Theories of Metastability

Oscillatory Activity and Coordination DynamicsThe dynamical system model, which represents networks composed of integrated neural systems communicating with one another between unstable and stable phases, has become an increasingly popular theory underpinning the understanding of metastability. Coordination dynamics forms the basis for this dynamical system model by describing mathematical formulae and paradigms governing the coupling of environmental stimuli to their effectors.History of Coordination Dynamics and the Haken-Kelso-Bunz (HKB) ModelThe so-named HKB model is one of the earliest and well-respected theories to describe coordination dynamics in the brain. In this model, the formation of neural networks can be partly described as self-organization, where individual neurons and small neuronal systems aggregate and coordinate to either adapt or respond to local stimuli or to divide labor and specialize in function.In the last 20 years, the HKB model has become a widely-accepted theory to explain the coordinated movements and behaviors of individual neurons into large, end-to-end neural networks. Originally the model described a system in which spontaneous transitions observed in finger movements could be described as a series of in-phase and out-of-phase movements.In the mid-1980s HKB model experiments, subjects were asked to wave one finger on each hand in two modes of direction: first, known as out of phase, both fingers moving in the same direction back and forth (as windshield wipers might move); and second, known as in-phase, where both fingers come together and move away to and from the midline of the body. To illustrate coordination dynamics, the subjects were asked to move their fingers out of phase with increasing speed until their fingers were moving as fast as possible. As movement approached its critical speed, the subjects’ fingers were found to move from out-of-phase (windshield-wiper-like) movement to in-phase (toward midline movement).The HKB model, which has also been elucidated by several complex mathematical descriptors, is still a relatively simple but powerful way to describe seemingly-independent systems that come to reach synchrony just before a state of self-organized criticality.

Metastability in molecules

Metastability is the ability of a non-equilibrium state to persist for some period of time.Metastability in molecules is the ability of a non-equilibrium chemical state to persist for a long period of time.Usually metastability is due to a relatively slow phase transformation. For example, at room temperature, diamonds are metastable because the phase transformation to the stable graphite form is extremely slow. At higher temperatures, the rate of phase transformation is increased and the diamond will transform to graphite.Martensite is a metastable phase used to control the hardness of most steel. The bonds between the building blocks of polymers such as DNA, RNA and proteins are also metastable.IUPAC recommend that the term "metastable" be avoided and "transient" be used instead because "metastable" can misleadingly associate a thermodynamic term to a kinetic property, even though most transients are thermodynamically unstable with

Metastable isomers

Metastable isomers can be produced through nuclear fusion or other nuclear reactions. A nucleus thus produced generally starts its existence in an excited state that de-excites through the emission of one or more gamma rays (or, equivalently, conversion electrons), usually in a time far shorter than a picosecond. However, sometimes it happens that the de-excitation does not proceed rapidly all the way to the nuclear ground state. This usually occurs because of the formation of an intermediate excited state with a spin far different from that of the ground state. Gamma-ray emission is far slower (is "hindered") if the spin of the post-emission state is very different from that of the emitting state, particularly if the excitation energy is low, than if the two states are of similar spin. The excited state in this situation is therefore a good candidate to be metastable, if there are no other states of intermediate spin with excitation energies less than that of the metastable state.Metastable isomers of a particular isotope are usually designated with an "m" (or, in the case of isotopes with more than one isomer, m2, m3, and so on). This designation is usually placed after the atomic symbol and number of the atom (e.g., Co-58m), but is sometimes placed as a superscript before (e.g., 58mCo). Increasing indices, m, m2, etc. correlate with increasing levels of excitation energy stored in each of the isomeric states (e.g., Hf-177m2 or 177m2Hf).A different kind of metastable nuclear state (isomer) is the fission isomer or shape isomer. Most actinide nuclei, in their ground states, are not spherical, but rather spheroidal — specifically, prolate, with an axis of symmetry longer than the other axes (similar to an American football or rugby ball, although with a less pronounced departure from spherical symmetry). In some of these, quantum-mechanical states can exist in which the distribution of protons and neutrons is farther yet from spherical (in fact, about as non-spherical as an American football), so much so that de-excitation to the nuclear ground state is strongly hindered. In general these states either de-excite to the ground state (albeit far more slowly than a "usual" excited state) or undergo spontaneous fission with half lives of the order of nanoseconds or microseconds— a very short time, but many orders of magnitude longer than the half life of a more usual nuclear excited state. Fission isomers are usually denoted with a postscript or superscript "f" rather than "m," so that a fission isomer in e.g. plutonium 240 is denoted Pu-240f or 240fPu

Nearly-stable isomers

Most nuclear isomers are very unstable, and radiate away the extra energy immediately (on the order of 10-12 seconds). As a result, the term is usually restricted to refer to isomers with half-lives of 10-9 seconds or more. Quantum mechanics predicts that certain atomic species will possess isomers with unusually long lifetimes even by this stricter standard, and so have interesting properties. By definition, there is no such thing as a "stable" isomer; however, some are so long-lived as to be nearly stable, and can be produced and observed in quantity.The only nearly-stable nuclear isomer occurring in nature is Ta-180m, which is present in all tantalum samples at about 1 part in 8,300. Its half-life is at least 1015 years, markedly longer than the age of the universe. This remarkable persistence results from the fact that the excitation energy of the isomeric state is low and both gamma de-excitation to the Ta-180 ground state (which is radioactive and not particularly long lived) and beta decay to hafnium or tungsten are suppressed owing to spin mismatches. The origin of this isomer is mysterious, though it is believed to have been formed in supernovas (as are most other heavy elements). When it relaxes to its ground state, it releases a photon with an energy of 75 keV. It was first reported in 1988 by Collinsthat Ta-180m can be forced to release its energy by weaker x-rays. After 11 years of controversy those claims were confirmed in 1999 by Belic and co-workers in the Stuttgart nuclear physics group.Another reasonably stable nuclear isomer (with a half-life of 31 years) is hafnium-178m2, which has the highest excitation energy of any comparably long-lived isomer. One gram of pure Hf-178-m2 contains approximately 1330 megajoules of energy, the equivalent of exploding about 317 kilograms (700 pounds) of TNT. Further, in the natural decay of Hf-178-m2, the energy is released as gamma rays with a total energy of 2.45 MeV. As with Ta-180m, there are disputed reports that Hf-178-m2 can be stimulated into releasing its energy, and as a result the substance is being studied as a possible source for gamma ray lasers. These reports also indicate that the energy is released very quickly, so that Hf-178-m2 can produce extremely high powers (on the order of exawatts. Other isomers have also been investigated as possible media for gamma-ray stimulated emission.

Applications

These hafnium and tantalum isomers have been considered in some quarters as weapons that could be used to circumvent the Nuclear Non-Proliferation Treaty, since they can be induced to emit very strong gamma radiation. DARPA has or has had a program to investigate this usage of both isomers. However, given the difference in speed between a photon and a neutron, they can't be induced to chain react like a nuclear weapon, so there will probably never be such a weapon. Ta-180m is also one of the most expensive substances to procure in the world: It costs approximately $17 million per gram. In 1999, the entire world's supply of Ta-180m was only 6.7 milligrams.Technetium isomers Tc-99m (with a half-life of 6.01 hours) and Tc-95m (with a half-life of 61 days) are used in medical and industrial applications.

Decay processes

Isomers decay to lower energy states of the nuclide through two isomeric transitions:γ (gamma) emission (emission of a high-energy photon)internal conversion (the energy is used to ionize the atom)