In
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
and
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
, permeation (also called imbuing) is the penetration of a
permeate
In physics and engineering, permeation (also called imbuing) is the penetration of a permeate (a fluid such as a liquid, gas, or vapor) through a solid. It is directly related to the concentration gradient of the permeate, a material's intrins ...
(a fluid such as a
liquid
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
,
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
, or
vapor
In physics, a vapor (American English) or vapour (British English and Canadian English; American and British English spelling differences#-our, -or, see spelling differences) is a substance in the gas phase at a temperature lower than its critic ...
) through a solid. It is directly related to the concentration gradient of the permeate, a material's
intrinsic permeability, and the materials'
mass diffusivity
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 ...
. Permeation is modeled by equations such as
Fick's laws of diffusion
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 equ ...
, and can be measured using tools such as a
minipermeameter
In petroleum engineering, a minipermeameter is a gas-based device for measuring permeability in porous rocks.
Minipermeametry has been used in the oil industry since the late 1960s (Eijpe and Weber, 1971) without becoming in any way a standard ...
.
Description
The process of permeation involves the
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 ...
of molecules, called the permeant, through a membrane or interface. Permeation works through diffusion; the permeant will move from high concentration to low concentration across the interface. A material can be semipermeable, with the presence of 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 ...
. Only molecules or ions with certain properties will be able to diffuse across such a membrane. This is a very important mechanism in biology where fluids inside a blood vessel need to be regulated and controlled. Permeation can occur through most materials including metals, ceramics and polymers. However, the permeability of metals is much lower than that of ceramics and polymers due to their crystal structure and porosity.
Permeation is something that must be considered carefully in many polymer applications, due to their high permeability. Permeability depends on the temperature of the interaction as well as the characteristics of both the polymer and the permeant component. Through the process of
sorption
Sorption is a physical and chemical process by which one substance becomes attached to another. Specific cases of sorption are treated in the following articles:
; Absorption: "the incorporation of a substance in one state into another of a dif ...
, molecules of the permeant can be either absorbed or desorbed at the interface. The permeation of a material can be measured through numerous methods that quantify the permeability of a substance through a specific material.
Permeability due to diffusion is measured in SI units of mol/(m・s・Pa) although Barrers are also commonly used. Permeability due to diffusion is not to be confused with
Permeability (earth sciences) due to fluid flow in porous solids measured in Darcy.
Related terms
* Permeant: The substance or species, ion, molecules permeating through the solid.
* Semipermeability: Property of a material to be permeable only for some substances and not for others.
* Permeation measurement: Method for the quantification of the permeability of a material for a specific substance.
History
Abbé Jean-Antoine Nollet (physicist, 1700–1770)
Nollet tried to seal wine containers with a
pig's bladder
Pig bladder (also pig's bladder) is the urinary bladder of a domestic pig, similar to the human urinary bladder. Today, this hollow organ has various applications in medicine, and in traditional cuisines and customs. Historically, the pig bladder ...
and stored them under water. After a while the bladder bulged outwards. He noticed the high pressure that discharged after he pierced the bladder. Curious, he did the experiment the other way round: he filled the container with water and stored it in wine. The result was a bulging inwards of the bladder. His notes about this experiment are the first scientific mention of permeation (later it would be called semipermeability).
Thomas Graham (chemist, 1805–1869)
Graham
Graham and Graeme may refer to:
People
* Graham (given name), an English-language given name
* Graham (surname), an English-language surname
* Graeme (surname), an English-language surname
* Graham (musician) (born 1979), Burmese singer
* Clan ...
experimentally proved the dependency of gas
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 ...
on
molecular weight
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
, which is now known as
Graham's law
Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham (chemist), Thomas Graham in 1848.Keith J. Laidler and John M. Meiser, ''Physical Chemistry'' (Benjamin/Cummings 1982), pp.&n ...
.
Richard Barrer (1910–1996)
Barrer developed the modern
Barrer Barrer is a non- SI unit of gas permeability (specifically, gas permeability) used in the membrane technology and contact lens industry. It is named after Richard Barrer.
Definition
\rm \ barrer = \frac
Here the 'cm3STP' is standard cubic c ...
measurement technique, and first used scientific methods for measuring permeation rates.
Applications
*
Packaging
Packaging is the science, art and technology of enclosing or protecting products for distribution, storage, sale, and use. Packaging also refers to the process of designing, evaluating, and producing packages. Packaging can be described as a co ...
: The permeability of the package (materials, seals, closures, etc.) needs to be matched with the sensitivity of the package contents and the specified
shelf life
Shelf life is the length of time that a commodity may be stored without becoming unfit for use, consumption, or sale. In other words, it might refer to whether a commodity should no longer be on a pantry shelf (unfit for use), or no longer on a ...
. Some packages must have nearly
hermetic seal
A hermetic seal is any type of sealing that makes a given object airtight (preventing the passage of air, oxygen, or other gases). The term originally applied to airtight glass containers, but as technology advanced it applied to a larger categor ...
s while others can (and sometimes must) be selectively permeable. Knowledge about the exact permeation rates is therefore essential.
![Fuel cell still](https://upload.wikimedia.org/wikipedia/commons/c/c3/Fuel_cell_still.gif)
*
Tires
A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
: Air pressure in tires should decrease as slowly as possible. A good tire is one that allows the least amount of gas to escape. Permeation will occur over time with the tires, so it is best to know the permeability of the material that will make up the tire with the desired gas to make the most efficient tires.
* Insulating material: Water vapour permeation of insulating material is important as well as for submarine cables to protect the conductor from
corrosion
Corrosion is a natural process that converts a refined metal into a more chemically stable oxide. It is the gradual deterioration of materials (usually a metal) by chemical or electrochemical reaction with their environment. Corrosion engine ...
.
*
Fuel cell
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most batteries in requ ...
s: Automobiles are equipped with Polymer Electrolyte Membrane (PEM) fuel cells to convert hydrogen fuel and oxygen found in the atmosphere to produce electricity. However, these cells only produce around 1.16 volts of electricity. In order to power a vehicle, multiple cells are arranged into a stack. A stack's power output depends on both the number and the size of the individual fuel cells.
* Thermoplastic and Thermosetting Piping: Pipes intended to transport water under high pressure can be considered as failed when there is a detectable permeation of water through the pipe wall to the outer surface of the pipe.
* Medical Uses: Permeation can also be seen in the medical field in drug delivery. Drug patches made up of polymer material contain a chemical reservoir that is loaded beyond its solubility, and then transferred to the body through contact. In order for the chemical to release itself into the body, it must permeate and diffuse through the polymer membrane, according to the concentration gradient. Due to the over solubility of the reservoir, transport of the drug follows the burst and lag mechanism. There is a high transfer rate of the drug when the patch makes contact with the skin, but as time increases a concentration gradient is established, meaning delivery of the drug settles to a constant rate. This is crucial in drug delivery and is used in cases such as the Ocusert System. But also the opposite case can be found in the medical field. As ampoules may contain highly sensitive pharmaceuticals for injection it is crucial that the used material prevents any kinds of substances to enter the pharmaceutical product or evaporate from it. For this, ampoules are often made from
glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
and less frequently from synthetic materials.
* Technical uses: At the production of
Halogen Lamps
A halogen lamp (also called tungsten halogen, quartz-halogen, and quartz iodine lamp) is an incandescent lamp consisting of a tungsten filament sealed in a compact transparent envelope that is filled with a mixture of an inert gas and a small ...
, halogen gases have to be encapsulated very closely.
Aluminosilicate glass can be the perfect barrier for the gas encapsulation. Hereby, the transition to the electrode is critical. But due to matching
thermal expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions.
Temperature is a monotonic function of the average molecular kinetic ...
s of the
glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
body and the metal, the transition is working.
Permeation measurement
Permeation measurement with sweep gas
The permeation of
films
A film also called a movie, motion picture, moving picture, picture, photoplay or (slang) flick is a work of visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, feelings, beauty, or atmosphere ...
and membranes can be measured with any gas or liquid. One method uses a central module which is separated by the test film: the testing gas is fed on the one side of the cell and the permeated gas is carried to the detector by a sweep gas. The diagram on the right shows a testing cell for films, normally made from metals like
stainless steel
Stainless steel is an alloy of iron that is resistant to rusting and corrosion. It contains at least 11% chromium and may contain elements such as carbon, other nonmetals and metals to obtain other desired properties. Stainless steel's corros ...
. The photo shows a testing cell for pipes made from
glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
, similar to a
Liebig condenser
The Liebig condenser (, ) or straight condenser is a piece of laboratory equipment, specifically a condenser consisting of a straight glass tube surrounded by a water jacket.
In typical laboratory operation, such as distillation, the condenser ...
. The testing medium (liquid or gas) is situated in the inner white pipe and the permeate is collected in the space between the pipe and the glass wall. It is transported by a sweep gas (connected to the upper and lower joint) to an analysing device.
Permeation can also be measured through intermittent contact. This method involves taking a sample of the test chemical and placing it on the surface of the material whose permeability is being observed while adding or removing specific amounts of the test chemical. After a known amount of time, the material is analyzed to find the concentration of the test chemical present throughout its structure. Along with the amount of time the chemical was on the material and the analysis of the test material, one can determine the cumulative permeation of the test chemical.
The following table gives examples of the calculated permeability coefficient of certain gases through a silicone membrane.
* 1 Barrer = 10
−10 cm
3 (STP) · cm /cm
2 · s · cm-Hg
Unless otherwise noted, permeabilities are measured and reported at 25 °C (RTP) and not (STP)
From W. L. Robb. Thin Silicone Membranes – Their Permeation Properties and Some Applications.
Annals of the New York Academy of Sciences, vol. 146, (January 1968) issue 1 Materials in, pp. 119–137
Approximation using Fick's First law
The flux or flow of mass of the permeate through the solid can be modeled by
Fick's first law.
:
This equation can be modified to a very simple formula that can be used in basic problems to approximate permeation through a membrane.
:
where
*
is the "diffusion flux"
*
is the diffusion coefficient or
mass diffusivity
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 ...
*
is the concentration of the permeate
*
is the thickness of the membrane
We can introduce
into this equation, which represents the sorption equilibrium parameter, which is the constant of proportionality between pressure (
) and
. This relationship can be represented as
.
:
The diffusion coefficient can be combined with the sorption equilibrium parameter to get the final form of the equation, where
is the permeability of the membrane. The relationship being
:
Solubility of a gas in a metal
In practical applications when looking at gases permeating metals, there is a way to relate gas pressure to concentration. Many gases exist as diatomic molecules when in the gaseous phase, but when permeating metals they exist in their singular ionic form.
Sieverts' law
Sieverts' law, in physical metallurgy and in chemistry, is a rule to predict the solubility of gases in metals. It is named after German chemist Adolf Sieverts (1874–1947). The law states that the solubility of a diatomic gas in metal is propor ...
states that the solubility of a gas, in the form of a diatomic molecule, in metal is proportional to the square root of the partial pressure of the gas.
The flux can be approximated in this case by the equation
:
We can introduce
into this equation, which represents the
reaction equilibrium constant. From the relationship
.
:
The diffusion coefficient can be combined with the reaction equilibrium constant to get the final form of the equation, where
is the permeability of the membrane. The relationship being
:
See also
*
*
*
*
*
*
References
Further reading
* Yam, K. L., ''Encyclopedia of Packaging Technology'', John Wiley & Sons, 2009,
* Massey, L K, ''Permeability Properties of Plastics and Elastomers'', 2003, Andrew Publishing,
* ASTM F1249 Standard Test Method for Water Vapor Transmission Rate Through Plastic Film and Sheeting Using a Modulated Infrared Sensor
* ASTM E398 Standard Test Method for Water Vapor Transmission Rate of Sheet Materials Using Dynamic Relative Humidity Measurement
* ASTM F2298 Standard Test Methods for Water Vapor Diffusion Resistance and Air Flow Resistance of Clothing Materials Using the Dynamic Moisture Permeation Cell
* F2622 Standard Test Method for Oxygen Gas Transmission Rate Through Plastic Film and Sheeting Using Various Sensors
* G1383: Standard Test Method for Permeation of Liquids and Gases through Protective Clothing Materials under Conditions of Intermittent Contact.
* "Thin silicone membranes – Their permeation properties and some applications", Annals of the New York Academy of Sciences, vol. 146, issue 1 Materials in, pp. 119–137 W. L. Robb
* ''Pharmaceutical Systems for Drug Delivery'', David Jones; Chien YW. 2nd ed. New York: Marcel Dekker, Inc; 1993. Novel drug delivery systems.
* O.V. Malykh, A.Yu. Golub, V.V. Teplyakov, "Polymeric membrane materials: New aspects of empirical approaches to prediction of gas permeability parameters in relation to permanent gases, linear lower hydrocarbons and some toxic gases", ''Advances in Colloid and Interface Science'', Volume 165, Issues 1–2, 11 May 2011, Pages 89–99 .
* Prediction of Mass Permeation in Polymers (and their Composites) based on Free Volume Theory and Sanchez-Lacombe Equation of State
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