Direct and quantitative AFM measurements of the concentration and temperature dependence of the hydrophobic force law at nanoscopic contacts.

By virtue of its importance for self-organization of biological matter the hydrophobic force law and the range of hydrophobic interactions (HI) have been debated extensively over the last 40 years. Here, we directly measure and quantify the hydrophobic force-distance law over large temperature and concentration ranges. In particular, we study the HI between molecularly smooth hydrophobic self-assembled monolayers, and similarly modified gold-coated AFM tips (radii∼8-50 nm). We present quantitative and direct evidence that the hydrophobic force is both long-ranged and exponential down to distances of about 1-2 nm. Therefore, we introduce a self-consistent radius-normalization for atomic force microscopy data. This approach allows quantitative data fitting of AFM-based experimental data to the recently proposed Hydra-model. With a statistical significance of r(2)⩾0.96 our fitting and data directly reveal an exponential HI decay length of 7.2±1.2 Å that is independent of the salt concentration up to 750 mM. As such, electrostatic screening does not have a significant influence on the HI in electrolyte concentrations ranging from 1 mM to 750 mM. In 1 M solutions the observed instability during approach shifts to longer distances, indicating ion correlation/adsorption effects at high salt concentrations. With increasing temperature the magnitude of HI decreases monotonically, while the range increases slightly. We compare our results to the large body of available literature, and shed new light into range and magnitude of hydrophobic interactions at very close distances and over wide temperature and concentration regimes.