Allotropy of Sulphur

Ever since the recognition of allotropy amongst the elements, sulphur has occupied the position of being the most marked example. So complex is the behaviour of the element, however, that even at the present time a complete interpretation is not possible.

Even in the state of vapour the problem presented by the behaviour of sulphur is far from simple. As soon as moderately accurate results for vapour density were available it became clear that with elevation of temperature from the boiling- point upwards the vapour molecules undergo reduction in weight, approaching the condition S₂ when near 1000° C., whilst in the neighbourhood of the boiling-point, under atmospheric pressure, the vapour density attains a value almost corresponding with the molecule S₈, which is the molecular condition of ordinary dissolved sulphur (see the following). More recent experiments have confirmed these results and have shown that even at the boiling-point the S₈ molecules of sulphur vapour are accompanied by smaller molecules, the proportion of the latter gradually increasing as the temperature rises until when near 900° C. only S₂ molecules are present. Above 1700° C. the S₂ molecules begin to suffer incipient dissociation into single atoms and at 2070° C. the vapour density corresponds to a molecular weight of only 50, indicating that the vapour contains a considerable percentage of monatomic molecules. From the pressure resulting during the explosion of "detonating gas" (2H₂ + O₂) mixed with hydrogen sulphide it has been calculated that at 2450° C., under atmospheric pressure, 50 per cent, of the diatomic sulphur molecules undergo further dissociation into single atoms.

Vapour density experiments conducted under reduced pressure and at temperatures below the normal boiling-point of sulphur have shown that under such conditions sulphur vapour gradually approaches the octa-atomic condition as the temperature is lowered; this is indicated by the following figures:

Temperature, ° C	Vapour Density (Air = 1)	Molecular Weight.	Apparent Number of Atoms per Molecule.
310	8.26	237.9	7.44
262	8.34	240.1	7.50
236	8.52	245.2	7.66
212	8.67	249.6	7.80
193	8.73	251.1	7.85

The gradual disintegration of the S₈ molecule at higher temperatures can also be observed by the alteration of the vapour density when the pressure is reduced and the temperature allowed to remain constant. Indeed, this method of examining the alteration in the molecular condition of sulphur vapour has yielded important information. At one time it was believed that the S₈ molecule disintegrated in successive stages to S₆ and S₄ before reaching the diatomic condition, but it now appears probable that there is only one intermediate stage, namely S₆, which form of sulphur vapour appears to stand in close relationship with one of the forms of liquid sulphur, namely S_μ.

External evidence is available in confirmation of the remarkable molecular alteration in sulphur vapour. Near the boiling-point sulphur vapour is orange-red, but the colour fades to a straw-yellow as the temperature is raised; indeed, above 1000° C. the vapour is said to become colourless and on reaching 1400° C. to assume a pale blue tint. The absorption spectrum of sulphur vapour3 has been examined over the range 400° to 1200° C., and it is found that absorption increases as the temperature is raised to about 650° C. but above this temperature it decreases as the vapour becomes more and more transparent. This

agrees with the view that the dissociation S₈ → S₂ is not direct, but that molecules of intermediate complexity and of greater absorptive power than S₂ are formed and in turn dissociated. No further change is observable above 900° C. The fluorescence observable in the vapour under reduced pressures also shows variations indicative of the alteration in molecular condition.

When the temperature of sulphur is gradually raised from the melting-point, a notable change is observable near 160° C., the colour of the liquid beginning to deepen, whilst the fluidity commences to decrease. The occurrence of this change, or at least its extent, is dependent on the previous history of the sulphur, for it may be delayed or be much less marked if the sulphur is of a high degree of purity; the reason for this is to be sought in the catalytic influence of certain impurities. Under ordinary conditions the viscosity attains a maximum between 170° and 220° C., the colour being then a very deep brown. Further rise in temperature causes,a partial restoration of the fluidity, but the deep colour is retained. These striking and exceptional changes are attributed to the presence of three different forms of sulphur in the liquid, and careful investigations of the phenomena have been made, especially by A. Smith and various collaborators.

A full interpretation of the results of the investigations is rendered difficult by the complications introduced by external influences such as those due to certain impurities which it is almost impossible to exclude. It is clearly recognisable, however, that the abnormal behaviour is due mainly to the existence of two distinct modifications of molten sulphur, side by side; these are commonly distinguished as λ-sulphur and μ-sulphur, and the equilibrium between them at any temperature may be expressed

λ-sulphur ⇔ μ-sulphur

The position of the equilibrium varies with the temperature, the proportion of μ -sulphur being less at lower temperatures; near the melting-point the proportion of μ-sulphur approximates to 4 per cent., and the maximum at higher temperatures generally does not much exceed 40 per cent. It was at one time believed that rapid cooling could effect the separation of molten sulphur into two distinct layers, but careful examination has shown the lack of homogeneity to be due only to temperature differences caused by the viscosity and the poor thermal conductivity of the liquid; the two modifications are completely miscible in the liquid state.

By rapidly cooling the fluid mixture it is possible to minimise the readjustment of the equilibrium and to attain a solid condition in which the original proportions of the mixture are approximately retained; in the solid state the allotropic change is so very slow as to allow careful and fairly prolonged examination of the mixture. It is then found that the normal mobile liquid constituent (S_λ) has given rise to crystalline sulphur, soluble in carbon disulphide, whereas the dark-coloured viscous constituent (S_μ) has produced an amorphous solid, insoluble in this solvent. A rough analysis of molten sulphur in this way becomes possible. Recent experiments, however, suggest that the insoluble μ-sulphur is not present as such in liquid sulphur, but makes its appearance, possibly as a gel, only when the liquid solidifies.

If sulphur is heated to 180° C. and then cooled, it becomes more soluble in carbon disulphide; also a saturated solution of sulphur chloride in toluene at the ordinary temperature will, after being heated to the neighbourhood of 180° C. and cooled again, dissolve yet more sulphur. These observations led to the discovery of a third modification in molten sulphur. This form of sulphur, distinguished as π-sulphur, is formed to some extent when ordinary sulphur is heated to 125° C. The optimum temperature for its formation is near 180° C., when the liquid contains approximately 6.5 per cent, of S_π with 20.5 per cent, of S_μ and 73 per cent, of S_λ. π-Sulphur exists as a definite and distinct modification both in the liquid and the solid state.2 It is especially notable on account of its deep orange-yellow colour, which is also seen in its solutions, a fairly concentrated solution in carbon disulphide having the colour of a concentrated aqueous solution of potassium dichromate. π-Sulphur is unstable at the ordinary temperature, its transformation being accelerated by ammonia solution and also by the influence of light; the products of its transformation are octahedral sulphur and some insoluble sulphur. A suggestion that π-sulphur has a molecular weight corresponding to S₄ needs further experimental confirmation.

The existence of yet another form of sulphur, designated φ-sulphur, formed together with π-sulphur but of a somewhat paler colour, although deeper than octahedral or monoclinic sulphur, is also suspected.

The presence of the μ- and π-modifications of sulphur dissolved in molten λ-sulphur naturally causes a depression of the freezing-point of the latter, and from the magnitude of this effect it has been possible to demonstrate the probability of a molecular weight corresponding to S₆ for the dark brown μ-allotrope, a result which is of especial interest as correlating this form of liquid sulphur with the hexatomic sulphur believed to occur in sulphur vapour (see before).

Kellas, however, from measurements of the surface tension of liquid sulphur, maintains that between 115° and 160° C. at least 95 per cent, of mobile sulphur is represented by the formula S₆, and that above 160° C. polymerisation occurs, resulting in the formation of S₁₈ or (S₆), molecules, which are stable nearly up to the boiling- point.

On account of the variability of the proportions of λ-sulphur, μ-sulphur and π-sulphur in the liquid, the solidifying-point of molten sulphur is not constant, but may range from 114° to 117° C. or even more widely. The freezing-point of pure λ-sulphur can be determined by calculation, the result, 119.25° C., almost coinciding with the temperature observed in the crystallisation of pure λ-sulphur and with the ideal melting-point of pure monoclinic sulphur.

Certain substances, especially ammonia, exert a catalytic influence on the two changes involved in the foregoing equilibrium, greatly facilitating the attainment of the equilibrium; on this account the presence of a little ammonia, or an organic base such as aniline or pyridine, causes soluble sulphur to be formed almost exclusively on solidification. On the other hand, several other substances, e.g. sulphur dioxide (or gases such as air or oxygen which can give rise to sulphur dioxide), halogen hydracids, phosphoric acid and organic acids, behave as negative catalysts, and when molten sulphur is cooled, cause the μ-sulphur to persist in a quantity in excess of the equilibrium proportion at lower temperatures, so that these substances raise the percentage of insoluble sulphur in the solidified mass. It is possible that the action of ammonia is merely due to its power of removing sulphur dioxide, traces of which are usually present in ordinary sulphur. Iodine not only exerts a catalytic effect of the same type as sulphur dioxide, but also causes an increase in the proportion of μ-sulphur in the liquid.

For the foregoing reasons it is seldom possible to obtain reproducible viscosity values for a given sample of sulphur. If, however, pure gas-free sulphur is prepared by distillation first in carbon dioxide and then in high vacuum, reliable values may be obtained. For such sulphur, protected from exposure to air, it has been found that the viscosity between 163° and 169° C., the interval of high viscosity variation, lies on the same curve whatever the previous thermal treatment of the sample may have been.

Exposure to bright light, for example to a concentrated beam of the sun's rays or to the electric arc, produces an increase in the proportion of the μ-modification in liquid sulphur. A similar effect is observable even in solution; if a solution of sulphur in carbon disulphide is similarly illuminated, insoluble sulphur gradually separates; the reverse change occurs in the dark. The conclusion can therefore be drawn that in solution also there is an equilibrium between the λ- and μ,-forms at the ordinary temperature, but that except under the influence of light the concentration of μ-sulphur is not sufficient to cause separation of the corresponding solid.

In spite of these allotropic changes, molten sulphur under certain conditions can be successfully used as a cryoscopic solvent. Soon after having been melted, the freezing-point of the liquid may be as high as 119° C., but after keeping for some hours at a temperature just above the melting-point, the freezing-point falls to 114.5° C., and in this condition the sulphur is suitable for cryoscopic determinations, the constant K being 213.

When molten sulphur is rapidly cooled from the neighbourhood of 400° C., an amber-coloured semi-elastic mass of density about 1.9 is obtained. This so-called " plastic sulphur " is in reality an under-cooled liquid sulphur and gradually hardens or solidifies to a mixture of soluble and insoluble sulphur, the change being hastened by kneading or by heating in boiling water. The rate of hardening is naturally dependent on the relative proportions of the two modifications and so will be influenced by the extent of the sudden fall in temperature; e.g. the higher the temperature of the sulphur as it is poured into cold water, the slower the solidification. If the cooling is still more rigorous, as by immersion in liquid air, a hard mass may be obtained, which on warming assumes the elastic character, possibly in greater degree, and finally solidifies in the usual manner. In its general character it will be seen that "plastic sulphur" resembles materials like glass or " barley sugar " which have been produced by cooling liquids much below their normal temperatures of crystallisation without any sharp change in state.

As is to be expected the equilibrium between the two above-mentioned forms of liquid sulphur affects other properties in addition to the colour and the viscosity. Thus, the electrical conductivity and the surface tension of molten sulphur exhibit abnormal variation with alteration in temperature; also the solubility curves for λ-sulphur and μ-sulphur in high-boiling solvents such as triphenylmethane are quite distinct, the solubility of the former increasing and that of the latter decreasing with rise of temperature; the respective coefficients of expansion are also quite independent. The reactivities of the two forms towards rubber are practically equal.

More or less drastic modifications of the above view of the nature of molten sulphur have been suggested, but none appears to be supported by sufficient evidence to deserve acceptance.

When molten sulphur is allowed to solidify, the modifications present give rise to corresponding solid forms, the liquid λ-sulphur producing crystalline sulphur (rhombic, monoclinic or nacreous, according to the conditions), whilst the deep brown viscous μ-sulphur yields an amorphous pale yellow solid which is very sparingly soluble (generally described as " insoluble ") in carbon disulphide and the other common solvents for sulphur. This amorphous form of sulphur, which is frequently termed γ-sulphur, has no definite melting-point and so may be regarded as " undercooled " μ-sulphur. As the crystalline forms of sulphur are commonly obtained by separation from a melt containing some μ-sulphur, crystalline sulphur ordinarily contains an appreciable quantity of insoluble y-sulphur in a state of solid solution. Mention has already been made of the formation of γ-sulphur as an insoluble powder when a carbon disulphide solution of sulphur is exposed to light.