Metastability

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A metastable state of weaker bond (1), a transitional "saddle" configuration (2) and a stable state of stronger bond (3). Meta-stability.svg
A metastable state of weaker bond (1), a transitional "saddle" configuration (2) and a stable state of stronger bond (3).

In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by (possibly large) barriers in the potential energy.

Contents

During a metastable state of finite lifetime, all state-describing parameters reach and hold stationary values. In isolation:

The metastability concept originated in the physics of first-order phase transitions. It then acquired new meaning in the study of aggregated subatomic particles (in atomic nuclei or in atoms) or in molecules, macromolecules or clusters of atoms and molecules. Later, it was borrowed for the study of decision-making and information transmission systems.

Metastability is common in physics and chemistry – from an atom (many-body assembly) to statistical ensembles of molecules (viscous fluids, amorphous solids, liquid crystals, minerals, etc.) at molecular levels or as a whole (see Metastable states of matter and grain piles below). The abundance of states is more prevalent as the systems grow larger and/or if the forces of their mutual interaction are spatially less uniform or more diverse.

In dynamic systems (with feedback) like electronic circuits, signal trafficking, decisional, neural and immune systems, the time-invariance of the active or reactive patterns with respect to the external influences defines stability and metastability (see brain metastability below). In these systems, the equivalent of thermal fluctuations in molecular systems is the "white noise" that affects signal propagation and the decision-making.

Statistical physics and thermodynamics

Non-equilibrium thermodynamics is a branch of physics that studies the dynamics of statistical ensembles of molecules via unstable states. Being "stuck" in a thermodynamic trough without being at the lowest energy state is known as having kinetic stability or being kinetically persistent. The particular motion or kinetics of the atoms involved has resulted in getting stuck, despite there being preferable (lower-energy) alternatives.

States of matter

Metastable states of matter (also referred as metastates) range from melting solids (or freezing liquids), boiling liquids (or condensing gases) and sublimating solids to supercooled liquids or superheated liquid-gas mixtures. Extremely pure, supercooled water stays liquid below 0 °C and remains so until applied vibrations or condensing seed doping initiates crystallization centers. This is a common situation for the droplets of atmospheric clouds.

Condensed matter and macromolecules

Metastable phases are common in condensed matter and crystallography. This is the case for anatase, a metastable polymorph of titanium dioxide, which despite commonly being the first phase to form in many synthesis processes due to its lower surface energy, is always metastable, with rutile being the most stable phase at all temperatures and pressures. [1] As another example, diamond is a stable phase only at very high pressures, but is a metastable form of carbon at standard temperature and pressure. It can be converted to graphite (plus leftover kinetic energy), but only after overcoming an activation energy – an intervening hill. Martensite is a metastable phase used to control the hardness of most steel. Metastable polymorphs of silica are commonly observed. In some cases, such as in the allotropes of solid boron, acquiring a sample of the stable phase is difficult. [2]

The bonds between the building blocks of polymers such as DNA, RNA, and proteins are also metastable. Adenosine triphosphate (ATP) is a highly metastable molecule, colloquially described as being "full of energy" that can be used in many ways in biology. [3]

Generally speaking, emulsions/colloidal systems and glasses are metastable. The metastability of silica glass, for example, is characterised by lifetimes on the order of 1098 years [4] (as compared with the lifetime of the universe, which is thought to be around 13.787×109 years). [5]

Sandpiles are one system which can exhibit metastability if a steep slope or tunnel is present. Sand grains form a pile due to friction. It is possible for an entire large sand pile to reach a point where it is stable, but the addition of a single grain causes large parts of it to collapse.

The avalanche is a well-known problem with large piles of snow and ice crystals on steep slopes. In dry conditions, snow slopes act similarly to sandpiles. An entire mountainside of snow can suddenly slide due to the presence of a skier, or even a loud noise or vibration.

Quantum mechanics

Aggregated systems of subatomic particles described by quantum mechanics (quarks inside nucleons, nucleons inside atomic nuclei, electrons inside atoms, molecules, or atomic clusters) are found to have many distinguishable states. Of these, one (or a small degenerate set) is indefinitely stable: the ground state or global minimum.

All other states besides the ground state (or those degenerate with it) have higher energies. [6] Of all these other states, the metastable states are the ones having lifetimes lasting at least 102 to 103 times longer than the shortest lived states of the set. [7]

A metastable state is then long-lived (locally stable with respect to configurations of 'neighbouring' energies) but not eternal (as the global minimum is). Being excited – of an energy above the ground state – it will eventually decay to a more stable state, releasing energy. Indeed, above absolute zero, all states of a system have a non-zero probability to decay; that is, to spontaneously fall into another state (usually lower in energy). One mechanism for this to happen is through tunnelling.

Nuclear physics

Some energetic states of an atomic nucleus (having distinct spatial mass, charge, spin, isospin distributions) are much longer-lived than others (nuclear isomers of the same isotope), e.g. technetium-99m. [8] The isotope tantalum-180m, although being a metastable excited state, is long-lived enough that it has never been observed to decay, with a half-life calculated to be least 4.5×1016 years, [9] [10] over 3 million times the current age of the universe.

Atomic and molecular physics

Some atomic energy levels are metastable. Rydberg atoms are an example of metastable excited atomic states. Transitions from metastable excited levels are typically those forbidden by electric dipole selection rules. This means that any transitions from this level are relatively unlikely to occur. In a sense, an electron that happens to find itself in a metastable configuration is trapped there. Since transitions from a metastable state are not impossible (merely less likely), the electron will eventually decay to a less energetic state, typically by an electric quadrupole transition, or often by non-radiative de-excitation (e.g., collisional de-excitation).

This slow-decay property of a metastable state is apparent in phosphorescence, the kind of photoluminescence seen in glow-in-the-dark toys that can be charged by first being exposed to bright light. Whereas spontaneous emission in atoms has a typical timescale on the order of 10−8 seconds, the decay of metastable states can typically take milliseconds to minutes, and so light emitted in phosphorescence is usually both weak and long-lasting.

Chemistry

In chemical systems, a system of atoms or molecules involving a change in chemical bond can be in a metastable state, which lasts for a relatively long period of time. Molecular vibrations and thermal motion make chemical species at the energetic equivalent of the top of a round hill very short-lived. Metastable states that persist for many seconds (or years) are found in energetic valleys which are not the lowest possible valley (point 1 in illustration). A common type of metastability is isomerism.

The stability or metastability of a given chemical system depends on its environment, particularly temperature and pressure. The difference between producing a stable vs. metastable entity can have important consequences. For instances, having the wrong crystal polymorph can result in failure of a drug while in storage between manufacture and administration. [11] The map of which state is the most stable as a function of pressure, temperature and/or composition is known as a phase diagram. In regions where a particular state is not the most stable, it may still be metastable. Reaction intermediates are relatively short-lived, and are usually thermodynamically unstable rather than metastable. The IUPAC recommends referring to these as transient rather than metastable. [12]

Metastability is also used to refer to specific situations in mass spectrometry [13] and spectrochemistry. [14]

Electronic circuits

A digital circuit is supposed to be found in a small number of stable digital states within a certain amount of time after an input change. However if an input changes at the wrong moment a digital circuit which employs feedback (even a simple circuit such as a flip-flop) can enter a metastable state and take an unbounded length of time to finally settle into a fully stable digital state.

Computational neuroscience

Metastability in the brain is a phenomenon studied in computational neuroscience to elucidate how the human brain recognizes patterns. Here, the term metastability is used rather loosely. There is no lower-energy state, but there are semi-transient signals in the brain that persist for a while and are different than the usual equilibrium state.

See also

Related Research Articles

<span class="mw-page-title-main">Atom</span> Smallest unit of a chemical element

Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.

A chemical element is a chemical substance that cannot be broken down into other substances by chemical reactions. The basic particle that constitutes a chemical element is the atom. Chemical elements are identified by the number of protons in the nuclei of their atoms, known as the element's atomic number. For example, oxygen has an atomic number of 8, meaning that each oxygen atom has 8 protons in its nucleus. Two or more atoms of the same element can combine to form molecules, in contrast to chemical compounds or mixtures, which contain atoms of different elements. Atoms can be transformed into different elements in nuclear reactions, which change an atom's atomic number.

<span class="mw-page-title-main">Diatomic molecule</span> Molecule composed of any two atoms

Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen or oxygen, then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide or nitric oxide, the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.

<span class="mw-page-title-main">Molecule</span> Electrically neutral group of two or more atoms

A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.

<span class="mw-page-title-main">Periodic table</span> Tabular arrangement of the chemical elements ordered by atomic number

The periodic table, also known as the periodic table of the elements, is an ordered arrangement of the chemical elements into rows ("periods") and columns ("groups"). It is an icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which states that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks. Elements in the same group tend to show similar chemical characteristics.

Spontaneous emission is the process in which a quantum mechanical system transits from an excited energy state to a lower energy state and emits a quantized amount of energy in the form of a photon. Spontaneous emission is ultimately responsible for most of the light we see all around us; it is so ubiquitous that there are many names given to what is essentially the same process. If atoms are excited by some means other than heating, the spontaneous emission is called luminescence. For example, fireflies are luminescent. And there are different forms of luminescence depending on how excited atoms are produced. If the excitation is effected by the absorption of radiation the spontaneous emission is called fluorescence. Sometimes molecules have a metastable level and continue to fluoresce long after the exciting radiation is turned off; this is called phosphorescence. Figurines that glow in the dark are phosphorescent. Lasers start via spontaneous emission, then during continuous operation work by stimulated emission.

An exotic atom is an otherwise normal atom in which one or more sub-atomic particles have been replaced by other particles of the same charge. For example, electrons may be replaced by other negatively charged particles such as muons or pions. Because these substitute particles are usually unstable, exotic atoms typically have very short lifetimes and no exotic atom observed so far can persist under normal conditions.

<span class="mw-page-title-main">Ionization</span> Process by which atoms or molecules acquire charge by gaining or losing electrons

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

<span class="mw-page-title-main">Electron configuration</span> Mode of arrangement of electrons in different shells of an atom

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, meaning that the 1s, 2s, and 2p subshells are occupied by two, two, and six electrons, respectively.

<span class="mw-page-title-main">Nuclear isomer</span> Metastable excited state of a nuclide

A nuclear isomer is a metastable state of an atomic nucleus, in which one or more nucleons (protons or neutrons) occupy excited state (higher energy) levels. "Metastable" describes nuclei whose excited states have half-lives 100 to 1000 times longer than the half-lives of the excited nuclear states that decay with a "prompt" half life (ordinarily on the order of 10−12 seconds). The term "metastable" is usually restricted to isomers with half-lives of 10−9 seconds or longer. Some references recommend 5 × 10−9 seconds to distinguish the metastable half life from the normal "prompt" gamma-emission half-life. Occasionally the half-lives are far longer than this and can last minutes, hours, or years. For example, the 180m
73Ta
 nuclear isomer survives so long (at least 1015 years) that it has never been observed to decay spontaneously. The half-life of a nuclear isomer can even exceed that of the ground state of the same nuclide, as shown by 180m
73Ta
 as well as 192m2
77Ir
, 210m
83Bi
, 242m
95Am
 and multiple holmium isomers.

<span class="mw-page-title-main">Ion source</span> Device that creates charged atoms and molecules (ions)

An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.

<span class="mw-page-title-main">Excited state</span> Quantum states with more energy than the lowest possible amount

In quantum mechanics, an excited state of a system is any quantum state of the system that has a higher energy than the ground state. Excitation refers to an increase in energy level above a chosen starting point, usually the ground state, but sometimes an already excited state. The temperature of a group of particles is indicative of the level of excitation.

<span class="mw-page-title-main">Intersystem crossing</span>

Intersystem crossing (ISC) is an isoenergetic radiationless process involving a transition between the two electronic states with different spin multiplicity.

<span class="mw-page-title-main">Mass number</span> Number of heavy particles in the atomic nucleus

The mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion). The mass number is different for each isotope of a given chemical element, and the difference between the mass number and the atomic number Z gives the number of neutrons (N) in the nucleus: N = A − Z.

In particle physics and nuclear physics, the branching fraction for a decay is the fraction of particles which decay by an individual decay mode or with respect to the total number of particles which decay. It applies to either the radioactive decay of atoms or the decay of elementary particles. It is equal to the ratio of the partial decay constant to the overall decay constant. Sometimes a partial half-life is given, but this term is misleading; due to competing modes, it is not true that half of the particles will decay through a particular decay mode after its partial half-life. The partial half-life is merely an alternate way to specify the partial decay constant λ, the two being related through:

<span class="mw-page-title-main">Isotopes of hydrogen</span> Hydrogen with different numbers of neutrons

Hydrogen (1H) has three naturally occurring isotopes, sometimes denoted 1
H
, 2
H
, and 3
H
. 1
H
 and 2
H
 are stable, while 3
H
 has a half-life of 12.32(2) years. Heavier isotopes also exist, all of which are synthetic and have a half-life of less than one zeptosecond (10−21 s). Of these, 5
H
 is the least stable, while 7
H
 is the most.

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<span class="mw-page-title-main">Helium dimer</span> Chemical compound

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References

  1. ↑ Hanaor, Dorian A. H.; Sorrell, Charles C. (2011-02-01). "Review of the anatase to rutile phase transformation". Journal of Materials Science. 46 (4): 855–874. Bibcode:2011JMatS..46..855H. doi: 10.1007/s10853-010-5113-0 . ISSN   1573-4803. S2CID   97190202.
  2. ↑ van Setten; Uijttewaal; de Wijs; de Groot (2007). "Thermodynamic stability of boron: the role of defects and zero point motion" (PDF). Journal of the American Chemical Society. 129 (9): 2458–2465. doi:10.1021/ja0631246. PMID   17295480. S2CID   961904. Archived from the original (PDF) on 2021-04-15. Retrieved 2019-07-08.
  3. ↑ Haldane, J. B. S. (1964). "Eighteen: Genesis of Life". In D. R., Bates (ed.). The Planet Earth (2nd ed.). Germany: Pergamon Press. p. 332. ISBN   1483135993 . Retrieved May 29, 2017. This is a highly stable molecule. About 11,500 calories of free energy are liberated when it is hydrolized to phosphate and adenosine-diphosphate (ADP).
  4. ↑ M.I. Ojovan, W.E. Lee, S.N. Kalmykov. An introduction to nuclear waste immobilisation. Third edition, Elsevier, Amsterdam, p.323 (2019)
  5. ↑ Planck Collaboration (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics. 641. page A6 (see PDF page 15, Table 2: "Age/Gyr", last column). arXiv: 1807.06209 . Bibcode:2020A&A...641A...6P. doi: 10.1051/0004-6361/201833910 . S2CID   119335614.
  6. ↑ Hobson, Art (2017). Tales of the Quantum: Understanding Physics' Most Fundamental Theory. Oxford University Press. ISBN   9780190679637.
  7. ↑ Hodgman, S. S.; Dall, R. G.; Byron, L. J.; Baldwin, K. G. H.; Buckman, S. J.; Truscott, A. G. (2009-07-31). "Metastable helium: a new determination of the longest atomic excited-state lifetime". Physical Review Letters. 103 (5): 053002. Bibcode:2009PhRvL.103e3002H. doi:10.1103/PhysRevLett.103.053002. hdl: 10440/978 . ISSN   0031-9007. PMID   19792494.
  8. ↑ "Technetium-99m". Hyperphysics.
  9. ↑ Conover, Emily (2016-10-03). "Rarest nucleus reluctant to decay". Science News. Retrieved 2016-10-05.
  10. ↑ Lehnert, Björn; Hult, Mikael; Lutter, Guillaume; Zuber, Kai (2017). "Search for the decay of nature's rarest isotope 180mTa". Physical Review C. 95 (4): 044306. arXiv: 1609.03725 . Bibcode:2017PhRvC..95d4306L. doi:10.1103/PhysRevC.95.044306. S2CID   118497863.
  11. ↑ Process Chemistry in the Pharmaceutical Industry. Kumar G. Gadamasetti, editor. 1999, pp. 375–378
  12. ↑ "transient (chemical) species". IUPAC Gold Book. 2014. doi: 10.1351/goldbook.T06451 .
  13. ↑ "metastable ion in mass spectrometry". IUPAC Gold Book. doi: 10.1351/goldbook.M03874 .
  14. ↑ "metastable state in spectrochemistry". IUPAC Gold Book. doi: 10.1351/goldbook.M03876 .
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