Rupture of molecular thin films observed in atomic force microscopy. I. Theory

Abstract

In atomic force microscope studies of molecular thin films, a defined jump of the tip through the film is often observed once a certain threshold force has been exceeded. Here, we present a theory to describe this film rupture and to relate microscopic parameters to measurable quantities. We assume that the tip has to overcome an activation energy before the film ruptures. A universal relation between the force dependence of the activation energy and the approaching velocity of the tip is derived. Two complementary models for calculating the activation energy are presented: a continuum nucleation model and a discrete molecular model. Both models predict a narrow distribution of yield forces in agreement with experimental results.

Mechanical Criterion for the Rupture of a Cell Membrane under Compression

“…Their results corresponded to a typical compressive stress for membrane rupture on the order of 3-6 kPa, again in reasonable agreement with the order of magnitude of the critical stress reported here (41). Rupturing lipid bilayers by compressing them with an AFM tip, Loi et al measured forces ranging from 2 to 12 nN for tip radii ranging between 26 and 86 nm (42,43). As their force curves imply a penetration of the AFM tip of a few nanometers, one can postulate that Eq.…”

“…However, unlike micropipette experiments, in our work the membrane is confined between the indenter and the substrate. Our setup thus resembles the configuration investigated by Butt et al, who investigated, both experimentally and theoretically, the rupture of a supported lipid bilayer compressed by an AFM tip (42,43). Following a reasoning similar to that of Butt et al, rupture occurs when release of the elastic energy stored in the indenter suffices to dislodge a sufficiently large number of membrane lipid molecules to nucleate a hole.…”

“…In another study using nanoneedle geometries, Xie et al (46,47) investigated the penetration of nanowires fixed to a substrate into cells that adhere to this substrate. They used a cell membrane rupture criterion based on activation energy theory and leading to a critical membrane tension to be reached before rupture (42,44). In the study of Xie et al, tensile forces of~1 nN are applied to the tips of nanowires of radius R ¼ 50 nm.…”

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…32). Such jumps were observed on a number of different bilayers [728,730,753,755,[769][770][771][772][773]. In a series of papers Schneider, Dufrêne, Lee et al [728,730,769] studied the influence of the tip chemistry on the tip-lipid bilayer interaction.…”

“…The aim of any theory of the jump-in is to calculate this distribution of yield forces and relate microscopic parameters to measurable quantities. Therefore, rupture of the layer can be described as an activated process [753]. An energy barrier has to be overcome for the formation of a hole in the layer, which is large enough to initiate tip penetration.…”