Schematic representation of mixing of two substances by diffusion

Molecular diffusion, often called simply diffusion, is a net transport of molecules from a region of higher concentration to one of lower concentration by random molecular motion. The result of diffusion is a gradual mixing of material. In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing or a state of equilibrium.

Molecular diffusion is typically described mathematically using Fick's laws.

[edit] Applications

Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion:

• Sintering to produce solid materials (powder metallurgy, production of ceramics)
• Chemical reactor design
• Catalyst design in chemical industry
• Steel can be diffused (e.g., with carbon or nitrogen) to modify its properties
• Doping during production of semiconductors.

[edit] Significance

Diffusion is part of the transport phenomena. Of mass transport mechanisms, molecular diffusion is known as a slower one.

[edit] In biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids within cells.^[1] Diffusion of a fluid (anything that moves like a liquid) through a partially permeable membrane is classified as osmosis.

Metabolism and respiration rely in part upon diffusion in addition to bulk or active processes. For example, in the alveoli of mammalian lungs, due to differences in partial pressures across the alveolar-capillary membrane, oxygen diffuses into the blood and carbon dioxide diffuses out. Lungs contain a large surface area to facilitate this gas exchange process.

[edit] Tracer and chemical diffusion

Self diffusion, exemplified with an isotopic tracer of radioactive isotope ²²Na

Example of chemical (classical, Fick's, or Fickian) diffusion of sodium chloride in water

Fundamentally, two types of diffusion are distinguished:

• Tracer diffusion, which is a spontaneous mixing of molecules taking place in the absence of concentration (or chemical potential) gradient. This type of diffusion can be followed using isotopic tracers, hence the name. The tracer diffusion is usually assumed to be identical to self-diffusion (assuming no significant isotopic effect). This diffusion can take place under equilibrium.
• Chemical diffusion occurs in a presence of concentration (or chemical potential) gradient and it results in net transport of mass. This is the process described by the diffusion equation. This diffusion is always a non-equilibrium process, increases the system entropy, and brings the system closer to equilibrium.

The diffusion coefficients for these two types of diffusion are generally different because the diffusion coefficient for chemical diffusion is binary and it includes the effects due to the correlation of the movement of the different diffusing species.

[edit] Non-equilibrium system

Illustration of low (top) and high (bottom) entropy.

Because chemical diffusion is a net transport process, the system in which it takes place is not an equilibrium system (i.e. it is not at rest yet). Many results in classical thermodynamics are not easily applied to non-equilibrium systems. However, there sometimes occur so-called quasi-steady states, where the diffusion process does not change in time, where classical results may locally apply. As the name suggests, this process is a not a true equilibrium since the system is still evolving.

Non-equilibrium fluid systems can be successfully modeled with Landau-Lifshitz fluctuating hydrodynamics. In this theoretical framework, diffusion is due to fluctuations whose dimensions range from the molecular scale to the macroscopic scale. ^[2]

Chemical diffusion increases the entropy of a system, i.e. diffusion is a spontaneous and irreversible process. Particles can spread out by diffusion, but will not spontaneously re-order themselves (absent changes to the system, assuming no creation of new chemical bonds, and absent external forces acting on the particles).

[edit] An experiment to demonstrate diffusion

Diffusion is not easy to observe, because other transport phenomena, especially convection, are more efficient on length scales above millimeters. Diffusion is most important on microscopic scales.

Diffusion can be demonstrated with a wide glass tube, paper, two corks, some cotton wool soaked in ammonia solution and some red litmus paper. By corking the two ends of the wide glass tube and plugging the wet cotton wool with one of the corks, and litmus paper can be hung with a thread within the tube. It will be observed that the red litmus papers turn blue.

This is because the ammonia molecules travel by diffusion from the higher concentration in the cotton wool to the lower concentration in the rest of the glass tube. As the ammonia solution is alkaline, the red litmus papers turn blue. By changing the concentration of ammonia, the rate of color change of the litmus papers can be changed.

[edit] concentration dependent "collective" diffusion

Collective diffusion is the diffusion of a large number of particles, most often within a solvent.

Contrary to brownian motion, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvent (ideal mix conditions correspond to the case where the interactions between the solvent and particles are identical to the interactions between particles and the interactions between solvent molecules; in this case, the particles do not interact when inside the solvent).

In case of an ideal mix, the particle diffusion equation holds true and the diffusion coefficient D the speed of diffusion in the particle diffusion equation is independent of particle concentration. In other cases, resulting interactions between particles within the solvent will amount for the following effects:

• the diffusion coefficient D in the particle diffusion equation becomes dependent of concentration. For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases. For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration increases.
• In the case of an attractive interaction between particles, particles exhibit a tendency to coalesce and form clusters if their concentration lies above a certain threshold. This is equivalent to a precipitation chemical reaction (and if the considered diffusing particles are chemical molecules in solution, then it is a precipitation).

[edit] See also

Look up diffusion in Wiktionary, the free dictionary.

[edit] References

[edit] External links

• Some pictures that display diffusion and osmosis
• An animation describing diffusion.
• A tutorial on the theory behind and solution of the Diffusion Equation.
• NetLogo Simulation Model for Educational Use (Java Applet)
• Short movie on brownian motion (includes calculation of the diffusion coefficient)
• Short movie about the diffusion process)
• A basic introduction to the classical theory of volume diffusion (with figures and animations)
• Diffusion on the nanoscale (with figures and animations)

[edit] Internal links

• A reference on doping semiconductors