tension using real-world materials is discussed.