2.1 Brownian motion

This plant was Clarkia pulchella, of which the grains of pollen, taken fromantherae full grown, but before bursting, were filled with particles or granules of unusually large size, varying from nearly1/4000th to 1/5000th of an inch in length, and of a figure between cylindrical and oblong, perhaps slightly flattened, and havingrounded and equal extremities. While examining the form of these particles immersed in water, I observed many of them very evidentlyin motion; their motion consisting not only of a change of place in the fluid, manifested by alterations in their relative positions,but also not unfrequently of a change of form in the particle itself; a contraction or curvature taking place repeatedly aboutthe middle of one side, accompanied by a corresponding swelling or convexity on the opposite side of the particle. In a few instancesthe particle was seen to turn on its longer axis. These motions were such as to satisfy me, after frequently repeated observation,that they arose neither from currents in the fluid, nor from its gradual evaporation, but belonged to the particle itself. -Robert Brown, 1828

Introduction

The physical phenomena described in the excerpt above by Robert Brown, the nineteenth-century Britishbotanist and surgeon, have come collectively to be known in his honor by the term Brownian motion.

Brownian motion, a simple stochastic process, can be modeled to mathematically characterize the random movementsof minute particles upon immersion in fluids. As Brown once noted in his observations under a microscope, particulate matter such as,for example, pollen granules, appear to be in a constant state of agitation and also seem to demonstrate a vivid, oscillatory motionwhen suspended in a solution such as water.

We now know that Brownian motion takes place as a result of thermal energy and that it is governed by thekinetic-molecular theory of heat, the properties of which have been found to be applicable to all diffusion phenomena.

But how are the random movement of flower gametes and a British plant enthusiast who has been dead for ahundred and fifty years relevant to the study and to the practice of nanotechnology? This is the main question that this module aimsto address. In order to arrive at an adequate answer, we must first examine the concept of Brownian motion from a number of differentperspectives, among them the historical, physical, mathematical, and biological.