# Brownian movement

Surface Chemistry: Brownian movement

One of the first pieces of evidence for how gases move was discovered by Robert Brown a botanist who noticed that pollen grains in the water moved about randomly. Robert Brown noticed that small grains of pollen (Clarkia) suspended in water, moved in a haphazard or random fashion. In 1905, Einstein developed a mathematical model for Brownian Motion. For small particles (d = 0.001mm), Einstein predicted the displacement of approximately 6 μm in 1 min. No individual particle movement can be predicted, but he means square displacement can be predicted.

Flashes of light or scintillations become visible when colloids are viewed under a microscope. Colloids scintillate as the particles reflect and scatter the light move erratically. Zig- zag and chaotic movement of colloidal particles in sol are defined as the Brownian movement.

Collisions of the molecules in the dispersion medium with the small, dispersed colloidal particles create Brownian motion.

Consider a plot of the smoke particles position over a period of time. This plot looks like zig-zag lines at random:

Note that

• There is no appreciable displacement of the particle
• The particle travels more or less in straight lines
• The motion is RANDOM

At any point in time, the forces on the smoke particle are unevenly causing a net force and therefore acceleration in that direction. The small weight helps in changing the direction quickly and easily. The motion is due to the collisions of the (invisible) air molecules with the much larger particles of smoke. Heating makes the smoke particles’ motion even more violent due to the increased velocity of the air molecules.

The term “Brownian motion” also refers to the mathematical model for describing random movements, often called a particle theory.

Suppose in two dimensions a displacement is

When displacements are observed for several particles, taking the average of these random values of r2

d: number of dimensions of movement

R: Universal gas constant

T: Temperature of the fluid in Kelvin

η: viscosity of the fluid

a: radius of the particle in the fluid

t: time of movement for each particle

 Observation of particles in Brownian motion Explanation Small bright dots are seen Tiny dark smoke particles scatter bright light in every direction. They consequently look brighter than their surroundings. Some disappear all of a sudden The microscope can only focus on a small plane within the smoke cell. If a smoke particle rises or falls far from the plane, it goes out of focus and seems to disappear. They move Because they are quite small, they can be hit by uneven numbers of air molecules on opposing sides. This causes a net force on them and they move. At random The tiny air molecules are in random motion (energy distributed randomly) so this process will occur without any pattern. Over small distances The molecules are small and light compared to the heavier, big smoke particles which are ‘quite’ close together.