Metastability

A metastable state of weaker bond (1), a transitional 'saddle' configuration (2) and a stable state of stronger bond (3).

In physics, Metastability denotes the phenomenon when a dynamical system spends an extended time in a configuration other than the system's state of least energy. During a metastable state of finite lifetime all state-describing parameters reach and hold stationary values. While in isolation:

• the state of least energy is the only one the system will inhabit for an indefinite length of time, until more external energy is added to the system (unique "absolutely stable" state);
• the system will spontaneously leave any other state (of higher energy) to eventually return (after a sequence of transitions) to the least energetic state.

A single particle analogy may be drawn with a ball resting in a hollow on a slope. With some perturbation the ball may start rolling again to lower levels. Isomerisation is another common example, where higher energy isomers are long lived as they are prevented from rearranging to the ground state by (possibly large) barriers in the potential energy.

The metastability concept originates in the physics of first-order phase transitions later to acquire new meanings in the study of aggregated subatomic particles (in atomic nuclei or in atoms) or in molecules, macromolecules or clusters of atoms and molecules. Later on it was borrowed for the study of decision-making and information transmitting systems.

Many complex natural and man-made systems can demonstrate metastability.

• Metastability is common in physics and chemistry - from an atom (many-body assembly) to statistical ensembles of molecules (viscous fluids, amorphous solids, liquid crystals 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 systems and neuroscience - it is the time-invariance of the active or reactive patterns with respect to the external influences that defines stability and metastability (see brain metastability below). Here the equivalent of the thermal fluctuations is the "white noise" affecting the 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 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. For example, diamond 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. The bonds between the building blocks of polymers such as DNA, RNA and proteins are also metastable. 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.^[1] Generally speaking, emulsions/colloidal systems and glasses are metastable.

Small avalanches demonstrate metastability at Mount Baker Ski Area.

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. 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.

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.^[2]

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. Of course, since transitions away from a metastable state are not impossible (merely unlikely), the electron will eventually be able to decay to a less energetic state by spontaneous emission.

This property of the electron is used in lasers. When light of suitable wavelength falls on atoms, their electrons jump to a higher energy state. When the incoming radiations are removed, the excited electron goes back to its original level, typically within a duration of around 10⁻⁸ seconds. However, when an electron goes to a metastable state, it remains there for a relatively longer duration of 10⁻³ seconds. This phenomenon leads to accumulation of electrons in the metastable state, since the rate of addition of electrons to the metastable state is higher than the rate of their de-excitation. This leads to the phenomenon called population inversion, which forms the basis of lasing action of lasers.

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 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.^[3] 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.^[4]

Metastability is also used to refer to specific situations in mass spectrometry^[5] and spectrochemistry.^[6]

Electron systems in biochemistry

The evolution of a many-body quantum system between its characteristic set of states may be influenced by the following external actions:

• The environment may act chaotically onto the system and add uncertainty to all state energies (while decreasing their lifetimes) — as in the spectral line broadening.
• Just as well, resonant exterior actions may nudge the system into a lower cohesive energy state while making it release an intrinsic amount or quanta of its energy — as in the stimulated emissions.
• Alternatively, external catalytic fields of forces may briefly flatten some of the barriers (ridges separating adjacent valleys) in the potential landscape of the system and help it tunnel through to lower energy states (see image above).
• Under the impact of thermal or directional external actions, some systems (see macromolecule complexes involving enzyme-cofactor association) may wander for extremely long periods of time among a certain sub-group of their states (all having distinct configurations but energy differences within the thermal fluctuation range). As such the enzymes will enter a biochemical reaction sequence with an initial configuration, perform through its many steps as catalysts while continuously contorting, and eventually leave that reaction sequence in the same configuration as they have entered it, ready to perform again.

Electronic circuits

Metastability in electronics is usually seen as a problem. A changing circuit is supposed to settle into one of a small number of desired states, but if the circuit is vulnerable to metastability, it can get stuck in an undesirable 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

• False vacuum
• Hysteresis

References