matter, anything that has mass and occupies space. Matter is sometimes called koinomatter (Gr. koinos=common) to distinguish it from antimatter, or matter composed of antiparticles.

The Properties of Matter

The general properties of matter result from its relationship with mass and space. Because of its mass, all matter has inertia (the mass being the measure of its inertia) and weight, if it is in a gravitational field (see gravitation). Because it occupies space, all matter has volume and impenetrability, since two objects cannot occupy the same space simultaneously.

The special properties of matter, on the other hand, depend on internal structure and thus differ from one form of matter, i.e., one substance, to another. Such properties include ductility, elasticity, hardness, malleability, porosity (ability to permit another substance to flow through it), and tenacity (resistance to being pulled apart).

The States of Matter

Matter is ordinarily observed in three different states, or phases (see states of matter), although scientists distinguish three additional states. Matter in the solid state has both a definite volume and a definite shape; matter in the liquid state has a definite volume but no definite shape, assuming the shape of whatever container it is placed in; matter in the gaseous state has neither a definite volume nor a definite shape and expands to fill any container. The properties of a plasma, or extremely hot, ionized gas, are sufficiently different from those of a gas at ordinary temperatures for scientists to consider them to be the fourth state of matter. So too are the properties of the Bose-Einstein and fermionic condensates, which exist only at temperatures approximating absolute zero (-273.15°C;), and they are considered the fifth and sixth states of matter respectively.

Early Theories of Matter

In ancient times various theories were suggested about the nature of matter. Empedocles held that all matter is made up of four "elements"—earth, air, fire, and water. Leucippus and his pupil Democritus proposed an atomic basis of matter, believing that all matter is built up from tiny particles differing in size and shape. Anaxagoras, however, rejected any theory in which matter is viewed as composed of smaller constituents, whether atoms or elements, and held instead that matter is continuous throughout, being entirely of a single substance.

Modern Theory of Matter

The modern theory of matter dates from the work of John Dalton at the beginning of the 19th cent. The atom is considered the basic unit of any element, and atoms may combine chemically to form molecules, the molecule being the smallest unit of any substance that possesses the properties of that substance. An element in modern theory is any substance all of whose atoms are the same (i.e., have the same atomic number), while a compound is composed of different types of atoms together in molecules.

Physical and Chemical Changes

The difference between a mixture and a compound helps to illustrate the difference between a physical change and a chemical change. Different atoms may also be present together in a mixture, but in a mixture they are not bound together chemically as they are in a compound. In a physical change, such as a change of state (e.g., from solid to liquid), the substance as a whole changes, but its underlying structure remains the same; water is still composed of molecules containing two hydrogen atoms and one oxygen atom whether it is in the form of ice, liquid water, or steam. In a chemical change, however, the substance participates in a chemical reaction, with a consequent reordering of its atoms. As a result, it becomes a different substance with a different set of properties.

Many of the physical properties and much of the behavior of matter can be understood without detailed assumptions about the structure of atoms and molecules. For example, the kinetic-molecular theory of gases provides a good explanation of the nature of temperature and the basis of the various gas laws and also gives insight into the different states of matter. Substances in different states vary in the strength of the forces between their molecules, with intermolecular forces being strongest in solids and weakest in gases. The force holding like molecules together is called cohesion, while that between unlike molecules is called adhesion (see adhesion and cohesion). Among the phenomena resulting from intermolecular forces are surface tension and capillarity. An even larger number of aspects of matter can be understood when the nature and structure of the atom are taken into account. The quantum theory has provided the key to understanding the atom, and most basic problems relating to the atom have been solved.

The Relationship of Matter and Energy

The atomic theory of matter does not answer the question of the basic nature of matter. It is now known that matter and energy are intimately related. According to the law of mass-energy equivalence, developed by Albert Einstein as part of his theory of relativity, a quantity of matter of mass m possesses an intrinsic rest mass energy E given by E = mc2, where c is the speed of light. This equivalence is dramatically demonstrated in the phenomena of nuclear fission and fusion (see nuclear energy; nucleus), in which a small amount of matter is converted to a rather large amount of energy. The converse reaction, the conversion of energy to matter, has been observed frequently in the creation of many new elementary particles. The study of elementary particles has not solved the question of the nature of matter but only shifted it to a smaller scale.


See V. H. Booth, Elements of Physical Science: The Nature of Matter and Energy (1970); G. Amaldi, The Nature of Matter: Physical Theory from Thales to Fermi (1982).

In the physical sciences, a phase is a set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e. density, crystal structure, index of refraction, and so forth).

Phases vs. states of matter

Phases are sometimes confused with states of matter, but there are significant differences. States of matter refers to the differences between gases, liquids, solids, plasma, etc. If there are two regions in a chemical system that are in different states of matter, then they must be different phases. However, the reverse is not true — a system can have multiple phases which are in equilibrium with each other and also in the same state of matter. This difference is especially important when considering the Gibbs' phase rule, which governs the number of allowed phases.

Mixtures can have multiple phases, which often happen when two immiscible substances dissolve into one another in small amounts. For example, a mixture might be composed of an oil phase (95% oil, 5% water) and a water phase (95% water, 5% oil).

Polymorphism is the ability of a solid to exist in more than one crystal form. For example, water ice is ordinarily found in the hexagonal form Ice Ih, but can also exist as the cubic ice Ic, the rhombohedral ice II, and many other forms.

Amorphous phases are also possible with the same molecule, such as amorphous ice. In this case, the phenomenon is known as polyamorphism.

For pure chemical elements, polymorphism is known as allotropy. For example, diamond, graphite, and fullerenes are different allotropes of carbon.

Types of phases

The most common dichotomy of liquid phases is aqueous phase vs. organic phase, where a water solution and an organic hydrophobic liquid, such as oil, spontaneously separate. However, more liquid phases are possible and the concept of phase separation also extends to solids.

Solubility is governed by Hildebrand's solubility parameter (δ), which is defined using molar volume, molar energy and molar enthalpy. The parameter describes the work needed to dissolve different solvents into each other. Solvents with very different parameter values are insoluble. As many as eight immiscible liquid phases are possible. One such a system is, from the top: paraffin oil, silicone oil, water, aniline, perfluoro(dimethylcyclohexane), white phosphorus, gallium and mercury. The system remains indefinitely separated at 45 C, where gallium and phosphorus are in the molten state.

Immiscible liquid phases are formed from:

  • Water, i.e. aqueous phase
  • Organic phase, i.e. hydrocarbons and their nonpolar, hydrophobic derivatives
  • Fluorous phase (perfluorocarbons)
  • Silicone oil
  • Metals
  • Other, such as molten phosphorus

Not all organic solvents are completely miscible. Ethylene glycol, for example, has limited solubility with toluene, and when neither is in excess, phases separate. This phenomenon can be used to help with catalyst recycle in Heck vinylation.

Also, solids may form solid solutions or remain immiscible, crystallizing into different crystals if cooled. In particular, some pairs of metals are soluble, forming alloys, and some are insoluble in each other.

General definition of phases

In general, two different states of a system are in different phases if there is an abrupt change in their physical properties while transforming from one state to the other. Conversely, two states are in the same phase if they can be transformed into one another without any abrupt changes. There are, however, exceptions to this statement -- for example the liquid-gas critical point discussed below in the Phase Diagrams section.

An important point is that different types of phases are associated with different physical qualities. When discussing the solid, liquid, and gaseous phases, we talked about rigidity and compressibility, and the effects of varying the pressure and volume, because those are the relevant properties that distinguish a solid, a liquid, and a gas. On the other hand, when discussing paramagnetism and ferromagnetism, we look at the magnetization, because that is what distinguishes the ferromagnetic phase from the paramagnetic phase. Several more examples of phases will be given in the following section.

In more technical language, a phase is a region in the parameter space of thermodynamic variables in which the free energy is analytic; between such regions there are abrupt changes in the properties of the system, which correspond to discontinuities in the derivatives of the free energy function. As long as the free energy is analytic, all thermodynamic properties (such as entropy, heat capacity, magnetization, and compressibility) will be well-behaved, because they can be expressed in terms of the free energy and its derivatives. For example, the entropy is the negative of the first derivative of the free energy with temperature (at constant pressure).

When a system goes from one phase to another, there will generally be a stage where the free energy is non-analytic. This is a phase transition. Due to this non-analyticity, the free energies on either side of the transition are two different functions, so one or more thermodynamic properties will behave very differently after the transition. The property most commonly examined in this context is the heat capacity. During a transition, the heat capacity may become infinite, jump abruptly to a different value, or exhibit a "kink" or discontinuity in its derivative. See also differential scanning calorimetry.

Phase diagrams

The different phases of a system may be represented using a phase diagram. The axes of the diagrams are the relevant thermodynamic variables. For simple mechanical systems, we generally use the pressure and temperature.

The markings on the phase diagram show the points where the free energy is non-analytic. The open spaces, where the free energy is analytic, correspond to the phases. The phases are separated by lines of non-analyticity, where phase transitions occur, which are called phase boundaries.

In the diagram, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the critical point. At temperatures and pressure above the critical point, the physical property differences that differentiate the liquid phase from the gas phase become less defined. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. In water, the critical point occurs at around 647 K (374 °C or 705 °F) and 22.064 MPa.

The existence of the liquid-gas critical point reveals a slight ambiguity in our above definitions. When going from the liquid to the gaseous phase, one usually crosses the phase boundary, but it is possible to choose a path that never crosses the boundary by going to the right of the critical point. Thus, phases can sometimes blend continuously into each other. This new phase which has some properties that are similar to a liquid and some properties that are similar to a gas is called a supercritical fluid. We should note, however, that this does not always happen. For example, it is impossible for the solid-liquid phase boundary to end in a critical point in the same way as the liquid-gas boundary, because the solid and liquid phases have different symmetry.

An interesting thing to note is that the solid-liquid phase boundary in the phase diagram of most substances, such as the one shown above, has a positive slope. This is due to the solid phase having a higher density than the liquid, so that increasing the pressure increases the melting temperature. However, in the phase diagram for water the solid-liquid phase boundary has a negative slope. This reflects the fact that ice has a lower density than water, which is an unusual property for a material.

Phase separation

Phase separation is transformation of a homogenous system into two (or more) phases and commonly encountered in many branches of science and technology. One example is the crystallization of a solid from a solution. A universal mathematical model of phase separation is provided by the Cahn–Hilliard equation.

Phase equilibrium

The distribution of kinetic energy among molecules is not uniform, and it changes randomly. This means that at, say, the surface of a liquid, there may be an individual molecule with enough kinetic energy to jump into the gas phase. Likewise, individual gas molecules may have low enough kinetic energy to join other molecules in the liquid phase. This phenomenon means that at any given temperature and pressure, multiple phases may co-exist.

For example, under standard conditions for temperature and pressure, a bowl of liquid water in dry air will evaporate until the partial pressure of gaseous water equals the vapor pressure of water. At this point, the rate of molecules leaving and entering the liquid phase becomes the same (due to the increased number of gaseous water molecules available to re-condense). The fact that liquid molecules with above-average kinetic energy have been removed from the bowl results in evaporative cooling. Similar processes may occur on other types of phase boundaries.

Gibbs' phase rule relates the number of possible phases, variables such as temperature and pressure, and whether or not an equilibrium will be reached.

Phase transition

A phase transition or, phase change, describes when a substance changes its state of matter - ex. ice melting to water is a phase change because a solid changed to a liquid. For a phase change to occur, energy must be added or removed from the substance. The heat energy, or enthalpy, associated with a solid to liquid transition is the enthalpy of fusion, that for liquid to gas is the enthalpy of vaporization, and for solid to gas is the heat of sublimation. Normally adding or removing energy will change the temperature of the substance as the kinetic energy of the particles will increase or decrease. During a phase change however, the potential energy of the substance changes as the particles are moved further apart or closer together. There is no change in kinetic energy of the particles and therefore no resulting change in temperature.


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