Colloids as model systems for problems in statistical physics

Abstract

Owing to their mesoscopic length scales, colloidal suspensions provide ideal model systems suitable for addressing many problems in the field of statistical physics. Exemplarily, we highlight the versatile nature of such systems by discussing experiments with stochastic resonance and a practical realization of a recently proposed ratchet cellular automaton. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1839311͔Colloidal systems, i.e., micron-sized particles which are suspended in liquids, share many properties with atomic systems. Therefore, they are often referred to as model systems to address novel concepts in the context of statistical physics in a convenient way. Owing to the Brownian motion of such particles, their trajectories can be experimentally studied and allow direct comparison with numerical and theoretical investigations. Here we report on two examples to highlight the use of colloidal particles. The first example is devoted to stochastic resonance, i.e., amplification of small periodic signals in a double-well potential in the presence of noise. The second example addresses a new type of a ratchet cellular automaton which has been recently suggested as a basic element in novel computing schemes. INTRODUCTIONMolecules and atoms are always in thermal motion thereby continuously swarming and colliding with each other. While it is difficult to directly observe this motion in experiments, it can be visualized with micron-sized particles suspended in a liquid. Due to its bombardment by molecules of the liquid, a mesoscopic particle undergoes a Brownian motion which can be directly observed with a conventional microscope. When the Scottish botanist Robert Brown ͑1773-1858͒ performed his famous experiments, he used pollen from Clarkia Pulchella whose cytoplasm contained particles of about 5 m in size. 1 Such particles, which are large compared to the molecules of the solvent so that the latter can be regarded as a homogeneous background but are small enough to exhibit Brownian motion, are known as colloids.At the beginning of the 20th century, Jean Perrin performed a simple yet brilliant experiment demonstrating that the Brownian motion of a colloidal particle is just the largescale manifestation of the thermal agitation of the molecules in the liquid. This means that the energy equipartition theorem, i.e., the fact that the total mean translational kinetic energy of a molecule equals 3 / 2 k B T holds for the molecules of the liquid as well as for the colloids. In 1926, Perrin was awarded the Nobel Prize for this observation which is the cornerstone for the concept of using colloidal particles as model systems for problems in statistical physics.With sizes comparable to the wavelength of visible light, colloidal systems can be conveniently investigated with optical methods. This allows to obtain direct positional information of individual particles. Apart from the length scale which distinguishes colloids from atoms by several orders of magnitude this also applies for the characteristic time sca...

Simulation of the active Brownian motion of a microswimmer

“…On the one hand, passive Brownian particles are often used to study random phenomena because their thermallydriven motion is due to random collisions with the surrounding fluid molecules; this provides a well-defined noisy background dependent on the temperature and the fluid viscosity. 20 On the other hand, the motion of active particles takes them out of equilibrium. 21 In order to start acquiring some first-hand experience with these phenomena, a good didactical approach is to perform numerical experiments, which have the advantage of being inexpensive and within the reach of every student with access to a computational device.…”

Identity of Distributions of Direct Uphill and Downhill Translocation Times for Particles Traversing Membrane Channels

“…Let fq j;f 0g and f _ q j;f 0g be the set of initial conditions for the bath oscillators that leads to the trajectory fx f t 0 ; v f t 0 g, 0 t 0 t. The realization probability of this trajectory is the Maxwell-Boltzmann probability of the corresponding set of initial conditions for the bath oscillators assuming that x f 0 x L Wfx f ; v f g Z ÿ1 expÿE osc fq j;f 0; _ q j;f 0gjx L ; (13) where Z is the partition function of the oscillator bath. When the trajectory reaches the channel boundary at time t, x f t x R , the bath oscillators have their final positions, fq j;f tg, and velocities, f _ q j;f tg.…”

Simulation of a Brownian particle in an optical trap

“…2 Brownian particles are often used to study random phenomena, because their motion due to thermal agitation from collisions with the surrounding fluid molecules provides a well-defined random background dependent on the temperature and the fluid viscosity. 3 By introducing optical forces to induce deterministic perturbations on the particles, 4 it is possible to study the interplay between random and deterministic forces. Optically trapped particles have been used as a model system for statistical physics, and have a wide range of applications, including, for example, the measurement of nanoscopic forces [5][6][7][8] and torques.…”