Diffusion Equilibrium
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Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
s above
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
. The rate of this movement is a function of temperature,
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
of the fluid and the size (mass) of the particles. Diffusion explains the net
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of
self-diffusion According to IUPAC definition, self-diffusion coefficient is the diffusion coefficient D_i^* of species i when the chemical potential gradient equals zero. It is linked to the diffusion coefficient D_i by the equation: D_i^*=D_i\frac. Here, a_i is ...
, originating from the random motion of the molecules. The result of diffusion is a gradual mixing of material such that the distribution of molecules is uniform. Since the molecules are still in motion, but an equilibrium has been established, the result of molecular diffusion is called a "dynamic equilibrium". In a
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing. Consider two systems; S1 and S2 at the same
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
and capable of exchanging
particles In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...
. If there is a change in the
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
of a system; for example μ12 (μ is
Chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
) an
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
flow will occur from S1 to S2, because nature always prefers low energy and maximum
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
. Molecular diffusion is typically described mathematically using Fick's laws of diffusion.


Applications

Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion: *
Sintering Clinker nodules produced by sintering Sintering or frittage is the process of compacting and forming a solid mass of material by pressure or heat without melting it to the point of liquefaction. Sintering happens as part of a manufacturing ...
to produce solid materials (
powder metallurgy Powder metallurgy (PM) is a term covering a wide range of ways in which materials or components are made from metal powders. PM processes can reduce or eliminate the need for subtractive processes in manufacturing, lowering material losses and ...
, production of
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
s) *
Chemical reactor A chemical reactor is an enclosed volume in which a chemical reaction takes place. In chemical engineering, it is generally understood to be a process vessel used to carry out a chemical reaction, which is one of the classic unit operations in chem ...
design *
Catalyst Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
design in chemical industry *
Steel Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant ty ...
can be diffused (e.g., with carbon or nitrogen) to modify its properties * Doping during production of
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s.


Significance

Diffusion is part of the
transport phenomena In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechan ...
. Of mass transport mechanisms, molecular diffusion is known as a slower one.


Biology

In
cell biology Cell biology (also cellular biology or cytology) is a branch of biology that studies the structure, function, and behavior of cells. All living organisms are made of cells. A cell is the basic unit of life that is responsible for the living and ...
, diffusion is a main form of transport for necessary materials such as
amino acid Amino acids are organic compounds that contain both amino and carboxylic acid functional groups. Although hundreds of amino acids exist in nature, by far the most important are the alpha-amino acids, which comprise proteins. Only 22 alpha am ...
s within cells. Diffusion of solvents, such as water, through a
semipermeable membrane Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecul ...
is classified as
osmosis Osmosis (, ) is the spontaneous net movement or diffusion of solvent molecules through a selectively-permeable membrane from a region of high water potential (region of lower solute concentration) to a region of low water potential (region of ...
.
Metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run cell ...
and
respiration Respiration may refer to: Biology * Cellular respiration, the process in which nutrients are converted into useful energy in a cell ** Anaerobic respiration, cellular respiration without oxygen ** Maintenance respiration, the amount of cellul ...
rely in part upon diffusion in addition to bulk or active processes. For example, in the
alveoli Alveolus (; pl. alveoli, adj. alveolar) is a general anatomical term for a concave cavity or pit. Uses in anatomy and zoology * Pulmonary alveolus, an air sac in the lungs ** Alveolar cell or pneumocyte ** Alveolar duct ** Alveolar macrophage * ...
of
mammal Mammals () are a group of vertebrate animals constituting the class Mammalia (), characterized by the presence of mammary glands which in females produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or ...
ian
lung The lungs are the primary organs of the respiratory system in humans and most other animals, including some snails and a small number of fish. In mammals and most other vertebrates, two lungs are located near the backbone on either side of t ...
s, due to differences in partial pressures across the alveolar-capillary membrane,
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as wel ...
diffuses into the blood and
carbon dioxide Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
diffuses out. Lungs contain a large surface area to facilitate this gas exchange process.


Tracer, self- and chemical diffusion

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 According to IUPAC definition, self-diffusion coefficient is the diffusion coefficient D_i^* of species i when the chemical potential gradient equals zero. It is linked to the diffusion coefficient D_i by the equation: D_i^*=D_i\frac. Here, a_i is ...
(assuming no significant isotopic effect). This diffusion can take place under equilibrium. An excellent method for the measurement of
self-diffusion According to IUPAC definition, self-diffusion coefficient is the diffusion coefficient D_i^* of species i when the chemical potential gradient equals zero. It is linked to the diffusion coefficient D_i by the equation: D_i^*=D_i\frac. Here, a_i is ...
coefficients is
pulsed field gradient A pulsed field gradient is a short, timed pulse with spatial-dependent field intensity. Any gradient is identified by four characteristics: axis, strength, shape and duration. Pulsed field gradient (PFG) techniques are key to magnetic resonance ...
(PFG)
NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
, where no isotopic tracers are needed. In a so-called NMR
spin echo In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect. The NMR ...
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. * ''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 coefficient Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is enco ...
s 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

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. Chemical diffusion increases the
entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
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 A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
. Contrary to
brownian motion Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas). This pattern of motion typically consists of random fluctuations in a particle's position insi ...
, 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 The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's la ...
holds true and the diffusion coefficient ''D'' the speed of
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
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 In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
lies above a certain threshold. This is equivalent to a
precipitation In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. ...
chemical reaction (and if the considered diffusing particles are chemical molecules in solution, then it is a
precipitation In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. ...
).


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 a 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 region 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 as -dCA/dx, where CA 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 -dCB/dx. The rate of diffusion of A, NA, 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 Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion eq ...
: N_= -D_ \frac (only applicable for no bulk motion) where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases. The rate of diffusion NA, is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, this indicates that the rate of force is directly proportional to the driving force, which is the concentration gradient. This basic equation applies to a number of situations. Restricting discussion exclusively to steady state conditions, in which neither dCA/dx or dCB/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 ideal gases (of similar molar volume) A and B must be equal and opposite, that is N_A=-N_B. The partial pressure of A changes by dPA over the distance dx. Similarly, the partial pressure of B changes dPB. As there is no difference in total pressure across the element (no bulk flow), we have : \frac=-\frac. For an ideal gas the partial pressure is related to the molar concentration by the relation : P_V=n_RT where nA is the number of moles of gas ''A'' in a volume ''V''. As the molar concentration ''CA'' is equal to ''nA/ V'' therefore : P_=C_RT Consequently, for gas A, : N_=-D_ \frac \frac where DAB is the diffusivity of A in B. Similarly, : N_=-D_ \frac \frac=D_ \frac\frac Considering that dPA/dx=-dPB/dx, it therefore proves that DAB=DBA=D. If the partial pressure of A at x1 is PA1 and x2 is PA2, integration of above equation, : N_=-\frac \frac A similar equation may be derived for the counterdiffusion of gas B.


See also

* * * * * * * * * * * * * * * * * * *


References


External links


Some pictures that display diffusion and osmosis



A tutorial on the theory behind and solution of the Diffusion Equation.




* ttp://dragon.unideb.hu/~zerdelyi/Diffusion-on-the-nanoscale/node2.html A basic introduction to the classical theory of volume diffusion (with figures and animations)
Diffusion on the nanoscale (with figures and animations)
{{authority control Transport phenomena Diffusion Underwater diving physics