Power Spectral Density Analysis of Nanowire-Anchored Fluctuating Microbead Reveals a Double Lorentzian Distribution

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.

Assessing the Viscoelasticity of Photopolymer Nanowires Using a Three-Parameter Solid Model for Bending Recovery Motion

“…Relying on the fluctuation-dissipation theorem, the proposed mechanical model was complemented by random forces to explain the stochastic motion of the microbeads attached to viscoelastic nanowires. The double-Lorentzian power spectral density, derived from the model, was well reproduced by experimental observations [28].…”

“…Subsequently, the trapping laser beam was switched off and the microbead motion was followed by video tracking. To suppress the effect of Brownian fluctuations [28], the results of twelve repetitive recovery actions were averaged for each glucose concentration.…”

“…The feasibility of the three-parameter approach for describing the viscoelasticity of photopolymer nanowires was also proved in relation to the Brownian fluctuations of the studied microstructures [28]. Relying on the fluctuation-dissipation theorem, the proposed mechanical model was complemented by random forces to explain the stochastic motion of the microbeads attached to viscoelastic nanowires.…”

3D-printed ultra-small Brownian viscometers

“…It was shown that the cantilever mechanics can be described by a three-parameter viscoelastic model. Furthermore, an analytical solution for the power spectral density of freely fluctuating viscoelastic cantilever/microsphere structures immersed in Newtonian liquids was obtained 42 . After being refined, this result serves as a theoretical basis for the presented viscometers.…”

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

“…al. [23] explained the process of development of the model in the domain of mechanics in a sophisticated way. Different types of computer simulation are delineated in a versatile way.…”