Physics and chemistry text books usually enumerate three states of matter: solids, liquids and gases. The criteria that distinguish them are shape and volume: solids retain a constant shape and volume, liquids only volume but not shape, gases neither volume nor shape.

Yet this neat scheme is an oversimplification. Only an ideal “Euclidian” solid retains an absolutely constant shape and volume; real solids have a whole range of rheological (flow) properties shading into liquids, while liquids in turn have another varied set of rheological behaviours. Real gases do not exactly obey the ideal gas laws, and near the critical point show a smooth transition to liquids with no phase change.

Turning to the internal molecular structure, solids, liquids and gases show different degrees of order: solids are crystalline (highly ordered), gases are chaotic (the word “chaos” means “gas” in Greek), liquids are intermediate (with short-range but not long-range order).

This, too, is an oversimplification: the glasses (a generic name, not a particular substance) are rigid non-crystalline phases, while soap films are crystalline liquids. Gases are chaotic (disordered) in the main, but not near the critical point, as already mentioned.

The ancient philosophers recognized four “elements”: earth, water, air and fire. The striking correspondence of “earth” with solid, “water” with liquid, and “air” with gas is obvious. The ancients did not mean “elements” in the modern chemical sense, but states of matter, In terms of the phase rule (discussed later), they meant “phases”, not “components”. Or at least, regardless of what their intended meaning was, it suits us now to interpret their theory in this way.

But what then corresponds to the fourth ancient “element”, i.e. fire? I would suggest “plasma”, a mix of electrically charged particles (ions and electrons). This is usually a high-temperature phase seen in electrical discharges (arcs, sparks, cathode ray tubes), around bodies heated by re-entry from space to the Earth’s atmosphere, in explosions and fireballs, and – yes – in flames. Plasmas have properties different from either solids, liquids or gases. They are the subject of intense study in many branches of pure and applied physics (e.g. magnetohydrodynamics). They should be acknowledged as the fourth distinct state of matter. This would complete the analogy with the ancient “elements”. Plasmas and gases are the most frequently occurring phases in the universe, while liquids and solids are far less common.

Just as high temperature enlarges the scope of states of matter by adding plasma to the list, so does very low temperature: superfluid helium has properties that differ markedly from ordinary liquids in several important aspects
(e.g. zero viscosity, zero surface tension).

Another extension of viewpoint comes in considering thin films, which are essentially two-dimensional structures. Nor are all films the same; they can be either condensed (a term comprising both solid and liquid) or gaseous, in analogy with three-dimensional matter.

Finally, extreme conditions of matter in collapsed stars must not be ignored. A star like the Sun can conveniently be described as plasma, but a white dwarf is composed of condensed plasma (fully ionized, with nuclei and electrons squeezed together until they are touching). Beyond that, a neutron star (the remnant of a supernova explosion) can be compared to a single giant nucleus, and is thus composed of “nuclear matter”, i.e. a phase in which the vast empty spaces in ordinary atoms have been eliminated. Beyond that, a black hole must be composed of a phase even more condensed, something similar to the universe before the Big Bang or during the first fractions of a micro-second, when the four forces of nature were still unified. But we don’t know for sure, because we can’t see inside – no message is received from inside a black hole.

After this quick overview, let us consider the relationships in greater detail, with the help of diagrams.

To clarify the relationships between solids, liquids and gases (the classical three states of matter), we can draw a simple 2×2 table.

Figure 1.
	Non-compressible	Compressible
Fluid	Liquid	Gas
Rigid	Solid	Empty cell

Here liquids and gases together are called “fluids” because they flow, and solids and liquids together are called “condensed phases” because they are denser than gases. There is no such thing as a rigid compressible phase, and so one cell of the 2×2 table must be left empty. Plasma, our fourth state of matter, does not fitr there.

Now let us explre the rheological properties of the condensed phases. There are two limiting ideal cases: one is a Euclidian solid, which never changes its shape or volume under any conditions of external pressure, shear or stress; the other is a Pascalian liquid, which, while incompressible with respoect to volume, flows (changes shape) without resistance under the slightest external shear or stress. (Superfluid helium approaches this state.)

A better approximation to a real solid is a Hookean solid, which can be extended (strained) by an external pulling force (stress) or distorted by a sideways force (shear) or compressed by pressure, but quickly returns to its original shape and volume when the external force is removed. It obeys Hooke’s law, which states that the strain (elongation) is proportional to the applied stress. This property and the previously mentioned rebound is called “elasticity”.

A good approximation to a real liquid is a Newtonian liquid, which flows with a certain resistance called “viscosity”. The law which expresses this, first formulated by Newton, states that the rate of flow is proportional to the external force, the proportionality constant being called the “viscosity coefficient”.

Hookean solids come with widely different elasticuty constants (strain/stress ratios), e.g. steel and vulcanized rubber. Newtonian liquids come in a wide range of viscosity, from ether to thick syrup. But these are only differences in the numerical values of the elasticity or viscosity coefficients. These coefficients remain constant, showing continued adherence to either Hooke’s law or Newton’s law.

Beyond that, there are also cases of non-Newtonian liquids (e.g. solutions of rubber in benzene or toluene) whose viscosity increases with shear, because the long polymer molecules tend to become aligned in the direction of shear. There are also non-Hookean solids; whose elasticity varies with stress. In fact, all elastic extensions have a limit; beyond it the solid either rearranges to a new shape if given the time to “relax”, or it breaks, as in a machine measuring tensile strength.

There are also possibilities of combining elastic and viscous behaviour; in this case, the distinction between a solid and a .liquid is blurred. These combinations can be elucidated by means of models using springs and pistons. If we represent perfect elasticity by a spring (which can be extended and let rebound), and perfect viscosity by a piston moving in a cylinder filled with liquid, we can have two types of arrangements: in series or in parallel. In a rapid application of a pulling force, the spring would respond intantaneously, while the piston responds slowly. In an arrangement of the spring and piston in series, the spring prevails; in an arrangement in parallel, the piston does. There could be multiple springs and pistons in various arrangements in more complex cases; somewhat like combinations of resistance, inductance and capacitance in electrical circuits.

The substances described by these models include for example raw (unvulcanized) rubber, which exhibits “creep” (tension relaxation) under a constant stressing force, and also “hysteresis”, in which the path followed by extension is different from the path exhibited in the return to the original position. (Vulcanized rubber differs from raw rubber in having more cross-links, in this case disulfide bridges, between the long polymer chains; this makes the cross-linked product closer to a solid, the raw product closer to a liquid.)

While the Hookean solid is definitely a solid and the Newtonian liquid is definitely a liquid, it is not clear how to designate the in-between combinations of springs and pistons. If elasticity characterizes a solid and viscosity a liquid, a body which exhibits both elasticity and viscosity can only be described as a hybrid condensed phase. The transition is continuous, or at least stepwise, through the range of different substances.

One other case of rheological behaviour will be noted, that of a thixotropic body. An example is a pot of some paints, which seem almost solid or at least very viscous when standing still, but become increasingly fluid when stirred rapidly. The properties exhibited include non-Newtonian flow, already mentioned, but also a “yield value”, i.e. there is no flow until a threshold shear velocity is reached. From the standpoint of molecular structure, what is involved here is the presence of a gel in the resting stage (lightly cross-linked with weak bonds, like hydrogen bonds or Van der Waals forces), and a gel-sol transformation on stirring, which breaks these weak bonds and removes the crosslinks.

We should examine then the molecular structures which might account for some of the other models. The ideal Euclidean solid might be approached by diamond, a structure held together completely by strong covalent bonds. The ideal Pascalian liquid, as already mentioned, might be represented by superfluid helium. A Hookean solid would be a polycrystalline body held together partly by covalent and partly by weaker bonds, or containing crystal imperfections. A Newtonian liquid would contain mainly weaker bonds: hydrogen bonds in the case of water, Van der Waals forces in oils. Raw rubber is composed of long tangled polymer chains, which can slide past each other (the piston element in the model), but whose tangles act somewhat as weak cross-links and stretch the intervening strands elestically when a pull is applied (like the springs in the model). The situation is similar to the tangles in uncombed hair.

This rheological discussion and the the Van der Waals type of deviation from ideal behaviour in gases can be summarized in Figure 2, which is a more complex version of Figure 1.

Figure 2.
^ fluidity	critical states
	Pascal liquid	Van der Waals gas	ideal gas
	Newton liquid
	spring and piston models
	Hooke solid	empty cell
	Euclid solid
compressibility >

In Figure 2, we have erased the boundary between liquid and solid, changing the fluid-rigid dichotomy into a fluidity dimension; and indicated where consideration of the critical state will similarly erase the boundary between liquid and gas. The boundaries do not really disappear; they are still very real in commonly observed phase transitions, such as ice to water and water to steam; but they are blurred in some other cases, where transitions occur gradually without phase change. Actually the various liquid-solid transition states in the diagram represent different substances, not blurred phase transitions of a single substance.

In Figure 3, we plot fluidity (which is the reciprocal of viscosity) against elasticity.

Figure 3
^ fluidity	superfluid	rubber
	mobile liquid
	viscous liquid
	glass
elasticity >

While glass is simply a very viscous liquid, rubber (as we have seen) is a more complex rheological state of matter. Here we use the terms “glass” and “rubber” in a generic sense, not referring to particular substances with which the terms originated, but to states of matter (phases) with certain properties. The rubbery state can be converted to the glassy state by increasing the density of crosslinks or bonds. Neither a glass nor a rubber are crystalline (ordered) structure like a real solid, but have only short-range order like a liquid, in spite of being relatively rigid like solids.

Notice that we have subtly changed the definition of a “solid”. Rigidity (no change in shape or volume under an external force) was the original definition. Now we specify crystallinity as the distinguishing characteristic of a solid. The text books do that too, this is not our innovation. There is a link between rigidity and crystallinity: a glass truly does flow if we wait long enough – years or decades. But this link is not absolute, for a crystal may flow too if we wait even longer.

Because of its importance in the revised definition, we must now consider crystallinity (order) as an additional determining factor in states of matter, in addition to rigidity/fluidity, compressibility, elasticity and viscosity. But the latter properties are empirically observable in macro dimensions, while crystallinity has to do with internal micro-structure of materials. However, we have already dealt with micro-structures in discussing the high polymer strands of rubber.

First of all, we must distinguish different kinds and degrees of crystallinity, as well as imperfections in crystalline order. Also we shall see that, while all true solids are crystalline in one kind or degree or other, not all crystals are solids; and so we will draw attention to liquid crystals. A final interesting phenomenon is “quasi-crystals” which occur in some recently discovered materials.

Figure 4.
^ rigidity	glasses	quasi crystals	defective crystals or poly crystals	single crystals
				liquid crystals
				nematic	smectic
crystallinity >

In Figure 4 we have another dimension, from glasses to single perfect crystals like the silicon from which chips are made, and from disordered to crystalline liquids. Deviations from single perfect crystals (three-dimensional lattices with no molecules or ions out of place).can occur in several different ways. (1) Most crystalline solids are composed of a mat of tiny crystallites; each crystallite may be perfect in itself, but they are oriented in different directions toward each other, and the boundaries are imperfect like earthquake faults. This is the polycrystalline state of matter. An example is steel. (2) There usually are crystal defects (deviations from perfect order) within monocrystals or the crystallites of polycrystals. These defects include various displacements, substitutions by other atoms or ions in the lattice, excess interstitial atoms or ions (not part of the lattice), or holes (missing atoms or ions) in the lattice. As these defects accumulate, order may gradually vanish and we will have a glass, with only short-range order among its constituent atoms, ions or molecules. The transition can be regarded as almost continuous, though it is conceptual only, involving different materials as examples along the way.

A somewhat different deviation is represented by the recently discovered quasi-crystals. Israeli scientist Dany Schechtman discovered five-fold symmetry (previously thought impossible) in an alloy of aluminum and manganese. The puzzle was solved when it was shown that the pattern was composed ot two kinds of unit cell (other crystal have only one unit cell) – “skinny” and “fat” rhombuses, and that these can fit together to “tile” (completely fill) three-dimensional space. This is a highly ordered structure, but does not periodically repeat like the three-dimensional chessboard of a cubic sodium chloride crystal, for example. There is only quasi-periodic order; hence the name “quasi crystals. Other materials with this kind of structure have since been discovered.

As for liquid crystals: how could a liquid be crystalline? Well, crystallinity is only another name for long-range order, and this can happen in liquids in two ways: In the nematic state, the elongated particles (e.g. soap molecules in a water solution) are aligned parallel to each other, but with their ends in random positions. In the more highly ordered smectic state, the long strings and their ends are both aligned, so that the strings form compact bundles. Both nematic and smectic liquids give X-ray diffraction patterns, as only crystals can do, but flow like normal liquids.

Briefly, we shall now turn our attention to mono-molecular or bi-molecular films (monolayers and bilayers). These are essentially two-dimensional structures. Examples are soap films, cell membranes (lipid bilayers with hydrophobic tails turned inwards and hydrophilic heads outwards), and any surface adsorbed layers that are very thin.

These films are termed either “gaseous” or “condensed” by analogy with three-dimensional structures. The relation between pressure and volume in a gas at constant temperature is inverse proportionality. In a liquid or solid, volume does not vary much with pressure. The two-dimensional analogue of pressure is surface tension, while volume corresponds to surface area. If the surface area of a film does not vary much with surface tension, the film is said to be in the condensed state. If the surface area shrinks as surface tension increases, we call it a gaseous film. Phase transitions in films have been observed under some circumstances.

This then completes the more detailed survey of states of matter, though of course much more could be said. Books have been written on separate aspects, such as rheology, crystal imperfections, and structure of membranes. They touch on many topics important in applied technologies, as well as giving insights of pure science.

We shall conclude with a few comments on phases commonly observed in the universe; but first, a brief note on miscibility of phases.

All gases are completely miscible, i.e. the molecules intermingle without discrimination. At the other pole, solid phases are always completely immiscible; each component, having its own specific crystal structure, forms its own phase. Liquids are the most interesting: they can be either miscible in all proportions, like ethyl alcohol and water; or immiscible like water and oil (forming two layers when put together); or partially miscible, forming two layers, each containing different proportions of each component. Complete or partial immiscibility is due to a preference of molecules for being close to their own kind rather than to the other kind; a sort of molecular apartheid. If a third component is introduced into a system consisting of oil and water, it may prefer the water phase (be hydrophilic) or the oil phase (be hydrophobic or lipophilic), or if it is a long molecule with a polar (hydrophilic) end and a non-polar (hydrophobic) end, like soap, it will accumulate in the interface between oil and water, and if shaken, may emulsify oil droplets in a continuous water phase by coating each oil droplet with a soap film. Inverse emulsions of water droplets in a continuous oil phase also exist, e.g. mayonnaise with egg as emulsifier. Cell membranes are complex oil-water systems in which various proteins are embedded with their non-polar portions in the oil-loving middle of the membrane and the polar ends sticking out of the membrane, either inside into the cytoplasm (aqueous medium) or outside the cell (another aqueous medium). The proteins perform various vital functions as hormone or neurotransmitter receptors, ion channels or pumps, and immune system signals. In some essential ways, life is an elaboration of the basic oil-water immiscible system; or at least that is the aspect of life in relation to a consideration of phase relations.

Gases and solids are too much “either-or” – complete miscibility or no miscibility. There is in the world only one gaseous phase and very numerous solid phases. But the number of liquid phases is limited, because of the phenomenon of partial miscibility. As usual, life thrives in the middle, in liquid (both aqueous and oily) media. (Somebody called life “wetware” in contrast to the “hardware” and “software” of computer science.) Life is also in the middle in the acid-base spectrum (middle pH range) and the redox (oxidation-reduction) spectrum between fully oxidized and fully reduced carbon compounds (CO2 and CH4, carbon dioxide and methane).

There is a simple and beautiful relationship between C, the number of components (pure chemical substances), P, the number of phases coexisting at equilibrium, and F, degrees of freedom, which determine whether the range of coexistence is a point (F=0), a line (F=1), or an area (F=2). This is called the Phase Rule, and it states that F = C-P+2. (The 2 stands for temperature and pressure as the determining variables.) On the basis of the phase rule, phase diagrams can be drawn to illustrate phase relationships and phase transitions. However, the diagrams represent equilibrium states only, and are not relevant to systems in transition or to far-from-equilibrium states which are involved in life processes

So far we have dealt with liquid immiscible systems at or near room temperature. If we go to high temperatures, as in a furnace, the common phases are molten metals and slag (silicates). But some molten metals are immiscible with each other , and “extractions” can be done (analogous to extracting plant products with ether from aqueous solutions), e.g. of gold and the platinum metals being extracted by molten silver from a lead button. (This must have intrigued the alchemists.)

Planets in the solar system are composed of rock (which is frozen slag), a metallic iron-alloy core, various liquids or ices (depending on the temperature), such as water, ammonia, or methane (completely reduced O, N, C compounds), and carbon dioxide; and gaseous atmospheres (same compounds as above plus free nitrogen and/or oxygen). So we have rock, metal, ice, and gas as planetary phases. Some of these are missing sometimes, such as the metallic core. The inner planets (Mercury, Venus. Earth, Mars) are rocky (the Earth alone also watery), the outer planets (Jupiter, Saturn, Neptune, maybe Pluto?) are probably largely hydrogen and helium gas, but their moons have rock and ice. The compressed hydrogen in the interior of Jupiter, Saturn and Neptune is thought to form a metallic phase; metallic hydrogen was only very recently obtained on Earth in a very high pressure experiment. We should add that Earth also contains oil as a phase in the biosphere, since oil is a product of life.

Unlike planets, stars are made of plasma, as already mentioned. Stellar phases, already described in the first part of the article, are represented in Figure 5.

Figure 5
^ Temperature	Main sequence star	White dwarf	Neutron star	Black hole
	Plasma	Condensed plasma	Nuclear matter	?
	Planet conditions
Pressure >

We have ranged widely in our discussions, taking in many sciences, many conditions, many localities. Many things were oversimplified, many others omitted altogether. Only superficial aspects could be mentioned in this brief treatment. However, perhaps what was lost in depth was gained in the width of perspective. Subtleties emerge in unexpected places, and will probably continue to do so as the science of the states of matter progresses.