NON-STABLE S. LEWIN South-West Essex Technical College, London, England
T H E R E are many states which are not in true thermodynamic equilibrium either within themselves or with their surroundings. Those which undergo perceptible continuous physical or chemical changes have been readily recognized and classified as unstable states of varying degrees of instability. There are, however, many cases in which the particular state or phase is only apparently in equilibrium either internally or wit,h its surroundings. I n this field precise classification is difficult and, consequently, the available terms have frequently been incorrectly used. This is exemplified by the incorrect use of the term "metastable states." This term was introduced by Ostwald in 1897 (1)to cover such cases as supersaturated solutions and supercooled liquids which could remain for prolonged periods in such a state in the absence of any nuclei of their stable phases. Following this, Findlay (2) adopted the definition: "A system which in itself is stable, and which becomes unstable only on contact with a part,icular phase is said to be metastable." He also agrees mit,h Othmer (3) that a very slow velocity of transformation of a given system cannot be used as a criterion for the system being truly metastable; the only criterion is that the addition of a nucleus of the "stable phase," or its spontaneous formation, should cause the change from the metastable into the unstable stat,e. The two statements represent, however, different definitions since a "particular phase" and a "stable phase" can be different. Thus, in the case of supersaturated solutions, addition of the stable phase or of isomorphous substances can cause precipitat,ion. However, the use of the word "particular" in the definition of metastable states, can lead to incorrect classification when it is used t,o refer to a nucleus which in itself is not the stable phase, but. which nevertheless causes the metastable state to become unstable and so be transformed into the stable phase. Such use would lead to classifying as metastable certain states which are in apparent equilibrium, but where reaction can take place on the addition of specific catalysts. Thus, Taylor (4) considers a mixture of O2and Hp at, room temperature to be in a state of partial or metastable equilibrium. However, the introduction of some H 2 0 vapor or a drop of water into the mixture does not cause any combination, though the introduction of some platinum black results in reaction. If Taylor's use of the term metastable equilibrium is accepted then the definition has heen extended to such an extent that it now implies that a metastable st,ate is one which is in apparent or
pseudo-equilibrium with the surroundings or within itself until energy of activation requirements have been met. If this be so, then the degree of metastability depends only on the magnitude of the energy of activation. Even finely divided solids would the0 have to he classified as metast,ahle, since, in order to be ahle to pass readily into t,he stable state possessing minimum surface area (and therefore minimum surface free energy), they would have to pass into the liquid-or vapor-&ate first, thus requiring a certain energy of activation. On the other hand, acceptance of such a definition would appear to exclude cases where apparently no energy of activation is required, but where removal of the available free energy of the reaction is the primary condition for reaction t,o take place. For example, atomic hydrogen reacts arcording to the equation H+H=HIX
where Hz* is a "quasi-molecule" complex of the hydrogen molecule so "supercharged" with the energy of of the reaction that it redissoriates into the two hydrogen atoms. The proress H+H-H2
cannot take place, therefore, uuless a three-body i'ollision occurs in which the third body removes the energy of the reaction ( 5 ) . The "particular phase" in this case is then the third body, and the molecular hydrogen in the excited state may .be termed metastable. Similar remarks apply to t.he rombination of other free atoms such as those of nitrogen, chlorine, or bromine. Indeed, Kneser (6) expressed the view that the properties of activated nitrogen are to be attributed to the presence of the ordinary N atoms along with metastable molecules. Other authors have extended the meaning of the term "metastable states" still further. Thus, Hackh's "Chemical Dictionary" (7) defines a metastable state as "an unstable condition which changes readily either to a more stable or a less stable condition," a metastable electron as "an electron moving in an excited orbit," and a metastable phase as "the existence of a substance as a solid, liquid, or vapor under conditions in which it is normally unstable in that state." This set of definitions has clearly extended the meaning of "metastable" to such an extent that it is synonymous with the term unstable. This, of course, is an unsatisfactory state of affairs. Some investigators have adopted the term "metas-
MARCH, 1953
table atoms" for those whose electrons are in axcited states and which, for some mason, remain rfnr some time in that state. This extension of the tenn metastable state seems to have been widely arcepted (S), probably for want of more suitable terms, despite the fact that excited atoms of this kind may proceed to emit radiation and therefore pass into a lower free energy state in absence of any specific nuclei. The main reason for placing these atoms in the category of metastable states would appear to he the consideration that the time interval between the attainment of this state and the eventual transformation into the lowest energy state is longer than usual. Several workers, including Findlay (Q), use the t e r n "metastahle metals" for metals whose properties have altered on being subjected to mechanical treatment. Yet it is not certain that these "metastable" metallic states would tend to break down only on the addition of-or self-fornation of-the required stahle state or some particular nuclei. The inclusion of these metallic states in the category of metastable ones may be considered correct, if we define a metastable state simply as an unstable one mhich proceeds very slowly t o an equilibrium state. But, acceptance of this latter definition would result in the original significance of the term metastable states heing completely lost, since no nuclei of the stable state are required, and would still leave unclassified the cases of atomic hydrogen, "metastahle atoms" (since if radiation is emitted, i t occurs instantaneously), and other cases. This unsatisfactory state of classification has resulted from loose use of the terms "metastable" and "unstable" and from the lack of suitable definitions of the various states which are not in t,rue thermodynamic equilibrium either internally or externally. A possible cont,rihntory factor has been the tendency to model the terminology of the various energy states on physical models where the usual terms employed are: st,able, un~t~able, metastable, and, sometimes, neutral, despite the care required in such analogies. Now, in all the previous rases the free energy content of each is above t,he minimum possible under the experiment,al conditions given. At present, such systems are said to be thermodynamically unstahle. But the significance generally attached to the word unstahle is that an unstable system is in the process of losing its excess free energy and is therefore undergoing transformation into the thermodynamically stable state. This leads to coufusion, because many systems which are not in equilibrium do not undergo such transformation, and hence t.hey have been classified as metastable. Any classification of non-equilibrium states would be made easier if the word unstable were reserved for cases such that can he shown to be undergoing, however slowly, transformation into the stable state. A new term would then be required to cover all non-equilibrium states; .and the various cases could t,hen be placed in subdivisions. To this purpose the following definitions are suggested.
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THmMODYNAMIC NON-STABILITY
A thermodynamically non-stable state is defined as a state which is not in true thermodynamic equilibrium either within itself or with its surroundings. Thermodynamically non-stable states are therefore those in which (AF),,, < 0, or (AS),., > 0. Such states may be divided into the following four categories : UNSTABLE STATES. An unstable state is a non-stable state which is nndergoing continuous transformation into states possessing lower free energy contents (or greater entropy contents). Examples are: Instability at Constant Temperatwe. (1) Any substance or substances nndergoing reaction a t a noticeable rate at constant temperature and pressure. (2) Isothermal expansion of a gas. (3) Vector distribution: e. g., a gas "at constant temperature" in which the average kinetic energy of the molecules obeys numerically the Maxwell-Boltzmann distribution, hut where the vector distribution is unequal (i. e., where the equipartition principle is: not obeyed). Thus, in the rase of a molecular beam, the molecules are at "constant temperature," but their direhonal movement is restricted. In a closed space they would tend to assume the Maxwell-Boltzmann distribution in all directions. (4) Diffusion of solutes from concentrated solutions into less concentrated solutions. Temperature Differences: e. g., a hot body in cont,act with the surroundings which are at a lower temperature. PSEUDO-STABLE STATES. A pseudo-stable state is a non-st,ahle state which appears t,o he in equilibrium within itself or with its surroundings, but which nevertheless is slowly, or very slowly, changing continuously into the lower free energy states possible. Examples of this are: (1) Lyophohic colloids: These tend to coagulate very slowly. (2) Finely divided solids: These tend to form large crystals having minimum surface area. (3) A mixture of Hz and 0% at room temperature: The formation of water, in the absence of a catalyst, is extremely slow. (4) A magnetized bar of steel: It tends to be demagnetized very slowly. QUASI-STABLE STATES. A quasi-stable state is a non-stable state in which "reaction" takesplace readily hut which is readily reversed, because the products retain in full the free energy of the reaction. This reversible reaction--or alternation of the system hetween two states which have the same free energy content--continues until the removal of the free energy change available takes place on the introduction of some suitable material. Examples are "quasimolecules" of hydrogen, . - . chlorine, bromine, or nitrogen. METASTABLE STATES. A metastahle state is a nonstable state in which no transformation into the stable
