# diffusion

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## diffusion,

in chemistry, the spontaneous migration of substances from regions where their concentration is high to regions where their concentration is low. Diffusion is important in many life processes. It occurs, for example, across the alveolar membrane of the lung, which separates the carbon-dioxide-rich blood from the oxygen-rich air. Oxygen diffuses across the membrane and becomes dissolved in the blood; carbon dioxide diffuses across the membrane into the air.

The spontaneous redistribution of a substance is due to the random motion of the molecules (or atoms or ions) of the substance. Because of the random nature of the motion of molecules, the rate of diffusion of molecules out of any region in a substance is proportional to the concentration of molecules in that region, and the rate of diffusion into the region is proportional to the concentration of molecules in the surrounding regions. Thus, while molecules continuously flow both into and out of all regions, the net flow is from regions of higher concentration to regions of lower concentration. Generally, the greater the difference in concentration, the faster the diffusion.

Since an increase in temperature represents an increase in the average molecular speed, diffusion occurs faster at higher temperatures. At any given temperature, small, light molecules (such as H2, hydrogen gas) diffuse faster than larger, more massive molecules (such as N2, nitrogen gas) because they are traveling faster, on the average (see heatheat,
nonmechanical energy in transit, associated with differences in temperature between a system and its surroundings or between parts of the same system. Measures of Heat
; kinetic-molecular theory of gaseskinetic-molecular theory of gases,
physical theory that explains the behavior of gases on the basis of the following assumptions: (1) Any gas is composed of a very large number of very tiny particles called molecules; (2) The molecules are very far apart compared to their sizes,
). According to Graham's law (for Thomas Graham), the rate at which a gas diffuses is inversely proportional to the square root of the density of the gas.

Diffusion often masks gravitational effects. For example, if a relatively dense gas (such as CO2, carbon dioxide) is introduced at the bottom of a vessel containing a less dense gas (such as H2, hydrogen gas), the dense gas will diffuse upward and the less dense gas will diffuse downward. It is true, however, that at equilibrium the two gases will not be uniformly mixed. There will be some variation in the density and composition of the gas mixture; at the top of the vessel the gas mixture will be slightly less concentrated, and there will be a slight preponderance of molecules of the less dense gas. These differences, which are due to gravity, are almost impossible to measure in the laboratory, although they interact with other factors in determining the distribution of gases in planetary atmosphere.

Diffusion is not confined to gases; it can take place with matter in any state. For example, salt diffuses (dissolves) into water; water diffuses (evaporates) into the air. It is even possible for a solid to diffuse into another solid; e.g., gold will diffuse into lead, although at room temperature this diffusion is very slow. Generally, gases diffuse much faster than liquids, and liquids much faster than solids. Diffusion may take place through a semipermeable membrane, which allows some, but not all, substances to pass. In solutions, when the liquid solvent passes through the membrane but the solute (dissolved solid) is retained, the process is called osmosisosmosis
, transfer of a liquid solvent through a semipermeable membrane that does not allow dissolved solids (solutes) to pass. Osmosis refers only to transfer of solvent; transfer of solute is called dialysis.
. Diffusion of a solute across a membrane is called dialysisdialysis
, in chemistry, transfer of solute (dissolved solids) across a semipermeable membrane. Strictly speaking, dialysis refers only to the transfer of the solute; transfer of the solvent is called osmosis.
, especially when some solutes pass and others are retained.

## Diffusion

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 Semiconductor

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 T3/2 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. See Kinetic theory of matter

#### 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. See Viscosity

#### 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 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. See Crystal defects

## diffusion

the spread of cultural traits (e.g. religious belief, technological ideas, language forms, etc.) or social practices from one society or group to another. The concept was first employed by the British anthropologist Edward TYLOR (in Primitive Culture, 1871) to explain the presence of non-indigenous cultural traits found within many societies. Such cultural diffusion has occurred on a wide scale throughout human history, so that, today, societies can even be said to exist as part of a single world society.

In social anthropology, and in sociology more generally, the existence of cultural diffusion is seen as presenting problems, especially for UNILINEAR theories of change which make the assumption that individual societies develop – mainly endogenously -through set stages (see also INTERSOCIETAL SYSTEMS). On the other hand, it should not be assumed that any cultural trait or social institution is compatible with any other, for this would be to assume that individual societies have no internal coherence.

The concept of diffusion has also been linked to the debate which emerged over theories of ECONOMIC AND SOCIAL DEVELOPMENT and MODERNIZATION. Theorists such as Talcott PARSONS (1964a) argued that the diffusion of social institutions (EVOLUTIONARY UNIVERSALS) and cultural values characteristic of Western capitalist democracies was essential if THIRD WORLD development was to occur. This position was trenchantly criticized by writers from the left, most notably Frank (1969), who pointed out that the diffusion of culture and institutions from Europe to the Third World was, in fact, centuries old, and rather than producing development, this colonial contact resulted in UNDERDEVELOPMENT.

In more mathematical usages of the term, similarities are seen as existing between patterns of social diffusion and those characteristic of EPIDEMIOLOGY, e.g. the logistical pattern of the spread of a contagious disease - proceeding slowly at first, with small numbers of persons involved, then more rapidly as more become involved and they also involve still others, but then slowing down as there are fewer new people to involve (see also DIFFUSION OF INNOVATIONS). However, although formal mathematical models of the type used in physical science can be illuminating, these are usually presented as ‘heuristic devices’, rather than models which will closely fit patterns of social diffusion which are likely to be seen as more complex and variable in form than those in the physical realm. One reason for this is that individual human beings and groups often resist change; and diffusion rarely occurs as the outcome of passive imitation (see also TWO-STEP FLOW OF COMMUNICATIONS; OPINION LEADERSHIP).

## Diffusion

the mutual penetration of adjoining substances because of the thermal motion of their particles. Diffusion occurs in the direction of decreasing concentration of a substance and leads to a uniform distribution of matter over the entire volume it occupies (to the equalization of the chemical potential of matter).

Diffusion occurs in gases, liquids, and solids; the particles of foreign materials, as well as the particles of the given substance (self-diffusion), may diffuse.

The diffusion of large particles suspended in a gas or liquid (for example, particles in smoke and suspensions) occurs because of the particles’ Brownian movement. Unless specifically noted, the following discussion will deal with molecular diffusion.

Diffusion proceeds most rapidly in gases, more slowly in liquids, and most slowly in solids because of the character of thermal motion in these mediums. The trajectory of motion of each particle in a gas is a broken line, since the particles change their direction and speed of motion during collisions.

The disorderliness of motion leads to the gradual movement of each particle away from the spot where it was originally located; its displacement along a straight line is much less than the path traversed along the broken line. For this reason, diffusion penetration is considerably slower than free motion (for example, the rate of diffusion propagation of odors is much lower than the speed of the molecules). Displacement of the particle changes in time in a random manner, but its mean square L̅2 increases over a large number of collisions proportional to thejime t. The proportionality coefficient D in the relationship 2 ~ Dt is called the diffusion coefficient. This relationship, which was found by A. Einstein, is valid for any diffusion process. In the simplest case of self-diffusion in a gas, the diffusion coefficient may be determined from the relationship D ~ L̅2/r applied to the mean free path length of the molecule . For a gas, I̅ c̄τ, where is the mean rate of particle motion and τ is the mean time between collisions. Thus, D ~ I2̅/τ ~ I̅c̄ (more exactly, D = 1/3 I̅c). The diffusion coefficient is inversely proportional to the pressure p of the gas (since I̅ ~ 1/p); with increasing temperature T (at constant volume), the diffusion coefficient increases proportionally to (since c̄ ~ ƲT). The diffusion coefficient decreases with increasing molecular weight.

In liquids, in accordance with the nature of the thermal motion of molecules, diffusion occurs through jumps of the molecules from one temporary equilibrium position to another. Every jump takes place by imparting to the molecule an energy sufficient to break its bonds with the neighboring molecules and to transfer it into the surroundings of other molecules (into another energetically advantageous position). The average jump does not exceed the inter-molecular distance. The diffusion motion of particles may be regarded as motion with friction to which Einstein’s second relationship is applicable: D ~ ukT. Here k is the Boltzmann constant and u is the mobility of the diffusing particles—that is, the proportionality coefficient between the particle velocity c and the moving force F during stationary motion with friction (c = uF). If the particles are spherically symmetrical, then u = 1/6 πƞr, where η is the viscosity coefficient of the liquid and r is the particle radius.

The diffusion coefficient in a liquid increases with the temperature, which is caused by the “loosening” of the structure of the liquid by heating and the consequent increase in the number of jumps per unit time.

Several diffusion mechanisms may act in a solid, including the interchange of atoms and vacancies (unoccupied points in the crystal lattice), the movement of atoms through the interstices, the simultaneous cyclical displacement of several atoms, and direct interchange of neighboring atoms. The first mechanism predominates in the formation of substitutional solid solutions; the second, in the formation of interstitial solid solutions.

The diffusion coefficient in solids is extremely sensitive to crystal lattice defects formed by heating, stresses, deformation, and other actions. The increase in the number of defects (mainly vacancies) facilitates the displacement of atoms in solids and leads to increasing diffusion coefficients. The diffusion coefficient in solids is characterized by a sharp (exponential) dependence on temperature. Thus, the diffusion coefficient for the diffusion of zinc into copper increases by a factor of 1014 when the temperature is increased from 20° to 300° C. (See Table 1 for values of the diffusion coefficient.)

For the majority of scientific and practical problems, the diffusional motion of the separate particles is of lesser importance than the resulting equalization of the concentration of matter in an initially heterogeneous medium. More particles depart from locations of high concentration than from locations of low concentration. An irreversible flow of matter, the diffusion flux j, passes through a unit area of a heterogeneous medium per unit time in the direction of lower concentration. The flux is equal to the difference in the number of particles traversing the area in both directions and is therefore proportional to the concentration gradient ∇C (the decrease in concentration per unit length). This relationship is expressed by Fick’s law (1855):

j = −D∇C

The unit of the flux j in the International System of Units is l/(m2·sec), or kg/(m’2·sec), and the unit of the concentration gradient is 1/m4, or kg/m4, from which the unit of the diffusion coefficient is m2/sec. Fick’s law is mathematically analogous to the Fourier thermal conductivity equation. A single mechanism of molecular transfer forms the basis for these phenomena: mass transfer in the former case and energy transfer in the latter.

Table 1. Values of diffusion coefficient (at atmospheric pressure)
Basic componentTemperature (°C)Diffusion coefficient (m2/sec)
Hydrogen (gas) ...............Oxygen (gas)00.70 × 10−4
Water vapor ...............Air00.23 × 10−4
Ethyl alcohol vapor ...............Air00.10 × 10−4
Salt (NaCl) ...............Water201.1 × 10−9
Sugar ...............Water200.3 × 10−9
Gold (solid) ...............Lead (solid)204 × 10−14

The presence of a concentration or chemical potential gradient in the medium is not the only condition under which diffusion occurs. The action of an external electrical field causes the diffusion of charged particles (electrodiffusion), the action of the gravitational field or pressure causes barodiffusion, and thermal diffusion occurs in a nonuniformly heated medium.

All the experimental methods for the determination of the diffusion coefficient contain two basic features, placement of the diffusing materials in contact and analysis of the composition of materials following diffusion. The composition (concentration of the diffused material) is determined chemically, optically (from the change in the index of refraction or the absorption coefficient), by methods of mass spectroscopy, or by the method of tracer atoms.

Diffusion plays an important role in chemical kinetics and technology. During a chemical reaction at the surface of a catalyst or of one of the reactants (for example, during the combustion of coal), diffusion may determine the rate of introduction of the other reactants and of removal of the reaction products—that is, it may be the limiting process.

Diffusion is usually the limiting process during evaporation and condensation, as well as the dissolution of crystals and crystallization. The diffusion of gases through porous membranes or into a stream of vapor is used for the separation of isotopes. Diffusion is the basis for many industrial processes, such as adsorption and case hardening. Diffusion welding and coating are widely used.

Diffusion of the molecules of solvent in liquid solutions through semipermeable membranes leads to the formation of osmotic pressure, which is used in the physicochemical separation method of dialysis.

D. A. FRANK-KAMENETSKII

Diffusion in biological systems. Diffusion plays an important role in the life processes of animal and plant tissues and cells (for example, diffusion of oxygen from the lungs into the blood, as well as from the blood into the tissues; absorption of the products of digestion from the digestive tract; absorption of elements of mineral nutrition by hair follicle cells; and the diffusion of ions during the generation of action potentials by the nerve and muscle cells). The various rates of diffusion of ions through cell membranes are among the physical factors affecting the selective accumulation of elements in the cells of organisms. The entry of dissolved materials into the cell may be expressed by Fick’s law, in which the value of the diffusion coefficient is replaced by the permeability coefficient of the membrane, and the concentration gradient is replaced by the difference in concentration on either side of the membrane. The diffusion penetration of the cell by gases and water is also described by Fick’s law. In this case, the values of the concentration differences are replaced by the values of the differences between the gas and osmotic pressures within and outside of the cell.

Four types of diffusion are distinguished: simple diffusion, osmosis (“limited diffusion”), active ion transport, and exchange diffusion. Simple diffusion consists of the free displacement of molecules and ions in the direction of the gradient of their chemical or electrochemical potential. Only materials of small molecular dimensions, such as water, methyl alcohol, and similar materials, may move in this way. Osmosis occurs when the cell membrane is charged and limits the diffusion of charged particles, even those of small size (for example, the weak penetration of anions into the cell). Active ion transport involves the transfer by specific “carriers” of molecules and ions that do not penetrate the membrane spontaneously or penetrate it only very weakly. Sugars and amino acids apparently penetrate the cell in this way. It is probable that both the carrier and the complex of the carrier and the substance diffuse through the membrane. The transfer of material determined by the carrier concentration gradient is called exchange diffusion; such diffusion is clearly detected in experiments using isotope tracers. The different concentrations of materials within the cell and in the surrounding medium cannot be explained exclusively by their diffusion through membranes caused by existing electrochemical and osmotic gradients. The distribution of ions is also influenced by the processes that may generate redistribution of materials in a direction opposite their electrochemical gradients with the expenditure of energy—so-called active ion transport (ionic “pumps”).

L. N. VOROB’EV and I. A. VOROB’EVA

### REFERENCES

Frenkel’, Ia. I. Sobr. izbr. trudov. Vol. 3: Kineticheskaia teoriia zhidkostei. Moscow-Leningrad, 1959.
Hirschfelder, J., C. Curtis, and R. Bird. Molekuliarnaia teoriia gazov i zhidkostei. Moscow, 1961. (Translated from English.)
Shewmon, P. Diffuziia v tverdykh telakh. Moscow, 1966. (Translated from English.)
Frank-Kamenetskii, D. A. Diffuziia i teploperedacha v khimicheskoi kinetike, 2nd ed. Moscow, 1967.
Bull, H. Fizicheskaia biokhimiia. Moscow, 1949. (Translated from English.)
Rukovodstvo po tsitologii, vol. 1. Moscow-Leningrad, 1965.
Khodorov, B. I. Problema vozbudimosti. Leningrad, 1969.

## diffusion

[də′fyü·zhən]
(acoustics)
The degree of variation in the propagation directions of sound waves over the volume of a sound field.
(electronics)
A method of producing a junction by difusing an impurity metal into a semiconductor at a high temperature.
(mechanical engineering)
The conversion of air velocity into static pressure in the diffuser casing of a centrifugal fan, resulting from increases in the radius of the air spin and in area.
(meteorology)
The exchange of fluid parcels (and hence the transport of conservative properties) between regions in space, in the apparently random motions of the parcels on a scale too small to be treated by the equations of motion; the diffusion of momentum (viscosity), vorticity, water vapor, heat (conduction), and gaseous components of the atmospheric mixture have been studied extensively.
(optics)
The distribution of incident light by reflection.
Transmission of light through a translucent material.
(physics)
The spontaneous movement and scattering of particles (atoms and molecules), of liquids, gases, and solids.
In particular, the macroscopic motion of the components of a system of fluids that is driven by differences in concentration.
(solid-state physics)
The actual transport of mass, in the form of discrete atoms, through the lattice of a crystalline solid.
The movement of carriers in a semiconductor.

## diffusion

1. Physics
a. the random thermal motion of atoms, molecules, clusters of atoms, etc., in gases, liquids, and some solids
b. the transfer of atoms or molecules by their random motion from one part of a medium to another
2. Physics the transmission or reflection of electromagnetic radiation, esp light, in which the radiation is scattered in many directions and not directly reflected or refracted; scattering
3. Physics the degree to which the directions of propagation of reverberant sound waves differ from point to point in an enclosure
4. Anthropol the transmission of social institutions, skills, and myths from one culture to another

## diffusion

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 This diagram shows the masking, etching and diffusion stages that build the tiny sublayers in a transistor.
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