Probing the validity of the Derjaguin approximation for heterogeneous colloidal particles

Abstract

The Derjaguin approximation states that the interaction force between two curved surfaces is proportional to their effective radius, whereby the inverse effective radius is the arithmetic mean of the inverse curvature radii of the surfaces involved. The present study investigates the validity of this approximation with an atomic force microscope (AFM) by measuring interaction forces between colloidal particles of different sizes, but of identical composition. Forces were measured between silica particles of 2.0, 4.8 and 6.8 mm in diameter in KCl electrolyte solution with and without adsorbed poly(amido amine) (PAMAM) dendrimers. The Derjaguin approximation could be confirmed at all distances investigated, including those comparable with the characteristic length scales of the surface roughness or the surface charge heterogeneities. For the conditions investigated, the Derjaguin approximation turns out to be surprisingly robust.

Dispersion forces acting between silica particles across water: influence of nanoscale roughness

“…The very small Hamaker constant for the untreated particles rationalizes the absence of dispersion forces reported by some authors. [22][23][24] Such weak dispersion forces could have simply remained undetected given an inferior force resolution in the previous studies to the one achieved here. Forces between the same silica particles heated at 1050 1C were investigated earlier.…”

“…The fact that forces between silica surfaces across water can be well described by DLVO theory may seem surprising, especially since some authors even claimed that dispersion forces are absent in such systems. [22][23][24] The reason for this unexpected behavior becomes obvious when one compares the force profiles for heat-treated particles with the untreated ones in 1.0 M KCl solution. In this medium, only dispersion forces contribute and the force profiles will not be influenced by different surface charge densities, which might have been induced by the different heat-treatments used.…”

“…20,21 Some studies even remark the absence dispersion forces altogether. [22][23][24] No satisfactory explanation of these discrepancies has been put forward so far. Given the widespread use of silica substrates in contact with water, a clarification of this discrepancy is imperative.…”

Numerical and experimental analysis of the sedimentation of spherical colloidal suspensions under centrifugal force

“…Equation (13) is constructed on the basis of Derjaguin's approximation, which has been shown to be valid for spherical colloidal particles. 39 Derjaguin's approximation requires s 0.5d, which is satisfied here since DLVO theory is only used to identify the minimum separation distance of colloidal particles. γ is given by 38…”

Micromechanical characterization of spider silk particles

“…11,12 In particular, a colloidal probe (CP) technique offers a valuable means of studying particle mechanics on a single particle level as well as surface interaction forces. [13][14][15] In biological investigations CP-AFM is even employed to analyze the stiffness and deformation behavior of entire cells. 16 Here, we investigated the swelling behavior of dried eADF4-(C16) particles upon hydration and their mechanical properties in the dry and wet state.…”