Reliable Measurements of Interfacial Slip by Colloid Probe Atomic Force Microscopy. I. Mathematical Modeling

Abstract

We developed a stable spread-sheet algorithm for the calculation of the hydrodynamic forces measured by colloid probe atomic force microscopy to be used in investigations of interfacial slip. The algorithm quantifies the effect on the slip hydrodynamic force for factors commonly encountered in experimental measurements such as nanoparticle contamination, nonconstant drag force due to cantilever bending that varies with different cantilevers, flattening of the microsphere, and calibration at large separations. We found that all of these experimental factors significantly affect the fitted slip length, approximately in the order listed. Our modeling is applied to fit new experimental data reproducibly. Using this new algorithm, it is shown that the fitting of hydrodynamic theories to experimental data is reliable and the fitted slip length is accurate. A "blind test" protocol was developed that produces a reliable estimate of the fitting error in the determination of both the slip length and spring constant. By this blind test, we estimate that our modeling determines the fitted slip length with an average systematic error of 2 nm and the fitted spring constant with a 3% error. Our exact calculation of the drag force may explain previous reports that the fitted slip length depends upon the shape and spring constant of the cantilever used to perform the measurements.

Boundary flow on end-grafted PEG brushes

“…Our group has recently dedicated significant attention to developing reliable and reproducible measurements and analysis of interfacial slip on rigid surfaces, [30][31][32][33] and here we expand this analysis to soft interfaces, presenting results which match well our molecular dynamic simulations on similar brush systems. 22 2 Experimental section…”

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path

“…Thanks to its simplicity, the model (5) finds broad application in the literature 6,10,12,26,[28][29][30][46][47][48] to extract the slip length λ s from experimental data. However, it is mostly employed in the limit k → 0, corresponding to equal slip lengths on both surfaces.…”

Casimir and hydrodynamic force influence on microelectromechanical system actuation in ambient conditions

“…Although other expressions for f à have been used in various studies depending on the nature of interacting surfaces, 17,[19][20][21][22][23][24][25] our tests indicated that the physical results remain qualitatively the same as those obtained with Eq. (2).…”

“…In different experiments for a sphere of radius R ¼ 10 lm the slip lengths in air were found to be b ¼ 23, 48, 80, and 98 nm, while for a larger sphere with R ¼ 50 lm were b ¼ 100 and 120 nm. 17,20,24,25 In any case, the force model for F h z ð Þ is valid for low Reynolds numbers (Re < 1) and short distances so that z ( R. 17,19 Here the mean Reynolds number Rehdz=dtið2RÞ= has values Re $ 0.005-0.07 for R ¼ 10-50 lm where % 15.68 Â 10 À6 m 2 /s is the kinematic viscosity of air and hdz/dti $ (2-3)10 À3 m/s is the mean velocity of the sphere (e.g., see Fig. 2).…”