Abstract
In this work, we investigate the properties of a stochastic model, in which two coupled degrees of freedom are subordinated to viscous, elastic, and also additive random forces. Our model, which builds on previous progress in Brownian motion theory, is designed to describe water-immersed microparticles connected to a cantilever nanowire prepared by polymerization using two-photon direct laser writing (TPP-DLW). The model focuses on insights into nanowires exhibiting viscoelastic behavior, which defines the specific conditions of the microbead. The nanowire bending is described by a three-parameter linear model. The theoretical model is studied from the point of view of the power spectrum density of Brownian fluctuations. Our approach also focuses on the potential energy equipartition, which determines random forcing parametrization. Analytical calculations are provided that result in a double-Lorentzian power density spectrum with two corner frequencies. The proposed model explained our preliminary experimental findings as a result of the use of regression analysis. Furthermore, an a posteriori form of regression efficiency evaluation was designed and applied to three typical spectral regions. The agreement of respective moments obtained by integration of regressed dependences as well as by summing experimental data was confirmed.
Highlights
Many of the problems addressed by current nanosciences can be traced back to statistical mechanics and the concept of fluctuations
Fundamental problems constantly arise in nanosciences that go beyond conventional findings, complementing the emphasis and motivations of statistical mechanics
Brownian motion has been used at a smaller scale in TPM experiments to investigate the properties of linear macromolecules such as DNA [9,10,11]
Summary
Many of the problems addressed by current nanosciences can be traced back to statistical mechanics and the concept of fluctuations. Fundamental problems constantly arise in nanosciences that go beyond conventional findings, complementing the emphasis and motivations of statistical mechanics. Stochastic oscillations of anchored mechanical systems immersed in fluidic media or kept in vacuum have attracted significant attention in the past and are important in many ways today. The thermal fluctuations of resonant micron-scale mechanical oscillators have been studied extensively, mostly in connection with AFM (atomic force microscopy) cantilevers and MEMS-based (micro- electromechanical) resonators [2,3,4,5,6]. Thermal fluctuations of glass nanofibers and silicon nitride cantilevers have been used to characterize and calibrate such systems for single-molecule force measurements [7,8]. Examples are inertial sensors [12,13] as well as recently proposed gravitational-wave and dark matter sensors [14,15,16]
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