A Medley of Potpourri

Platinum is a chemical element; it has symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish platina, a diminutive of plata "silver".

Platinum is a member of the platinum group of elements and group 10 of the periodic table of elements. It has six naturally occurring isotopes. It is one of the rarer elements in Earth's crust, with an average abundance of approximately 5 μg/kg. It occurs in some nickel and copper ores along with some native deposits, mostly in South Africa, which accounts for ~80% of the world production. Because of its scarcity in Earth's crust, only a few hundred tonnes are produced annually, and given its important uses, it is highly valuable and is a major precious metal commodity.

Platinum is one of the least reactive metals. It has remarkable resistance to corrosion, even at high temperatures, and is therefore considered a noble metal. Consequently, platinum is often found chemically uncombined as native platinum. Because it occurs naturally in the alluvial sands of various rivers, it was first used by pre-Columbian South American natives to produce artifacts. It was referenced in European writings as early as the 16th century, but it was not until Antonio de Ulloa published a report on a new metal of Colombian origin in 1748 that it began to be investigated by scientists.

Platinum is used in catalytic converters, laboratory equipment, electrical contacts and electrodes, platinum resistance thermometers, dentistry equipment, and jewelry. Platinum is used in the glass industry to manipulate molten glass, which does not "wet" platinum. As a heavy metal, it leads to health problems upon exposure to its salts; but due to its corrosion resistance, metallic platinum has not been linked to adverse health effects. Compounds containing platinum, such as cisplatin, oxaliplatin and carboplatin, are applied in chemotherapy against certain types of cancer.

Pure platinum is currently less expensive than pure gold, having been so continuously since 2015, but has been twice as expensive or more, mostly prior to 2008. In early 2021, the value of platinum ranged from US$1,055 to US$1,320 per troy ounce.

Characteristics

Physical

Pure platinum is a lustrous, ductile, and malleable, silver-white metal. Platinum is more ductile than gold, silver or copper, thus being the most ductile of pure metals, but it is less malleable than gold.Its physical characteristics and chemical stability make it useful for industrial applications. Its resistance to wear and tarnish is well suited to use in fine jewellery.

Chemical

Platinum has excellent resistance to corrosion. Bulk platinum does not oxidize in air at any temperature, but it forms a thin surface film of PtO₂ that can be easily removed by heating to about 400 °C.

The most common oxidation states of platinum are +2 and +4. The +1 and +3 oxidation states are less common, and are often stabilized by metal bonding in bimetallic (or polymetallic) species. Tetracoordinate platinum(II) compounds tend to adopt 16-electron square planar geometries. Although elemental platinum is generally unreactive, it is attacked by chlorine, bromine, iodine, and sulfur. It reacts vigorously with fluorine at 500 °C (932 °F) to form platinum tetrafluoride. Platinum is insoluble in hydrochloric and nitric acid, but dissolves in hot aqua regia (a mixture of nitric and hydrochloric acids), to form aqueous chloroplatinic acid, H₂PtCl₆:

Pt + 4 HNO₃ + 6 HCl → H₂PtCl₆ + 4 NO₂ + 4 H₂O

As a soft acid, the Pt²⁺ ion has a great affinity for sulfide and sulfur ligands. Numerous DMSO complexes have been reported and care is taken in the choosing of reaction solvents.

In 2007, the German scientist Gerhard Ertl won the Nobel Prize in Chemistry for determining the detailed molecular mechanisms of the catalytic oxidation of carbon monoxide over platinum (catalytic converter).

Isotopes

Platinum has six naturally occurring isotopes: ¹⁹⁰
Pt, ¹⁹²
Pt, ¹⁹⁴
Pt, ¹⁹⁵
Pt, ¹⁹⁶
Pt, and ¹⁹⁸
Pt. The most abundant of these is ¹⁹⁵
Pt, comprising 33.83% of all platinum. It is the only stable isotope with a non-zero spin. The spin of ¹/₂ and other favourable magnetic properties of the nucleus are utilised in ¹⁹⁵
Pt NMR. Due to its spin and large abundance, ¹⁹⁵
Pt satellite peaks are also often observed in ¹
H and ³¹
P NMR spectroscopy (e.g., for Pt-phosphine and Pt-alkyl complexes). ¹⁹⁰
Pt is the least abundant at only 0.01%. Of the naturally occurring isotopes, only ¹⁹⁰
Pt is unstable, though it decays with a half-life of 6.5×10¹¹ years, causing an activity of 15 Bq/kg of natural platinum. Other isotopes can undergo alpha decay, but their decay has never been observed, therefore they are considered stable. Platinum also has 38 synthetic isotopes ranging in atomic mass from 165 to 208, making the total number of known isotopes 44. The least stable of these are ¹⁶⁵
Pt and ¹⁶⁶
Pt, with half-lives of 260 µs, whereas the most stable is ¹⁹³
Pt with a half-life of 50 years. Most platinum isotopes decay by some combination of beta decay and alpha decay. ¹⁸⁸
Pt, ¹⁹¹
Pt, and ¹⁹³
Pt decay primarily by electron capture. ¹⁹⁰
Pt and ¹⁹⁸
Pt are predicted to have energetically favorable double beta decay paths.

Occurrence

A native platinum nugget, Kondyor mine, Khabarovsk Krai

Platinum is an extremely rare metal, occurring at a concentration of only 0.005 ppm in Earth's crust. Sometimes mistaken for silver, platinum is often found chemically uncombined as native platinum and as alloy with the other platinum-group metals and iron mostly. Most often the native platinum is found in secondary deposits in alluvial deposits. The alluvial deposits used by pre-Columbian people in the Chocó Department, Colombia are still a source for platinum-group metals. Another large alluvial deposit is in the Ural Mountains, Russia, and it is still mined.

In nickel and copper deposits, platinum-group metals occur as sulfides (e.g., (Pt,Pd)S), tellurides (e.g., PtBiTe), antimonides (PdSb), and arsenides (e.g. PtAs₂), and as end alloys with nickel or copper. Platinum arsenide, sperrylite (PtAs₂), is a major source of platinum associated with nickel ores in the Sudbury Basin deposit in Ontario, Canada. At Platinum, Alaska, about 17,000 kg (550,000 ozt) was mined between 1927 and 1975. The mine ceased operations in 1990. The rare sulfide mineral cooperite, (Pt,Pd,Ni)S, contains platinum along with palladium and nickel. Cooperite occurs in the Merensky Reef within the Bushveld complex, Gauteng, South Africa.

In 1865, chromites were identified in the Bushveld region of South Africa, followed by the discovery of platinum in 1906. In 1924, the geologist Hans Merensky discovered a large supply of platinum in the Bushveld Igneous Complex in South Africa. The specific layer he found, named the Merensky Reef, contains around 75% of the world's known platinum. The large copper–nickel deposits near Norilsk in Russia, and the Sudbury Basin, Canada, are the two other large deposits. In the Sudbury Basin, the huge quantities of nickel ore processed make up for the fact platinum is present as only 0.5 ppm in the ore. Smaller reserves can be found in the United States, for example in the Absaroka Range in Montana. In 2010, South Africa was the top producer of platinum, with an almost 77% share, followed by Russia at 13%; world production in 2010 was 192,000 kg (423,000 lb).

Large platinum deposits are present in the state of Tamil Nadu, India.

Platinum exists in higher abundances on the Moon and in meteorites. Correspondingly, platinum is found in slightly higher abundances at sites of bolide impact on Earth that are associated with resulting post-impact volcanism, and can be mined economically; the Sudbury Basin is one such example.

Compounds

Halides

Hexachloroplatinic acid mentioned above is probably the most important platinum compound, as it serves as the precursor for many other platinum compounds. By itself, it has various applications in photography, zinc etchings, indelible ink, plating, mirrors, porcelain coloring, and as a catalyst.

Treatment of hexachloroplatinic acid with an ammonium salt, such as ammonium chloride, gives ammonium hexachloroplatinate, which is relatively insoluble in ammonium solutions. Heating this ammonium salt in the presence of hydrogen reduces it to elemental platinum. Potassium hexachloroplatinate is similarly insoluble, and hexachloroplatinic acid has been used in the determination of potassium ions by gravimetry.

When hexachloroplatinic acid is heated, it decomposes through platinum(IV) chloride and platinum(II) chloride to elemental platinum, although the reactions do not occur stepwise:

(H₃O)₂PtCl₆·nH₂O ⇌ PtCl₄ + 2 HCl + (n + 2) H₂O

PtCl₄ ⇌ PtCl₂ + Cl₂

PtCl₂ ⇌ Pt + Cl₂

All three reactions are reversible. Platinum(II) and platinum(IV) bromides are known as well. Platinum hexafluoride is a strong oxidizer capable of oxidizing oxygen.

Oxides

Platinum(IV) oxide, PtO₂, also known as "Adams' catalyst", is a black powder that is soluble in potassium hydroxide (KOH) solutions and concentrated acids. PtO₂ and the less common PtO both decompose upon heating. Platinum(II,IV) oxide, Pt₃O₄, is formed in the following reaction:

2 Pt²⁺ + Pt⁴⁺ + 4 O²⁻ → Pt₃O₄

Other compounds

Unlike palladium acetate, platinum(II) acetate is not commercially available. Where a base is desired, the halides have been used in conjunction with sodium acetate. The use of platinum(II) acetylacetonate has also been reported.

Several barium platinides have been synthesized in which platinum exhibits negative oxidation states ranging from −1 to −2. These include BaPt, Ba
₃Pt
₂, and Ba
₂Pt. Caesium platinide, Cs
₂Pt, a dark-red transparent crystalline compound has been shown to contain Pt²⁻
anions. Platinum also exhibits negative oxidation states at surfaces reduced electrochemically. The negative oxidation states exhibited by platinum are unusual for metallic elements, and they are attributed to the relativistic stabilization of the 6s orbitals.

It is predicted that even the cation PtO²⁺
₄ in which platinum exists in the +10 oxidation state may be achievable.

Zeise's salt, containing an ethylene ligand, was one of the first organometallic compounds discovered. Dichloro(cycloocta-1,5-diene)platinum(II) is a commercially available olefin complex, which contains easily displaceable cod ligands ("cod" being an abbreviation of 1,5-cyclooctadiene). The cod complex and the halides are convenient starting points to platinum chemistry.

Cisplatin, or cis-diamminedichloroplatinum(II) is the first of a series of square planar platinum(II)-containing chemotherapy drugs. Others include carboplatin and oxaliplatin. These compounds are capable of crosslinking DNA, and kill cells by similar pathways to alkylating chemotherapeutic agents. (Side effects of cisplatin include nausea and vomiting, hair loss, tinnitus, hearing loss, and nephrotoxicity.)

Organoplatinum compounds such as the above antitumour agents, as well as soluble inorganic platinum complexes, are routinely characterised using ¹⁹⁵
Pt nuclear magnetic resonance spectroscopy.

The hexachloroplatinate ion
The anion of Zeise's salt
Dichloro(cycloocta-1,5-diene)platinum(II)
Cisplatin

History

Early uses

Archaeologists have discovered traces of platinum in the gold used in ancient Egyptian burials as early as 1200 BCE. For example, a small box from burial of Shepenupet II was found to be decorated with gold-platinum hieroglyphics. However, the extent of early Egyptians' knowledge of the metal is unclear. It is quite possible they did not recognize there was platinum in their gold.

The metal was used by Native Americans near modern-day Esmeraldas, Ecuador to produce artifacts of a white gold-platinum alloy. Archeologists usually associate the tradition of platinum-working in South America with the La Tolita Culture (c. 600 BCE – 200 CE), but precise dates and location are difficult, as most platinum artifacts from the area were bought secondhand through the antiquities trade rather than obtained by direct archeological excavation. To work the metal, they would combine gold and platinum powders by sintering. The resulting gold–platinum alloy would then be soft enough to shape with tools. The platinum used in such objects was not the pure element, but rather a naturally occurring mixture of the platinum group metals, with small amounts of palladium, rhodium, and iridium.

European discovery

The first European reference to platinum appears in 1557 in the writings of the Italian humanist Julius Caesar Scaliger as a description of an unknown noble metal found between Darién and Mexico, "which no fire nor any Spanish artifice has yet been able to liquefy". From their first encounters with platinum, the Spanish generally saw the metal as a kind of impurity in gold, and it was treated as such. It was often simply thrown away, and there was an official decree forbidding the adulteration of gold with platinum impurities.

In 1735, Antonio de Ulloa and Jorge Juan y Santacilia saw Native Americans mining platinum while the Spaniards were travelling through Colombia and Peru for eight years. Ulloa and Juan found mines with the whitish metal nuggets and took them home to Spain. Antonio de Ulloa returned to Spain and established the first mineralogy lab in Spain and was the first to systematically study platinum, which was in 1748. His historical account of the expedition included a description of platinum as being neither separable nor calcinable. Ulloa also anticipated the discovery of platinum mines. After publishing the report in 1748, Ulloa did not continue to investigate the new metal. In 1758, he was sent to superintend mercury mining operations in Huancavelica.

In 1741, Charles Wood, a British metallurgist, found various samples of Colombian platinum in Jamaica, which he sent to William Brownrigg for further investigation.

In 1750, after studying the platinum sent to him by Wood, Brownrigg presented a detailed account of the metal to the Royal Society, stating that he had seen no mention of it in any previous accounts of known minerals. Brownrigg also made note of platinum's extremely high melting point and refractoriness toward borax. Other chemists across Europe soon began studying platinum, including Andreas Sigismund Marggraf, Torbern Bergman, Jöns Jakob Berzelius, William Lewis, and Pierre Macquer. In 1752, Henrik Scheffer published a detailed scientific description of the metal, which he referred to as "white gold", including an account of how he succeeded in fusing platinum ore with the aid of arsenic. Scheffer described platinum as being less pliable than gold, but with similar resistance to corrosion.

Means of malleability

Karl von Sickingen researched platinum extensively in 1772. He succeeded in making malleable platinum by alloying it with gold, dissolving the alloy in hot aqua regia, precipitating the platinum with ammonium chloride, igniting the ammonium chloroplatinate, and hammering the resulting finely divided platinum to make it cohere. Franz Karl Achard made the first platinum crucible in 1784. He worked with the platinum by fusing it with arsenic, then later volatilizing the arsenic.

Because the other platinum-family members were not discovered yet (platinum was the first in the list), Scheffer and Sickingen made the false assumption that due to its hardness—which is slightly more than for pure iron—platinum would be a relatively non-pliable material, even brittle at times, when in fact its ductility and malleability are close to that of gold. Their assumptions could not be avoided because the platinum they experimented with was highly contaminated with minute amounts of platinum-family elements such as osmium and iridium, amongst others, which embrittled the platinum alloy. Alloying this impure platinum residue called "plyoxen" with gold was the only solution at the time to obtain a pliable compound, but nowadays, very pure platinum is available and extremely long wires can be drawn from pure platinum, very easily, due to its crystalline structure, which is similar to that of many soft metals.

In 1786, Charles III of Spain provided a library and laboratory to Pierre-François Chabaneau to aid in his research of platinum. Chabaneau succeeded in removing various impurities from the ore, including gold, mercury, lead, copper, and iron. This led him to believe he was working with a single metal, but in truth the ore still contained the yet-undiscovered platinum-group metals. This led to inconsistent results in his experiments. At times, the platinum seemed malleable, but when it was alloyed with iridium, it would be much more brittle. Sometimes the metal was entirely incombustible, but when alloyed with osmium, it would volatilize. After several months, Chabaneau succeeded in producing 23 kilograms of pure, malleable platinum by hammering and compressing the sponge form while white-hot. Chabeneau realized the infusibility of platinum would lend value to objects made of it, and so started a business with Joaquín Cabezas producing platinum ingots and utensils. This started what is known as the "platinum age" in Spain.

Production

Platinum, along with the rest of the platinum-group metals, is obtained commercially as a by-product from nickel and copper mining and processing. During electrorefining of copper, noble metals such as silver, gold and the platinum-group metals as well as selenium and tellurium settle to the bottom of the cell as "anode mud", which forms the starting point for the extraction of the platinum-group metals.

If pure platinum is found in placer deposits or other ores, it is isolated from them by various methods of subtracting impurities. Because platinum is significantly denser than many of its impurities, the lighter impurities can be removed by simply floating them away in a liquid. Platinum is paramagnetic, whereas nickel and iron are both ferromagnetic. These two impurities are thus removed by running an electromagnet over the mixture. Because platinum has a higher melting point than most other substances, many impurities can be burned or melted away without melting the platinum. Finally, platinum is resistant to hydrochloric and sulfuric acids, whereas other substances are readily attacked by them. Metal impurities can be removed by stirring the mixture in either of the two acids and recovering the remaining platinum.

One suitable method for purification for the raw platinum, which contains platinum, gold, and the other platinum-group metals, is to process it with aqua regia, in which palladium, gold and platinum are dissolved, whereas osmium, iridium, ruthenium and rhodium stay unreacted. The gold is precipitated by the addition of iron(II) chloride and after filtering off the gold, the platinum is precipitated as ammonium chloroplatinate by the addition of ammonium chloride. Ammonium chloroplatinate can be converted to platinum by heating. Unprecipitated hexachloroplatinate(IV) may be reduced with elemental zinc, and a similar method is suitable for small scale recovery of platinum from laboratory residues. Mining and refining platinum has environmental impacts.

Applications

Of the 218 tonnes of platinum sold in 2014, 98 tonnes were used for vehicle emissions control devices (45%), 74.7 tonnes for jewelry (34%), 20.0 tonnes for chemical production and petroleum refining (9.2%), and 5.85 tonnes for electrical applications such as hard disk drives (2.7%). The remaining 28.9 tonnes went to various other minor applications, such as medicine and biomedicine, glassmaking equipment, investment, electrodes, anticancer drugs, oxygen sensors, spark plugs and turbine engines.

Catalyst

The most common use of platinum is as a catalyst in chemical reactions, often as platinum black. It has been employed as a catalyst since the early 19th century, when platinum powder was used to catalyze the ignition of hydrogen. Its most important application is in automobiles as a catalytic converter, which allows the complete combustion of low concentrations of unburned hydrocarbons from the exhaust into carbon dioxide and water vapor. Platinum is also used in the petroleum industry as a catalyst in a number of separate processes, but especially in catalytic reforming of straight-run naphthas into higher-octane gasoline that becomes rich in aromatic compounds. PtO₂, also known as Adams' catalyst, is used as a hydrogenation catalyst, specifically for vegetable oils. Platinum also strongly catalyzes the decomposition of hydrogen peroxide into water and oxygen and it is used in fuel cells as a catalyst for the reduction of oxygen.

Green energy transition

As a fuel cell catalyst, platinum enables hydrogen and oxygen reactions to take place at an optimum rate. It is used in platinum-based proton exchange memebrane (PEM) technologies required in green hydrogen production as well as fuel cell electric vehicle adoption (FCEV).

Standard

From 1889 to 1960, the meter was defined as the length of a platinum-iridium (90:10) alloy bar, known as the international prototype meter. The previous bar was made of platinum in 1799. Until May 2019, the kilogram was defined as the mass of the international prototype of the kilogram, a cylinder of the same platinum-iridium alloy made in 1879.

The Standard Platinum Resistance Thermometer (SPRT) is one of the four types of thermometers used to define the International Temperature Scale of 1990 (ITS-90), the international calibration standard for temperature measurements. The resistance wire in the thermometer is made of pure platinum (NIST manufactured the wires from platinum bar stock with a chemical purity of 99.999% by weight).In addition to laboratory uses, Platinum Resistance Thermometry (PRT) also has many industrial applications, industrial standards include ASTM E1137 and IEC 60751.

The standard hydrogen electrode also uses a platinized platinum electrode due to its corrosion resistance, and other attributes.

As an investment

Platinum is a precious metal commodity; its bullion has the ISO currency code of XPT. Coins, bars, and ingots are traded or collected. Platinum finds use in jewellery, usually as a 90–95% alloy, due to its inertness. It is used for this purpose for its prestige and inherent bullion value. Jewellery trade publications advise jewellers to present minute surface scratches (which they term patina) as a desirable feature in an attempt to enhance value of platinum products.

In watchmaking, Vacheron Constantin, Patek Philippe, Rolex, Breitling, and other companies use platinum for producing their limited edition watch series. Watchmakers appreciate the unique properties of platinum, as it neither tarnishes nor wears out (the latter quality relative to gold).

During periods of sustained economic stability and growth, the price of platinum tends to be as much as twice the price of gold, whereas during periods of economic uncertainty, the price of platinum tends to decrease due to reduced industrial demand, falling below the price of gold. Gold prices are more stable in slow economic times, as gold is considered a safe haven. Although gold is also used in industrial applications, especially in electronics due to its use as a conductor, its demand is not so driven by industrial uses. In the 18th century, platinum's rarity made King Louis XV of France declare it the only metal fit for a king.

1,000 cubic centimeters of 99.9% pure platinum, worth about US$696,000 at 29 Jun 2016 prices
Platinum price 1970–2022

Other uses

In the laboratory, platinum wire is used for electrodes; platinum pans and supports are used in thermogravimetric analysis because of the stringent requirements of chemical inertness upon heating to high temperatures (~1000 °C). Platinum is used as an alloying agent for various metal products, including fine wires, noncorrosive laboratory containers, medical instruments, dental prostheses, electrical contacts, and thermocouples. Platinum-cobalt, an alloy of roughly three parts platinum and one part cobalt, is used to make relatively strong permanent magnets. Platinum-based anodes are used in ships, pipelines, and steel piers. Platinum drugs are used to treat a wide variety of cancers, including testicular and ovarian carcinomas, melanoma, small-cell and non-small-cell lung cancer, myelomas and lymphomas.

Symbol of prestige in marketing

Platinum's rarity as a metal has caused advertisers to associate it with exclusivity and wealth. "Platinum" debit and credit cards have greater privileges than "gold" cards. "Platinum awards" are the second highest possible, ranking above "gold", "silver" and "bronze", but below diamond. For example, in the United States, a musical album that has sold more than 1 million copies will be credited as "platinum", whereas an album that has sold more than 10 million copies will be certified as "diamond". Some products, such as blenders and vehicles, with a silvery-white color are identified as "platinum". Platinum is considered a precious metal, although its use is not as common as the use of gold or silver. The frame of the Crown of Queen Elizabeth The Queen Mother, manufactured for her coronation as Consort of King George VI, is made of platinum. It was the first British crown to be made of this particular metal.

Health problems

According to the Centers for Disease Control and Prevention, short-term exposure to platinum salts may cause irritation of the eyes, nose, and throat, and long-term exposure may cause both respiratory and skin allergies. The current OSHA standard is 2 micrograms per cubic meter of air averaged over an 8-hour work shift. The National Institute for Occupational Safety and Health has set a recommended exposure limit (REL) for platinum as 1 mg/m³ over an 8-hour workday.

As platinum is a catalyst in the manufacture of the silicone rubber and gel components of several types of medical implants (breast implants, joint replacement prosthetics, artificial lumbar discs, vascular access ports, etc.), the possibility that platinum could enter the body and cause adverse effects has merited study. The Food and Drug Administration and other institutions have reviewed the issue and found no evidence to suggest toxicity in vivo.Chemically unbounded platinum has been identified by the FDA as a "fake cancer 'cure'". The misunderstanding is created by healthcare workers who are using inappropriately the name of the metal as a slang term for platinum-based chemotherapy medications like cisplatin. They are platinum compounds, not the metal itself.

Cellular automaton

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cellular_automaton

Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton.

The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete.

The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogeneity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolve in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class is thought to be computationally universal, or capable of simulating a Turing machine. Special types of cellular automata are reversible, where only a single configuration leads directly to a subsequent one, and totalistic, in which the future value of individual cells only depends on the total value of a group of neighboring cells. Cellular automata can simulate a variety of real-world systems, including biological and chemical ones.

Overview

The red cells are the Moore neighborhood for the blue cell.

The red cells are the von Neumann neighborhood for the blue cell. The range-2 "cross neighborhood" includes the pink cells as well.

One way to simulate a two-dimensional cellular automaton is with an infinite sheet of graph paper along with a set of rules for the cells to follow. Each square is called a "cell" and each cell has two possible states, black and white. The neighborhood of a cell is the nearby, usually adjacent, cells. The two most common types of neighborhoods are the von Neumann neighborhood and the Moore neighborhood. The former, named after the founding cellular automaton theorist, consists of the four orthogonally adjacent cells. The latter includes the von Neumann neighborhood as well as the four diagonally adjacent cells. For such a cell and its Moore neighborhood, there are 512 (= 2⁹) possible patterns. For each of the 512 possible patterns, the rule table would state whether the center cell will be black or white on the next time interval. Conway's Game of Life is a popular version of this model. Another common neighborhood type is the extended von Neumann neighborhood, which includes the two closest cells in each orthogonal direction, for a total of eight. The general equation for the total number of automata possible is k^{k^s}, where k is the number of possible states for a cell, and s is the number of neighboring cells (including the cell to be calculated itself) used to determine the cell's next state. Thus, in the two-dimensional system with a Moore neighborhood, the total number of automata possible would be 2^2⁹, or 1.34×10¹⁵⁴.

It is usually assumed that every cell in the universe starts in the same state, except for a finite number of cells in other states; the assignment of state values is called a configuration. More generally, it is sometimes assumed that the universe starts out covered with a periodic pattern, and only a finite number of cells violate that pattern. The latter assumption is common in one-dimensional cellular automata.

Cellular automata are often simulated on a finite grid rather than an infinite one. In two dimensions, the universe would be a rectangle instead of an infinite plane. The obvious problem with finite grids is how to handle the cells on the edges. How they are handled will affect the values of all the cells in the grid. One possible method is to allow the values in those cells to remain constant. Another method is to define neighborhoods differently for these cells. One could say that they have fewer neighbors, but then one would also have to define new rules for the cells located on the edges. These cells are usually handled with periodic boundary conditions resulting in a toroidal arrangement: when one goes off the top, one comes in at the corresponding position on the bottom, and when one goes off the left, one comes in on the right. (This essentially simulates an infinite periodic tiling, and in the field of partial differential equations is sometimes referred to as periodic boundary conditions.) This can be visualized as taping the left and right edges of the rectangle to form a tube, then taping the top and bottom edges of the tube to form a torus (doughnut shape). Universes of other dimensions are handled similarly. This solves boundary problems with neighborhoods, but another advantage is that it is easily programmable using modular arithmetic functions. For example, in a 1-dimensional cellular automaton like the examples below, the neighborhood of a cell x_i^t is {x_i−1^t−1, x_i^t−1, x_i+1^t−1}, where t is the time step (vertical), and i is the index (horizontal) in one generation.

History

Stanislaw Ulam, while working at the Los Alamos National Laboratory in the 1940s, studied the growth of crystals, using a simple lattice network as his model. At the same time, John von Neumann, Ulam's colleague at Los Alamos, was working on the problem of self-replicating systems. Von Neumann's initial design was founded upon the notion of one robot building another robot. This design is known as the kinematic model. As he developed this design, von Neumann came to realize the great difficulty of building a self-replicating robot, and of the great cost in providing the robot with a "sea of parts" from which to build its replicant. Neumann wrote a paper entitled "The general and logical theory of automata" for the Hixon Symposium in 1948. Ulam was the one who suggested using a discrete system for creating a reductionist model of self-replication. Nils Aall Barricelli performed many of the earliest explorations of these models of artificial life.

Ulam and von Neumann created a method for calculating liquid motion in the late 1950s. The driving concept of the method was to consider a liquid as a group of discrete units and calculate the motion of each based on its neighbors' behaviors. Thus was born the first system of cellular automata. Like Ulam's lattice network, von Neumann's cellular automata are two-dimensional, with his self-replicator implemented algorithmically. The result was a universal copier and constructor working within a cellular automaton with a small neighborhood (only those cells that touch are neighbors; for von Neumann's cellular automata, only orthogonal cells), and with 29 states per cell. Von Neumann gave an existence proof that a particular pattern would make endless copies of itself within the given cellular universe by designing a 200,000 cell configuration that could do so. This design is known as the tessellation model, and is called a von Neumann universal constructor.

Also in the 1940s, Norbert Wiener and Arturo Rosenblueth developed a model of excitable media with some of the characteristics of a cellular automaton. Their specific motivation was the mathematical description of impulse conduction in cardiac systems. However their model is not a cellular automaton because the medium in which signals propagate is continuous, and wave fronts are curves. A true cellular automaton model of excitable media was developed and studied by J. M. Greenberg and S. P. Hastings in 1978; see Greenberg-Hastings cellular automaton. The original work of Wiener and Rosenblueth contains many insights and continues to be cited in modern research publications on cardiac arrhythmia and excitable systems.

In the 1960s, cellular automata were studied as a particular type of dynamical system and the connection with the mathematical field of symbolic dynamics was established for the first time. In 1969, Gustav A. Hedlund compiled many results following this point of view in what is still considered as a seminal paper for the mathematical study of cellular automata. The most fundamental result is the characterization in the Curtis–Hedlund–Lyndon theorem of the set of global rules of cellular automata as the set of continuous endomorphisms of shift spaces.

In 1969, German computer pioneer Konrad Zuse published his book Calculating Space, proposing that the physical laws of the universe are discrete by nature, and that the entire universe is the output of a deterministic computation on a single cellular automaton; "Zuse's Theory" became the foundation of the field of study called digital physics.

Also in 1969 computer scientist Alvy Ray Smith completed a Stanford PhD dissertation on Cellular Automata Theory, the first mathematical treatment of CA as a general class of computers. Many papers came from this dissertation: He showed the equivalence of neighborhoods of various shapes, how to reduce a Moore to a von Neumann neighborhood or how to reduce any neighborhood to a von Neumann neighborhood. He proved that two-dimensional CA are computation universal, introduced 1-dimensional CA, and showed that they too are computation universal, even with simple neighborhoods. He showed how to subsume the complex von Neumann proof of construction universality (and hence self-reproducing machines) into a consequence of computation universality in a 1-dimensional CA. Intended as the introduction to the German edition of von Neumann's book on CA, he wrote a survey of the field with dozens of references to papers, by many authors in many countries over a decade or so of work, often overlooked by modern CA researchers.

In the 1970s a two-state, two-dimensional cellular automaton named Game of Life became widely known, particularly among the early computing community. Invented by John Conway and popularized by Martin Gardner in a Scientific American article, its rules are as follows:

Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
Any live cell with two or three live neighbours lives on to the next generation.
Any live cell with more than three live neighbours dies, as if by overpopulation.
Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Despite its simplicity, the system achieves an impressive diversity of behavior, fluctuating between apparent randomness and order. One of the most apparent features of the Game of Life is the frequent occurrence of gliders, arrangements of cells that essentially move themselves across the grid. It is possible to arrange the automaton so that the gliders interact to perform computations, and after much effort it has been shown that the Game of Life can emulate a universal Turing machine. It was viewed as a largely recreational topic, and little follow-up work was done outside of investigating the particularities of the Game of Life and a few related rules in the early 1970s.

Stephen Wolfram independently began working on cellular automata in mid-1981 after considering how complex patterns seemed formed in nature in violation of the Second Law of Thermodynamics. His investigations were initially spurred by a desire to model systems such as the neural networks found in brains. He published his first paper in Reviews of Modern Physics investigating elementary cellular automata (Rule 30 in particular) in June 1983. The unexpected complexity of the behavior of these simple rules led Wolfram to suspect that complexity in nature may be due to similar mechanisms. His investigations, however, led him to realize that cellular automata were poor at modelling neural networks. Additionally, during this period Wolfram formulated the concepts of intrinsic randomness and computational irreducibility, and suggested that rule 110 may be universal—a fact proved later by Wolfram's research assistant Matthew Cook in the 1990s.

Classification

Wolfram, in A New Kind of Science and several papers dating from the mid-1980s, defined four classes into which cellular automata and several other simple computational models can be divided depending on their behavior. While earlier studies in cellular automata tended to try to identify types of patterns for specific rules, Wolfram's classification was the first attempt to classify the rules themselves. In order of complexity the classes are:

Class 1: Nearly all initial patterns evolve quickly into a stable, homogeneous state. Any randomness in the initial pattern disappears.
Class 2: Nearly all initial patterns evolve quickly into stable or oscillating structures. Some of the randomness in the initial pattern may filter out, but some remains. Local changes to the initial pattern tend to remain local.
Class 3: Nearly all initial patterns evolve in a pseudo-random or chaotic manner. Any stable structures that appear are quickly destroyed by the surrounding noise. Local changes to the initial pattern tend to spread indefinitely.
Class 4: Nearly all initial patterns evolve into structures that interact in complex and interesting ways, with the formation of local structures that are able to survive for long periods of time. Class 2 type stable or oscillating structures may be the eventual outcome, but the number of steps required to reach this state may be very large, even when the initial pattern is relatively simple. Local changes to the initial pattern may spread indefinitely. Wolfram has conjectured that many class 4 cellular automata, if not all, are capable of universal computation. This has been proven for Rule 110 and Conway's Game of Life.

These definitions are qualitative in nature and there is some room for interpretation. According to Wolfram, "...with almost any general classification scheme there are inevitably cases which get assigned to one class by one definition and another class by another definition. And so it is with cellular automata: there are occasionally rules...that show some features of one class and some of another." Wolfram's classification has been empirically matched to a clustering of the compressed lengths of the outputs of cellular automata.

There have been several attempts to classify cellular automata in formally rigorous classes, inspired by Wolfram's classification. For instance, Culik and Yu proposed three well-defined classes (and a fourth one for the automata not matching any of these), which are sometimes called Culik–Yu classes; membership in these proved undecidable. Wolfram's class 2 can be partitioned into two subgroups of stable (fixed-point) and oscillating (periodic) rules.

The idea that there are 4 classes of dynamical system came originally from Nobel-prize winning chemist Ilya Prigogine who identified these 4 classes of thermodynamical systems: (1) systems in thermodynamic equilibrium, (2) spatially/temporally uniform systems, (3) chaotic systems, and (4) complex far-from-equilibrium systems with dissipative structures (see figure 1 in the 1974 paper of Nicolis, Prigogine's student).

Reversible

A cellular automaton is reversible if, for every current configuration of the cellular automaton, there is exactly one past configuration (preimage). If one thinks of a cellular automaton as a function mapping configurations to configurations, reversibility implies that this function is bijective. If a cellular automaton is reversible, its time-reversed behavior can also be described as a cellular automaton; this fact is a consequence of the Curtis–Hedlund–Lyndon theorem, a topological characterization of cellular automata. For cellular automata in which not every configuration has a preimage, the configurations without preimages are called Garden of Eden patterns.

For one-dimensional cellular automata there are known algorithms for deciding whether a rule is reversible or irreversible. However, for cellular automata of two or more dimensions reversibility is undecidable; that is, there is no algorithm that takes as input an automaton rule and is guaranteed to determine correctly whether the automaton is reversible. The proof by Jarkko Kari is related to the tiling problem by Wang tiles.

Reversible cellular automata are often used to simulate such physical phenomena as gas and fluid dynamics, since they obey the laws of thermodynamics. Such cellular automata have rules specially constructed to be reversible. Such systems have been studied by Tommaso Toffoli, Norman Margolus and others. Several techniques can be used to explicitly construct reversible cellular automata with known inverses. Two common ones are the second-order cellular automaton and the block cellular automaton, both of which involve modifying the definition of a cellular automaton in some way. Although such automata do not strictly satisfy the definition given above, it can be shown that they can be emulated by conventional cellular automata with sufficiently large neighborhoods and numbers of states, and can therefore be considered a subset of conventional cellular automata. Conversely, it has been shown that every reversible cellular automaton can be emulated by a block cellular automaton.

Totalistic

A special class of cellular automata are totalistic cellular automata. The state of each cell in a totalistic cellular automaton is represented by a number (usually an integer value drawn from a finite set), and the value of a cell at time t depends only on the sum of the values of the cells in its neighborhood (possibly including the cell itself) at time t − 1. If the state of the cell at time t depends on both its own state and the total of its neighbors at time t − 1 then the cellular automaton is properly called outer totalistic. Conway's Game of Life is an example of an outer totalistic cellular automaton with cell values 0 and 1; outer totalistic cellular automata with the same Moore neighborhood structure as Life are sometimes called life-like cellular automata.

Related automata

There are many possible generalizations of the cellular automaton concept.

A cellular automaton based on hexagonal cells instead of squares (rule 34/2)

One way is by using something other than a rectangular (cubic, etc.) grid. For example, if a plane is tiled with regular hexagons, those hexagons could be used as cells. In many cases the resulting cellular automata are equivalent to those with rectangular grids with specially designed neighborhoods and rules. Another variation would be to make the grid itself irregular, such as with Penrose tiles.

Also, rules can be probabilistic rather than deterministic. Such cellular automata are called probabilistic cellular automata. A probabilistic rule gives, for each pattern at time t, the probabilities that the central cell will transition to each possible state at time t + 1. Sometimes a simpler rule is used; for example: "The rule is the Game of Life, but on each time step there is a 0.001% probability that each cell will transition to the opposite color."

The neighborhood or rules could change over time or space. For example, initially the new state of a cell could be determined by the horizontally adjacent cells, but for the next generation the vertical cells would be used.

In cellular automata, the new state of a cell is not affected by the new state of other cells. This could be changed so that, for instance, a 2 by 2 block of cells can be determined by itself and the cells adjacent to itself.

There are continuous automata. These are like totalistic cellular automata, but instead of the rule and states being discrete (e.g. a table, using states {0,1,2}), continuous functions are used, and the states become continuous (usually values in [0,1]). The state of a location is a finite number of real numbers. Certain cellular automata can yield diffusion in liquid patterns in this way.

Continuous spatial automata have a continuum of locations. The state of a location is a finite number of real numbers. Time is also continuous, and the state evolves according to differential equations. One important example is reaction–diffusion textures, differential equations proposed by Alan Turing to explain how chemical reactions could create the stripes on zebras and spots on leopards. When these are approximated by cellular automata, they often yield similar patterns. MacLennan considers continuous spatial automata as a model of computation.

There are known examples of continuous spatial automata, which exhibit propagating phenomena analogous to gliders in the Game of Life.

Graph rewriting automata are extensions of cellular automata based on graph rewriting systems.

Elementary cellular automata

The simplest nontrivial cellular automaton would be one-dimensional, with two possible states per cell, and a cell's neighbors defined as the adjacent cells on either side of it. A cell and its two neighbors form a neighborhood of 3 cells, so there are 2³ = 8 possible patterns for a neighborhood. A rule consists of deciding, for each pattern, whether the cell will be a 1 or a 0 in the next generation. There are then 2⁸ = 256 possible rules.

An animation of the way the rules of a 1D cellular automaton determine the next generation

These 256 cellular automata are generally referred to by their Wolfram code, a standard naming convention invented by Wolfram that gives each rule a number from 0 to 255. A number of papers have analyzed and compared these 256 cellular automata. The rule 30, rule 90, rule 110, and rule 184 cellular automata are particularly interesting. The images below show the history of rules 30 and 110 when the starting configuration consists of a 1 (at the top of each image) surrounded by 0s. Each row of pixels represents a generation in the history of the automaton, with t=0 being the top row. Each pixel is colored white for 0 and black for 1.

Rule 30 cellular automaton
(binary 00011110 = decimal 30)
current pattern	111	110	101	100	011	010	001	000
new state for center cell	0	0	0	1	1	1	1	0

Rule 30 exhibits class 3 behavior, meaning even simple input patterns such as that shown lead to chaotic, seemingly random histories.

Rule 110 cellular automaton
(binary 01101110 = decimal 110)
current pattern	111	110	101	100	011	010	001	000
new state for center cell	0	1	1	0	1	1	1	0

Rule 110, like the Game of Life, exhibits what Wolfram calls class 4 behavior, which is neither completely random nor completely repetitive. Localized structures appear and interact in various complicated-looking ways. In the course of the development of A New Kind of Science, as a research assistant to Wolfram in 1994, Matthew Cook proved that some of these structures were rich enough to support universality. This result is interesting because rule 110 is an extremely simple one-dimensional system, and difficult to engineer to perform specific behavior. This result therefore provides significant support for Wolfram's view that class 4 systems are inherently likely to be universal. Cook presented his proof at a Santa Fe Institute conference on Cellular Automata in 1998, but Wolfram blocked the proof from being included in the conference proceedings, as Wolfram did not want the proof announced before the publication of A New Kind of Science. In 2004, Cook's proof was finally published in Wolfram's journal Complex Systems (Vol. 15, No. 1), over ten years after Cook came up with it. Rule 110 has been the basis for some of the smallest universal Turing machines.

Rule space

An elementary cellular automaton rule is specified by 8 bits, and all elementary cellular automaton rules can be considered to sit on the vertices of the 8-dimensional unit hypercube. This unit hypercube is the cellular automaton rule space. For next-nearest-neighbor cellular automata, a rule is specified by 2⁵ = 32 bits, and the cellular automaton rule space is a 32-dimensional unit hypercube. A distance between two rules can be defined by the number of steps required to move from one vertex, which represents the first rule, and another vertex, representing another rule, along the edge of the hypercube. This rule-to-rule distance is also called the Hamming distance.

Cellular automaton rule space allows us to ask the question concerning whether rules with similar dynamical behavior are "close" to each other. Graphically drawing a high dimensional hypercube on the 2-dimensional plane remains a difficult task, and one crude locator of a rule in the hypercube is the number of bit-1 in the 8-bit string for elementary rules (or 32-bit string for the next-nearest-neighbor rules). Drawing the rules in different Wolfram classes in these slices of the rule space show that class 1 rules tend to have lower number of bit-1s, thus located in one region of the space, whereas class 3 rules tend to have higher proportion (50%) of bit-1s.

For larger cellular automaton rule space, it is shown that class 4 rules are located between the class 1 and class 3 rules. This observation is the foundation for the phrase edge of chaos, and is reminiscent of the phase transition in thermodynamics.

Applications

Biology

Several biological processes occur—or can be simulated—by cellular automata.

Some examples of biological phenomena modeled by cellular automata with a simple state space are:

Patterns of some seashells, like the ones in the genera Conus and Cymbiola, are generated by natural cellular automata. The pigment cells reside in a narrow band along the shell's lip. Each cell secretes pigments according to the activating and inhibiting activity of its neighbor pigment cells, obeying a natural version of a mathematical rule. The cell band leaves the colored pattern on the shell as it grows slowly. For example, the widespread species Conus textile bears a pattern resembling Wolfram's rule 30 cellular automaton.
Plants regulate their intake and loss of gases via a cellular automaton mechanism. Each stoma on the leaf acts as a cell.
Moving wave patterns on the skin of cephalopods can be simulated with a two-state, two-dimensional cellular automata, each state corresponding to either an expanded or retracted chromatophore.
Threshold automata have been invented to simulate neurons, and complex behaviors such as recognition and learning can be simulated.
Fibroblasts bear similarities to cellular automata, as each fibroblast only interacts with its neighbors.

Additionally, biological phenomena which require explicit modeling of the agents' velocities (for example, those involved in collective cell migration) may be modeled by cellular automata with a more complex state space and rules, such as biological lattice-gas cellular automata. These include phenomena of great medical importance, such as:

Characterization of different modes of metastatic invasion.
The role of heterogeneity in the development of aggressive carcinomas.
Phenotypic switching during tumor proliferation.

Chemistry

The Belousov–Zhabotinsky reaction is a spatio-temporal chemical oscillator that can be simulated by means of a cellular automaton. In the 1950s A. M. Zhabotinsky (extending the work of B. P. Belousov) discovered that when a thin, homogenous layer of a mixture of malonic acid, acidified bromate, and a ceric salt were mixed together and left undisturbed, fascinating geometric patterns such as concentric circles and spirals propagate across the medium. In the "Computer Recreations" section of the August 1988 issue of Scientific American, A. K. Dewdney discussed a cellular automaton developed by Martin Gerhardt and Heike Schuster of the University of Bielefeld (Germany). This automaton produces wave patterns that resemble those in the Belousov-Zhabotinsky reaction.

Physics

Probabilistic cellular automata are used in statistical and condensed matter physics to study phenomena like fluid dynamics and phase transitions. The Ising model is a prototypical example, in which each cell can be in either of two states called "up" and "down", making an idealized representation of a magnet. By adjusting the parameters of the model, the proportion of cells being in the same state can be varied, in ways that help explicate how ferromagnets become demagnetized when heated. Moreover, results from studying the demagnetization phase transition can be transferred to other phase transitions, like the evaporation of a liquid into a gas; this convenient cross-applicability is known as universality.The phase transition in the two-dimensional Ising model and other systems in its universality class has been of particular interest, as it requires conformal field theory to understand in depth. Other cellular automata that have been of significance in physics include lattice gas automata, which simulate fluid flows.

Computer science, coding, and communication

Cellular automaton processors are physical implementations of CA concepts, which can process information computationally. Processing elements are arranged in a regular grid of identical cells. The grid is usually a square tiling, or tessellation, of two or three dimensions; other tilings are possible, but not yet used. Cell states are determined only by interactions with adjacent neighbor cells. No means exists to communicate directly with cells farther away. One such cellular automaton processor array configuration is the systolic array. Cell interaction can be via electric charge, magnetism, vibration (phonons at quantum scales), or any other physically useful means. This can be done in several ways so that no wires are needed between any elements. This is very unlike processors used in most computers today (von Neumann designs) which are divided into sections with elements that can communicate with distant elements over wires.

Rule 30 was originally suggested as a possible block cipher for use in cryptography. Two-dimensional cellular automata can be used for constructing a pseudorandom number generator.

Cellular automata have been proposed for public-key cryptography. The one-way function is the evolution of a finite CA whose inverse is believed to be hard to find. Given the rule, anyone can easily calculate future states, but it appears to be very difficult to calculate previous states. Cellular automata have also been applied to design error correction codes.

Other problems that can be solved with cellular automata include:

Generative art and music

Cellular automata have been used in generative music and evolutionary music composition and procedural terrain generation in video games.

Maze generation

Certain types of cellular automata can be used to generate mazes. Two well-known such cellular automata, Maze and Mazectric, have rulestrings B3/S12345 and B3/S1234. In the former, this means that cells survive from one generation to the next if they have at least one and at most five neighbours. In the latter, this means that cells survive if they have one to four neighbours. If a cell has exactly three neighbours, it is born. It is similar to Conway's Game of Life in that patterns that do not have a living cell adjacent to 1, 4, or 5 other living cells in any generation will behave identically to it. However, for large patterns, it behaves very differently from Life.

For a random starting pattern, these maze-generating cellular automata will evolve into complex mazes with well-defined walls outlining corridors. Mazecetric, which has the rule B3/S1234 has a tendency to generate longer and straighter corridors compared with Maze, with the rule B3/S12345. Since these cellular automaton rules are deterministic, each maze generated is uniquely determined by its random starting pattern. This is a significant drawback since the mazes tend to be relatively predictable.

Like some of the graph-theory based methods described above, these cellular automata typically generate mazes from a single starting pattern; hence it will usually be relatively easy to find the way to the starting cell, but harder to find the way anywhere else.

Solvent effects

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Solvent_effects

In chemistry, solvent effects are the influence of a solvent on chemical reactivity or molecular associations. Solvents can have an effect on solubility, stability and reaction rates and choosing the appropriate solvent allows for thermodynamic and kinetic control over a chemical reaction.

A solute dissolves in a solvent when solvent-solute interactions are more favorable than solute-solute interaction.

Effects on stability

Different solvents can affect the equilibrium constant of a reaction by differential stabilization of the reactant or product. The equilibrium is shifted in the direction of the substance that is preferentially stabilized. Stabilization of the reactant or product can occur through any of the different non-covalent interactions with the solvent such as H-bonding, dipole-dipole interactions, van der Waals interactions etc.

Acid-base equilibria

The ionization equilibrium of an acid or a base is affected by a solvent change. The effect of the solvent is not only because of its acidity or basicity but also because of its dielectric constant and its ability to preferentially solvate and thus stabilize certain species in acid-base equilibria. A change in the solvating ability or dielectric constant can thus influence the acidity or basicity.

Solvent properties at 25 °C
Solvent	Dielectric constant
Acetonitrile	37
Dimethylsulfoxide	47
Water	78

In the table above, it can be seen that water is the most polar-solvent, followed by DMSO, and then acetonitrile. Consider the following acid dissociation equilibrium:

HA ⇌ A⁻ + H⁺

Water, being the most polar-solvent listed above, stabilizes the ionized species to a greater extent than does DMSO or Acetonitrile. Ionization - and, thus, acidity - would be greatest in water and lesser in DMSO and Acetonitrile, as seen in the table below, which shows pK_a values at 25 °C for acetonitrile (ACN) and dimethyl sulfoxide (DMSO) and water.

pK_a values of acids
HA ⇌ A⁻ + H⁺	ACN	DMSO	water
p-Toluenesulfonic acid	8.5	0.9	strong
2,4-Dinitrophenol	16.66	5.1	3.9
Benzoic acid	21.51	11.1	4.2
Acetic acid	23.51	12.6	4.756
Phenol	29.14	18.0	9.99

Keto–enol equilibria

Keto enol tautomerization (diketo form on left, *cis*-enol form on right)

Many carbonyl compounds exhibit keto–enol tautomerism. This effect is especially pronounced in 1,3-dicarbonyl compounds that can form hydrogen-bonded enols. The equilibrium constant is dependent upon the solvent polarity, with the cis-enol form predominating at low polarity and the diketo form predominating at high polarity. The intramolecular H-bond formed in the cis-enol form is more pronounced when there is no competition for intermolecular H-bonding with the solvent. As a result, solvents of low polarity that do not readily participate in H-bonding allow cis-enolic stabilization by intramolecular H-bonding.

Solvent	$K_{T} = \frac{[c i s - e n o l]}{[d i k e t o]}$
Gas phase	11.7
Cyclohexane	42
Tetrahydrofuran	7.2
Benzene	14.7
Ethanol	5.8
Dichloromethane	4.2
Water	0.23

Effects on reaction rates

Often, reactivity and reaction mechanisms are pictured as the behavior of isolated molecules in which the solvent is treated as a passive support. However, the nature of the solvent can actually influence reaction rates and order of a chemical reaction.

Performing a reaction without solvent can affect reaction-rate for reactions with bimolecular mechanisms, for example, by maximizing the concentration of the reagents. Ball milling is one of several mechanochemical techniques where physical methods are used to control reactions rather than solvents are methods are methods for affecting reactions in the absence of solvent.

Equilibrium-solvent effects

Solvents can affect rates through equilibrium-solvent effects that can be explained on the basis of the transition state theory. In essence, the reaction rates are influenced by differential solvation of the starting material and transition state by the solvent. When the reactant molecules proceed to the transition state, the solvent molecules orient themselves to stabilize the transition state. If the transition state is stabilized to a greater extent than the starting material then the reaction proceeds faster. If the starting material is stabilized to a greater extent than the transition state then the reaction proceeds slower. However, such differential solvation requires rapid reorientational relaxation of the solvent (from the transition state orientation back to the ground-state orientation). Thus, equilibrium-solvent effects are observed in reactions that tend to have sharp barriers and weakly dipolar, rapidly relaxing solvents.

Frictional solvent effects

The equilibrium hypothesis does not stand for very rapid chemical reactions in which the transition state theory breaks down. In such cases involving strongly dipolar, slowly relaxing solvents, solvation of the transition state does not play a very large role in affecting the reaction rate. Instead, dynamic contributions of the solvent (such as friction, density, internal pressure, or viscosity) play a large role in affecting the reaction rate.

Hughes–Ingold rules

The effect of solvent on elimination and nucleophillic substitution reactions was originally studied by British chemists Edward D. Hughes and Christopher Kelk Ingold. Using a simple solvation model that considered only pure electrostatic interactions between ions or dipolar molecules and solvents in initial and transition states, all nucleophilic and elimination reactions were organized into different charge types (neutral, positively charged, or negatively charged). Hughes and Ingold then made certain assumptions about the extent of solvation to be expected in these situations:

increasing magnitude of charge will increase solvation
increasing delocalization will decrease solvation
loss of charge will decrease solvation more than the dispersal of charge

The applicable effect of these general assumptions are shown in the following examples:

An increase in solvent polarity accelerates the rates of reactions where a charge is developed in the activated complex from neutral or slightly charged reactant
An increase in solvent polarity decreases the rates of reactions where there is less charge in the activated complex in comparison to the starting materials
A change in solvent polarity will have little or no effect on the rates of reaction when there is little or no difference in charge between the reactants and the activated complex.

Reaction examples

Substitution reactions

The solvent used in substitution reactions inherently determines the nucleophilicity of the nucleophile; this fact has become increasingly more apparent as more reactions are performed in the gas phase. As such, solvent conditions significantly affect the performance of a reaction with certain solvent conditions favoring one reaction mechanism over another. For S_N1 reactions the solvent's ability to stabilize the intermediate carbocation is of direct importance to its viability as a suitable solvent. The ability of polar solvents to increase the rate of S_N1 reactions is a result of the polar solvent's solvating the reactant intermediate species, i.e., the carbocation, thereby decreasing the intermediate energy relative to the starting material. The following table shows the relative solvolysis rates of tert-butyl chloride with acetic acid (CH₃CO₂H), methanol (CH₃OH), and water (H₂O).

Solvent	Dielectric Constant, ε	Relative Rate
CH₃CO₂H	6	1
CH₃OH	33	4
H₂O	78	150,000

The case for S_N2 reactions is quite different, as the lack of solvation on the nucleophile increases the rate of an S_N2 reaction. In either case (S_N1 or S_N2), the ability to either stabilize the transition state (S_N1) or destabilize the reactant starting material (S_N2) acts to decrease the ΔG^‡_activation and thereby increase the rate of the reaction. This relationship is according to the equation ΔG = –RT ln K (Gibbs free energy). The rate equation for S_N2 reactions are bimolecular being first order in Nucleophile and first order in Reagent. The determining factor when both S_N2 and S_N1 reaction mechanisms are viable is the strength of the Nucleophile. Nuclephilicity and basicity are linked and the more nucleophilic a molecule becomes the greater said nucleophile's basicity. This increase in basicity causes problems for S_N2 reaction mechanisms when the solvent of choice is protic. Protic solvents react with strong nucleophiles with good basic character in an acid/base fashion, thus decreasing or removing the nucleophilic nature of the nucleophile. The following table shows the effect of solvent polarity on the relative reaction rates of the S_N2 reaction of 1-bromobutane with azide (N₃^–). There is a noticeable increase in reaction rate when changing from a protic solvent to an aprotic solvent. This difference arises from acid/base reactions between protic solvents (not aprotic solvents) and strong nucleophiles. While it is true that steric effects also affect the relative reaction rates, however, for demonstration of principle for solvent polarity on S_N2 reaction rates, steric effects may be neglected.

Solvent	Dielectric Constant, ε	Relative Rate	Type
CH₃OH	33	1	Protic
H₂O	78	7	Protic
DMSO	49	1,300	Aprotic
DMF	37	2800	Aprotic
CH₃CN	38	5000	Aprotic

A comparison of S_N1 to S_N2 reactions is to the right. On the left is an S_N1 reaction coordinate diagram. Note the decrease in ΔG^‡_activation for the polar-solvent reaction conditions. This arises from the fact that polar solvents stabilize the formation of the carbocation intermediate to a greater extent than the non-polar-solvent conditions. This is apparent in the ΔE_a, ΔΔG^‡_activation. On the right is an S_N2 reaction coordinate diagram. Note the decreased ΔG^‡_activation for the non-polar-solvent reaction conditions. Polar solvents stabilize the reactants to a greater extent than the non-polar-solvent conditions by solvating the negative charge on the nucleophile, making it less available to react with the electrophile.

Transition-metal-catalyzed reactions

The reactions involving charged transition metal complexes (cationic or anionic) are dramatically influenced by solvation, especially in the polar media. As high as 30-50 kcal/mol changes in the potential energy surface (activation energies and relative stability) were calculated if the charge of the metal species was changed during the chemical transformation.

Free radical syntheses

Many free radical-based syntheses show large kinetic solvent effects that can reduce the rate of reaction and cause a planned reaction to follow an unwanted pathway.

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Thursday, May 9, 2024

Platinum

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Cellular automaton

Overview

History

Classification

Reversible

Totalistic

Related automata

Elementary cellular automata

Rule space

Applications

Biology

Chemistry

Physics

Computer science, coding, and communication

Generative art and music

Maze generation

Solvent effects

Effects on stability

Acid-base equilibria

Keto–enol equilibria

Effects on reaction rates

Equilibrium-solvent effects

Frictional solvent effects

Hughes–Ingold rules

Reaction examples

Substitution reactions

Transition-metal-catalyzed reactions

Free radical syntheses

Operator (computer programming)