Effect of adhesion on the dynamics of an AFM cantilever
Rojin Mathews, Sreesastharam Thachamoochikkal Rajithan, Soney Varghese, U. B. JayadeepPurpose
This study aims to investigate the impact of adhesion forces on the dynamic behaviour of an atomic force microscopy (AFM) cantilever, particularly focusing on amplitude variation and phase shifts in tapping-mode operation. A finite element (FE) model using a body-force formulation and lumped parameter algorithm is used to simulate adhesive interactions efficiently. By adopting an axisymmetric model, the computational cost is reduced while maintaining accuracy. The findings highlight the significant influence of adhesion on cantilever vibration dynamics, offering insights valuable for interpreting AFM measurements and guiding future developments in modelling adhesive interactions between deformable bodies.
Design/methodology/approach
This study uses an FE approach using a body-force formulation to model adhesive interactions in an AFM cantilever system. Adhesion is represented as a volumetric body force rather than a surface force for improved accuracy. An axisymmetric model interacting with a semi-infinite rigid substrate is developed to reduce computational load. A lumped parameter algorithm is used to represent the distributed body force as an equivalent nodal force. The model simulates tapping-mode AFM dynamics to quantify vibrational parameters – particularly phase shift due to adhesion – revealing measurable changes that correlate with adhesive interactions at the tip–sample interface.
Findings
This study demonstrates that adhesion significantly influences the vibrational behaviour of an AFM cantilever operating in tapping mode. Using a volumetric body force model within an axisymmetric FE framework and a lumped parameter algorithm, the analysis revealed notable variations in amplitude and phase shift due to adhesive interactions. The presence of adhesion caused a reduction in the cantilever’s natural frequency, leading to a distinguishable phase shift at resonance. These results confirm that phase shift serves as a sensitive and reliable indicator of tip–sample adhesion, enhancing the accuracy of dynamic characterisation in AFM-based material analysis.
Research limitations/implications
The current study models adhesive interactions between an elastic AFM cantilever and a rigid half-space, which limits the analysis of coupled effects arising from the sample’s material properties. As a result, it does not capture the full complexity of adhesion between two deformable bodies. Future work involves extending the model to simulate interactions between deformable bodies, enabling more realistic predictions of adhesion-driven dynamics, energy dissipation and their influence on AFM-based property measurements and nanoscale friction analysis.
Originality/value
This work presents a novel FE-based framework for analysing adhesion effects in tapping-mode AFM using a volumetric body-force formulation, surpassing conventional surface-based models in accuracy. By using an axisymmetric representation with a lumped parameter approach, it achieves significant computational efficiency without compromising fidelity. This study quantitatively links phase-shift variations to adhesive interactions, offering a sensitive and practical metric for characterising adhesion in nanoscale contact. This methodology advances current AFM simulation practices and provides foundational insight for future models involving deformable bodies, with implications for material characterisation, energy dissipation and nanoscale friction analysis.