In 1886 R. Eötvös (Wied. Ann. 27, p. 452), assuming that two liquids may be compared when the ratios of the volumes of the liquids to the volumes of the saturated vapours are the same, deduced that γV2/3 (where γ is the surface tension, and V the molecular volume of the liquid) causes all liquids to have the same temperature coefficients. This theorem was investigated by Sir W. Ramsay and J. Shields (Journ. Chem. Soc. 63, p. 1089; 65, p. 167), whose results have thrown considerable light on the subject of the molecular complexity of liquids. Ramsay and Shields suggested that there exists an equation for the surface energy of liquids, analogous to the volume-energy equation of gases, PV = RT. The relation they suspected to be of the form γS = KT, where K is a constant analogous to R, and S the surface containing one gramme-molecule, γ and T being the surface tension and temperature respectively. Obviously equimolecular surfaces are given by (Mv)2/3, where M is the molecular weight of the substance, for equimolecular volumes are Mv, and corresponding surfaces the two-thirds power of this. Hence S may be replaced by (Mv)2/3. Ramsay and Shields found from investigations of the temperature coefficient of the surface energy that T in the equation γ(Mv)2/3 = KT must be counted downwards from the critical temperature T less about 6°. Their surface energy equation therefore assumes the form γ(Mv)2/3 = K(τ - 6°). Now the value of K, γ being measured in dynes and M being the molecular weight of the substance as a gas, is in general 2.121; this value is never exceeded, but in many cases it is less. This diminution implies an association of molecules, the surface containing fewer molecules than it is supposed to. Suppose the coefficient of association be n, i.e. n is the mean number of molecules which associate to form one molecule, then by the normal equation we have γ(Mnv)2/3 = 2.121(τ - 6°); if the calculated constant be K1, then we have also γ(Mv)2/3 = K1(τ-6°). By division we obtain n2/3 = 2.121/K1, or n = (2.121/K1)3/2 the coefficient of association being thus determined.
The apparatus devised by Ramsay and Shields consisted of a capillary tube, on one end of which was blown a bulb provided with a minute hole. Attached to the bulb was a glass rod and then a tube containing iron wire. This tube was placed in an outer tube containing the liquid to be experimented with; the liquid is raised to its boiling-point, and then hermetically sealed. The whole is enclosed in a jacket connected with a boiler containing a liquid, the vapour of which serves to keep the inner tube at any desired temperature. The capillary tube can be raised or lowered at will by running a magnet outside the tube, and the heights of the columns are measured by a cathetometer or micrometer microscope.
Normal values of K were given by nitrogen peroxide, N2O4, sulphur chloride, S2Cl2, silicon tetrachloride, SiCl4, phosphorus chloride, PCl3, phosphoryl chloride, POCl3, nickel carbonyl, Ni(CO)4, carbon disulphide, benzene, pyridine, ether, methyl propyl ketone; association characterized many hydroxylic compounds: for ethyl alcohol the factor of association was 2.74-2-43, for n-propyl alcohol 2.86-2.72, acetic acid 3.62-2.77, acetone 1.26, water 3.81-2.32; phenol, nitric acid, sulphuric acid, nitroethane, and propionitril, also exhibit association.
Crystalline Form and Composition.
The development of the theory of crystal structure, and the fundamental principles on which is based the classification of crystal forms, are treated in the article [Crystallography]; in the same place will be found an account of the doctrine of isomorphism, polymorphism and morphotropy. Here we shall treat the latter subjects in more detail, viewed from the standpoint of the chemist. Isomorphism may be defined as the existence of two or more different substances in the same crystal form and structure, polymorphism as the existence of the same substance in two or more crystal modifications, and morphotropy (after P. von Groth) as the change in crystal form due to alterations in the molecule of closely (chemically) related substances. In order to permit a comparison of crystal forms, from which we hope to gain an insight into the prevailing molecular conditions, it is necessary that some unit of crystal dimensions must be chosen. A crystal may be regarded as built up of primitive parallelepipeda, the edges of which are in the ratio of the crystallographic axes, and the angles the axial angles of the crystals. To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters[18] (χ,ψ,ω), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules. The actual values of the topic parameters can then readily be expressed in terms of the elements of the crystals (the axial ratios and angles), the density, and the molecular weight (see Groth, Physikalische Krystallographie, or Chemical Crystallography).
Polymorphism.—On the theory that crystal form and structure are the result of the equilibrium between the atoms and molecules composing the crystals, it is probable, a priori, that the same substance may possess different equilibrium configurations of sufficient stability, under favourable conditions, to form different crystal structures. Broadly this phenomenon is termed polymorphism; however, it is necessary to examine closely the diverse crystal modifications in order to determine whether they are really of different symmetry, or whether twinning has occasioned the apparent difference. In the article [Crystallography] the nature and behaviour of twinned crystals receives full treatment; here it is sufficient to say that when the planes and axes of twinning are planes and axes of symmetry, a twin would exhibit higher symmetry (but remain in the same crystal system) than the primary crystal; and, also, if a crystal approximates in its axial constants to a higher system, mimetic twinning would increase the approximation, and the crystal would be pseudo-symmetric.
In general, polysymmetric and polymorphous modifications suffer transformation when submitted to variations in either temperature or pressure, or both. The criterion whether a pseudo-symmetric form is a true polymorph or not consists in the determination of the scalar properties (e.g. density, specific heat, &c.) of the original and the resulting modification, a change being in general recorded only when polymorphism exists. Change of temperature usually suffices to determine this, though in certain cases a variation in pressure is necessary; for instance, sodium magnesium uranyl acetate, NaMg(UO2)3(C2H3O2)9·9H2O shows no change in density unless the observations are conducted under a considerable pressure. Although many pseudo-symmetric twins are transformable into the simpler form, yet, in some cases, a true polymorph results, the change being indicated, as before, by alterations in scalar (as well as vector) properties.
For example, boracite forms pseudo-cubic crystals which become truly cubic at 265°, with a distinct change in density; leucite behaves similarly at about 560°. Again, the pyroxenes, RSiO3 (R = Fe, Mg, Mn, &c.), assume the forms (1) monoclinic, sometimes twinned so as to become pseudo-rhombic; (2) rhombic, resulting from the pseudo-rhombic structure of (1) becoming ultramicroscopic; and (3) triclinic, distinctly different from (1) and (2); (1) and (2) are polysymmetric modifications, while (3) and the pair (1) and (2) are polymorphs.
While polysymmetry is solely conditioned by the manner in which the mimetic twin is built up from the single crystals, there being no change in the scalar properties, and the vector properties being calculable from the nature of the twinning, in the case of polymorphism entirely different structures present themselves, both scalar and vector properties being altered; and, in the present state of our knowledge, it is impossible to foretell the characters of a polymorphous modification. We may conclude that in polymorphs the substance occurs in different phases (or molecular aggregations), and the equilibrium between these phases follows definite laws, being dependent upon temperature and pressure, and amenable to thermodynamic treatment (cf. [Chemical Action] and [Energetics]). The transformation of polymorphs presents certain analogies to the solidification of a liquid. Liquids may be cooled below their freezing-point without solidification, the metastable (after W. Ostwald) form so obtained being immediately solidified on the introduction of a particle of the solid modification; and supersaturated solutions behave in a similar manner. At the same time there may be conditions of temperature and pressure at which polymorphs may exist side by side.
