Quantitative surface free energy with micro-colloid probe pairs

Measurement of the surface free energy (SFE) of a material allows the prediction of its adhesion properties. Materials can have microscale or sub-microscale surface inhomogeneities, engineered or random, which affect the surface macroscopic behaviour. However, quantitative characterization of the SFE at such length scales remains challenging in view of the variety of instruments and techniques available, the poor knowledge of critical variables and parameters during measurements and the need for appropriate contact models to derive the SFE from the measurements. Failure to characterize adhesion correctly may result in defective components or lengthy process optimization costing billions to industry. Conversely, for planar and homogeneous surfaces, contact angle (CA) measurements are standardized and allow for calculating the SFE using for example the Owen–Wendt model, relying only on the properties of the probing liquids. As such, we assessed and report here a method to correlate quantitative measurements of force–distance curves made with an atomic force microscope (AFM) and with silica and polystyrene (PS) colloidal probe pairs, with quantitative CA measurements and CA-derived SFE values. We measured five surfaces (mica, highly oriented pyrolytic graphite, thermally grown silica on silicon, silicon, and silicon with a super-hydrophobic coating), ranging from hydrophilic to super-hydrophobic, and found an excellent classification of the AFM measurements when these are represented by a set of principal components (PCs), and when both silica and PS colloidal probes are considered together. A regression of the PCs onto the CA measurements allows recovery of the SFE at the length scale of the colloidal probes, which is here ca. 1 micron. We found that once the PC-regression model is built, test sets of only ten AFM force–distance curves are sufficient to predict the local SFE with the calibrated silica and PS colloidal probes.