Hydrogen production

From Wikipedia, the free encyclopedia

Hydrogen production is the family of industrial methods for generating hydrogen. Hydrogen is primarily produced by steam reforming of natural gas. Other major sources include naphtha or oil reforming of refinery or other industrial off-gases, and partial oxidation of coal and other hydrocarbons. A small amount is obtained by water electrolysis and other sources.

 

Steam-methane reforming is a mature production process in which high-temperature steam (700 °C–1,000 °C) is used to produce hydrogen from natural gas. Methane reacts with steam under 3–25 bar pressure in the presence of a catalyst to produce hydrogen, carbon monoxide, and a relatively small amount of carbon dioxide. For steam reforming to proceed, heat must be supplied to the process. In a separate reactor vessel, the carbon monoxide and steam are reacted using a catalyst to produce carbon dioxide and more hydrogen. In a final process step called "pressure-swing adsorption," carbon dioxide and other impurities are removed from the gas stream, leaving essentially pure hydrogen. Steam reforming can also be used to produce hydrogen from other fuels, such as coal and oil products.

There are no natural hydrogen deposits, but hydrogen is required for essential chemical processes. Therefore, the production of hydrogen plays a key role in any industrialized society. The hydrogen generation market is expected to be valued at $115.25 billion USD in 2017. Millions of tons of hydrogen were consumed on-site in oil refining, and in the production of ammonia (Haber process) and methanol (reduction of carbon monoxide). Hydrogen is also produced as a by-product of the chlor-alkali process.

As of 1999, the majority of hydrogen (∼95%) is produced from fossil fuels by steam reforming or partial oxidation of methane and coal gasification with only a small quantity by other routes such as biomass gasification or electrolysis of water. Around 8GW of electrolysis capacity is installed worldwide, accounting for around 4% of global hydrogen production. Developing affordable methods for producing hydrogen with less damage to the environment is a goal of the hydrogen economy. Electrolysis of water using electricity produced from fossil fuels emits significant amounts of CO2.

Steam reforming

There are four main sources for the commercial production of hydrogen: natural gas, oil, coal, and electrolysis; which account for 48%, 30%, 18% and 4% of the world’s hydrogen production respectively. Fossil fuels are the dominant source of industrial hydrogen. Carbon dioxide can be separated from natural gas with a 70-85% efficiency for hydrogen production and from other hydrocarbons to varying degrees of efficiency. Specifically, bulk hydrogen is usually produced by the steam reforming of methane or natural gas. The production of hydrogen from natural gas is the cheapest source of hydrogen currently. This process consists of heating the gas to between 700-1100 °C in the presence of steam and a nickel catalyst. The resulting endothermic reaction breaks up the methane molecules and forms carbon monoxide CO and hydrogen H₂. The carbon monoxide gas can then be passed with steam over iron oxide or other oxides and undergo a water gas shift reaction to obtain further quantities of H₂. The downside to this process is that its major byproducts are CO, CO₂ and other greenhouse gases. Depending on the quality of the feedstock (natural gas, rich gases, naphtha, etc.), one ton of hydrogen produced will also produce 9 to 12 tons of CO₂.

For this process high temperature (700–1100 °C) steam (H₂O) reacts with methane (CH₄) in an endothermic reaction to yield syngas.

Gasification

CH₄ + H₂O → CO + 3 H₂

In a second stage, additional hydrogen is generated through the lower-temperature, exothermic, water gas shift reaction, performed at about 360 °C:

CO + H₂O → CO₂ + H₂

Essentially, the oxygen (O) atom is stripped from the additional water (steam) to oxidize CO to CO₂. This oxidation also provides energy to maintain the reaction. Additional heat required to drive the process is generally supplied by burning some portion of the methane.

CO₂ sequestration

Steam reforming generates carbon dioxide (CO₂). Since the production is concentrated in one facility, it is possible to separate the CO₂ and dispose of it without atmospheric release, for example by injecting it in an oil or gas reservoir, although this is not currently done in most cases. A carbon dioxide injection project has been started by the Norwegian company Statoil in the North Sea, at the Sleipner field.

Integrated steam reforming / co-generation - It is possible to combine steam reforming and co-generation of steam and power into a single plant. This can deliver benefits for an oil refinery because it is more efficient than separate hydrogen, steam and power plants. Air Products recently built an integrated steam reforming / co-generation plant in Port Arthur, Texas.

Other production methods from fossil fuels

Partial oxidation

Hydrogen production from natural gas or other hydrocarbons is achieved by partial oxidation. A fuel-air or fuel-oxygen mixture is partially combusted resulting in a hydrogen rich syngas. Hydrogen and carbon monoxide are obtained via the water-gas shift reaction. Carbon dioxide can be co-fed to lower the hydrogen to carbon monoxide ratio. 

The partial oxidation reaction occurs when a substoichiometric fuel-air mixture or fuel-oxygen is partially combusted in a reformer or partial oxidation reactor. A distinction is made between thermal partial oxidation (TPOX) and catalytic partial oxidation (CPOX). The chemical reaction takes the general form:

C_nH_m + ⁿ/₂ O₂ → n CO + ^m/₂ H₂

Idealized examples for heating oil and coal, assuming compositions C₁₂H₂₄ and C₂₄H₁₂ respectively, are as follows:

C₁₂H₂₄ + 6 O₂ → 12 CO + 12 H₂

C₂₄H₁₂ + 12 O₂ → 24 CO + 6 H₂

Plasma reforming

The Kværner-process or Kvaerner carbon black & hydrogen process (CB&H) is a plasma reforming method, developed in the 1980s by a Norwegian company of the same name, for the production of hydrogen and carbon black from liquid hydrocarbons (C_nH_m). Of the available energy of the feed, approximately 48% is contained in the hydrogen, 40% is contained in activated carbon and 10% in superheated steam. CO₂ is not produced in the process. 

A variation of this process is presented in 2009 using plasma arc waste disposal technology for the production of hydrogen, heat and carbon from methane and natural gas in a plasma converter.

Coal

For the production of hydrogen from coal, coal gasification is used. The process of coal gasification uses steam and a carefully controlled concentration of gases to break molecular bonds in coal and form a gaseous mix of hydrogen and carbon monoxide. This source of hydrogen is advantageous since its main product is coal-derived gas which can be used for fuel. The gas obtained from coal gasification can later be used to produce electricity more efficiently and allow a better capture of greenhouse gases than the traditional burning of coal.

Another method for conversion is low temperature and high temperature coal carbonization.

Petroleum coke

Similarly to coal, petroleum coke can also be converted in hydrogen rich syngas, via coal gasification. The syngas in this case consists mainly of hydrogen, carbon monoxide and H₂S, depending on the sulfur content of the coke feed. Gasification is an attractive option for producing hydrogen from almost any carbon source, while providing attractive hydrogen utilization alternatives through process integration.

From water

Many technologies have been explored but, as of 2007, "Thermal, thermochemical, biochemical and photochemical processes have so far not found industrial applications." High temperature electrolysis of alkaline solutions has been used for the industrial scale production of hydrogen and there are now a number of small scale polymer electrolyte membrane (PEM) electrolysis units available commercially.

Gas Extraction

Electrolysis consists of using electricity to split water into hydrogen and oxygen. Electrolysis of water is 70-80% efficient (a 20-30% conversion loss) while steam reforming of natural gas has a thermal efficiency between 70-85%. The (electrical) efficiency of electrolysis is expected to reach 82-86% before 2030, while also maintaining durability as progress in this area continues at a pace. Water electrolysis can operate between 50-80 °C, while steam methane reforming requires temperatures between 700-1100 °C. The difference between the two methods is the primary energy used; either electricity (for electrolysis) or natural gas (for steam methane reforming). Due to their use of water, a readily available resource, electrolysis and similar water-splitting methods have attracted the interest of the scientific community. With the objective of reducing the cost of hydrogen production, renewable sources of energy have been targeted to allow electrolysis. There are three main types of cells, solid oxide electrolysis cells (SOECs), polymer electrolyte membrane cells (PEM) and alkaline electrolysis cells (AECs). SOECs operate at high temperatures, typically around 800 °C. At these high temperatures a significant amount of the energy required can be provided as thermal energy (heat), and as such is termed High temperature electrolysis. The heat energy can be provided from a number of different sources, including waste industrial heat, nuclear power stations or concentrated solar thermal plants. This has the potential to reduce the overall cost of the hydrogen produced by reducing the amount of electrical energy required for electrolysis. PEM electrolysis cells typically operate below 100 °C and are becoming increasingly available commercially. These cells have the advantage of being comparatively simple and can be designed to accept widely varying voltage inputs which makes them ideal for use with renewable sources of energy such as solar PV. AECs optimally operate at high concentrations electrolyte (KOH or potassium carbonate) and at high temperatures, often near 200 °C.

Industrial output and efficiency

Efficiency of modern hydrogen generators is measured by energy consumed per standard volume of hydrogen (MJ/m³), assuming standard temperature and pressure of the H₂. The lower the energy used by a generator, the higher would be its efficiency; a 100%-efficient electrolyser would consume 39.4 kilowatt-hours per kilogram (142 MJ/kg) of hydrogen, 12,749 joules per litre (12.75 MJ/m³). Practical electrolysis (using a rotating electrolyser at 15 bar pressure) may consume 50 kilowatt-hours per kilogram (180 MJ/kg), and a further 15 kilowatt-hours (54 MJ) if the hydrogen is compressed for use in hydrogen cars.

Electrolyser vendors provide efficiencies based on enthalpy. To assess the claimed efficiency of an electrolyser it is important to establish how it was defined by the vendor (i.e. what enthalpy value, what current density, etc.). 

There are two main technologies available on the market, alkaline and proton exchange membrane (PEM) electrolysers. Traditionally, alkaline electrolysers are cheaper in terms of investment (they generally use nickel catalysts), but less efficient; PEM electrolysers, conversely, are more expensive (they generally use expensive platinum-group metal catalysts) but are more efficient and can operate at higher current densities, and can therefore be possibly cheaper if the hydrogen production is large enough. 

Conventional alkaline electrolysis has an efficiency of about 70%, however thyssenkrupp have recently developed an advanced alkaline water electrolyser with an efficiency of 82%. Accounting for the use of the higher heat value (because inefficiency via heat can be redirected back into the system to create the steam required by the catalyst), average working efficiencies for PEM electrolysis are around 80%, or 82% using the most modern alkaline electrolysers. PEM efficiency is expected to increase to approximately 86% before 2030. Theoretical efficiency for PEM electrolysers are predicted up to 94%.

H₂ production cost ($-gge untaxed) at varying natural gas prices

 

Considering the industrial production of hydrogen, and using current best processes for water electrolysis (PEM or alkaline electrolysis) which have an effective electrical efficiency of 70-82%, producing 1 kg of hydrogen (which has a specific energy of 143 MJ/kg or about 40 kWh/kg) requires 50–55 kWh of electricity. At an electricity cost of $0.06/kWh, as set out in the Department of Energy hydrogen production targets for 2015, the hydrogen cost is $3/kg. With the range of natural gas prices from 2016 as shown in the graph (Hydrogen Production Tech Team Roadmap, November 2017) putting the cost of SMR hydrogen at between $1.20 and $1.50, the cost price of hydrogen via electrolysis is still over double 2015 DOE hydrogen target prices. The US DOE target price for hydrogen in 2020 is $2.30/kg, requiring an electricity cost of $0.037/kWh, which is achievable given recent PPA tenders for wind and solar in many regions. This puts the $4/gge H2 dispensed objective well within reach, and close to a slightly elevated natural gas production cost for SMR. 

In many cases, the advantage of electrolysis over SMR hydrogen is that the hydrogen can be produced on-site, meaning that the costly process of delivery via truck or pipeline is avoided. 

In other parts of the world, steam methane reforming is between $1–3/kg on average. This makes production of hydrogen via electrolysis cost competitive in many regions already, as outlined by Nel Hydrogen and others, including an article by the IEA examining the conditions which could lead to a competitive advantage for electrolysis.

Chemically assisted electrolysis (Carbon/hydrocarbon assisted water electrolysis; CAWE)

In addition to reducing the voltage required for electrolysis via the increasing of the temperature of the electrolysis cell it is also possible to electrochemically consume the oxygen produced in an electrolyser by introducing a fuel (such as carbon/coal, methanol, ethanol, formic acid, glycerol, etc.) into the oxygen side of the reactor. This reduces the required electrical energy and has the potential to reduce the cost of hydrogen to less than 40~60% with the remaining energy provided in this manner. In addition, carbon/hydrocarbon assisted electrolysis has the potential to offer a less energy intensive, cleaner method of using chemical energy in various sources of carbon, such as low-rank and high sulfur coals, biomass, alcohols and methane (Natural Gas), where pure CO2 produced can be easily sequestered without the need for separation.

Radiolysis

Nuclear radiation can break water bonds(citation needed). In the Mponeng gold mine, South Africa, researchers found in a naturally high radiation zone a community dominated by a new phylotype of Desulfotomaculum, feeding on primarily radiolytically produced H₂. Spent nuclear fuel is also being looked at as a potential source of hydrogen.

Thermolysis

Water spontaneously dissociates at around 2500 °C, but this thermolysis occurs at temperatures too high for usual process piping and equipment. Catalysts are required to reduce the dissociation temperature.

Thermochemical cycle

Thermochemical cycles combine solely heat sources (thermo) with chemical reactions to split water into its hydrogen and oxygen components. The term cycle is used because aside from water, hydrogen and oxygen, the chemical compounds used in these processes are continuously recycled. If electricity is partially used as an input, the resulting thermochemical cycle is defined as a hybrid one.

The sulfur-iodine cycle (S-I cycle) is a thermochemical cycle processes which generates hydrogen from water with an efficiency of approximately 50%. The sulfur and iodine used in the process are recovered and reused, and not consumed by the process. The cycle can be performed with any source of very high temperatures, approximately 950 °C, such as by Concentrating solar power systems (CSP) and is regarded as being well suited to the production of hydrogen by high-temperature nuclear reactors, and as such, is being studied in the High Temperature Test Reactor in Japan. There are other hybrid cycles that use both high temperatures and some electricity, such as the Copper–chlorine cycle, it is classified as a hybrid thermochemical cycle because it uses an electrochemical reaction in one of the reaction steps, it operates at 530 °C and has an efficiency of 43 percent.

Ferrosilicon method

Ferrosilicon is used by the military to quickly produce hydrogen for balloons. The chemical reaction uses sodium hydroxide, ferrosilicon, and water. The generator is small enough to fit a truck and requires only a small amount of electric power, the materials are stable and not combustible, and they do not generate hydrogen until mixed. The method has been in use since World War I. A heavy steel pressure vessel is filled with sodium hydroxide and ferrosilicon, closed, and a controlled amount of water is added; the dissolving of the hydroxide heats the mixture to about 93 °C and starts the reaction; sodium silicate, hydrogen and steam are produced.

Photobiological water splitting

An algae bioreactor for hydrogen production.

Biological hydrogen can be produced in an algae bioreactor. In the late 1990s it was discovered that if the algae are deprived of sulfur it will switch from the production of oxygen, i.e. normal photosynthesis, to the production of hydrogen. It seems that the production is now economically feasible by surpassing the 7–10 percent energy efficiency (the conversion of sunlight into hydrogen) barrier. with a hydrogen production rate of 10-12 ml per liter culture per hour.

Photocatalytic water splitting

The conversion of solar energy to hydrogen by means of water splitting process is one of the most interesting ways to achieve clean and renewable energy systems. However, if this process is assisted by photocatalysts suspended directly in water instead of using photovoltaic and an electrolytic system the reaction is in just one step, it can be made more efficient.

Biohydrogen routes

Biomass and waste streams can in principle be converted into biohydrogen with biomass gasification, steam reforming, or biological conversion like biocatalysed electrolysis or fermentative hydrogen production.

Among hydrogen production methods such as steam methane reforming, thermal cracking, coal and biomass gasification and pyrolysis, electrolysis, and photolysis, biological ones are more eco-friendly and less energy intensive. In addition, a wide variety of waste and low-value materials such as agricultural biomass as renewable sources can be utilized to produce hydrogen via biochemical pathways. Nevertheless, at present hydrogen is produced mainly from fossil fuels, in particular, natural gas which are non-renewable sources. Hydrogen is not only the cleanest fuel but also widely used in a number of industries, especially fertilizer, petrochemical and food ones. This makes it logical to investigate alternative sources for hydrogen production. The main biochemical technologies to produce hydrogen are dark and photo fermentation processes. In dark fermentation, carbohydrates are converted to hydrogen by fermentative microorganisms including strict anaerobe and facultative anaerobe bacteria. A theoretical maximum of 4 mol H₂/mol glucose can be produced and, besides hydrogen, sugars are converted to volatile fatty acids (VFAs) and alcohols as by-products during this process. Photo fermentative bacteria are able to generate hydrogen from VFAs. Hence, metabolites formed in dark fermentation can be used as feedstock in photo fermentation to enhance the overall yield of hydrogen.

Fermentative hydrogen production

Fermentative hydrogen production is the fermentative conversion of organic substrate to biohydrogen manifested by a diverse group of bacteria using multi enzyme systems involving three steps similar to anaerobic conversion. Dark fermentation reactions do not require light energy, so they are capable of constantly producing hydrogen from organic compounds throughout the day and night. Photofermentation differs from dark fermentation because it only proceeds in the presence of light. For example, photo-fermentation with Rhodobacter sphaeroides SH2C can be employed to convert small molecular fatty acids into hydrogen.

Fermentative hydrogen production can be done using direct biophotolysis by green algae, indirect biophotolysis by cyanobacteria, photo-fermentation by anaerobic photosynthetic bacteria and dark fermentation by anaerobic fermentative bacteria. For example, studies on hydrogen production using H. salinarium, an anaerobic photosynthetic bacteria, coupled to a hydrogenase donor like E. coli, are reported in literature.

Enterobacter aerogenes is an outstanding hydrogen producer. It is an anaerobic facultative and mesophilic bacterium that is able to consume different sugars and in contrast to cultivation of strict anaerobes, no special operation is required to remove all oxygen from the fermenter. E. aerogenes has a short doubling time and high hydrogen productivity and evolution rate. Furthermore, hydrogen production by this bacterium is not inhibited at high hydrogen partial pressures; however, its yield is lower compared to strict anaerobes like Clostridia. A theoretical maximum of 4 mol H₂/mol glucose can be produced by strict anaerobic bacteria. Facultative anaerobic bacteria such as E. aerogenes have a theoretical maximum yield of 2 mol H₂/mol glucose.

Biohydrogen can be produced in bioreactors that utilize feedstocks, the most common feedstock being waste streams. The process involves bacteria feeding on hydrocarbons and exhaling hydrogen and CO₂. The CO₂ can be sequestered successfully by several methods, leaving hydrogen gas. In 2006-2007, NanoLogix first demonstrated a prototype hydrogen bioreactor using waste as a feedstock at Welch's grape juice factory in Pennsylvania (U.S.).

Enzymatic hydrogen generation

Due to the Thauer limit (four H₂/glucose) for dark fermentation, a non-natural enzymatic pathway was designed that can generate 12 moles of hydrogen per mole of glucose units of polysaccharides and water in 2007. The stoichiometric reaction is:

C₆H₁₀O₅ + 7 H₂O → 12 H₂ + 6 CO₂

The key technology is cell-free synthetic enzymatic pathway biotransformation (SyPaB). A biochemist can understand it as "glucose oxidation by using water as oxidant". A chemist can describe it as "water splitting by energy in carbohydrate". A thermodynamics scientist can describe it as the first entropy-driving chemical reaction that can produce hydrogen by absorbing waste heat. In 2009, cellulosic materials were first used to generate high-yield hydrogen. Furthermore, the use of carbohydrate as a high-density hydrogen carrier was proposed so to solve the largest obstacle to the hydrogen economy and propose the concept of sugar fuel cell vehicles.

Biocatalysed electrolysis

A microbial electrolysis cell

Besides dark fermentation, electrohydrogenesis (electrolysis using microbes) is another possibility. Using microbial fuel cells, wastewater or plants can be used to generate power. Biocatalysed electrolysis should not be confused with biological hydrogen production, as the latter only uses algae and with the latter, the algae itself generates the hydrogen instantly, where with biocatalysed electrolysis, this happens after running through the microbial fuel cell and a variety of aquatic plants can be used. These include reed sweetgrass, cordgrass, rice, tomatoes, lupines and algae.

Xylose

In 2014 a low-temperature 50 °C (122 °F), atmospheric-pressure enzyme-driven process to convert xylose into hydrogen with nearly 100% of the theoretical yield was announced. The process employs 13 enzymes, including a novel polyphosphatexylulokinase (XK).

Carbon-neutral hydrogen

Currently there are two practical ways of producing hydrogen in a renewable industrial process. One is to use power to gas, in which electric power is used to produce hydrogen from electrolysis, and the other is to use landfill gas to produce hydrogen in a steam reformer. Hydrogen fuel, when produced by renewable sources of energy like wind or solar power, is a renewable fuel.

Use of hydrogen

Hydrogen is mainly used for the conversion of heavy petroleum fractions into lighter ones via the process of hydrocracking and other processes (dehydrocyclization and the aromatization process). It is also required for cleaning fossil fuels via hydrodesulfurization.

Hydrogen is mainly used for the production of ammonia via Haber process. In this case, the hydrogen is produced in situ. Ammonia is the major component of most fertilizers. 

Earlier it was common to vent the surplus hydrogen off, nowadays the process systems are balanced with hydrogen pinch to collect hydrogen for further use. 

Hydrogen may be used in fuel cells for local electricity generation, making it possible for hydrogen to be used as a transportation fuel for an electric vehicle. 

Hydrogen is also produced as a by-product of industrial chlorine production by electrolysis. Although requiring expensive technologies, hydrogen can be cooled, compressed and purified for use in other processes on site or sold to a customer via pipeline, cylinders or trucks. The discovery and development of less expensive methods of production of bulk hydrogen is relevant to the establishment of a hydrogen economy.

Galvanic cell

From Wikipedia, the free encyclopedia

Galvanic cell with no cation flow

 

A galvanic cell or voltaic cell, named after Luigi Galvani or Alessandro Volta, respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reactions taking place within the cell. It generally consists of two different metals immersed in an electrolyte, or of individual half-cells with different metals and their ions in solution connected by a salt bridge or separated by a porous membrane. 

Volta was the inventor of the voltaic pile, the first electrical battery. In common usage, the word "battery" has come to include a single galvanic cell, but a battery properly consists of multiple cells.

History

In 1780, Luigi Galvani discovered that when two different metals (e.g., copper and zinc) are in contact and then both are touched at the same time to two different parts of a muscle of a frog leg, to close the circuit, the frog's leg contracts. He called this "animal electricity". The frog's leg, as well as being a detector of electrical current, was also the electrolyte (to use the language of modern chemistry). 

A year after Galvani published his work (1790), Alessandro Volta showed that the frog was not necessary, using instead a force-based detector and brine-soaked paper (as electrolyte). (Earlier Volta had established the law of capacitance C =  Q/V with force-based detectors). In 1799 Volta invented the voltaic pile, which is a pile of galvanic cells each consisting of a metal disk, an electrolyte layer, and a disk of a different metal. He built it entirely out of non-biological material to challenge Galvani's (and the later experimenter Leopoldo Nobili)'s animal electricity theory in favor of his own metal-metal contact electricity theory. Carlo Matteucci in his turn constructed a battery entirely out of biological material in answer to Volta. Volta's contact electricity view characterized each electrode with a number that we would now call the work function of the electrode. This view ignored the chemical reactions at the electrode-electrolyte interfaces, which include H₂ formation on the more noble metal in Volta's pile. 

Although Volta did not understand the operation of the battery or the galvanic cell, these discoveries paved the way for electrical batteries; Volta's cell was named an IEEE Milestone in 1999.

Some forty years later, Faraday showed that the galvanic cell -- now often called a voltaic cell -- was chemical in nature. Faraday introduced new terminology to the language of chemistry: electrode (cathode and anode), electrolyte, and ion (cation and anion). Thus Galvani incorrectly thought the source of electricity (or source of emf, or seat of emf) was in the animal, Volta incorrectly thought it was in the physical properties of the isolated electrodes, but Faraday correctly identified the source of emf as the chemical reactions at the two electrode-electrolyte interfaces. The authoritative work on the intellectual history of the voltaic cell remains that by Ostwald.

It was suggested by Wilhelm König in 1940 that the object known as the Baghdad battery might represent galvanic cell technology from ancient Parthia. Replicas filled with citric acid or grape juice have been shown to produce a voltage. However, it is far from certain that this was its purpose—other scholars have pointed out that it is very similar to vessels known to have been used for storing parchment scrolls.

Basic description

Schematic of Zn-Cu galvanic cell

 

In its simplest form, a half-cell consists of a solid metal (called an electrode) that is submerged in a solution; the solution contains cations (+) of the electrode metal and anions (−) to balance the charge of the cations. The full cell consists of two half-cells, usually connected by a semi-permeable membrane or by a salt bridge that prevents the ions of the more noble metal from plating out at the other electrode. 

A specific example is the Daniell cell (see figure), with a zinc (Zn) half-cell containing a solution of ZnSO₄ (zinc sulfate) and a copper (Cu) half-cell containing a solution of CuSO₄ (copper sulfate). A salt bridge is used here to complete the electric circuit. 

If an external electrical conductor connects the copper and zinc electrodes, zinc from the zinc electrode dissolves into the solution as Zn²⁺ ions (oxidation), releasing electrons that enter the external conductor. To compensate for the increased zinc ion concentration, via the salt bridge zinc ions leave and anions enter the zinc half-cell. In the copper half-cell, the copper ions plate onto the copper electrode (reduction), taking up electrons that leave the external conductor. Since the Cu²⁺ ions (cations) plate onto the copper electrode, the latter is called the cathode. Correspondingly the zinc electrode is the anode. The electrochemical reaction is:

Zn + Cu²⁺ → Zn²⁺ + Cu

In addition, electrons flow through the external conductor, which is the primary application of the galvanic cell. 

The EMF of the cell is the difference of the half-cell potentials, a measure of the relative ease of dissolution of the two electrodes into the electrolyte. The emf depends on both the electrodes and on the electrolyte, an indication that the emf is chemical in nature.

Electrochemical thermodynamics of galvanic cell reactions

The electrochemical processes in a galvanic cell occur because reactants of high free energy (e.g. metallic Zn and hydrated Cu²⁺ in the Daniell cell) are converted to lower-energy products (metallic Cu and hydrated Zn²⁺ in this example). The difference in the lattice cohesive energies  of the electrode metals is sometimes the dominant energetic driver of the reaction, specifically in the Daniell cell. Metallic Zn, Cd, Li, and Na, which are not stabilized by d-orbital bonding, have higher cohesive energies (i.e. they are more weakly bonded) than all transition metals, including Cu, and are therefore useful as high-energy anode metals.

The difference between the metals' ionization energies in water  is the other energetic contribution that can drive the reaction in a galvanic cell; it is not important in the Daniell cell because the energies of hydrated Cu²⁺ and Zn²⁺ ions happen to be similar. Both atom transfer, e.g. of zinc from the metal electrode into the solution, and electron transfer, from metal atoms or to metal ions, play important roles in a galvanic cell. Concentration cells, whose electrodes and ions are made of the same metal and which are driven by an entropy increase and free-energy decrease as ion concentrations equalize, show that the electronegativity difference of the metals is not the driving force of electrochemical processes. 

Galvanic cells and batteries are typically used as a source of electrical power. The energy derives from a high-cohesive-energy metal dissolving while to a lower-energy metal is deposited, and/or from high-energy metal ions plating out while lower-energy ions go into solution. 

Quantitatively, the electrical energy produced by a galvanic cell is approximately equal to the standard free-energy difference of the reactants and products, denoted as Δ_rG^o. In the Daniell cell, most of the electrical energy of Δ_rG^o = -213 kJ/mol can be attributed to the -207 kJ/mol difference between Zn and Cu lattice cohesive energies.

Half reactions and conventions

A half-cell contains a metal in two oxidation states. Inside an isolated half-cell, there is an oxidation-reduction (redox) reaction that is in chemical equilibrium, a condition written symbolically as follows (here, "M" represents a metal cation, an atom that has a charge imbalance due to the loss of "n" electrons):

Mⁿ⁺ (oxidized species) + ne⁻ ⇌ M (reduced species)

A galvanic cell consists of two half-cells, such that the electrode of one half-cell is composed of metal A, and the electrode of the other half-cell is composed of metal B; the redox reactions for the two separate half-cells are thus:

Aⁿ⁺ + ne⁻ ⇌ A

B^m+ + me⁻ ⇌ B

The overall balanced reaction is

m A + n B^m+ ⇌ n B + m Aⁿ⁺

In other words, the metal atoms of one half-cell are oxidized while the metal cations of the other half-cell are reduced. By separating the metals in two half-cells, their reaction can be controlled in a way that forces transfer of electrons through the external circuit where they can do useful work.

• The electrodes are connected with a metal wire in order to conduct the electrons that participate in the reaction.

In one half-cell, dissolved metal-B cations combine with the free electrons that are available at the interface between the solution and the metal-B electrode; these cations are thereby neutralized, causing them to precipitate from solution as deposits on the metal-B electrode, a process known as plating.

This reduction reaction causes the free electrons throughout the metal-B electrode, the wire, and the metal-A electrode to be pulled into the metal-B electrode. Consequently, electrons are wrestled away from some of the atoms of the metal-A electrode, as though the metal-B cations were reacting directly with them; those metal-A atoms become cations that dissolve into the surrounding solution.

As this reaction continues, the half-cell with the metal-A electrode develops a positively charged solution (because the metal-A cations dissolve into it), while the other half-cell develops a negatively charged solution (because the metal-B cations precipitate out of it, leaving behind the anions); unabated, this imbalance in charge would stop the reaction. The solutions of the half-cells are connected by a salt bridge or a porous plate that allows ions to pass from one solution to the other, which balances the charges of the solutions and allows the reaction to continue.

By definition:

• The anode is the electrode where oxidation (loss of electrons) takes place (metal-A electrode); in a galvanic cell, it is the negative electrode, because when oxidation occurs, electrons are left behind on the electrode. These electrons then flow through the external circuit to the cathode (positive electrode) (while in electrolysis, an electric current drives electron flow in the opposite direction and the anode is the positive electrode).
• The cathode is the electrode where reduction (gain of electrons) takes place (metal-B electrode); in a galvanic cell, it is the positive electrode, as ions get reduced by taking up electrons from the electrode and plate out (while in electrolysis, the cathode is the negative terminal and attracts positive ions from the solution). In both cases, the statement 'the cathode attracts cations' is true.

Galvanic cells, by their nature, produce direct current. The Weston cell has an anode composed of cadmium mercury amalgam, and a cathode composed of pure mercury. The electrolyte is a (saturated) solution of cadmium sulfate. The depolarizer is a paste of mercurous sulfate. When the electrolyte solution is saturated, the voltage of the cell is very reproducible; hence, in 1911, it was adopted as an international standard for voltage. 

A battery is a set of galvanic cells that are connected together to form a single source of voltage. For instance, a typical 12V lead–acid battery has six galvanic cells connected in series with the anodes composed of lead and cathodes composed of lead dioxide, both immersed in sulfuric acid. Large battery rooms, for instance in a telephone exchange providing central office power to user's telephones, may have cells connected in both series and parallel.

Cell voltage

The voltage (electromotive force E^o) produced by a galvanic cell can be estimated from the standard Gibbs free energy change in the electrochemical reaction according to 

${\displaystyle E_{cell}^{o}=-\Delta _{r}G^{o}/(\nu _{e}F)}$

where ν_e is the number of electrons transferred in the balanced half reactions, and F is Faraday's constant. However, it can be determined more conveniently by the use of a standard potential table for the two half cells involved. The first step is to identify the two metals and their ions reacting in the cell. Then one looks up the standard electrode potential, E^o, in volts, for each of the two half reactions. The standard potential of the cell is equal to the more positive E^o value minus the more negative E^o value. 

For example, in the figure above the solutions are CuSO₄ and ZnSO₄. Each solution has a corresponding metal strip in it, and a salt bridge or porous disk connecting the two solutions and allowing SO²⁻
₄ ions to flow freely between the copper and zinc solutions. To calculate the standard potential one looks up copper and zinc's half reactions and finds:

Cu²⁺ + 2
e⁻ ⇌ Cu   E^o = +0.34 V

Zn²⁺ + 2
e⁻ ⇌ Zn   E^o = −0.76 V

Thus the overall reaction is:

Cu²⁺ + Zn ⇌ Cu + Zn²⁺

The standard potential for the reaction is then +0.34 V − (−0.76 V) = 1.10 V. The polarity of the cell is determined as follows. Zinc metal is more strongly reducing than copper metal because the standard (reduction) potential for zinc is more negative than that of copper. Thus, zinc metal will lose electrons to copper ions and develop a positive electrical charge. The equilibrium constant, K, for the cell is given by

${\displaystyle \ln K={\frac {\nu _{e}FE_{cell}^{o}}{RT}}}$

where F is the Faraday constant, R is the gas constant and T is the temperature in kelvins. For the Daniell cell K is approximately equal to 1.5×10³⁷. Thus, at equilibrium, a few electrons are transferred, enough to cause the electrodes to be charged.

Actual half-cell potentials must be calculated by using the Nernst equation as the solutes are unlikely to be in their standard states,

${\displaystyle E_{\text{half-cell}}=E^{o}-{\frac {RT}{\nu _{e}F}}\ln _{e}Q}$

where Q is the reaction quotient. When the charges of the ions in the reaction are equal, this simplifies to

${\displaystyle E_{\text{half-cell}}=E^{o}-2.303{\frac {RT}{\nu _{e}F}}\log _{10}\left\{{\text{M}}^{n+}\right\}}$

where {Mⁿ⁺} is the activity of the metal ion in solution. In practice concentration in mol/L is used in place of activity. The metal electrode is in its standard state so by definition has unit activity. The potential of the whole cell is obtained as the difference between the potentials for the two half-cells, so it depends on the concentrations of both dissolved metal ions. If the concentrations are the same, ${\displaystyle E_{cell}=E_{cell}^{o}}$and the Nernst equation is not needed under the conditions assumed here.

The value of 2.303R/F is 1.9845×10⁻⁴ V/K, so at 25 °C (298.15 K) the half-cell potential will change by only 0.05918 V/ν_e if the concentration of a metal ion is increased or decreased by a factor of 10.

${\displaystyle E_{\text{half-cell}}=E^{o}-{\frac {0.05918\ {\text{V}}}{\nu _{e}}}\log _{10}\left[{\text{M}}^{n+}\right]}$

These calculations are based on the assumption that all chemical reactions are in equilibrium. When a current flows in the circuit, equilibrium conditions are not achieved and the cell voltage will usually be reduced by various mechanisms, such as the development of overpotentials. Also, since chemical reactions occur when the cell is producing power, the electrolyte concentrations change and the cell voltage is reduced. A consequence of the temperature dependency of standard potentials is that the voltage produced by a galvanic cell is also temperature dependent.

Galvanic corrosion

Galvanic corrosion is a process that degrades metals electrochemically. This corrosion occurs when two dissimilar metals are in contact with each other in the presence of an electrolyte, such as salt water, forming a galvanic cell with H₂ formation on the more noble metal. The resulting electrochemical potential then develops an electric current that electrolytically dissolves the less noble material. A concentration cell can be formed if the same metal is exposed to two different concentrations of electrolyte.

Membrane potential

From Wikipedia, the free encyclopedia

Differences in the concentrations of ions on opposite sides of a cellular membrane lead to a voltage called the membrane potential. Typical values of membrane potential are in the range –40 mV to –70 mV. Many ions have a concentration gradient across the membrane, including potassium (K⁺), which is at a high concentration inside and a low concentration outside the membrane. Sodium (Na⁺) and chloride (Cl⁻) ions are at high concentrations in the extracellular region, and low concentrations in the intracellular regions. These concentration gradients provide the potential energy to drive the formation of the membrane potential. This voltage is established when the membrane has permeability to one or more ions. In the simplest case, illustrated here, if the membrane is selectively permeable to potassium, these positively charged ions can diffuse down the concentration gradient to the outside of the cell, leaving behind uncompensated negative charges. This separation of charges is what causes the membrane potential. Note that the system as a whole is electro-neutral. The uncompensated positive charges outside the cell, and the uncompensated negative charges inside the cell, physically line up on the membrane surface and attract each other across the lipid bilayer. Thus, the membrane potential is physically located only in the immediate vicinity of the membrane. It is the separation of these charges across the membrane that is the basis of the membrane voltage. Note also that this diagram is only an approximation of the ionic contributions to the membrane potential. Other ions including sodium, chloride, calcium, and others play a more minor role, even though they have strong concentration gradients, because they have more limited permeability than potassium. Key: Blue pentagons – sodium ions; Purple squares – potassium ions; Yellow circles – chloride ions; Orange rectangles – membrane-impermeable anions (these arise from a variety of sources including proteins). The large purple structure with an arrow represents a transmembrane potassium channel and the direction of net potassium movement.

 

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.

Physical basis

The membrane potential in a cell derives ultimately from two factors: electrical force and diffusion. Electrical force arises from the mutual attraction between particles with opposite electrical charges (positive and negative) and the mutual repulsion between particles with the same type of charge (both positive or both negative). Diffusion arises from the statistical tendency of particles to redistribute from regions where they are highly concentrated to regions where the concentration is low.

Voltage

Electric field (arrows) and contours of constant voltage created by a pair of oppositely charged objects. The electric field is at right angles to the voltage contours, and the field is strongest where the spacing between contours is the smallest.

 

Voltage, which is synonymous with difference in electrical potential, is the ability to drive an electric current across a resistance. Indeed, the simplest definition of a voltage is given by Ohm's law: V=IR, where V is voltage, I is current and R is resistance. If a voltage source such as a battery is placed in an electrical circuit, the higher the voltage of the source the greater the amount of current that it will drive across the available resistance. The functional significance of voltage lies only in potential differences between two points in a circuit. The idea of a voltage at a single point is meaningless. It is conventional in electronics to assign a voltage of zero to some arbitrarily chosen element of the circuit, and then assign voltages for other elements measured relative to that zero point. There is no significance in which element is chosen as the zero point—the function of a circuit depends only on the differences not on voltages per se. However, in most cases and by convention, the zero level is most often assigned to the portion of a circuit that is in contact with ground.

 

The same principle applies to voltage in cell biology. In electrically active tissue, the potential difference between any two points can be measured by inserting an electrode at each point, for example one inside and one outside the cell, and connecting both electrodes to the leads of what is in essence a specialized voltmeter. By convention, the zero potential value is assigned to the outside of the cell and the sign of the potential difference between the outside and the inside is determined by the potential of the inside relative to the outside zero. 

In mathematical terms, the definition of voltage begins with the concept of an electric field E, a vector field assigning a magnitude and direction to each point in space. In many situations, the electric field is a conservative field, which means that it can be expressed as the gradient of a scalar function V, that is, E = –∇V. This scalar field V is referred to as the voltage distribution. Note that the definition allows for an arbitrary constant of integration—this is why absolute values of voltage are not meaningful. In general, electric fields can be treated as conservative only if magnetic fields do not significantly influence them, but this condition usually applies well to biological tissue.

Because the electric field is the gradient of the voltage distribution, rapid changes in voltage within a small region imply a strong electric field; on the converse, if the voltage remains approximately the same over a large region, the electric fields in that region must be weak. A strong electric field, equivalent to a strong voltage gradient, implies that a strong force is exerted on any charged particles that lie within the region.

Ions and the forces driving their motion

Ions (pink circles) will flow across a membrane from the higher concentration to the lower concentration (down a concentration gradient), causing a current. However, this creates a voltage across the membrane that opposes the ions' motion. When this voltage reaches the equilibrium value, the two balance and the flow of ions stops.

 

Electrical signals within biological organisms are, in general, driven by ions. The most important cations for the action potential are sodium (Na⁺) and potassium (K⁺). Both of these are monovalent cations that carry a single positive charge. Action potentials can also involve calcium (Ca²⁺), which is a divalent cation that carries a double positive charge. The chloride anion (Cl⁻) plays a major role in the action potentials of some algae, but plays a negligible role in the action potentials of most animals.

Ions cross the cell membrane under two influences: diffusion and electric fields. A simple example wherein two solutions—A and B—are separated by a porous barrier illustrates that diffusion will ensure that they will eventually mix into equal solutions. This mixing occurs because of the difference in their concentrations. The region with high concentration will diffuse out toward the region with low concentration. To extend the example, let solution A have 30 sodium ions and 30 chloride ions. Also, let solution B have only 20 sodium ions and 20 chloride ions. Assuming the barrier allows both types of ions to travel through it, then a steady state will be reached whereby both solutions have 25 sodium ions and 25 chloride ions. If, however, the porous barrier is selective to which ions are let through, then diffusion alone will not determine the resulting solution. Returning to the previous example, let's now construct a barrier that is permeable only to sodium ions. Now, only sodium is allowed to diffuse cross the barrier from its higher concentration in solution A to the lower concentration in solution B. This will result in a greater accumulation of sodium ions than chloride ions in solution B and a lesser number of sodium ions than chloride ions in solution A.

This means that there is a net positive charge in solution B from the higher concentration of positively charged sodium ions than negatively charged chloride ions. Likewise, there is a net negative charge in solution A from the greater concentration of negative chloride ions than positive sodium ions. Since opposite charges attract and like charges repel, the ions are now also influenced by electrical fields as well as forces of diffusion. Therefore, positive sodium ions will be less likely to travel to the now-more-positive B solution and remain in the now-more-negative A solution. The point at which the forces of the electric fields completely counteract the force due to diffusion is called the equilibrium potential. At this point, the net flow of the specific ion (in this case sodium) is zero.

Plasma membranes

The cell membrane, also called the plasma membrane or plasmalemma, is a semipermeable lipid bilayer common to all living cells. It contains a variety of biological molecules, primarily proteins and lipids, which are involved in a vast array of cellular processes.

 

Every animal cell is enclosed in a plasma membrane, which has the structure of a lipid bilayer with many types of large molecules embedded in it. Because it is made of lipid molecules, the plasma membrane intrinsically has a high electrical resistivity, in other words a low intrinsic permeability to ions. However, some of the molecules embedded in the membrane are capable either of actively transporting ions from one side of the membrane to the other or of providing channels through which they can move.

In electrical terminology, the plasma membrane functions as a combined resistor and capacitor. Resistance arises from the fact that the membrane impedes the movement of charges across it. Capacitance arises from the fact that the lipid bilayer is so thin that an accumulation of charged particles on one side gives rise to an electrical force that pulls oppositely charged particles toward the other side. The capacitance of the membrane is relatively unaffected by the molecules that are embedded in it, so it has a more or less invariant value estimated at about 2 µF/cm² (the total capacitance of a patch of membrane is proportional to its area). The conductance of a pure lipid bilayer is so low, on the other hand, that in biological situations it is always dominated by the conductance of alternative pathways provided by embedded molecules. Thus, the capacitance of the membrane is more or less fixed, but the resistance is highly variable. 

The thickness of a plasma membrane is estimated to be about 7-8 nanometers. Because the membrane is so thin, it does not take a very large transmembrane voltage to create a strong electric field within it. Typical membrane potentials in animal cells are on the order of 100 millivolts (that is, one tenth of a volt), but calculations show that this generates an electric field close to the maximum that the membrane can sustain—it has been calculated that a voltage difference much larger than 200 millivolts could cause dielectric breakdown, that is, arcing across the membrane.

Facilitated diffusion and transport

Facilitated diffusion in cell membranes, showing ion channels and carrier proteins

 

The resistance of a pure lipid bilayer to the passage of ions across it is very high, but structures embedded in the membrane can greatly enhance ion movement, either actively or passively, via mechanisms called facilitated transport and facilitated diffusion. The two types of structure that play the largest roles are ion channels and ion pumps, both usually formed from assemblages of protein molecules. Ion channels provide passageways through which ions can move. In most cases, an ion channel is permeable only to specific types of ions (for example, sodium and potassium but not chloride or calcium), and sometimes the permeability varies depending on the direction of ion movement. Ion pumps, also known as ion transporters or carrier proteins, actively transport specific types of ions from one side of the membrane to the other, sometimes using energy derived from metabolic processes to do so.

Ion pumps

The sodium-potassium pump uses energy derived from ATP to exchange sodium for potassium ions across the membrane.

Ion pumps are integral membrane proteins that carry out active transport, i.e., use cellular energy (ATP) to "pump" the ions against their concentration gradient. Such ion pumps take in ions from one side of the membrane (decreasing its concentration there) and release them on the other side (increasing its concentration there). 

The ion pump most relevant to the action potential is the sodium–potassium pump, which transports three sodium ions out of the cell and two potassium ions in. As a consequence, the concentration of potassium ions K⁺ inside the neuron is roughly 20-fold larger than the outside concentration, whereas the sodium concentration outside is roughly ninefold larger than inside. In a similar manner, other ions have different concentrations inside and outside the neuron, such as calcium, chloride and magnesium.

If the numbers of each type of ion were equal, the sodium–potassium pump would be electrically neutral, but, because of the three-for-two exchange, it gives a net movement of one positive charge from intracellular to extracellular for each cycle, thereby contributing to a positive voltage difference. The pump has three effects: (1) it makes the sodium concentration high in the extracellular space and low in the intracellular space; (2) it makes the potassium concentration high in the intracellular space and low in the extracellular space; (3) it gives the intracellular space a negative voltage with respect to the extracellular space. 

The sodium-potassium pump is relatively slow in operation. If a cell were initialized with equal concentrations of sodium and potassium everywhere, it would take hours for the pump to establish equilibrium. The pump operates constantly, but becomes progressively less efficient as the concentrations of sodium and potassium available for pumping are reduced. 

Ion pumps influence the action potential only by establishing the relative ratio of intracellular and extracellular ion concentrations. The action potential involves mainly the opening and closing of ion channels not ion pumps. If the ion pumps are turned off by removing their energy source, or by adding an inhibitor such as ouabain, the axon can still fire hundreds of thousands of action potentials before their amplitudes begin to decay significantly. In particular, ion pumps play no significant role in the repolarization of the membrane after an action potential.

Another functionally important ion pump is the sodium-calcium exchanger. This pump operates in a conceptually similar way to the sodium-potassium pump, except that in each cycle it exchanges three Na⁺ from the extracellular space for one Ca⁺⁺ from the intracellular space. Because the net flow of charge is inward, this pump runs "downhill", in effect, and therefore does not require any energy source except the membrane voltage. Its most important effect is to pump calcium outward—it also allows an inward flow of sodium, thereby counteracting the sodium-potassium pump, but, because overall sodium and potassium concentrations are much higher than calcium concentrations, this effect is relatively unimportant. The net result of the sodium-calcium exchanger is that in the resting state, intracellular calcium concentrations become very low.

Ion channels

Despite the small differences in their radii, ions rarely go through the "wrong" channel. For example, sodium or calcium ions rarely pass through a potassium channel.

 

Ion channels are integral membrane proteins with a pore through which ions can travel between extracellular space and cell interior. Most channels are specific (selective) for one ion; for example, most potassium channels are characterized by 1000:1 selectivity ratio for potassium over sodium, though potassium and sodium ions have the same charge and differ only slightly in their radius. The channel pore is typically so small that ions must pass through it in single-file order. Channel pores can be either open or closed for ion passage, although a number of channels demonstrate various sub-conductance levels. When a channel is open, ions permeate through the channel pore down the transmembrane concentration gradient for that particular ion. Rate of ionic flow through the channel, i.e. single-channel current amplitude, is determined by the maximum channel conductance and electrochemical driving force for that ion, which is the difference between the instantaneous value of the membrane potential and the value of the reversal potential.

Depiction of the open potassium channel, with the potassium ion shown in purple in the middle, and hydrogen atoms omitted. When the channel is closed, the passage is blocked.

 

A channel may have several different states (corresponding to different conformations of the protein), but each such state is either open or closed. In general, closed states correspond either to a contraction of the pore—making it impassable to the ion—or to a separate part of the protein, stoppering the pore. For example, the voltage-dependent sodium channel undergoes inactivation, in which a portion of the protein swings into the pore, sealing it. This inactivation shuts off the sodium current and plays a critical role in the action potential. 

Ion channels can be classified by how they respond to their environment. For example, the ion channels involved in the action potential are voltage-sensitive channels; they open and close in response to the voltage across the membrane. Ligand-gated channels form another important class; these ion channels open and close in response to the binding of a ligand molecule, such as a neurotransmitter. Other ion channels open and close with mechanical forces. Still other ion channels—such as those of sensory neurons—open and close in response to other stimuli, such as light, temperature or pressure.

Leakage channels

Leakage channels are the simplest type of ion channel, in that their permeability is more or less constant. The types of leakage channels that have the greatest significance in neurons are potassium and chloride channels. It should be noted that even these are not perfectly constant in their properties: First, most of them are voltage-dependent in the sense that they conduct better in one direction than the other (in other words, they are rectifiers); second, some of them are capable of being shut off by chemical ligands even though they do not require ligands in order to operate.

Ligand-gated channels

Ligand-gated calcium channel in closed and open states

 

Ligand-gated ion channels are channels whose permeability is greatly increased when some type of chemical ligand binds to the protein structure. Animal cells contain hundreds, if not thousands, of types of these. A large subset function as neurotransmitter receptors—they occur at postsynaptic sites, and the chemical ligand that gates them is released by the presynaptic axon terminal. One example of this type is the AMPA receptor, a receptor for the neurotransmitter glutamate that when activated allows passage of sodium and potassium ions. Another example is the GABA_A receptor, a receptor for the neurotransmitter GABA that when activated allows passage of chloride ions. 

Neurotransmitter receptors are activated by ligands that appear in the extracellular area, but there are other types of ligand-gated channels that are controlled by interactions on the intracellular side.

Voltage-dependent channels

Voltage-gated ion channels, also known as voltage dependent ion channels, are channels whose permeability is influenced by the membrane potential. They form another very large group, with each member having a particular ion selectivity and a particular voltage dependence. Many are also time-dependent—in other words, they do not respond immediately to a voltage change but only after a delay. 

One of the most important members of this group is a type of voltage-gated sodium channel that underlies action potentials—these are sometimes called Hodgkin-Huxley sodium channels because they were initially characterized by Alan Lloyd Hodgkin and Andrew Huxley in their Nobel Prize-winning studies of the physiology of the action potential. The channel is closed at the resting voltage level, but opens abruptly when the voltage exceeds a certain threshold, allowing a large influx of sodium ions that produces a very rapid change in the membrane potential. Recovery from an action potential is partly dependent on a type of voltage-gated potassium channel that is closed at the resting voltage level but opens as a consequence of the large voltage change produced during the action potential.

Reversal potential

The reversal potential (or equilibrium potential) of an ion is the value of transmembrane voltage at which diffusive and electrical forces counterbalance, so that there is no net ion flow across the membrane. This means that the transmembrane voltage exactly opposes the force of diffusion of the ion, such that the net current of the ion across the membrane is zero and unchanging. The reversal potential is important because it gives the voltage that acts on channels permeable to that ion—in other words, it gives the voltage that the ion concentration gradient generates when it acts as a battery. 

The equilibrium potential of a particular ion is usually designated by the notation E_ion.The equilibrium potential for any ion can be calculated using the Nernst equation. For example, reversal potential for potassium ions will be as follows:

${\displaystyle E_{eq,K^{+}}={\frac {RT}{zF}}\ln {\frac {[K^{+}]_{o}}{[K^{+}]_{i}}},}$

where

• E_eq,K⁺ is the equilibrium potential for potassium, measured in volts
• R is the universal gas constant, equal to 8.314 joules·K⁻¹·mol⁻¹
• T is the absolute temperature, measured in kelvins (= K = degrees Celsius + 273.15)
• z is the number of elementary charges of the ion in question involved in the reaction
• F is the Faraday constant, equal to 96,485 coulombs·mol⁻¹ or J·V⁻¹·mol⁻¹
• [K⁺]_o is the extracellular concentration of potassium, measured in mol·m⁻³ or mmol·l⁻¹
• [K⁺]_i is the intracellular concentration of potassium

Even if two different ions have the same charge (i.e., K⁺ and Na⁺), they can still have very different equilibrium potentials, provided their outside and/or inside concentrations differ. Take, for example, the equilibrium potentials of potassium and sodium in neurons. The potassium equilibrium potential E_K is −84 mV with 5 mM potassium outside and 140 mM inside. On the other hand, the sodium equilibrium potential, E_Na, is approximately +66 mV with approximately 12 mM sodium inside and 140 mM outside.

Changes to membrane potential during development

A neuron’s resting membrane potential actually changes during the development of an organism. In order for a neuron to eventually adopt its full adult function, its potential must be tightly regulated during development. As an organism progresses through development the resting membrane potential becomes more negative. Glial cells are also differentiating and proliferating as development progresses in the brain. The addition of these glial cells increases the organism’s ability to regulate extracellular potassium. The drop in extracellular potassium can lead to a decrease in membrane potential of 35 mV.

Equivalent circuit

Equivalent circuit for a patch of membrane, consisting of a fixed capacitance in parallel with four pathways each containing a battery in series with a variable conductance

 

Electrophysiologists model the effects of ionic concentration differences, ion channels, and membrane capacitance in terms of an equivalent circuit, which is intended to represent the electrical properties of a small patch of membrane. The equivalent circuit consists of a capacitor in parallel with four pathways each consisting of a battery in series with a variable conductance. The capacitance is determined by the properties of the lipid bilayer, and is taken to be fixed. Each of the four parallel pathways comes from one of the principal ions, sodium, potassium, chloride, and calcium. The voltage of each ionic pathway is determined by the concentrations of the ion on each side of the membrane; see the Reversal potential section above. The conductance of each ionic pathway at any point in time is determined by the states of all the ion channels that are potentially permeable to that ion, including leakage channels, ligand-gated channels, and voltage-gated ion channels.

Reduced circuit obtained by combining the ion-specific pathways using the Goldman equation

 

For fixed ion concentrations and fixed values of ion channel conductance, the equivalent circuit can be further reduced, using the Goldman equation as described below, to a circuit containing a capacitance in parallel with a battery and conductance. In electrical terms, this is a type of RC circuit (resistance-capacitance circuit), and its electrical properties are very simple. Starting from any initial state, the current flowing across either the conductance or the capacitance decays with an exponential time course, with a time constant of τ = RC, where C is the capacitance of the membrane patch, and R = 1/g_net is the net resistance. For realistic situations, the time constant usually lies in the 1—100 millisecond range. In most cases, changes in the conductance of ion channels occur on a faster time scale, so an RC circuit is not a good approximation; however, the differential equation used to model a membrane patch is commonly a modified version of the RC circuit equation.

Resting potential

When the membrane potential of a cell goes for a long period of time without changing significantly, it is referred to as a resting potential or resting voltage. This term is used for the membrane potential of non-excitable cells, but also for the membrane potential of excitable cells in the absence of excitation. In excitable cells, the other possible states are graded membrane potentials (of variable amplitude), and action potentials, which are large, all-or-nothing rises in membrane potential that usually follow a fixed time course. Excitable cells include neurons, muscle cells, and some secretory cells in glands. Even in other types of cells, however, the membrane voltage can undergo changes in response to environmental or intracellular stimuli. For example, depolarization of the plasma membrane appears to be an important step in programmed cell death.

The interactions that generate the resting potential are modeled by the Goldman equation. This is similar in form to the Nernst equation shown above, in that it is based on the charges of the ions in question, as well as the difference between their inside and outside concentrations. However, it also takes into consideration the relative permeability of the plasma membrane to each ion in question.

${\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {P_{\mathrm {K} }[\mathrm {K} ^{+}]_{\mathrm {out} }+P_{\mathrm {Na} }[\mathrm {Na} ^{+}]_{\mathrm {out} }+P_{\mathrm {Cl} }[\mathrm {Cl} ^{-}]_{\mathrm {in} }}{P_{\mathrm {K} }[\mathrm {K} ^{+}]_{\mathrm {in} }+P_{\mathrm {Na} }[\mathrm {Na} ^{+}]_{\mathrm {in} }+P_{\mathrm {Cl} }[\mathrm {Cl} ^{-}]_{\mathrm {out} }}}\right)}}$

The three ions that appear in this equation are potassium (K⁺), sodium (Na⁺), and chloride (Cl⁻). Calcium is omitted, but can be added to deal with situations in which it plays a significant role. Being an anion, the chloride terms are treated differently from the cation terms; the intracellular concentration is in the numerator, and the extracellular concentration in the denominator, which is reversed from the cation terms. P_i stands for the relative permeability of the ion type i.

In essence, the Goldman formula expresses the membrane potential as a weighted average of the reversal potentials for the individual ion types, weighted by permeability. (Although the membrane potential changes about 100 mV during an action potential, the concentrations of ions inside and outside the cell do not change significantly. They remain close to their respective concentrations when then membrane is at resting potential.) In most animal cells, the permeability to potassium is much higher in the resting state than the permeability to sodium. As a consequence, the resting potential is usually close to the potassium reversal potential. The permeability to chloride can be high enough to be significant, but, unlike the other ions, chloride is not actively pumped, and therefore equilibrates at a reversal potential very close to the resting potential determined by the other ions.

Values of resting membrane potential in most animal cells usually vary between the potassium reversal potential (usually around -80 mV) and around -40 mV. The resting potential in excitable cells (capable of producing action potentials) is usually near -60 mV—more depolarized voltages would lead to spontaneous generation of action potentials. Immature or undifferentiated cells show highly variable values of resting voltage, usually significantly more positive than in differentiated cells. In such cells, the resting potential value correlates with the degree of differentiation: undifferentiated cells in some cases may not show any transmembrane voltage difference at all. 

Maintenance of the resting potential can be metabolically costly for a cell because of its requirement for active pumping of ions to counteract losses due to leakage channels. The cost is highest when the cell function requires an especially depolarized value of membrane voltage. For example, the resting potential in daylight-adapted blowfly (Calliphora vicina) photoreceptors can be as high as -30 mV. This elevated membrane potential allows the cells to respond very rapidly to visual inputs; the cost is that maintenance of the resting potential may consume more than 20% of overall cellular ATP.

On the other hand, the high resting potential in undifferentiated cells can be a metabolic advantage. This apparent paradox is resolved by examination of the origin of that resting potential. Little-differentiated cells are characterized by extremely high input resistance, which implies that few leakage channels are present at this stage of cell life. As an apparent result, potassium permeability becomes similar to that for sodium ions, which places resting potential in-between the reversal potentials for sodium and potassium as discussed above. The reduced leakage currents also mean there is little need for active pumping in order to compensate, therefore low metabolic cost.

Graded potentials

As explained above, the potential at any point in a cell's membrane is determined by the ion concentration differences between the intracellular and extracellular areas, and by the permeability of the membrane to each type of ion. The ion concentrations do not normally change very quickly (with the exception of Ca²⁺, where the baseline intracellular concentration is so low that even a small influx may increase it by orders of magnitude), but the permeabilities of the ions can change in a fraction of a millisecond, as a result of activation of ligand-gated ion channels. The change in membrane potential can be either large or small, depending on how many ion channels are activated and what type they are, and can be either long or short, depending on the lengths of time that the channels remain open. Changes of this type are referred to as graded potentials, in contrast to action potentials, which have a fixed amplitude and time course. 

As can be derived from the Goldman equation shown above, the effect of increasing the permeability of a membrane to a particular type of ion shifts the membrane potential toward the reversal potential for that ion. Thus, opening Na⁺ channels shifts the membrane potential toward the Na⁺ reversal potential, which is usually around +100 mV. Likewise, opening K⁺ channels shifts the membrane potential toward about –90 mV, and opening Cl⁻ channels shifts it toward about –70 mV (resting potential of most membranes). Thus, Na⁺ channels shift the membrane potential in a positive direction, K⁺ channels shift it in a negative direction (except when the membrane is hyperpolarized to a value more negative than the K⁺ reversal potential), and Cl⁻ channels tend to shift it towards the resting potential. 

Graph displaying an EPSP, an IPSP, and the summation of an EPSP and an IPSP

 

Graded membrane potentials are particularly important in neurons, where they are produced by synapses—a temporary change in membrane potential produced by activation of a synapse by a single graded or action potential is called a postsynaptic potential. Neurotransmitters that act to open Na⁺ channels typically cause the membrane potential to become more positive, while neurotransmitters that activate K⁺ channels typically cause it to become more negative; those that inhibit these channels tend to have the opposite effect. 

Whether a postsynaptic potential is considered excitatory or inhibitory depends on the reversal potential for the ions of that current, and the threshold for the cell to fire an action potential (around –50mV). A postsynaptic current with a reversal potential above threshold, such as a typical Na⁺ current, is considered excitatory. A current with a reversal potential below threshold, such as a typical K⁺ current, is considered inhibitory. A current with a reversal potential above the resting potential, but below threshold, will not by itself elicit action potentials, but will produce subthreshold membrane potential oscillations. Thus, neurotransmitters that act to open Na⁺ channels produce excitatory postsynaptic potentials, or EPSPs, whereas neurotransmitters that act to open K⁺ or Cl⁻ channels typically produce inhibitory postsynaptic potentials, or IPSPs. When multiple types of channels are open within the same time period, their postsynaptic potentials summate (are added together).

Other values

From the viewpoint of biophysics, the resting membrane potential is merely the membrane potential that results from the membrane permeabilities that predominate when the cell is resting. The above equation of weighted averages always applies, but the following approach may be more easily visualized. At any given moment, there are two factors for an ion that determine how much influence that ion will have over the membrane potential of a cell:

1. That ion's driving force
2. That ion's permeability

If the driving force is high, then the ion is being "pushed" across the membrane. If the permeability is high, it will be easier for the ion to diffuse across the membrane.

• Driving force is the net electrical force available to move that ion across the membrane. It is calculated as the difference between the voltage that the ion "wants" to be at (its equilibrium potential) and the actual membrane potential (E_m). So, in formal terms, the driving force for an ion = E_m - E_ion
• For example, at our earlier calculated resting potential of −73 mV, the driving force on potassium is 7 mV : (−73 mV) − (−80 mV) = 7 mV. The driving force on sodium would be (−73 mV) − (60 mV) = −133 mV.
• Permeability is a measure of how easily an ion can cross the membrane. It is normally measured as the (electrical) conductance and the unit, siemens, corresponds to 1 C·s⁻¹·V⁻¹, that is one coulomb per second per volt of potential.

So, in a resting membrane, while the driving force for potassium is low, its permeability is very high. Sodium has a huge driving force but almost no resting permeability. In this case, potassium carries about 20 times more current than sodium, and thus has 20 times more influence over E_m than does sodium. 

However, consider another case—the peak of the action potential. Here, permeability to Na is high and K permeability is relatively low. Thus, the membrane moves to near E_Na and far from E_K. 

The more ions are permeant the more complicated it becomes to predict the membrane potential. However, this can be done using the Goldman-Hodgkin-Katz equation or the weighted means equation. By plugging in the concentration gradients and the permeabilities of the ions at any instant in time, one can determine the membrane potential at that moment. What the GHK equations means is that, at any time, the value of the membrane potential will be a weighted average of the equilibrium potentials of all permeant ions. The "weighting" is the ions relative permeability across the membrane.

Effects and implications

While cells expend energy to transport ions and establish a transmembrane potential, they use this potential in turn to transport other ions and metabolites such as sugar. The transmembrane potential of the mitochondria drives the production of ATP, which is the common currency of biological energy. 

Cells may draw on the energy they store in the resting potential to drive action potentials or other forms of excitation. These changes in the membrane potential enable communication with other cells (as with action potentials) or initiate changes inside the cell, which happens in an egg when it is fertilized by a sperm. 

In neuronal cells, an action potential begins with a rush of sodium ions into the cell through sodium channels, resulting in depolarization, while recovery involves an outward rush of potassium through potassium channels. Both of these fluxes occur by passive diffusion.