Gibbs–Donnan effect

The Gibbs–Donnan effect (also known as the Donnan's effect, Donnan law, Donnan equilibrium, or Gibbs–Donnan equilibrium) is a name for the behaviour of charged particles near a semi-permeable membrane that sometimes fail to distribute evenly across the two sides of the membrane.[1] The usual cause is the presence of a different charged substance that is unable to pass through the membrane and thus creates an uneven electrical charge.[2] For example, the large anionic proteins in blood plasma are not permeable to capillary walls. Because small cations are attracted, but are not bound to the proteins, small anions will cross capillary walls away from the anionic proteins more readily than small cations.

Thus, some ionic species can pass through the barrier while others cannot. The solutions may be gels or colloids as well as solutions of electrolytes, and as such the phase boundary between gels, or a gel and a liquid, can also act as a selective barrier. The electric potential arising between two such solutions is called the Donnan potential.

The effect is named after the American physicist Josiah Willard Gibbs and the British chemist Frederick G. Donnan.[3]

The Donnan equilibrium is prominent in the triphasic model for articular cartilage proposed by Mow and Lai, as well as in electrochemical fuel cells and dialysis.

The Donnan effect is extra osmotic pressure attributable to cations (Na+ and K+) attached to dissolved plasma proteins.

Donnan equilibrium across a cell membrane (schematic)


The presence of a charged impermeant ion (for example, a protein) on one side of a membrane will result in an asymmetric distribution of permeant charged ions. The Gibbs–Donnan equation at equilibrium states (assuming permeant ions are Na+ and Cl):

[NaSide 1] × [ClSide 1] = [NaSide 2] × [ClSide 2]


Start Equilibrium Osmolarity
Side 1: 9 Na, 9 Cl
Side 2: 9 Na, 9 Protein
Side 1: 6 Na, 6 Cl
Side 2: 12 Na, 3 Cl, 9 Protein
Side 1: 12
Side 2: 24

Double Donnan

Note that Sides 1 and 2 are no longer in osmotic equilibrium (i.e. the total osmolytes on each side are not the same)

In vivo, ion balance does not equilibriate at the proportions that would be predicted by the Gibbs-Donnan model, because the cell cannot tolerate the attendant large influx of water. This is balanced by instating a functionally impermeant cation, Na+, extracellularly to counter the anionic protein. Na+ does cross the membrane via leak channels (the permeability is approximately 1/10 that of K+, the most permeant ion) but, as per the pump-leak model, it is extruded by the Na+/K+-ATPase[4].

pH change

Because there is a difference in concentration of ions on either side of the membrane, the pH may also differ when protons are involved. In many instances, from ultrafiltration of proteins to ion exchange chromatography, the pH of the buffer adjacent to the charged groups of the membrane is different from the pH of the rest of the buffer solution.[5] When the charged groups are negative (basic), then they will attract protons so that the pH will be lower than the surrounding buffer. When the charged groups are positive (acidic), then they will repel protons so that the pH will be higher than the surrounding buffer.

Physiological Applications

Red Blood Cells

When tissue cells are in a protein-containing fluid, the Donnan effect of the cytoplasmic proteins is equal and opposite to the Donnan effect of the extracellular proteins. The opposing Donnan effects cause chloride ions to migrate inside the cell, increasing the intracellular chloride concentration. The Donnan effect may explain why some red blood cells do not have active sodium pumps; the effect relieves the osmotic pressure of plasma proteins, which is why sodium pumping is less important for maintaining the cell volume .[6]


Brain tissue swelling, known as cerebral oedema, results from brain injury and other traumatic head injuries that can increase intracranial pressure (ICP). Negatively charged molecules within cells create a fixed charge density, which increases intracranial pressure through the Donnan effect. ATP pumps maintain a negative membrane potential even though negative charges leak across the membrane; this action establishes a chemical and electrical gradient.[7]

The negative charge in the cell and ions outside the cell creates a thermodynamic potential; if damage occurs to the brain and cells lose their membrane integrity, ions will rush into the cell to balance chemical and electrical gradients that were previously established. The membrane voltage will become zero, but the chemical gradient will still exist. To neutralize the negative charges within the cell, cations flow in, which increases the osmotic pressure inside relative to the outside of the cell. The increased osmotic pressure forces water to flow into the cell and tissue swelling occurs.[8]

See also


  1. ^ "Gibbs-Donnan effect". Archived from the original on 2007-06-18. Retrieved 2006-08-28.
  2. ^ The Gibbs–Donnan Equilibrium..., D.C. Mikulecky, retrieved 28 August 2006
  3. ^ Donnan, F.G. (1911). "Theorie der Membrangleichgewichte und Membranpotentiale bei Vorhandensein von nicht dialysierenden Elektrolyten. Ein Beitrag zur physikalisch-chemischen Physiologie" [The theory of membrane equilibrium and membrane potential in the presence of a non-dialyzable electrolyte. A contribution to physical-chemical physiology]. Zeitschrift für Elektrochemie und Angewandte Physikalische Chemie. 17 (10): 572–581.
  4. ^ Leaf, Alexander (1959). "Maintenance of Concentration Gradients and Regulation of Cell Volume". Annals of the New York Academy of Sciences. 72 (12): 396–404. doi:10.1111/j.1749-6632.1959.tb44168.x. PMID 13627925.
  5. ^ Bolton, Glen R.; Boesch, Austin W.; Basha, Jonida; LaCasse, Daniel P.; Kelley, Brian D.; Acharya, Hari (2011-01-01). "Effect of protein and solution properties on the donnan effect during the ultrafiltration of proteins". Biotechnology Progress. 27 (1): 140–152. doi:10.1002/btpr.523. ISSN 1520-6033. PMID 21312362.
  6. ^ Kurbel, S. (2011). Donnan effect on chloride ion distribution as a determinant of body fluid composition that allows action potentials to spread via fast sodium channels. Theoretical Biology & Medical Modelling, 8, 16.
  7. ^ Elkin, Benjamin S.; Shaik, Mohammed A.; Morrison, Barclay (13 February 2010). "Fixed negative charge and the Donnan effect: a description of the driving forces associated with brain tissue swelling and oedema". Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences. 368 (1912): 585–603. doi:10.1098/rsta.2009.0223. PMC 2944388. PMID 20047940.
  8. ^ Elkin, B. S., Shaik, M. A., & Morrison, B. (2010). Fixed negative charge and the Donnan effect: a description of the driving forces associated with brain tissue swelling and oedema. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences, 368(1912), 585–603.
  • IUPAC Compendium of Chemical Terminology 2nd Edition (1997)
  • Van C. Mow Basic orthopaedic biomechanics and mechano-biology, 2nd Ed. Lippincott Williams & Wilkins, Philadelphia, 2005
  • Mapleson WW. "Computation of the effect of Donnan equilibrium on pH in equilibrium dialysis". Journal of Pharmacological Methods, May 1987.

External links

Extracellular fluid

Extracellular fluid (ECF) denotes all body fluid outside the cells. Total body water in humans makes up between 45 to 75% of total body weight. About two thirds of this is intracellular fluid within cells, and one third is the extracellular fluid. The main component of the extracellular fluid is the interstitial fluid that bathes cells.

Extracellular fluid is the internal environment of all multicellular animals, and in those animals with a blood circulatory system a proportion of this fluid is blood plasma. Plasma and interstitial fluid are the two components that make up at least 97% of the ECF. Lymph makes up a small percentage of the interstitial fluid. The remaining small portion of the ECF includes the transcellular fluid (about 2.5%). The ECF can also be seen as having two components – plasma and lymph as a delivery system, and interstitial fluid for water and solute exchange with the cells.The extracellular fluid, in particular the interstitial fluid, constitutes the body's internal environment that bathes all of the cells in the body. The ECF composition is therefore crucial for their normal functions, and is maintained by a number of homeostatic mechanisms involving negative feedback. Homeostasis regulates, among others, the pH, sodium, potassium, and calcium concentrations in the ECF. The volume of body fluid, blood glucose, oxygen, and carbon dioxide levels are also tightly homeostatically maintained.

The volume of extracellular fluid in a young adult male of 70 kg (154 lbs) is 20% of body weight – about fourteen litres. Eleven litres is interstitial fluid and the remaining three litres is plasma.

Frederick G. Donnan

Frederick George Donnan CBE FRS FRSE (6 September 1870 – 16 December 1956) was an Irish physical chemist who is known for his work on membrane equilibria, and commemorated in the Donnan equilibrium describing ionic transport in cells. He spent most of his career at University College London.

Index of physics articles (G)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Ion chromatography

Ion chromatography (or ion-exchange chromatography) is a chromatography process that separates ions and polar molecules based on their affinity to the ion exchanger. It works on almost any kind of charged molecule—including large proteins, small nucleotides, and amino acids. However, ion chromatography must be done in conditions that are one unit away from the isoelectric point of a protein.The two types of ion chromatography are anion-exchange and cation-exchange. Cation-exchange chromatography is used when the molecule of interest is positively charged. The molecule is positively charged because the pH for chromatography is less than the pI. In this type of chromatography, the stationary phase is negatively charged and positively charged molecules are loaded to be attracted to it. Anion-exchange chromatography is when the stationary phase is positively charged and negatively charged molecules (meaning that pH for chromatography is greater than the pI) are loaded to be attracted to it. It is often used in protein purification, water analysis, and quality control. The water-soluble and charged molecules such as proteins, amino acids, and peptides bind to moieties which are oppositely charged by forming ionic bonds to the insoluble stationary phase. The equilibrated stationary phase consists of an ionizable functional group where the targeted molecules of a mixture to be separated and quantified can bind while passing through the column—a cationic stationary phase is used to separate anions and an anionic stationary phase is used to separate cations. Cation exchange chromatography is used when the desired molecules to separate are cations and anion exchange chromatography is used to separate anions. The bound molecules then can be eluted and collected using an eluant which contains anions and cations by running higher concentration of ions through the column or changing pH of the column.

One of the primary advantages for the use of ion chromatography is only one interaction involved during the separation as opposed to other separation techniques; therefore, ion chromatography may have higher matrix tolerance. Another advantage of ion exchange, is the predictably of elution patterns (based on the presence of the ionizable group). For example, when cation exchange chromatography is used, cations will elute out last. Meanwhile, the negative charged molecules will elute out first. However, there are also disadvantages involved when performing ion-exchange chromatography, such as constant evolution with the technique which leads to the inconsistency from column to column. A major limitation to this purification technique is that it is limited to ionizable group.

Josiah Willard Gibbs

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period).

In 1863, Yale awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his career at Yale, where he was professor of mathematical physics from 1871 until his death. Working in relative isolation, he became the earliest theoretical scientist in the United States to earn an international reputation and was praised by Albert Einstein as "the greatest mind in American history". In 1901, Gibbs received what was then considered the highest honor awarded by the international scientific community, the Copley Medal of the Royal Society of London, "for his contributions to mathematical physics".Commentators and biographers have remarked on the contrast between Gibbs's quiet, solitary life in turn of the century New England and the great international impact of his ideas. Though his work was almost entirely theoretical, the practical value of Gibbs's contributions became evident with the development of industrial chemistry during the first half of the 20th century. According to Robert A. Millikan, in pure science, Gibbs "did for statistical mechanics and for thermodynamics what Laplace did for celestial mechanics and Maxwell did for electrodynamics, namely, made his field a well-nigh finished theoretical structure".

List of effects

This is a list of names for observable phenomena that contain the word effect, amplified by reference(s) to their respective fields of study.

List of things named after Josiah W. Gibbs

Things named after American scientist Josiah Willard Gibbs:

Gibbs–Donnan effect

Gibbs–Duhem equation

Gibbs–Helmholtz equation

Gibbs–Marangoni effect

Gibbs–Thomson effect

Gibbs algorithm

Gibbs distribution

Gibbs energy, see Gibbs free energy

Gibbs ensemble

Gibbs entropy

Gibbs free energy

Gibbs H-theorem

Gibbs' inequality

Gibbs isotherm

Gibbs lemma

Gibbs measure

Gibbs phase rule

Gibbs paradox

Gibbs phenomenon

Gibbs random field

Gibbs sampling

Gibbs state

Gibbs's thermodynamic surface

Gibbs vector

Massieu–Gibbs function, see Massieu function

Membrane potential

Membrane potential (also transmembrane potential or membrane voltage) is the difference in electric potential between the interior and the exterior of a biological cell. With respect to the exterior of the cell, typical values of membrane potential, normally given in millivolts, range from –40 mV to –80 mV.

All animal cells are surrounded by a membrane composed of a lipid bilayer with proteins embedded in it. The membrane serves as both an insulator and a diffusion barrier to the movement of ions. Transmembrane proteins, also known as ion transporter or ion pump proteins, actively push ions across the membrane and establish concentration gradients across the membrane, and ion channels allow ions to move across the membrane down those concentration gradients. Ion pumps and ion channels are electrically equivalent to a set of batteries and resistors inserted in the membrane, and therefore create a voltage between the two sides of the membrane.

Almost all plasma membranes have an electrical potential across them, with the inside usually negative with respect to the outside. The membrane potential has two basic functions. First, it allows a cell to function as a battery, providing power to operate a variety of "molecular devices" embedded in the membrane. Second, in electrically excitable cells such as neurons and muscle cells, it is used for transmitting signals between different parts of a cell. Signals are generated by opening or closing of ion channels at one point in the membrane, producing a local change in the membrane potential. This change in the electric field can be quickly affected by either adjacent or more distant ion channels in the membrane. Those ion channels can then open or close as a result of the potential change, reproducing the signal.

In non-excitable cells, and in excitable cells in their baseline states, the membrane potential is held at a relatively stable value, called the resting potential. For neurons, typical values of the resting potential range from –70 to –80 millivolts; that is, the interior of a cell has a negative baseline voltage of a bit less than one-tenth of a volt. The opening and closing of ion channels can induce a departure from the resting potential. This is called a depolarization if the interior voltage becomes less negative (say from –70 mV to –60 mV), or a hyperpolarization if the interior voltage becomes more negative (say from –70 mV to –80 mV). In excitable cells, a sufficiently large depolarization can evoke an action potential, in which the membrane potential changes rapidly and significantly for a short time (on the order of 1 to 100 milliseconds), often reversing its polarity. Action potentials are generated by the activation of certain voltage-gated ion channels.

In neurons, the factors that influence the membrane potential are diverse. They include numerous types of ion channels, some of which are chemically gated and some of which are voltage-gated. Because voltage-gated ion channels are controlled by the membrane potential, while the membrane potential itself is influenced by these same ion channels, feedback loops that allow for complex temporal dynamics arise, including oscillations and regenerative events such as action potentials.


Nanofiltration (NF) is a relatively recent membrane filtration process used most often with low total dissolved solids water such as surface water and fresh groundwater, with the purpose of softening (polyvalent cation removal) and removal of disinfection by-product precursors such as natural organic matter and synthetic organic matter.Nanofiltration is also becoming more widely used in food processing applications such as dairy, for simultaneous concentration and partial (monovalent ion) demineralisation.

Osmotic pressure

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 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.

Osmosis occurs when two solutions, containing different concentration of solute, are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules will continue until equilibrium is attained.


Osteoarthritis (OA) is a type of joint disease that results from breakdown of joint cartilage and underlying bone. The most common symptoms are joint pain and stiffness. Initially, symptoms may occur only following exercise, but over time may become constant. Other symptoms may include joint swelling, decreased range of motion, and, when the back is affected, weakness or numbness of the arms and legs. The most commonly involved joints are those near the ends of the fingers, at the base of the thumb, neck, lower back, knee, and hips. Joints on one side of the body are often more affected than those on the other. Usually the symptoms come on over years. It can affect work and normal daily activities. Unlike other types of arthritis, only the joints are typically affected.Causes include previous joint injury, abnormal joint or limb development, and inherited factors. Risk is greater in those who are overweight, have one leg of a different length, and have jobs that result in high levels of joint stress. Osteoarthritis is believed to be caused by mechanical stress on the joint and low grade inflammatory processes. It develops as cartilage is lost and the underlying bone becomes affected. As pain may make it difficult to exercise, muscle loss may occur. Diagnosis is typically based on signs and symptoms, with medical imaging and other tests occasionally used to either support or rule out other problems. In contrast to rheumatoid arthritis, which is primarily an inflammatory condition, in osteoarthritis, the joints do not become hot or red.Treatment includes exercise, efforts to decrease joint stress, support groups, and pain medications. Efforts to decrease joint stress include resting and the use of a cane. Weight loss may help in those who are overweight. Pain medications may include paracetamol (acetaminophen) as well as NSAIDs such as naproxen or ibuprofen. Long-term opioid use is generally discouraged due to lack of information on benefits as well as risks of addiction and other side effects. If pain interferes with normal life despite other treatments, joint replacement surgery may help. An artificial joint typically lasts 10 to 15 years.Osteoarthritis is the most common form of arthritis, affecting about 237 million (3.3% of the population). Among those over 60 years old, about 10% of males and 18% of females are affected. It is the cause of about 2% of years lived with disability. In Australia, about 1.9 million people are affected, and in the United States, 30 to 53 million people are affected. It becomes more common in both sexes as people become older.

Scientific phenomena named after people

This is a list of scientific phenomena and concepts named after people (eponymous phenomena). For other lists of eponyms, see eponym.

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