ADHESIVE CONTACT MODELLING BASED ON LENNARD-JONES FORCE LAW
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2015-10-11 |
| Journal | Jurnal Teknologi |
| Authors | W.G. Lee, William Woei Fong Chong |
| Institutions | University of Southampton Malaysia |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Diamond Substrates for Nanoscale Adhesion Studies
Section titled âTechnical Documentation & Analysis: Diamond Substrates for Nanoscale Adhesion StudiesâThis document analyzes the research on adhesive contact modeling using the Lennard-Jones force law, focusing on the critical role of the Diamond (111) substrate. This application falls directly within 6CCVDâs expertise in providing high-precision, single-crystal diamond materials for advanced tribology and nanomechanics research.
Executive Summary
Section titled âExecutive SummaryâThe analyzed research validates a numerical model for predicting nanoscale adhesive forces, a critical requirement for advancing miniaturized systems (MEMS/NEMS) and tribology.
- Core Application: Simulation of Atomic Force Microscopy (AFM) indentation and pull-off force measurement between a Tungsten Carbide (WC) tip and a Diamond (111) surface.
- Material Requirement: The study relies on the highly stable and well-characterized mechanical properties of Diamond (111) (Youngâs Modulus: 1164 GPa; Poissonâs Ratio: 0.079).
- Key Achievement: The proposed model, utilizing Weirâs method for theoretical work of adhesion, predicted the pull-off force (8.6 nN) with an acceptable deviation (17.8%) from the measured experimental value (7.3 nN).
- Scientific Domain: The contact was confirmed to operate within the Derjaguin-Muller-Toporov (DMT) adhesion domain (Taborâs parameter = 0.014), requiring extremely high surface quality.
- 6CCVD Value Proposition: 6CCVD specializes in providing the necessary Single Crystal Diamond (SCD) substrates with precise (111) orientation and ultra-low surface roughness (Ra < 1 nm) essential for replicating and extending this high-fidelity nanoscale research.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the simulation and validation parameters used in the study.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Substrate Material | Diamond (111) | N/A | Target surface for AFM indentation |
| Indenter Material | Tungsten Carbide (WC) | N/A | AFM tip coating |
| Measured Pull-off Force | -7.3 | nN | Experimental validation target |
| Predicted Pull-off Force | 8.6 | nN | Numerical model result |
| Prediction Deviation | 17.8 | % | Deviation from measured value |
| Diamond Youngâs Modulus | 1164 | GPa | Input parameter for (111) orientation |
| Diamond Poissonâs Ratio | 0.079 | N/A | Input parameter |
| WC Youngâs Modulus | 600 | GPa | Input parameter |
| WC Density | 15250 | kg m-3 | Input parameter |
| Equilibrium Spacing (z0) | 1.65 | Ă | Between two parallel flat surfaces |
| Taborâs Parameter (”) | 0.014 | N/A | Confirms contact in DMT domain |
| Numerical Tolerance | < 1 x 10-3 | N/A | Residual solution convergence criterion |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized a numerical scheme validated against established experimental AFM data, focusing on theoretical calculation of surface energy.
- Physical Modeling: Simulation of a spherical cap AFM tip (WC coated) indenting a planar Diamond (111) surface, focusing on asperity pair interaction.
- Force Law Application: The Lennard-Jones force law (using powers m=6 and n=12) was applied to describe the adhesive contact behavior.
- Theoretical Adhesion Calculation: Weirâs method was employed to compute the theoretical work of adhesion (λ), avoiding the reliance on empirically obtained surface energy terms (Îł).
- Numerical Discretization: The contact problem was solved for a domain of 128 elements using a discretization scheme (Feng [10]).
- Iterative Solution: The residual equation (R) was solved iteratively using a successive over-relaxation method until the residual was lower than the tolerance (R < 1 x 10-3).
- Validation: The predicted pull-off force was compared directly against measured force-cantilever displacement curves obtained from experimental AFM studies on the same material interface.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the critical need for high-quality, precisely oriented diamond substrates for fundamental studies in nanoscale tribology and adhesion. 6CCVD is uniquely positioned to supply the materials required to replicate, validate, and extend this work.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate the high-fidelity AFM measurements and simulations described, researchers require the highest quality diamond with controlled crystal orientation.
- Optical Grade Single Crystal Diamond (SCD): Required for the Diamond (111) surface used in the study. 6CCVD provides SCD with precise crystal orientations, including (111), (100), and (110), ensuring consistent mechanical and surface energy properties necessary for accurate tribological modeling.
- Ultra-Low Roughness Polishing: Since the contact operates in the DMT domain (where surface forces dominate), surface roughness is paramount. 6CCVD guarantees Ra < 1 nm polishing on SCD substrates, minimizing surface asperities that could interfere with ideal contact modeling.
Customization Potential
Section titled âCustomization Potentialâ6CCVDâs MPCVD capabilities allow for the precise tailoring of substrates to meet the exact needs of advanced tribology research.
- Custom Dimensions and Thickness: We provide SCD plates/wafers in custom dimensions and thicknesses ranging from 0.1 ”m up to 500 ”m, allowing researchers to select the optimal size for AFM stages or integration into larger experimental setups.
- Specific Crystal Orientation: We guarantee the required (111) orientation used in this study, crucial for matching the anisotropic mechanical properties (Youngâs Modulus, Poissonâs Ratio) cited in the paper.
- Advanced Metalization Services: While the paper focused on a WC tip, future experiments involving electrical contact or thermal management may require custom pads. 6CCVD offers in-house metalization capabilities, including Ti, W, Pt, Au, Pd, and Cu, patterned to customer specifications.
Engineering Support
Section titled âEngineering SupportâUnderstanding the complex interplay between material properties (like the anisotropic Youngâs Modulus of diamond) and nanoscale contact mechanics is essential for accurate modeling.
- Material Selection Consultation: 6CCVDâs in-house PhD engineering team provides expert consultation on material selection, ensuring the chosen SCD or PCD grade meets the specific mechanical, thermal, or electrical requirements for similar Nanoscale Tribology and Adhesion projects.
- Property Matching: We assist researchers in selecting substrates that accurately match the required Youngâs Modulus and Poissonâs Ratio for specific crystal planes, critical for input parameters in numerical models like the one presented here.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
At diminishing separations, the load carrying capacity of opposing rough surfaces is distributed among asperities across a smaller contact area as compared with the apparent contact area. An improved understanding on asperity interactions is therefore required in order to better predict the tribological behaviour of a rough surface contact. In this paper, based on Weirâs method for computing the work of adhesion, a simplistic adhesive contact model is proposed, applying the Lennard-Jones force law, to study an asperity pair interaction. Assuming that the tip represents an asperity, the numerical model is subsequently applied to simulate a Tungsten Carbide (WC) coated AFM tip indenting on a Diamond (111) surface. It was found that the simulated pull-off force agrees with the measured value by Enachescu et al for a WC AFM tip on a Diamond (111).