Brownian motion studied with an optical trap

Abstract

This thesis describes measurements of Brownian motion of a colloidal particle using optical trapping. Two aspects are investigated: (i) influence of inertial effects on Brownian motion, and (ii) effect of the optical trap on Brownian motion. The first part describes the experimental setup used: in short, a focused infrared laser beam is used to create an optical trap, and also provides the light source for the position detection. A single particle is trapped by the laser if it is brought near the focus, but it still moves due to Brownian motion. By analyzing the power spectral density of the position signal, the detection limit of the experimental setup is estimated to be 2 µs. The second part contains a study of inertial effects in Brownian motion of a colloidal particle at the microsecond time scale. Measurements are performed for three cases: a particle in a bulk fluid, a particle next to a wall and a particle in a confined fluid. For a particle in a bulk fluid, power law decay of t-3/2 is observed in the particle's velocity autocorrelation function. This power law decay has its origin in the non-negligible fluid inertia. A small effect caused by the particle's inertia is also observed. For the case of a particle placed next to a wall, a faster decay with power law of t-5/2 is observed in the velocity correlations parallel to the wall. Finally, for a particle in a confined fluid, absence of power law decay is observed, and the data instead agree with the model of an exponential decay of velocity correlations. These experimental observations are in accord with the theoretical predictions and show that the effect of the fluid's inertia is most significant in the case of a particle in a bulk fluid, less significant in the case of a particle next to a wall and completely absent in the case of a particle in a confined fluid. The third part is devoted to the characterization of the Brownian motion of a colloidal particle in an optical trap. Data for the mean-square displacement 〈[Δx(t)]2〉 and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential, which also accounts for inertial effects. The motion of the particle is dominated by inertial effects at short times and by the trap potential at longer times. We find the time below which the particle's motion is not influenced by the potential to be approximately τκ/20, where τκ is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion, 〈[Δx(t)]2〉 ∝ t , even for a spherical particle with a radius as small as 0.27 µm in a potential with a spring constant as small as 1.5 µN/m. In the experiment with a micron-sized sphere in the weakest trap potential, estimation of the time below which the particle motion is not influenced by the potential gives τκ/20 ≈ 100 µs. In the time range 2-100 µs, the experimental setup then functions as a position detector probing the motion of a free Brownian particle. Moreover, it is shown that such a detector is achieved for any sphere size in the range between 0.53 µm to 4.16 µm. Hence, the results open up a possibility for using optically trapped Brownian particle as a local reporter its environment on microsecond time scales. This technique could be applied in more complex environments, like polymer networks, cell interiors or bacterial solutions.