No abstract

The thermal position fluctuations of a single micron-sized sphere immersed in a fluid were recorded by optical trapping interferometry with nanometer spatial and microsecond temporal resolution. We find, in accord with the theory of Brownian motion including hydrodynamic memory effects, that the transition from ballistic to diffusive motion is delayed to significantly longer times than predicted by the standard Langevin equation. This delay is a consequence of the inertia of the fluid. On the shortest time scales investigated, the sphere's inertia has a small, but measurable, effect.

The motion of an optically trapped sphere constrained by the vicinity of a wall is investigated at times where hydrodynamic memory is significant. First, we quantify, in bulk, the influence of confinement arising from the trapping potential on the sphere's velocity autocorrelation function C(t). Next, we study the splitting of C(t) into C_{parallel}(t) and C_{perpendicular}(t), when the sphere is approached towards a surface. Thereby, we monitor the crossover from a slow t{-3/2} long-time tail, away from the wall, to a faster t{-5/2} decay, due to the subtle interplay between hydrodynamic backflow and wall effects. Finally, we discuss the resulting asymmetric time-dependent diffusion coefficients.

Thermal position fluctuations of a colloidal particle in an optical trap are measured with microsecond resolution using back-focal-plane interferometry. The mean-square displacement and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential that accounts for hydrodynamic memory effects. The motion of a particle is dominated at short times by memory effects and at longer times by the potential. We identify the time below which the particle's motion is not influenced by the potential, and find it to be approximately tau(k)/20 , where tau(k) is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion, proportional to t, even for a sphere with a radius as small as 0.27 microm in a potential as weak as 1.5 microN/m. As the physics of Brownian motion can be used to calibrate an optical trap, we show that neglecting memory effects leads to an underestimation of more than 10% in the detector sensitivity and the trap stiffness for an experiment with a micrometer-sized particle and a sampling frequency above 200kHz . Furthermore, these calibration errors increase in a nontrivial fashion with particle size, trap stiffness, and sampling frequency. Finally, we present a method to evaluate calibration errors caused by memory effects for typical optical trapping experiments.

We measured the elastic modulus of individual multiwalled carbon nanotubes (MWCNTs) grown by catalytic chemical vapor deposition (CVD) over a broad diameter range (10-25 nm). Alternating current (ac) dielectrophoresis was used for efficient tube deposition, and atomic force microscope (AFM) force-displacement curve technique was used for stiffness measurements. The elastic modulus exhibits a strong diameter dependence, showing a difference of nearly 2 orders of magnitude in the 10-20 nm diameter range (thinner MWCNTs have higher elastic modulus). Our results support the metastable-catalyst model in which the catalyst's molten skin plays a key role.