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TECHNICAL PAPERS

# A Hybrid Continuum-Molecular Analysis of Interfacial Force Microscope Experiments on a Self-Assembled Monolayer

[+] Author and Article Information
Mingji Wang, Kenneth M. Liechti

Center for the Mechanics of Solids, Structures and Materials,Department of Aerospace Engineering and Engineering Mechanics

Vibha Srinivasan

Institute for Theoretical Chemistry

John M. White

Center for Nanomolecular Science and Technology

Peter J. Rossky

Institute for Theoretical Chemistry, The University of Texas, Austin, TX 78712

Matthew T. Stone

Exxon Mobil Upstream Research Company, Houston, TX 77252-2189

DḺPOLY 2.0 package was developed at Daresbury Laboratory, U.K. and is available free, under license, to academic institutions on a worldwide basis 28.

J. Appl. Mech 73(5), 769-777 (Nov 24, 2004) (9 pages) doi:10.1115/1.1943435 History: Received May 24, 2004; Revised November 24, 2004

## Abstract

Nanoindentation experiments were performed on a defect-free, molecular self-assembled monolayer of octadecyltrichlorosilane (OTS) on silicon using an interfacial force microscope (IFM). The IFM provided repeatable and elastic force profiles corresponding to the adhesive and compressive response of these $2.5nm$ thick monolayers. As a first step in the analysis of the force profiles, the OTS was assumed to be linearly elastic and isotropic, and adhesive interactions were accounted for via a cohesive zone model. However, the assumption of linearity gave rise to force profiles that did not match the measurements. As a result, the mechanical behavior of the OTS was extracted from molecular-dynamics simulations and represented as a hypoelastic material, which, when used in finite element analyses of the IFM experiments, was able to fully reproduce the force profiles. This suggests that the continuum representation of the mechanical and adhesive behavior of self-assembled monolayers may be directly obtained from molecular analyses.

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## Figures

Figure 1

Figure 2

(a) Cohesive zone model geometry showing the contact radius a, cohesive zone size (c−a) and the normal traction and separation σ and δ between the surfaces and (b) a triangular traction-separation law specifying σ(δ)

Figure 3

(a) A three-dimensional representation of the atomic structure of silica terminated with hydroxyl groups (O is red, Si is yellow, and H is white.); (b) plan view, (29); and (c) molecular dynamics simulation cell for OTS on silica—the small solid circles represent oxygen atoms, large solid circles represent silicon atoms on lower plane, and the remaining open circles represent the silicon atoms with OTS molecules on them

Figure 4

FEM analysis of IFM experiments on OTS with different Poisson’s ratio for OTS: (a) νOTS=0.0 and (b) νOTS=0.44. The insets show the disagreement between measurements and analyses at low force levels.

Figure 5

Comparison of the stress-strain (nominal) behavior of OTS from the molecular dynamics simulation and the hypoelastic model: (a) low stress, (b) full range

Figure 6

Derivation of nonlinear material properties based on a uniaxial strain state: (a) tangent modulus, (b) tangent Poisson’s ratio

Figure 7

Nonlinear finite element analysis of the IFM experiment on OTS

Figure 8

Contact radii from classical contact mechanics and finite element analyses of an IFM probing of an OTS monolayer

## Errata

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