Optical Tweezers Study Alters Einstein’s Theory of Motion

Anne L. Fischer

Brownian motion, first described theoretically by Albert Einstein 100 years ago, is the concept that the irregular motion of particles in a fluid is caused by random thermal agitation of the surrounding molecules. Since then, scientists have hypothesized that the random motion Einstein described does not occur as predicted when a particle is much larger than the molecules surrounding it.

The position of a microsphere surrounded by water molecules is tracked using a focused laser beam. The velocities of the water molecules close to the sphere are randomly oriented (a). When a molecule hits the sphere, its momentum transfers to the surrounding water molecules, so their velocities depend on when and where they were nudged by the sphere (b). Because the molecules keep the memory of the particle's motion for a limited time, their velocities again become randomly oriented (c). Courtesy of Ecole Polytechnique Fédérale de Lausanne.

Now a group of researchers from Ecole Polytechnique Fédérale de Lausanne in Switzerland, the University of Texas at Austin and the European Molecular Biology Laboratory in Heidelberg, Germany, has experimentally confirmed this by using optical tweezers to study the effect on Brownian motion of a single particle in water.

The scientists have shown that a particle gains momentum from surrounding particles and that it displaces the water in its immediate vicinity. Einstein described Brownian motion as coming from the white noise of molecules in motion. What he did not say is that, when the water is disturbed, it bounces back to nudge the particle.

The investigators’ setup included a weak optical trap created by focusing a 20× expanded beam of 1064-nm radiation from an Nd:YAG laser with a 1.2-NA, 63× water-immersion objective. It followed the trajectory of a polystyrene or silica sphere in a fluid with temporal resolution short enough to see nondiffusive Brownian motion. According to Sylvia Jeney of the Swiss research institution, the micron-size particles move about 1 nm in 1 μs, so the time scales must be short enough to observe it in that period. The optical trap keeps the particle within the InGaAs quadrant photodiode detector’s range and provides a light source for the position detection.

They found that the friction force — the force between the particle and the solvent molecules — had to be rewritten so as to describe Brownian motion at short time intervals. Einstein’s theory could not take hydrodynamic memory into account, of course, because scientists at the time were not yet working in a nanoworld, Jeney explained. But now that biophysicists and other scientists are working with such tiny particles, deviations in the standard Langevin theory are significant when high-resolution experiments are performed.

Because Brownian motion drives molecules such as proteins and living systems such as cellular vesicles, detailed information can be gained about a protein’s or a cell’s environment by analyzing the trajectory of a probing particle. By validating the corrected form of the equation used to describe Brownian motion, researchers will be better able to develop high-resolution techniques for probing nanoparticles in a variety of environments.

Physical Review Letters, Oct. 14, 2005, 160601.