Contact of Single Asperities with Varying Adhesion: Comparing Continuum Mechanics to Atomistic Simulations

Atomistic simulations are used to test the equations of continuum contact mechanics in nanometer scale contacts. Nominally spherical tips, made by bending crystals or cutting crystalline or amorphous solids, are pressed into a flat, elastic substrate. The normal displacement, contact radius, stress distribution, friction and lateral stiffness are examined as a function of load and adhesion. The atomic scale roughness present on any tip made of discrete atoms is shown to have profound effects on the results. Contact areas, local stresses, and the work of adhesion change by factors of two to four, and the friction and lateral stiffness vary by orders of magnitude. The microscopic factors responsible for these changes are discussed. The results are also used to test methods for analyzing experimental data with continuum theory to determine information, such as contact area, that can not be measured directly in nanometer scale contacts. Even when the data appear to be fit by continuum theory, extracted quantities can differ substantially from their true values

Slippery nanoworld

Quantum Matter and Optic

Thermodynamics of ferrofluids in applied magnetic fields

The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B2 and B3) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B3 for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ≤2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust. © 2013 American Physical Society

Pair Correlations in a Bidisperse Ferrofluid in an External Magnetic Field:Theory and Computer Simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole–dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole–dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation func-tion g(r) – 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small[1]angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional com-position of a ferrofluid, interparticle correlations, and external magnetic field. © Pleiades Publishing, Inc., 2014

Ripple formation induced in localized abrasion

The formation of nanometer-scale patterns while scratching a KBr(001) surface with a scanning force microscope in ultrahigh vacuum is reported. Wear of single atomic layers has been observed when the microscope tip is repeatedly scanned across a line. The initially flat surface is rearranged in a quasiperiodic pattern of mounds and pits. The distance between the pits is about 40 nm when normal forces of a few nanonewtons are applied, and it slowly increases with the load. If a square area is scanned, a pattern of ripples is formed. These features can be interpreted within an erosion process induced by a periodic increase of the strain produced by the scanning tip