Permeation

Last updated August 22, 2024

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 intrinsic permeability, and the materials' mass diffusivity.^[1] Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.

Description

The process of permeation involves the diffusion 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. 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, 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.^[2]^[3]

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 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 experimentally proved the dependency of gas diffusion on molecular weight, which is now known as Graham's law.

Richard Barrer (1910–1996)

Barrer developed the modern Barrer measurement technique, and first used scientific methods for measuring permeation rates.

Applications

Packaging: 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. Some packages must have nearly hermetic seals while others can (and sometimes must) be selectively permeable. Knowledge about the exact permeation rates is therefore essential.

Tires: 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.
Fuel cells: 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 and less frequently from synthetic materials.
Technical uses: At the production of Halogen Lamps, 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 expansions of the glass body and the metal, the transition is working.

Permeation measurement

The permeation of films 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. The photo shows a testing cell for pipes made from glass, similar to a Liebig 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.

Gas Name	Chemical Formula	Silicone Permeability Coefficient (Barrer)*
Oxygen	O₂	600
Hydrogen	H₂	650
Carbon Dioxide	CO₂	3250
Methanol	CH₃OH	13900
Water	H₂O	36000

* 1 Barrer = 10⁻¹⁰ cm³ (STP) · cm /cm² · 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 ^[4]

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.

{\bigg .}J=-D{\frac {\partial \phi }{\partial x}}{\bigg .}

This equation can be modified to a very simple formula that can be used in basic problems to approximate permeation through a membrane.

{\bigg .}J=-D{\frac {(C_{2}-C_{1})}{\delta }}{\bigg .}

where

$J$ is the "diffusion flux"
$\,D$ is the diffusion coefficient or mass diffusivity
$C$ is the concentration of the permeate
$\,\delta$ is the thickness of the membrane

We can introduce $S$ into this equation, which represents the sorption equilibrium parameter, which is the constant of proportionality between pressure ( $p$ ) and $C$ . This relationship can be represented as $C=Sp$ .

{\bigg .}J=-D{\frac {S(p_{2}-p_{1})}{\delta }}{\bigg .}

The diffusion coefficient can be combined with the sorption equilibrium parameter to get the final form of the equation, where $P$ is the permeability of the membrane. The relationship being $P=SD$

{\bigg .}J=-{\frac {P(p_{2}-p_{1})}{\delta }}{\bigg .}

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 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

{\bigg .}J=-D{\frac {(S_{1}-S_{2})}{\delta }}{\bigg .}

We can introduce $K$ into this equation, which represents the reaction equilibrium constant. From the relationship $S={K{\sqrt {p_{N}}}}$ .

{\bigg .}J=-D{\frac {K({\sqrt {p_{1}}}-{\sqrt {p_{2}}})}{\delta }}{\bigg .}

The diffusion coefficient can be combined with the reaction equilibrium constant to get the final form of the equation, where $P$ is the permeability of the membrane. The relationship being $P=KD$

{\bigg .}J=-{\frac {P({\sqrt {p_{1}}}-{\sqrt {p_{2}}})}{\delta }}{\bigg .}

Related Research Articles

<span class="mw-page-title-main">Molecular diffusion</span> Thermal motion of liquid or gas particles at temperatures above absolute zero

Molecular diffusion, often simply called diffusion, is the thermal motion of all 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. 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, 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 with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.

<span class="mw-page-title-main">Fick's laws of diffusion</span> Mathematical descriptions of molecular diffusion

Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, $D$ . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in its pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane.

Permeability, permeable, and semipermeable may refer to:

Adsorption is the adhesion of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. This process creates a film of the adsorbate on the surface of the adsorbent. This process differs from absorption, in which a fluid is dissolved by or permeates a liquid or solid. While adsorption does often precede absorption, which involves the transfer of the absorbate into the volume of the absorbent material, alternatively, adsorption is distinctly a surface phenomenon, wherein the adsorbate does not penetrate through the material surface and into the bulk of the adsorbent. The term sorption encompasses both adsorption and absorption, and desorption is the reverse of sorption.

Semipermeable membrane is a type of synthetic or biologic, polymeric membrane that allows certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecules or solutes on either side, as well as the permeability of the membrane to each solute. Depending on the membrane and the solute, permeability may depend on solute size, solubility, properties, or chemistry. How the membrane is constructed to be selective in its permeability will determine the rate and the permeability. Many natural and synthetic materials which are rather thick are also semipermeable. One example of this is the thin film on the inside of an egg.

Permeability in fluid mechanics, materials science and Earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.

A relatively static membrane potential which is usually referred to as the ground value for trans-membrane voltage.

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference via the hydraulic conductivity. In fact, the Darcy's law is a special case of the Stokes equation for the momentum flux, in turn deriving from the momentum Navier-Stokes equation.

Gas mixtures can be effectively separated by synthetic membranes made from polymers such as polyamide or cellulose acetate, or from ceramic materials.

The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the Resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane.

Absorption is the journey of a drug travelling from the site of administration to the site of action.

The Glossary of fuel cell terms lists the definitions of many terms used within the fuel cell industry. The terms in this fuel cell glossary may be used by fuel cell industry associations, in education material and fuel cell codes and standards to name but a few.

<span class="mw-page-title-main">Diffusion</span> Transport of dissolved species from the highest to the lowest concentration region

Diffusion is the net movement of anything 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 potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing.

A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Membranes can be generally classified into synthetic membranes and biological membranes. Biological membranes include cell membranes ; nuclear membranes, which cover a cell nucleus; and tissue membranes, such as mucosae and serosae. Synthetic membranes are made by humans for use in laboratories and industry.

In electrochemistry, the Randles–Ševčík equation describes the effect of scan rate on the peak current for a cyclic voltammetry experiment. For simple redox events where the reaction is electrochemically reversible, and the products and reactants are both soluble, such as the ferrocene/ferrocenium couple, $i p$ depends not only on the concentration and diffusional properties of the electroactive species but also on scan rate.

Membraneless Fuel Cells convert stored chemical energy into electrical energy without the use of a conducting membrane as with other types of Fuel Cells. In Laminar Flow Fuel Cells (LFFC) this is achieved by exploiting the phenomenon of non-mixing laminar flows where the interface between the two flows works as a proton/ion conductor. The interface allows for high diffusivity and eliminates the need for costly membranes. The operating principles of these cells mean that they can only be built to millimeter-scale sizes. The lack of a membrane means they are cheaper but the size limits their use to portable applications which require small amounts of power.

Membrane technology encompasses the scientific processes used in the construction and application of membranes. Membranes are used to facilitate the transport or rejection of substances between mediums, and the mechanical separation of gas and liquid streams. In the simplest case, filtration is achieved when the pores of the membrane are smaller than the diameter of the undesired substance, such as a harmful microorganism. Membrane technology is commonly used in industries such as water treatment, chemical and metal processing, pharmaceuticals, biotechnology, the food industry, as well as the removal of environmental pollutants.

<span class="mw-page-title-main">Membrane osmometer</span>

A membrane osmometer is a device used to indirectly measure the number average molecular weight of a polymer sample. One chamber contains pure solvent and the other chamber contains a solution in which the solute is a polymer with an unknown $. The osmotic pressure of the solvent across the semipermeable membrane is measured by the membrane osmometer. This osmotic pressure measurement is used to calculate for the sample.$

The solution-friction model is a mechanistic transport model developed to describe the transport processes across porous membranes, such as reverse osmosis (RO) and nanofiltration (NF). Unlike traditional models, such as those based on Darcy’s law, which primarily describes pressure-driven solvent (water) transport in homogeneous porous mediums, the SF model also accounts for the coupled transport of both solvent (water) and solutes (salts).

References

↑ Fu, Jinlong; Thomas, Hywel R.; Li, Chenfeng (January 2021). "Tortuosity of porous media: Image analysis and physical simulation" (PDF). Earth-Science Reviews. 212: 103439. Bibcode:2021ESRv..21203439F. doi:10.1016/j.earscirev.2020.103439. S2CID 229386129.
↑ Carley, James F. Whittington's dictionary of plastics. CRC Press, 1993.
↑ Carley, James F. (8 October 1993). Whittington's Dictionary of Plastics, Third Edition. CRC Press. ISBN 9781566760904 . Retrieved 20 September 2017– via Google Books.
↑ Robb, W. L. (1968). "Thin Silicone Membranes-Their Permeation Properties and Some Applications". Annals of the New York Academy of Sciences. 146 (1): 119–137. Bibcode:1968NYASA.146..119R. doi:10.1111/j.1749-6632.1968.tb20277.x. PMID 5238627. S2CID 28605088.