Elastic moduli in monolayers

Abstract

The surface elastic moduli are the two-dimensional analogs of the elastic moduli in three dimensions. Experimental methods are reviewed briefly, and it is shown that Fourt's "elasticity index" for an oscillating vane or needle is dimensionally incorrect, whereas the formula proposed by Trapeznikov for an oscillating disk or ring is correct and can be derived exactly by regarding the film as an elastic annulus sheared in its own plane. A dimensionally correct formula is proposed for an oscillating needle as well as for an aperiodic needle type surface torsion pendulum. The relationships between the four two-dimensional elastic constants of homogeneous isotropic films are derived and are shown to be different from the three-dimensional formulas. The maximal value of the surface Poisson's ratio is unity instead of one half.

Additional details