Optimizing the methodology for accurate and accessible slip length measurement with atomic force microscopy

The remarkable performance of cooling devices employing nano- and microscale channels has drawn considerable interest, highlighting the need for surfaces with large slip lengths to improve their efficiency. However, the large errors in slip length associated with existing techniques hinder a clear understanding of slip phenomena. In this paper, we evaluate existing analytical methods for slip length measurement with atomic force microscopy (AFM) and propose a new reliable method. We performed force curve measurements on mica, silica and highly ordered pyrolytic graphite surfaces in water using an AFM equipped with a colloidal probe. The obtained force curves were analyzed through three methods: two commonly utilized procedures, namely the recursive and intercept methods, and a novel one called the two-parameter method which we developed. Our analyses showed that the recursive method yielded slip lengths with relatively large errors, fluctuation of ±5.8 nm, which were due to inaccuracies in the cantilever's spring constant and the fluid viscosity. On the other hand, it was found that the intercept method leads to restrictions on the choice of fitting range because of the simplified formula for viscous drag. As a result, by altering the data range, the calculated slip length shows significant variations within the ranges of ±27.5 nm. The two-parameter method, unlike the standard ones, overcome these drawbacks. This method requires no pre-measured parameters, and the slip length fluctuation is independent of the fitting range and only ±3.6 nm, which is around 2/3 of that observed in the recursive method and 1/8 of that in the intercept method. Our study optimizes existing analytical protocols and offers a new way for accessible and reliable calculations of slip lengths.