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International Journal of Fracture

, Volume 208, Issue 1–2, pp 131–143 | Cite as

Multi-scale model of effects of roughness on the cohesive strength of self-assembled monolayers

  • Chen Zhang
  • Amnaya P. Awasthi
  • Jeauk Sung
  • Philippe H. GeubelleEmail author
  • Nancy R. Sottos
IUTAM Baltimore
  • 249 Downloads

Abstract

Self-assembled monolayers (SAMs) are aggregates of small molecular chains that form highly ordered assemblies at the nanoscale. They are excellent contenders of molecular-level tailoring of interfaces because of the wide choice of terminal groups. Molecular dynamics (MD) simulations and experimental observations of spallation of two SAM-enhanced gold-film/fused silica-substrate interfaces have shown that the cohesive strength of SAM-enriched transfer-printed interfaces is strongly dependent on the choice of terminal groups. Though the MD results of perfectly ordered atomistic surfaces show the same qualitative trend as the experiments, they over-predict the interfacial cohesive strengths by a factor of about 50. Previous studies have revealed that the roughness of these interfaces may significantly impact their cohesive strength. In this manuscript, we perform a multiscale study to investigate the influence of surface roughness on cohesive strength of an interface between a Si/SAM substrate and a transfer-printed gold film. We approximate the film as a 2D deformable medium while the rough SAM-enhanced substrate is modeled using 2D harmonic functions with the cohesive interaction between the SAM and the film described by a simple exponential relation. Spallation is simulated on this system to evaluate the effective traction-separation response for the rough SAM-gold interface. Beyond the idealized harmonic interface, we extend our studies to real surface profiles obtained by AFM. We demonstrate how interfacial roughness can reduce the cohesive strength of the SAM-enhanced interface by more than an order of magnitude.

Keywords

Self-assembled monolayers Nano-scale interfacial roughness Cohesive model Thin films Spallation Interfacial strength 

List of symbols

A

Amplitude of idealized surface roughness represented by a 2D harmonic function

D

Distance of a point to the peak of surface

E

Young’s modulus of the thin film

\(E_b\)

Bending energy stored in the film due to initial deformation after being transfer-printed onto the roughness substrate

\(\widetilde{E}_b\)

The ratio of bending energy to the interface cohesive energy

\(E_c\)

Interface cohesive energy

\(\widetilde{E}_c\)

The ratio of interface cohesive energy of the thin film on a rough substrate to the cohesive energy of a flat interface

e

exp(1)

H

Thickness of the thin film

h

Distance between a point on the surface and the bottom of the surface

\(h_{max}\)

Maximum height of the surface

\(h_{min}\)

Minimum height of the surface

\(K_n\)

Penalty parameter for the compressive force between the thin film and substrate

\(L_i\)

Wavelength in \(x_i(i=1,2)\) direction of the surface

\(S_r\)

Surface bearing ratio

T

The traction on the thin film due to the interaction between the film and the substrate

\(\overline{T}\)

Effective cohesive traction with respect to \(\sigma _c\)

\(\overline{T}^R\)

Effective cohesive traction with respect to \(\sigma _c\) for the thin film with infinite rigidity

\(\overline{T}_{max}\)

Maximum effective cohesive traction with respect to \(\sigma _c\)

\(T_a\)

Attractive cohesive force between thin film and substrate

\(T_c\)

Compressive cohesive force between thin film and substrate

w

Displacement of a point on the surface after initial deformation

\(\widetilde{w}\)

\(\tfrac{w}{A}\)

\(x_i\)

Position of a point on the surface in \(L_i(i=1,2)\) direction

\(\widetilde{x}_i\)

\(\tfrac{x_i}{L_i}(i=1,2)\)

\(\beta \)

Non-dimensional parameter, which considers mechanical properties of the thin film, cohesive response of the interface, and wavelength in the substrate

\(\delta \)

Uniform separation of the thin film

\(\widetilde{\delta }\)

\(\tfrac{\delta }{A}\)

\(\delta _c\)

Critical separation of the interface

\(\delta _i\)

Separation between a point on the substrate and the thin film

\(\widetilde{\delta }_i\)

\(\tfrac{\delta _i}{A}\)

\(\eta \)

Non-dimensional parameter, which considers the amplitude of the surface roughness to \(\delta _c\)

\(\nu \)

Poisson’s ratio of the thin film

\(\xi \)

The ratio of wavelength in the two directions of the substrate \(\dfrac{L_2}{L_1}\)

\(\sigma _c\)

Maximum cohesive force of a flat interface

Notes

Acknowledgements

The financial support of the National Science Foundation (Award Number 1161517) is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringUniversity of Illinois at Urbana-ChampaignChampaignUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Materials Science and EngineeringUniversity of Illinois at Urbana-ChampaignChampaignUSA

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