Nanoadhesion of elastic bodies: Roughness and temperature effects

Abstract

We present a simple model which illustrates the nature of the contact between an elastic solid and a hard surface with cosine-corrugation profile. In the continuum limit, the contact mechanics depends only on two dimensionless parameters, namely the ratio between the height and wavelength of the substrate corrugation, and the ratio between a surface energy and an elastic energy. The theory shows that the complete contact state is always a local energy minima ͑in the zero temperature limit͒, but for large enough surface roughness the global minima correspond to a partial contact state. We show that at nonzero temperature, the contribution to the free energy from the vibrational entropy is very important, and favors the detached state. Computer simulations results are also presented where we study more complicated roughness geometries and the influence of temperature on the adhesion. Simulation results agrees well with the analytical predictions.

Analytical solution of adhesion contact for a rigid sinusoidal surface on a semi-infinite elastic body

“…We have confirmed our results with the total energy calculated by Zilberman and Persson's equation [4] and the equilibrium condition calculated by Johnson's equation [2]. It is shown that our results conform to those of Zilberman and In Fig.…”

“…In the case of a rigid body in contact with an elastic body, the elastic modulus, * E is given by The net surface displacement on the elastic body within the contact region is given by [3], [4]…”

“…Zilberman and Persson [3,4] investigated an adhesion contact of a largely wavy surface and solved it numerically. They considered the curvature rather than the straight line of the contact area in the calculation of interfacial term of the total energy.…”

“…Considering the limitations of the work of Johnson [2] and Zilberman and Persson [3,4], the present work is intended to obtain an analytical solution for an equilibrium condition of the system for combination of their works under zero external pressure. In addition, the effect of the thermodynamic work of adhesion as well as the effect of the surface roughness on the system is investigated.…”

Quantum Size Effects Induced Novel Properties in Two-Dimensional Electronic Systems: Pb Thin Films on Si(111)

“…57) An important factor influencing the measurement of adhesive force is the surface roughness, as discussed in the previous theoretical and experimental works. [150][151][152][153][154][155] When two rough surfaces are brought into contact, the real contact can happen only on the protruding points of the interface. That is, the real area of contact can be decreased as a result of surface roughness, which subsequently decreases the adhesive force.…”