diffusion

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The transport of matter from one point to another by random molecular motions. It occurs in gases, liquids, and solids.

Diffusion plays a key role in processes as diverse as permeation through membranes, evaporation of liquids, dyeing textile fibers, drying timber, doping silicon wafers to make semiconductors, and transporting of thermal neutrons in nuclear power reactors. Rates of important chemical reactions are limited by how fast diffusion can bring reactants together or deliver them to reaction sites on enzymes or catalysts. The forces between molecules and molecular sizes and shapes can be studied by making diffusion measurements. See also Evaporation.

Molecules in fluids (gases and liquids) are constantly moving. Even in still air, for example, nitrogen and oxygen molecules ricochet off each other at bullet speeds. Molecular diffusion is easily demonstrated by pouring a layer of water over a layer of ink in a narrow glass tube. The boundary between the ink and water is sharp at first, but it slowly blurs as the ink diffuses upward into the clear water. Eventually, the ink spreads evenly along the tube without any help from stirring.

Gases

A number of techniques are used to measure diffusion in gases. In a two-bulb experiment, two vessels of gas are connected by a narrow tube through which diffusion occurs. Diffusion is followed by measuring the subsequent changes in the composition of gas in each vessel. Excellent results are also obtained by placing a lighter gas mixture on top of a denser gas mixture in a vertical tube and then measuring the composition along the tube after a timed interval.

Rates of diffusion in gases increase with the temperature (T) approximately as T^3/2 and are inversely proportional to the pressure. The interdiffusion coefficients of gas mixtures are almost independent of the composition.

Kinetic theory shows that the self-diffusion coefficient of a pure gas is inversely proportional to both the square root of the molecular weight and the square of the molecular diameter. Interdiffusion coefficients for pairs of gases can be estimated by taking averages of the molecular weights and collision diameters. Kinetic-theory predictions are accurate to about 5% at pressures up to 10 atm (1 megapascal). Theories which take into account the forces between molecules are more accurate, especially for dense gases.

Liquids

The most accurate diffusion measurements on liquids are made by layering a solution over a denser solution and then using optical methods to follow the changes in refractive index along the column of solution. Excellent results are also obtained with cells in which diffusion occurs between two solution compartments through a porous diaphragm. Many other reliable experimental techniques have been devised.

Room-temperature liquids usually have diffusion coefficients in the range 0.5–5 × 10⁻⁵ cm² s⁻¹. Diffusion in liquids, unlike diffusion in gases, is sensitive to changes in composition but relatively insensitive to changes in pressure. Diffusion of high-viscosity, syrupy liquids and macromolecules is slower. The diffusion coefficient of aqueous serum albumin, a protein of molecular weight 60,000 atomic mass units, is only 0.06 × 10⁻⁵ cm² s⁻¹ at 25°C (77°F).

When solute molecules diffuse through a solution, solvent molecules must be pushed out of the way. For this reason, liquid-phase interdiffusion coefficients are inversely proportional to both the viscosity of the solvent and the effective radius of the solute molecules. Accurate theories of diffusion in liquids are still under development.

Solids

Diffusion in solids is an important topic of physical metallurgy and materials science since diffusion processes are ubiquitous in solid matter at elevated temperatures. They play a key role in the kinetics of many microstructural changes that occur during the processing of metals, alloys, ceramics, semiconductors, glasses, and polymers. Typical examples of such changes include nucleation of new phases, diffusive phase transformations, precipitation and dissolution of a second phase, recrystallization, high-temperature creep, and thermal oxidation. Direct technological applications concern diffusion doping during the fabrication of microelectronic devices, solid electrolytes for battery and fuel cells, surface hardening of steels through carburization or nitridation, diffusion bonding, and sintering. See also Fuel cell; Phase transitions.

The atomic mechanisms of diffusion are closely connected with defects in solids. Point defects such as vacancies and interstitials are the simplest defects and often mediate diffusion in an otherwise perfect crystal. Dislocations, grain boundaries, phase boundaries, and free surfaces are other types of defects in a crystalline solid. They can act as diffusion short circuits because the mobility of atoms along such defects is usually much higher than in the lattice.

A semiconductor manufacturing process that infuses tiny quantities of impurities into a base material, such as silicon, to change its electrical characteristics. See chip.

Diffusion Process

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Process by which a new product or idea attracts the attention and interest of a market and is gradually adopted by the many individuals making up that market. Unlike individual adoption decisions, diffusion is influenced by communication about a product between an ever-widening group of consumers and is affected by the social dynamics of the group. See also adoption process; innovation; early adopter; innovator.

The name applied to a physical process by which individual particles move randomly, within a fluid, from areas of high concentration to lower concentration until the particles are evenly distributed throughout the space. The particles referred to can be molecules or ions and the fluid can be either gaseous or liquid. For example, a person wearing perfume can be noticed on entering a room because molecules of the odiferous substances contained within the perfume diffuse in the air and are detected by the nose. Similarly, a drop of dye dropped into a glass of water will eventually colour the whole volume as the molecules of dye diffuse evenly throughout the volume. Because of thermal motion and vibration, a molecule, ion, or small particle undergoes 10¹³ to 10¹⁵ collisions per second with molecules of the fluid. The particle is said to undergo a random walk, in which the result of a particular collision is independent of the effects of previous collisions. The statistical consequence of this is that the displacement of a particle from its original position will depend on the elapsed time. Where the diffusing particles are at high concentration, many collisions will be between the diffusing species, so that they will move away from each other, thus creating a flux from high concentration to low until the concentration is even throughout the volume. Diffusion is influenced by many factors, such as viscosity and electric charge. Thus diffusion in treacle will be slower than diffusion in water, and particles carrying the same charge will exert mutual repulsion.

Diffusion is an important process for bodily function. Important substances, such as oxygen and carbon dioxide, not only need to diffuse within a particular fluid volume but need to diffuse from one bodily compartment to another across barriers, where generally diffusion will be slower than within a fluid. Consider the position in the lungs; oxygen from the air has to diffuse across the walls of the alveoli and of the capillaries within the lungs to reach the blood, and then across the walls of the red cells to reach the haemoglobin. Fortunately it combines with the haemoglobin to form oxyhaemoglobin, thus maintaining a steep concentration gradient. At the same time carbon dioxide, released from the venous blood, needs to diffuse in the opposite direction, down its concentration gradient, into the lungs, in order to be exhaled. As the transit time of blood in the lungs is just a few seconds, the diffusive process needs to be rapid. (If, for example, the lungs are filled with thick, viscid mucus, as in bronchiectasis or cystic fibrosis, then the diffusive process is impaired and full oxygenation will not occur). Conversely, when oxygenated blood arrives at the tissues the conditions are such that oxygen is released and needs to diffuse into the cells to maintain tissue respiration, whilst carbon dioxide, a product of tissue respiration, needs to be loaded into the blood for conveyance back to the lungs.

Diffusion is similarly important in the absorptive processes in the gut. The purpose of digestion is to break down complex molecules into simple ones such as sugars, fats, and peptides. The lining of the gut wall has many specialized transporters to take the breakdown products into the cells and to transfer them to the blood, for delivery to tissues where they can be used as a source of energy, stored, or used for growth and repair. However, to arrive at the transporters the products of digestion need to diffuse from the gut contents, through the aqueous stationary layer closest to the lining of the gut, to reach the transporters. Diffusion therefore is a universally important process affecting every aspect of living tissue. A single living cell is a hive of activity. Substances produced within the cell which are important for its normal functioning may be produced at one site but then interact with another part of the cell, which they reach by diffusion, moving from high concentration to low by way of thermal motion, an inherent physical property.

— Alan W. Cuthbert

noun

Words or the use of words in excess of those needed for clarity or precision: diffuseness, long-windedness, pleonasm, prolixity, redundancy, verbiage, verboseness, verbosity, windiness, wordage, wordiness. See excess/insufficiency/enough, style/good style/bad style, words.

Definition: spread; wide distribution
Antonyms: centralization, collection, concentration

The widespread dispersal of an innovation from a centre or centres. This innovation may be anything from an epidemic disease to a political belief, or even the wearing of reversed baseball caps.

T. Hägerstrand's model of diffusion (1968) implies the existence of a mean information field which regulates the flows of information around a regional system. These flows are moderated by barriers which can obstruct the evolution of information into innovation, and thus mould the diffusion wave; the ripple of innovation which spreads from one location to another.

Various categories of diffusion have been recognized: expansion diffusion is the spread of a factor from a centre with the concentration of the things being diffused also remaining, and possibly intensifying, at the point of origin. One example is the spread of girls' public day schools in the nineteenth century, which started in London. As new schools developed further and further away from London, new schools also opened in the capital. Relocation diffusion similarly spreads from a centre but the innovation moves outwards, leaving the centre. An example of this is the movement of a bush fire, which has burned out at the origin but continues to spread at the periphery. Hierarchic diffusion passes through a regular sequence of orders as when an innovation in a metropolis spreads out to cities, then towns, and finally to villages. A good example is the introduction of video hire shops. The order of the diffusion may also be based on class—the spread of wine-drinking in Britain is a good example. The innovation may spread up a hierarchy, but cascade diffusion is a form of hierarchic diffusion which only moves down an order or hierarchy.

The Hägerstrand model has shortcomings: it does not explain why some adopt an innovation and others do not, and it is based on the notion of a uniform cognitive region through which innovation diffuses, whereas access to information is socially structured.

Recent work on diffusion has focused on the transmission of epidemics; the diffusion of HIV/AIDS, for example, seems to depend on: distance from a transmission pathway; access to travel facilities; and the propensity to travel. See spatial diffusion analysis.

1. The net movement of molecules of a fluid from a high concentration to a low concentration. Diffusion is a passive process resulting from the random movement of molecules as a result of their kinetic energy. Gaseous exchange in the lungs and tissues takes place by diffusion through biological membranes. The rate of diffusion depends on the concentration gradient, diffusion distance, and the surface area and properties of the membrane.

2. The spread of cultural traits, such as language, technological ideas, or social practices from one society to another.

Tendency of conduction band electrons to wander across a pn junction to combine with valence band holes.

The spreading of atoms or molecules of one substance through those of another, especially into liquids or gases.

1. the net flow of molecules from a region of high concentration, or high chemical potential, to one of low concen-tration, or low chemical potential, due only to random thermal motion. See also facilitated diffusion.
2. the irregular reflection or transmission of light or other electromagnetic radiation; scattering.
3. the act or process of dispersing or of being dispersed widely.

1. the state or process of being widely spread.
2. the spontaneous mixing of the molecules or ions of two or more substances resulting from random thermal motion; its rate is proportional to the concentrations of the substances and it increases with the temperature.
In the body fluids the molecules of water, gases, and the ions of substances in solution are in constant motion. As each molecule moves about, it bounces off other molecules and loses some of its energy to each molecule it hits, but at the same time it gains energy from the molecules that collide with it.
The rate of diffusion is influenced by the size of the molecules; larger molecules move less rapidly, because they require more energy to move about. Molecules of a solution of higher concentration move more rapidly toward those of a solution of lesser concentration; in other words, the rate of movement from higher to lower concentration is greater than the movement in the opposite direction.

• d. coefficient — the number of milliliters of a gas that will diffuse at a distance of 0.001 mm over a square centimeter surface per minute, at 1 atmosphere of pressure. The diffusion coefficient for any given gas is proportional to the solubility and molecular weight of the gas. The diffusion coefficient for oxygen is 1.0, for carbon dioxide it is 20.3, and for nitrogen it is 0.53. The diffusion capacity of a gas varies directly with the diffusion coefficient.
• facilitated d. — mechanisms in intestinal absorption which assist the passage of those products of digestion, which cannot occur by simple diffusion, across the intestinal cell membranes. They include a carrier mechanism involving proteins, and active transport which provides energy from the breakdown of high-energy phosphate bonds.
• Fick's first law of d. — see fick's first law of diffusion.
• d. hypoxia — a transient hypoxic episode after the cessation of nitrous oxide anesthesia if air is inhaled instead of pure oxygen; caused by the rapid diffusion of nitrous oxide out into the alveoli diluting the oxygen that is there.

A property of ions or molecules of a solute that permits them to pass through a membrane or to intermingle by rapid or gradual permeation with the molecules of a solvent.

• Cell Structure and Function - diffusion: movement of molecules by random motion from region of higher to one of lower concentration
• Physical Properties and Changes - diffusion: mixture of one substance with another throughout a given volume as a result of random molecular motion

This article is about spontaneous dispersion of mass. For a more generic treatment of diffusion, see Diffusion.

Diffusion from a microscopic and macroscopic point of view. Initially, there are solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the whole container. Top: A single molecule moves around randomly. Middle: With more molecules, there is a clear trend where the solute fills the container more and more uniformly. Bottom: With an enormous number of solute molecules, all randomness is gone: The solute appears to move smoothly and systematically from high-concentration areas to low-concentration areas, following Fick's laws.

Molecular diffusion, often called simply diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration, but it is important to note that diffusion also occurs when there is no concentration gradient. 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.

Diffusive equilibrium is reached when the concentrations of the diffusing substance in the two compartments becomes equal.

Consider two systems; S₁ and S₂ at the same temperature and capable of exchanging particles. If there is a change in the potential energy of a system; for example μ₁>μ₂ (μ is Chemical potential) an energy flow will occur from S₁ to S₂, because nature always prefers low energy and maximum entropy.

Though the different systems are at equilibrium, there is still water passing through the semipermeable membrane. So if food coloring is put in system A, eventually it would be of equal color to system B.

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

Contents 1 Applications 2 Significance 2.1 Biology 3 Tracer, self- and chemical diffusion 4 Non-equilibrium system 5 Concentration dependent "collective" diffusion 6 Molecular Diffusion of Gases 7 Equimolecular Counterdiffusion 8 See also 9 References 10 External links 11 Internal links

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.

Significance

Schematic representation of mixing of two substances by diffusion

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

Biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids within cells.^[1] Diffusion of water (H₂O) 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.

Tracer, self- 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 and Self-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. An excellent method for the measurement of self-diffusion coefficients is pulsed field gradient (PFG) NMR, where no isotopic tracers are needed. In a so-called NMR spin echo experiment this technique uses the nuclear spin precession phase, allowing to distinguish chemically and physically completely identical species e.g. in the liquid phase, as for example water molecules within liquid water. The self-diffusion coefficient of water has been experimentally determined with high accuracy and thus serves often as a reference value for measurements on other liquids. The self-diffusion coefficient of neat water is: 2.299·10⁻⁹ m²·s⁻¹ at 25 °C and 1.261·10⁻⁹ m²·s⁻¹ at 4 °C.^[2]

• 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.

Non-equilibrium system

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

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.^[3]

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 particle).

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 account 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).

Molecular Diffusion of Gases

Transport of material in stagnant fluid or across streamlines of a fluid in a laminar flow occurs by molecular diffusion.Two adjacent compartments, separated by partition containing pure gases A or B may be envisaged. Random movement of all molecules occurs so that after a period molecules are found remote from their original positions. If the partition is removed, some molecules of A move towards the region occupied by B, their number depends on the number of molecules at the point considered. Concurrently, molecules of B diffuse toward regimens formerly occupied by pure A. Finally, complete mixing occurs. Before this point in time, a gradual variation in the concentration of A occurs along an axis, designated x, which joins the original compartments. This variation, expressed mathematically -dC_A/dx, where C_A is the concentration of A. The negative sign arises because the concentration of A decreases as the distance x increases. Similarly, the variation in the concentration of gas B is -dC_B/dx. The rate of diffusion of A, N_A, depend on concentration gradient and the average velocity with which the molecules of A moves in the x direction. This relationship is expressed by Fick's Law

"only applicable for no bulk motion"

where D is the Diffusivity of A through B, proportional to the average (squared?) molecular velocity and, therefore depend on the temperature and pressure of gases. The rate of Diffusion N_A,is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, indicates that the rate of force is directly proportional to the driving force, which is the concentration gradient.

This basic equation applied to a number of situations. Restricting discussion exclusively to steady state conditions, in which neither dC_A/dx or dC_B/dx change with time, equimolecular counterdiffusion is considered first.

Equimolecular Counterdiffusion

If no bulk flow occurs in an element of length dx, the rates of diffusion of two gases A and B must be equal and opposite, that is .

The partial pressure of A changes by dP_A over the distance dx. Similarly, the partial pressure of B changes dP_B. As there is no difference in total pressure across the element (no bulk flow), dP_A/dx must equal . For an ideal gas the partial pressure is related to the molar concentration by the relation

where n_A is the number of moles of gas A in a volume V. As the molar concentration C_A is equal to n_A/ V therefore

Consequently, for gas A,

where D_AB is the diffusivity of A in B. Similarly,

It therefore allows that D_AB=D_BA=D. If the partial pressure of A at x₁ is P_A1 and x₂ is P_A2, integration of above equation,

A similar equation may be derived for the counterdiffusion of gas B.

See also

Underwater diving portal

• Molecular diffusion of gases
• Equimolecular counterdiffusion
• Ambipolar diffusion
• Anomalous diffusion
• Batchelor scale
• Bohm diffusion
• Diffusion MRI
• Double diffusive convection
• Drag (physics)
• Fick's laws of diffusion
• Local time (mathematics)
• Mass transfer
• Mass flux
• Osmosis
• Permeation
• Relativistic heat conduction
• Transport phenomena
• Turbulent diffusion
• Viscosity

References

1. ^ Maton, Anthea; Jean Hopkins, Susan Johnson, David LaHart, Maryanna Quon Warner, Jill D. Wright (1997). Cells Building Blocks of Life. Upper Saddle River, New Jersey: Prentice Hall. pp. 66–67. 
2. ^ M. Holz, S.R. Heil, A. Sacco: Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate 1H NMR PFG Measurements. In: Phys. Chem. Chem. Phys. 2,, 2000, S. 4740–4742.
3. ^ D. Brogioli and A. Vailati, Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited, Phys. Rev. E 63, 012105/1-4 (2001)

External links

Look up diffusion in Wiktionary, the free dictionary.

• 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)
• A basic introduction to the classical theory of volume diffusion (with figures and animations)
• Diffusion on the nanoscale (with figures and animations)

Internal links

• Doping (semiconductor) – A reference on doping semiconductors

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