Precise Analysis of the Brownian Dynamics of Optically Trapped Particles in Time and Frequency Domain

Bera, Sudipta Kumar (2018) Precise Analysis of the Brownian Dynamics of Optically Trapped Particles in Time and Frequency Domain. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

The study of Brownian motion in optical tweezers plays an important role in the field of biology, physics, chemistry etc. In this doctoral thesis, we are trying to develop a complete set of algorithms to analyze Brownian motion data in general and apply those algorithms to analyze the trajectory of a trapped particle in optical tweezers. Different challenges appear in analyzing Brownian motion data in an experimental situation. The types of data are also numerous - ranging from free and confined diffusive Brownian motion, free and confined ballistic Brownian motion, anomalous Brownian motion, rotational Brownian motion, hot Brownian motion, Lévy process etc. Again, length of data sets may be less, the confining potential may be weak, and experimental noise may be large. We have also developed Bayesian inference technique, time domain autoregressive analysis, power spectral density estimated by autoregressive technique to analyze data of Brownian motion of a particle confined in an optical trap to measure trap stiffness and particle diffusion coefficient. The main advantages of these time techniques are accurate results for low trap stiffness and requirement of less no of data points. We have developed a frequency domain analysis technique to analyze anomalous Brownian motion. We perform exhaustive theoretical simulations by solving the fractional Langevin equation with time series corresponding to different color noise and confirm that a linear fit to the power spectral density (PSD) recovers the input. We check the theoretical simulations with experimental data where we measure the displacement of a single microscopic polystyrene bead in water and viscoelastic medium inside optical tweezers. In addition, we have also measured and analyzed Brownian motion in the ballistic domain. We measure the Brownian motion of a trapped absorbing particle cluster in air and determine the power spectral density, mean squared displacement, normalized position, and velocity auto-correlation functions to characterize the photophoretic body force in a quantitative fashion for the first time. Here, the Langevin equation with the inertia term is applied. We fit the spectral density to the well-known analytical function derived from the Langevin equation, measure the resonance and rotation frequencies, and determine the values of mass for the particle. We have tried to measure rotational Brownian motion as well. We study rotation of particle due to imbalanced scattering in great detail by evaluating the Maxwell stress tensor in the case of different asymmetric and compared with the experimental result of single trapped asymmetric quartz microparticles. We have also worked on the optical trapping of a silver nanowire to measure hot Brownian motion, time domain noise reduction technique etc.

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