Quantification of the interactions between nanoparticles is important in understanding their dynamic behaviors and many related phenomena. In this study, molecular dynamics simulation is used to calculate the interaction potentials (i.e., van der Waals attraction, Born repulsion, and electrostatic interaction) between two silica nanospheres of equal radius in the range of 0.975 to 5.137 nm. The results are compared with those obtained from the conventional Hamaker approach, leading to the development of modified formulas to calculate the van der Waals attraction and Born repulsion between nanospheres, respectively. Moreover, Coulomb's law is found to be valid for calculating the electrostatic potential between nanospheres. The developed formulas should be useful in the study of the dynamic behaviors of nanoparticle systems under different conditions.

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.

The rich behaviors of high-speed mechanical contacts at the nanoscale have been studied. The seldom observed elastic-plastic transition governed by Hertz and Thornton models has been clearly unveiled, the origins of the hardening effect and the deformation mechanism of nanoscale plasticity have been discussed in terms of structural changes after compression and a series of physical quantities are measured including contact forces, contact radius, contact stress, coefficient of restitution and total impact time. Our simulation results closely resemble experiments and/or theoretical predictions: (i) when impact speed v is higher than Y/ρc0, the elastic-plastic deformation transition occurs, (ii) the yielded apparent elastic modulus and hardness are larger than those of the bulk, (iii) the initiating yield stress Y and hardness P0 still satisfy P0 ≈ 1.6Y, (iv) particle's volume decreases during compression, (v) contact radius a follows a [proportionality] v(2/5), (vi) at v ≥ 2000 m s(-1), the coefficient of restitution follows e [proportionality] v(-1/4) and (vii) the total time of impact follows Tc [proportionality] v(-1/5). However, there also exist many quantitative differences. The contact radius and final contact radius are underestimated by the continuum predictions while the total impact time is overestimated, but all of them reasonably agree with theoretical predictions with an increase of contact area and impact speed. The theoretical equation is adapted to predict the final contact radius during normal impact, in which the contact radius at zero load is also formulated.

Due to the breakdown of Derjaguin approximation at the nanoscale level apart from the neglect of the atomic discrete structure, the underestimated number density of atoms, and surface effects, the continuum Hamaker model does not hold to describe interactions between a spherical nanoparticle and a flat surface. In this work, the interaction forces including van der Waals (vdW) attraction, Born repulsion and mechanical contact forces between a spherical nanoparticle and a flat substrate have been studied using molecular dynamic (MD) simulations. The MD simulated results are compared with the Hamaker approach and it is found that the force ratios for one nanosphere interacting with a flat surface are different from those for two interacting nanospheres, both qualitatively and quantitatively. Thus two separate formulas have been proposed to estimate the vdW attraction and Born repulsion forces between a nanosphere and a flat surface. Besides, it is revealed that the mechanical contact forces between a spherical nanoparticle and a flat surface still can be described by the continuum Hertz model.