Reliable measurement of slip using colloid probe atomic force microscopy

Abstract

Recent research has shown that Newtonian liquids can slip at solid surfaces in confined geometries, which contradicts the classical no-slip boundary condition in which the liquid is stationary at the solid surface. The study of liquid boundary conditions that provides a fundamental understanding of the physics of liquid flow in confined geometries, such as in porous media, and also could benefit various commercial applications, such as micro and nanofluidic applications. The aim of our work was to build a reliable experimental and theoretical framework to investigate liquids slip on solid surfaces by colloid probe atomic force microscopy (AFM). Colloid probe AFM provides an accurate way to study slip at a solid surface by measuring the hydrodynamic drainage force between a colloid probe and a solid substrate as the two surfaces approach to contact. In our studies, we have investigated the slip of a one-component viscous liquid (di-n-octylphthalate) on bare silicon substrates and hydrophobised silicon substrates. In order to obtain reliable slip results, we solved experimental problems in previously published experiments and improved the theoretical modeling which affects the reliability and accuracy of the measured slip lengths. In the new improved experimental protocol we used a closed loop scanner to produce a constant driving velocity, minimised the virtual deflection due to top-scan AFM by removing a constant slope in the force curve, and clarified the true compliance and zero separation in the force curve. The need for tight control over experimental conditions in slip measurements was highlighted, such as extremely careful surface cleaning, the use of a one-component liquid, continuous monitoring of the liquid temperature, and repeat measurements in different locations of the substrate. By performing slip measurements in symmetric and asymmetric systems, a new method was developed to self-assess the accuracy and reproducibility of the slip force measurements. A new mathematical algorithm was built to predict the hydrodynamic drainage force independently of experimental data. This new mathematical algorithm reduced the noise greatly in the theoretical forces over that in the previous treatments; it was demonstrated by blind test that this new calculation method provides reproducible and reliable slip length values and spring constant values with the uncertainty within 3%. The new mathematical algorithm can be easily applied to simulate slip lengths and hydrodynamic forces in different experimental conditions, such as the presence of nanoparticle contamination on the substrate surface and the flattening of the colloid probe, which were both demonstrated to affect the measured slip lengths. The exact variable drag force on soft cantilevers was calculated for the first time and applied to fit the experimental force. This calculation revealed that the dependence of slip on the driving velocity and the cantilever shape found in literature could be a spurious effect due to the assumption that the drag force on the cantilever is constant during force measurements. In our studies, it was also shown that the measured slip length actually decreases with increasing shear rate, rather than being a constant value as commonly assumed. A new shear dependent model for slip fitted well experimental hydrodynamic forces for all separations down to a few nanometres. A possible molecular explanation was proposed for the mechanism of shear rate dependent slip in our experiments.