Calculation of Normal Contact Forces between Silica Nanospheres

Abstract

In this work, interaction forces between two silica nanospheres after contact, including the van der Waals (vdW) attraction, Born repulsion, and mechanical contact forces are studied by molecular dynamics (MD) simulations. The effects of interaction path (approach or departure), initial relative velocity, and relative orientations of two nanospheres are first examined. The results show that the interparticle forces are, to a large degree, independent of these variables. Then, emphasis is given to other important variables. At a small contact deformation, the size dependence of the vdW attraction and Born repulsion qualitatively agrees with the prediction based on the conventional theories, but this becomes vague upon further deformation due to the gradually flattened shape of deformed particles. An alternative approach is provided to calculate the interparticle vdW attraction and Born repulsion forces. Moreover, the MD simulations show that the Hertz model still holds to describe the mechanical contact force at low compression, which is obtained by subtracting the vdW attraction and Born repulsion forces from the total normal force. Comparisons with the Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) models, in terms of force-displacement relationships and contact radius, show that the two models can be used to provide the first approximation, but there is some deviation from the MD simulated results. The origins of the quantitative difference are analyzed. New equations are formulated to estimate the interaction forces between silica nanospheres, which should be useful in the dynamic simulation of silica nanoparticle systems.

Reinforcing nanocolloidal crystals by tuning interparticle bonding via atomic layer deposition

“…Based on Eq. (3b) and H i = 30 MPa for the 289 nm NCC, the intrinsic shear resistance force of each NCJ is f i = 140 nN, suggesting capillary [48,49] and/or van der Waals forces [42][43][44][45]. In fact, Gallego-Gómez et al [7] found that a wet SiO 2 NCC is twice as hard as its dry counterpart, implying that the magnitudes of the capillary and van der Waals forces are similar for wet SiO 2 NCCs.…”

“…Fig. 4(b) shows that the pristine NCCs exhibit granular behavior: rigid-granule-like NCs are dislodged upon indentation, suggesting weak IPB, likely associated with van der Waals forces and/or capillary interactions [42][43][44][45]. Thus, although each SiO 2 NC is very hard and stiff, the as-assembled NCC is soft and compliant.…”

Interaction forces between carbon nanospheres: A molecular dynamics simulation study

“…Details can be found in our previous studies. For brevity, the major simulation procedures are as follows (Sun et al, 2013a(Sun et al, , 2013b:…”

“…On the other hand, it is known that the continuum models, developed at the macroscale (Feke et al, 1984;Hamaker, 1937;Johnson, 1985), cannot generally apply to nanoparticles due to the neglect of discrete atomic structure and surface effects (Bishop et al, 2009;Girifalco et al, 2000;Luan and Robbins, 2005). Recently, molecular dynamics (MD) simulation has been developed to calculate the interaction forces between α-quartz silica nanospheres, including the van der Waals (vdW) attraction, Born repulsion and mechanical contact forces during a normal impact (Sun et al, 2013a(Sun et al, , 2013bZeng et al, 2010). Such MD studies can help clarify a series of fundamental issues from atomic level.…”

A probabilistic model for predicting the uncertainties of the humid stiction phenomenon on hard materials

“…Besides those asperity models, the adhesive contact, due to vdW forces, between asperities has also been studying using molecular dynamics (MD) methods [8]. MD methods were also used to study the adhesive interactions due to vdW forces of silicon [9], silica [10], and silicon carbide [11] nano-particles. These studies have shown that the JKR and DMT models are valid up to given contact interference distances.…”