Effect of the Interparticle Interactions on Adsorption- Induced Frequency Shift of Nano-beam-Based Nanoscale Mass-Sensors: A Theoretical Study

It is well-known that the Interparticle interactions between adsorbates and surface of an adsorbent can affect the surface morphology. One of the consequences of this issue is that the resonant frequency of a nanoscale resonator can be changed due to adsorption. In this study we have chosen a cantilever-based nanoscale mass-sensor with a single nanoparticle at its tip. Using the classical continuum mechanics and the Euler-Bernoulli beam theory we have derived the governing equation of free vibration of the proposed sensor. By the assumption of physisorption, the weak van der Waals forces between the attached nanoparticle and the upper surface atoms have been taken into account. Effect of this interparticle interaction on the frequency response of the mass sensor is examined. Accordingly, the classical equation of motion has been modified by an additional term on the dynamics behavior of the sensor with a variable coefficient. It has been shown that the effect of this additional term is the same as that of an elastic foundation with variable modulus. Numerical results have shown that this additional term has significant effect on the frequency shift of a nanoscale mass-sensor in such a way that by approaching the nanoparticle towards the sensor, the frequency shift of the sensor will increase significantly. The smaller is the nanoparticle, the higher is the frequency shift.