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Surface Forces
Published in Arthur T. Hubbard, The Handbook of Surface Imaging and Visualization, 2022
Using the Derjaguin approximation, Equation 58.6, we may immediately write the expression for the force F between two spheres of radius R as F = πRE, from which the double-layer interaction free energy between two spheres is obtained by integration as: () W=4.61×10–11Rtanh[Ψ0(mV/103)]e-kDJ(for1:1electrolytes)
Surface Forces and Adhesion
Published in Bharat Bhushan, Handbook of Micro/Nano Tribology, 2020
Nancy A. Burnham, Andrzej J. Kulik
The Derjaguin approximation is a useful method by which to arrive at a force law for the sphere—flat geometry. It states that if the interaction energy per unit area, ϖ, as a function of separation for two semi-infinite parallel planes is known, then the force law for a sphere near a flat surface becomes F(δ)sphere−flat=2πRϖ(δ)planes.
Nanoscale Charge Nonuniformity on Colloidal Particles
Published in Stoyl P. Stoylov, Maria V. Stoimenova, Molecular and Colloidal Electro-Optics, 2016
The interparticle potential of mean force (Φ) is commonly given by the DLVO model, which accounts for electrostatic forces (usually repulsive) and van der Waals forces (usually attractive). A model is developed for the potential of mean force between two flat plates, and then the Derjaguin approximation is used to evaluate the potential of mean force. Hogg et al. showed that for low potentials one obtains approximately the following for the electrostatic potential (ΦES) between identical spheres ΦES=2πεaψ02e−κδ
Interactions between apolar, basic and acidic model oils and a calcite surface
Published in Journal of Dispersion Science and Technology, 2019
Xiaoyan Liu, Karen L. Feilberg, Wei Yan, Erling H. Stenby, Esben Thormann
The force versus separation between model oil probes and the calcite surface were measured using a NanoWizard 3 AFM (JPK Instrument, Germany). Before each experiment, the cantilever holder, O-rings and all other tools were cleaned by immersion in 2% Hellmanex (Hellma GmbH, Germany) solution for approximately 1 hour, followed by rinsing several times with plenty of Milli-Q water and then blow-drying with compressed air. The surface forces between the different surface pairs, apolar model oil-calcite, basic model oil-calcite and acidic model oil-calcite, were measured in the aqueous salt solutions and 200 force curves were recorded at a regular spacing over a 2 × 2 μm2 area for each condition. All surface force measurements were executed at a constant approach and separation speed of 0.5 μm/s, and the reported forces were normalized by the probe radius, F/R, according to the Derjaguin approximation. Tapping mode images of the calcite surface were obtained with air using a rectangular silicon cantilever (NSC15/Al BS, Mikromasch, Germany) and a scan rate of 0.3 Hz per line. To characterize the silica probe, it was first glued on a tipless cantilever; and then ‘reverse imaged’ by contact mode using a PA01 grating (Mikromasch, Germany) and a scan rate of 1 Hz per line. The JPK SPM data processing software was employed to analyze the recorded images.
Nanoparticle–membrane interactions
Published in Journal of Experimental Nanoscience, 2018
Claudia Contini, Matthew Schneemilch, Simon Gaisford, Nick Quirke
The adhesion energy per unit area, estimated from the maximum attractive force within the Derjaguin approximation [90], was 0.5 and 1 mN⋅m−1 for the vesicle fusion and Langmuir–Blodgett deposition SLB, respectively.