I.Bivariant Systems: One component in one phase.(a) Rhombic sulphur.(b) Monoclinic sulphur.(c) Sulphur vapour.(d) Liquid sulphur.II.Univariant Systems: One component in two phases.(a) Rhombic sulphur and vapour.(b) Monoclinic sulphur and vapour.(c) Rhombic sulphur and liquid.(d) Monoclinic sulphur and liquid.(e) Rhombic and monoclinic sulphur.(f) Liquid and vapour.III.Invariant Systems: One component in three phases.(a) Rhombic and monoclinic sulphur and vapour.(b) Rhombic sulphur, liquid and vapour.(c) Monoclinic sulphur, liquid and vapour.(d) Rhombic and monoclinic sulphur and liquid.
I.Bivariant Systems: One component in one phase.(a) Rhombic sulphur.(b) Monoclinic sulphur.(c) Sulphur vapour.(d) Liquid sulphur.
I.Bivariant Systems: One component in one phase.
(a) Rhombic sulphur.
(b) Monoclinic sulphur.
(c) Sulphur vapour.
(d) Liquid sulphur.
II.Univariant Systems: One component in two phases.(a) Rhombic sulphur and vapour.(b) Monoclinic sulphur and vapour.(c) Rhombic sulphur and liquid.(d) Monoclinic sulphur and liquid.(e) Rhombic and monoclinic sulphur.(f) Liquid and vapour.
II.Univariant Systems: One component in two phases.
(a) Rhombic sulphur and vapour.
(b) Monoclinic sulphur and vapour.
(c) Rhombic sulphur and liquid.
(d) Monoclinic sulphur and liquid.
(e) Rhombic and monoclinic sulphur.
(f) Liquid and vapour.
III.Invariant Systems: One component in three phases.(a) Rhombic and monoclinic sulphur and vapour.(b) Rhombic sulphur, liquid and vapour.(c) Monoclinic sulphur, liquid and vapour.(d) Rhombic and monoclinic sulphur and liquid.
III.Invariant Systems: One component in three phases.
(a) Rhombic and monoclinic sulphur and vapour.
(b) Rhombic sulphur, liquid and vapour.
(c) Monoclinic sulphur, liquid and vapour.
(d) Rhombic and monoclinic sulphur and liquid.
Fig. 5Fig.5.
Triple Point—Rhombic and Monoclinic Sulphur and Vapour. Transition Point.—In the case of ice, water and vapour, we saw that at the triple point the vapour pressures of ice and water are equal; below this point, ice is stable; above this point, water is stable. We saw, further, that below 0° the vapour pressure of the stable system is lower than that of the metastable, and therefore that at the triple point there is a break in the vapour pressure curve of such a kind that abovethe triple point the vapour-pressure curve ascends more slowly than below it. Now, although the vapour pressure of solid sulphur has not been determined, we can nevertheless consider that it does possess a certain, even if very small, vapour pressure,[50]and that at the temperature at which the vapour pressures of rhombic and monoclinic sulphur become equal, we can have these two solid forms existing in equilibrium with the vapour. Below that point only one form, that with the lower vapour pressure, will be stable; above that point only the other form will be stable. On passing through the triple point, therefore, there will be a change of the one form into the other. This point is represented in our diagram (Fig. 5) by the point O, the two curves AO and OB representing diagrammatically the vapour pressures of rhombic and monoclinic sulphur respectively. If the vapour phase is absent and the system maintained under a constant pressure,e.g.atmospheric pressure, there will also be a definite temperature at which the two solid forms are in equilibrium, and on passing through which complete and reversible transformation of one form into the other occurs. This temperature, which refers to equilibrium in absence of the vapour phase, is known as thetransition temperatureorinversion temperature.
Were we dependent on measurements of pressure and temperature, the determination of the transition point might be a matter of great difficulty. When we consider, however, that the other physical properties of the solid phases,e.g.the density, undergo an abrupt change on passing through the transition point, owing to the transformation of one form into the other, then any method by which this abrupt change in the physical properties can be detected may be employed for determining the transition point. A considerable number of such methods have been devised, and a description of the most important of these is given in the Appendix.
In the case of sulphur, the transition point of rhombic into monoclinic sulphur was found by Reicher[51]to lie at 95.5°. Below this temperature the octahedral, above it the monoclinic, is the stable form.
Condensed Systems.—We have already seen that in the change of the melting point of water with the pressure, a very great increase of the latter was necessary in order to produce a comparatively small change in the temperature of equilibrium. This is a characteristic of all systems from which the vapour phase is absent, and which are composed only of solid and liquid phases. Such systems are calledcondensed systems,[52]and in determining the temperature of equilibrium of such systems, practically the same point will be obtained whether the measurements are carried out under atmospheric pressure or under the pressure of the vapour of the solid or liquid phases. The transition point, therefore, as determined in open vessels at atmospheric pressure, will differ only by a very slight amount from the triple point, or point at which the two solid or liquid phases are in equilibrium under the pressure of their vapour.The determination of the transition point is thereby greatly simplified.
Suspended Transformation.—In many respects the transition point of two solid phases is analogous to the melting point of a solid, or point at which the solid passes into a liquid. In both cases the change of phase is associated with a definite temperature and pressure in such a way that below the point the one phase, above the point the other phase, is stable. The transition point, however, differs in so far from a point of fusion, that while it is possible to supercool a liquid, no definite case is known where the solid has been heated above the triple point without passing into the liquid state. Transformation, therefore, is suspended only on one side of the melting point. In the case of two solid phases, however, the transition point can be overstepped in both directions, so that each phase can be obtained in the metastable condition. In the case of supercooled water, further, we saw that the introduction of the stable, solid phase caused the speedy transformation of the metastable to the stable condition of equilibrium; but in the case of two solid phases the change from the metastable to the stable modification may occur with great slowness, even in presence of the stable form. This tardiness with which the stable condition of equilibrium is reached greatly increases in many cases the difficulty of accurately determining the transition point. The phenomena of suspended transformation will, however, receive a fuller discussion later (p.68).
Transition Curve—Rhombic and Monoclinic Sulphur.—Just as we found the melting point of ice to vary with the pressure, so also do we find that change of pressure causes an alteration in the transition point. In the case of the transition point of rhombic into monoclinic sulphur, increase of pressure by 1 atm. raises the transition point by 0.04°-0.05°.[53]The transition curve, or curve representing the change of the transition point with pressure, will therefore slope to the right away from the pressure axis. This is curve OC (Fig. 5).
Triple Point—Monoclinic Sulphur, Liquid, and Vapour. Melting Point of Monoclinic Sulphur.—Above 95.5°, monoclinic sulphur is, as we have seen, the stable form. On being heated to 120°, under atmospheric pressure, it melts. This temperature is, therefore, the point of equilibrium between monoclinic sulphur and liquid sulphur under atmospheric pressure. Since we are dealing with a condensed system, this temperature may be regarded as very nearly that at which the solid and liquid are in equilibrium with their vapour,i.e.the triple point, solid (monoclinic)—liquid—vapour. This point is represented in the diagram by B.
Triple Point—Rhombic and Monoclinic Sulphur and Liquid.—In contrast with that of ice, the fusion point of monoclinic sulphur israisedby increase of pressure, and the fusion curve, therefore, slopes to the right. The transition curve of rhombic and monoclinic sulphur, as we have seen, also slopes to the right, and more so than the fusion curve of monoclinic sulphur. There will, therefore, be a certain pressure and temperature at which the two curves will cut. This point lies at 151°, and a pressure of 1320 kilogm. per sq. cm., or about 1288 atm.[54]It, therefore, forms another triple point, the existence of which had been predicted by Roozeboom,[55]at which rhombic and monoclinic sulphur are in equilibrium with liquid sulphur. It is represented in our diagram by the point C.Beyond this point monoclinic sulphur ceases to exist in a stable condition.At temperatures and pressures above this triple point, rhombic sulphur will be the stable modification, and this fact is of mineralogical interest, because it explains the occurrence in nature of well-formed rhombic crystals. Under ordinary conditions, prismatic sulphur separates out on cooling fused sulphur, but at temperatures above 151° and under pressures greater than 1288 atm., the rhombic form would be produced.[56]
Triple Point—Rhombic Sulphur, Liquid, and Vapour. Metastable Triple Point.—On account of the slowness withwhich transformation of one form into the other takes place on passing the transition point, it has been found possible to heat rhombic sulphur up to its melting point (114.5°). At this temperature, not only is rhombic sulphur in a metastable condition, but the liquid is also metastable, its vapour pressure being greater than that of solid monoclinic sulphur. This point is represented in our diagram by the pointb.
From the relative positions of the metastable melting point of rhombic sulphur and the stable melting point of monoclinic sulphur at 120°, we see that, of the two forms, the metastable form has the lower melting point. This, of course, is valid only for the relative stability in the neighbourhood of the melting point; for we have already learned that at lower temperatures rhombic sulphur is the stable, monoclinic sulphur the metastable (or unstable) form.
Fusion Curve of Rhombic Sulphur.—Like any other melting point, that of rhombic sulphur will be displaced by increase of pressure; increase of pressure raises the melting point, and we can therefore obtain a metastable fusion curve representing the conditions under which rhombic sulphur is in equilibrium with liquid sulphur. This metastable fusion curve must pass through the triple point for rhombic sulphur—monoclinic sulphur—liquid sulphur, and on passing this point it becomes a stable fusion curve. The continuation of this curve, therefore, above 151° forms the stable fusion curve of rhombic sulphur (curve CD).
These curves have been investigated at high pressures by Tammann, and the results are represented according to scale in Fig. 6,[57]abeing the curve for monoclinic sulphur and liquid;b, that for rhombic sulphur and liquid; andc, that for rhombic and monoclinic sulphur.
Bivariant Systems.—Just as in the case of the diagram of states of water, the areas in Fig. 5 represent the conditions for the stable existence of the single phases: rhombic sulphur in the area to the left of AOCD; monoclinic sulphur in the area OBC; liquid sulphur in the area EBCD; sulphur vapour below the curves AOBE. As can be seen from the diagram,the existence of monoclinic sulphur is limited on all sides, its area being bounded by the curves OB, OC, BC. At any point outside this area, monoclinic sulphur can exist only in a metastable condition.
Fig. 6Fig. 6.
Other crystalline forms of sulphur have been obtained,[58]so that the existence of other systems of the one-component sulphur besides those already described is possible. Reference will be made to these later (p.51).
C.Tin.
Another substance capable of existing in more than one crystalline form, is the metal tin, and although the general behaviour, so far as studied, is analogous to that of sulphur, a short account of the two varieties of tin may be given here, not only on account of their metallurgical interest, but also on account of the importance which the phenomena possess for the employment of this metal in everyday life.
After a winter of extreme severity in Russia (1867-1868), the somewhat unpleasant discovery was made that a number of blocks of tin, which had been stored in the Customs House at St. Petersburg, had undergone disintegration and crumbled to a grey powder.[59]That tin undergoes change on exposure to extreme cold was known, however, before that time, even as far back as the time of Aristotle, who spoke of the tin as "melting."[60]Ludicrous as that term may now appear, Aristotle nevertheless unconsciously employed a strikingly accurate analogy, for the conditions under which ordinary white tin passes into the grey modification are, in many ways, quite analogous to those under which a substance passes from the solid to the liquid state. The knowledge of this was, however, beyond the wisdom of the Greek philosopher.
For many years there existed considerable confusion both as to the conditions under which the transformation of white tin into its allotropic modification occurs, and to the reason of the change. Under the guidance of the Phase Rule, however, the confusion which obtained has been cleared away, and the "mysterious" behaviour of tin brought into accord with other phenomena of transformation.[61]
Transition Point.—Just as in the case of sulphur, so also in the case of tin, there is a transition point above which theone form, ordinary white tin, and below which the other form, grey tin, is the stable variety. In the case of this metal, the transition point was found by Cohen and van Eyk, who employed both the dilatometric and the electrical methods (Appendix) to be 20°. Below this temperature, grey tin is the stable form. But, as we have seen in the case of sulphur, the change of the metastable into the stable solid phase occurs with considerable slowness, and this behaviour is found also in the case of tin. Were it not so, we should not be able to use this metal for the many purposes to which it is applied in everyday life; for, with the exception of a comparatively small number of days in the year, the temperature of our climate is below 20°, andwhite tin is, therefore, at the ordinary temperature, in a metastable condition. The change, however, into the stable form at the ordinary temperature, although slow, nevertheless takes place, as is shown by the partial or entire conversion of articles of tin which have lain buried for several hundreds of years.
On lowering the temperature, the velocity with which the transformation of the tin occurs is increased, and Cohen and van Eyk found that the temperature of maximum velocity is about -50°. Contact with the stable form will, of course, facilitate the transformation.
The change of white tin into grey takes place also with increased velocity in presence of a solution of tin ammonium chloride (pink salt), which is able to dissolve small quantities of tin. In presence of such a solution also, it was found that the temperature at which the velocity of transformation was greatest was raised to 0°. At this temperature, white tin in contact with a solution of tin ammonium chloride, and the grey modification, undergoes transformation to an appreciable extent in the course of a few days.
Fig. 7 is a photograph of a piece of white tin undergoing transformation into the grey variety.[62]The bright surface of the tin becomes covered with a number of warty masses, formed of the less dense grey form, and the number and size of these continue to grow until the whole of the white tin has passedinto a grey powder. On account of the appearance which is here seen, this transformation of tin has been called by Cohen the "tin plague."
Fig. 7Fig. 7.
Enantiotropy and Monotropy.—In the case of sulphur and tin, we have met with two substances existing in polymorphic forms, and we have also learned that these forms exhibit a definite transition point at which their relative stability is reversed. Each form, therefore, possesses a definite range of stable existence, and is capable of undergoing transformation into the other, at temperatures above or below that of the transition point.
Another class of dimorphous substances is, however, met with as, for instance, in the case of the well-known compounds iodine monochloride and benzophenone. Each crystalline form has its own melting point, the dimorphous forms of iodine monochloride melting at 13.9° and 27.2°,[63]and those of benzophenone at 26° and 48°.[64]This class of substance differs from that which we have already studied (e.g.sulphur and tin), in that at all temperatures up to the melting point, only one of the forms is stable, the other being metastable. There is, therefore, no transition point, and transformation of the crystalline forms can be observedonly in one direction. These two classes of phenomena are distinguished by the namesenantiotropyandmonotropy; enantiotropic substances being such that the change of one form into the other is a reversible process (e.g.rhombic sulphur into monoclinic, and monoclinic sulphur into rhombic), and monotropic substances, those in which the transformation of the crystalline forms is irreversible.
Fig. 9Fig. 9.
Fig. 8Fig. 8.
These differences in the behaviour can be explained very well in many cases by supposing that in the case of enantiotropic substances the transition point lies below the melting point, while in the case of monotropic substances, it lies above the melting point.[65]These conditions would be represented by the Figs. 8 and 9.
In these two figures, O3is the transition point, O1and O2the melting points of the metastable and stable formsrespectively. From Fig. 9 we see that the crystalline form I. at all temperatures up to its melting point is metastable with respect to the form II. In such cases the transition point could be reached only at higher pressures.
Although, as already stated, this explanation suffices for many cases, it does not prove that in all cases of monotropy the transition point is above the melting point of the two forms. It is also quite possible that the transition point may lie below the melting points;[66]in this case we have what is known aspseudomonotropy. It is possible that graphite and diamond,[67]perhaps also the two forms of phosphorus, stand in the relation of pseudomonotropy (v.p.49).
The disposition of the curves in Figs. 8 and 9 also explains the phenomenon sometimes met with, especially in organic chemistry, that the substance first melts, then solidifies, and remelts at a higher temperature. On again determining the melting point after re-solidification, only the higher melting point is obtained.
The explanation of such a behaviour is, that if the determination of the melting point is carried out rapidly, the point O1, the melting point of the metastable solid form, may be realized. At this temperature, however, the liquid is metastable with respect to the stable solid form, and if the temperature isnot allowed to rise above the melting point of the latter, the liquid may solidify. The stable solid modification thus obtained will melt only at a higher temperature.
D.Phosphorus.
An interesting case of a monotropic dimorphous substance is found in phosphorus, which occurs in two crystalline forms; white phosphorus belonging to the regular system, and red phosphorus belonging to the hexagonal system. From determinations of the vapour pressures of liquid white phosphorus, and of solid red phosphorus,[68]it was found that the vapour pressure of red phosphorus was considerably lower than that of liquid white phosphorus at the same temperature, the values obtained being given in the following table.
Vapour Pressures of White and Red Phosphorus.
These values are also represented graphically in Fig. 10.
Fig. 10Fig. 10.
At all temperatures above about 260°, transformation of the white into the red modification takes place with appreciable velocity, and this velocity increases as the temperature is raised. Even at lower temperatures,e.g.at the ordinary temperature, the velocity of transformation is increased under the influenceof light,[69]or by the presence of certain substances,e.g.iodine,[70]just as the velocity of transformation of white tin into the grey modification was increased by the presence of a solution of tin ammonium chloride (p.40). At the ordinary temperature, therefore, white phosphorus must be considered as the less stable (metastable) form, for although it can exist in contact with red phosphorus for a long period, its vapour pressure, as we have seen, is greater than that of the red modification, and also, its solubility in different solvents is greater[71]than that of the red modification; as we shall find later, the solubility of the metastable form is always greater than that of the stable.
The relationships which are met with in the case of phosphorus can be best represented by the diagram, Fig. 11.[72]
In this figure, BO1represents the conditions of equilibrium of the univariant system red phosphorus and vapour, which ends at O1, the melting point of red phosphorus. By heating in capillary tubes of hard glass, Chapman[73]found that red phosphorus melts at the melting point of potassium iodide,i.e.about 630°,[74]but the pressure at this temperature is unknown.
At O1, then, we have the triple point, red phosphorus, liquid, and vapour, and starting from it, we should have thevaporization curve of liquid phosphorus, O1A, and the fusion curve of red phosphorus, O1F. Although these have not been determined, the latter curve must, from theoretical considerations (v.p.58), slope slightly to the right;i.e.increase of pressure raises the melting point of red phosphorus.
Fig. 11Fig. 11.
When white phosphorus is heated to 44°, it melts. At this point, therefore, we shall have another triple point, white phosphorus—liquid—vapour; the pressure at this point has been calculated to be 3 mm.[75]This point is the intersection of three curves, viz. sublimation curve, vaporization curve, and the fusion curve of white phosphorus. The fusion curve, O2E, has been determined by Tammann[76]and by G. A. Hulett,[77]and it was found that increase of pressure by 1 atm. raises the melting point by 0.029°. The sublimation curve of white phosphorus has not yet been determined.
As can be seen from the table of vapour pressures (p.46), the vapour pressure of white phosphorus has been determined up to 500°; at temperatures above this, however, the velocity with which transformation into red phosphorus takes place is so great as to render the determination of the vapour pressureat higher temperatures impossible. Since, however, the difference between white phosphorus and red phosphorus disappears in the liquid state, the vapour pressure curve of white phosphorus must pass through the point O1, the melting point of red phosphorus, and must be continuous with the curve O1A, the vapour pressure curve of liquid phosphorus (vide infra). Since, as Fig. 10 shows, the vapour pressure curve of white phosphorus ascends very rapidly at higher temperatures, the "break" between BO1and O1A must be very slight.
As compared with monotropic substances like benzophenone, phosphorus exhibits the peculiarity that transformation of the metastable into the stable modification takes place with great slowness; and further, the time required for the production of equilibrium between red phosphorus and phosphorus vapour is great compared with that required for establishing the same equilibrium in the case of white phosphorus. This behaviour can be best explained by the assumption that change in the molecular complexity (polymerization) occurs in the conversion of white into red phosphorus, and when red phosphorus passes into vapour (depolymerization).[78]
This is borne out by the fact that measurements of the vapour density of phosphorus vapour at temperatures of 500° and more, show it to have the molecular weight represented by P4,[79]and the same molecular weight has been found for phosphorus in solution.[80]On the other hand, it has recently been shown by R. Schenck,[81]that the molecular weight of red phosphorus is at least P8, and very possibly higher.
In the case of phosphorus, therefore, it is more than possible that we are dealing, not simply with two polymorphicforms of the same substance, but with polymeric forms, and that there is no transition point at temperatures above the absolute zero, unless we assume the molecular complexity of the two forms to become the same. The curve for red phosphorus would therefore lie below that of white phosphorus, for the vapour pressure of the polymeric form, if produced from the simpler form with evolution of heat, must be lower than that of the latter. A transition point would, of course, become possible if the sign of the heat effect in the transformation of the one modification into the other should change. If, further, the liquid which is produced by the fusion of red phosphorus at 630° under high pressure also exists in a polymeric form, greater than P4, then the metastable vaporization curve of white phosphorus would not pass through the melting point of red phosphorus, as was assumed above.[82]
We have already seen in the case of water (p.31) that the vapour pressure of supercooled water is greater than that of ice, and that therefore it is possible, theoretically at least, by a process of distillation, to transfer the water from one end of a closed tube to the other, and to there condense it as ice. On account of the very small difference between the vapour pressure of supercooled water and ice, this distillation process has not been experimentally realized. In the case of phosphorus, however, where the difference in the vapour pressures is comparatively great, it has been found possible to distil white phosphorus from one part of a closed tube to another, and to there condense it as red phosphorus; and since the vapour pressure of red phosphorus at 350° is less than the vapour pressure of white phosphorus at 200°, it is possible to carry out the distillation from acolderpart of the tube to ahotter, by having white phosphorus at the former and red phosphorus at the latter. Such a process of distillation has been carried out by Troost and Hautefeuille between 324° and 350°.[83]
Relationships similar to those found in the case of phosphorus are also met with in the case of cyanogen andparacyanogen, which have been studied by Chappuis,[84]Troost and Hautefeuille,[85]and Dewar,[86]and also in the case of other organic substances.
Enantiotropy combined with Monotropy.—Not only can polymorphic substances exhibit enantiotropy or monotropy, but, if the substance is capable of existing in more than two crystalline forms, both relationships may be found, so that some of the forms may be enantiotropic to one another, while the other forms exhibit only monotropy. This behaviour is seen in the case of sulphur, which can exist in as many as eight different crystalline varieties. Of these only monoclinic and rhombic sulphur exhibit the relationship of enantiotropy,i.e.they possess a definite transition point, while the other forms are all metastable with respect to rhombic and monoclinic sulphur, and remain so up to the melting point; that is to say, they are monotropic modifications.[87]
E.Liquid Crystals.
Phenomena observed.—In 1888 it was discovered by Reinitzer[88]that the two substances, cholesteryl acetate and cholesteryl benzoate, possess the peculiar property of melting sharply at a definite temperature to milky liquids; and that the latter, on being further heated, suddenly become clear, also at a definite temperature. Other substances, more especiallyp-azoxyanisole andp-azoxyphenetole, were, later, found to possess the same property of having apparently a double melting point.[89]On cooling the clear liquids, the reverse series of changes occurred.
The turbid liquids which were thus obtained were found to possess not only the usual properties of liquids (such as theproperty of flowing and of assuming a perfectly spherical shape when suspended in a liquid of the same density), but also those properties which had hitherto been observed only in the case of solid crystalline substances, viz. the property of double refraction and of giving interference colours when examined by polarized light; the turbid liquids areanisotropic. To such liquids, the optical properties of which were discovered by O. Lehmann,[90]the nameliquid crystals, or crystalline liquids, was given.
Nature of Liquid Crystals.—During the past ten years the question as to the nature of liquid crystals has been discussed by a number of investigators, several of whom have contended strongly against the idea of the term "liquid" being applied to the crystalline condition; and various attempts have been made to prove that the turbid liquids are in reality heterogeneous and are to be classed along with emulsions.[91]This view was no doubt largely suggested by the fact that the anisotropic liquids were turbid, whereas the "solid" crystals were clear. Lehmann found, however, that, when examined under the microscope, the "simple" liquid crystals were also clear,[92]the apparent turbidity being due to the aggregation of a number of differently oriented crystals, in the same way as a piece of marble does not appear transparent although composed of transparent crystals.[93]
Further, no proof of the heterogeneity of liquid crystals has yet been obtained, but rather all chemical and physical investigations indicate that they are homogeneous.[94]No separationof a solid substance from the milky, anisotropic liquids has been effected; the anisotropic liquid is in some cases less viscous than the isotropic liquid formed at a higher temperature; and the temperature of liquefaction is constant, and is affected by pressure and admixture with foreign substances exactly as in the case of a pure substance.[95]
Fig. 12Fig. 12.
Equilibrium Relations in the Case of Liquid Crystals.—Since, now, we have seen that we are dealing here with substances in two crystalline forms (which we may call the solid and liquid[96]crystalline form), which possess a definite transition point, at which, transformation of the one form into the other occurs in both directions, we can represent the conditions of equilibrium by a diagram in all respects similar to that employed in the case of other enantiotropic substances,e.g.sulphur (p.35).
In Fig. 12 there is given a diagrammatic representation of the relationships found in the case ofp-azoxyanisole.[97]
Although the vapour pressure of the substance in the solid, or liquid state, has not been determined, it will be understood from what we have already learned, that the curves AO, OB, BC, representing the vapour pressure of solid crystals, liquid crystals, isotropic liquid, must have the relative positions shown in the diagram. Point O, the transition point of the solid into the liquid crystals, lies at 118.27°, and the change of the transition point with the pressure is +0.032° pro 1 atm. The transition curve OE slopes, therefore, slightly to the right. The point B, the melting point of the liquid crystals, lies at 135.85°, and the melting point is raised 0.0485° pro 1 atm. The curve BD, therefore, also slopes to the right, and more so than the transition curve. In this respect azoxyanisole is different from sulphur.
The areas bounded by the curves represent the conditions for the stable existence of the four single phases, solid crystals, liquid crystals, isotropic liquid and vapour.
The most important substances hitherto found to form liquid crystals are[98]:—
GENERAL SUMMARY
In the preceding pages we have learned how the principles of the Phase Rule can be applied to the elucidation of various systems consisting of one component. In the present chapter it is proposed to give a short summary of the relationships we have met with, and also to discuss more generally how the Phase Rule applies to other one-component systems. On account of the fact that beginners are sometimes inclined to expect too much of the Phase Rule; to expect, for example, that it will inform them as to the exact behaviour of a substance, it may here be emphasized that the Phase Rule is a general rule; it informs us only as to the general conditions of equilibrium, and leaves the determination of the definite, numerical data to experiment.
Triple Point.—We have already (p.28) defined a triple point in a one-component system, as being that pressure and temperature at which three phases coexist in equilibrium; it represents, therefore, an invariant system (p.16). At the triple point also, three curves cut, viz. the curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs. The most common triple point of a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V), but other triple points[99]are also possible when, as in the case ofsulphur or benzophenone, polymorphic forms occur. Whether or not all the triple points can be experimentally realized will, of course, depend on circumstances. We shall, in the first place, consider only the triple point S-L-V.
As to the general arrangement of the three univariant curves around the triple point, the following rules may be given. (1) The prolongation of each of the curves beyond the triple point must lie between the other two curves. (2) The middle position at one and the same temperature in the neighbourhood of the triple point is taken by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.[100]That is to say, if a line of constant temperature is drawn immediately above or below the triple point so as to cut the three curves—two stable curves and the metastable prolongation of the third—the position of the curves at that temperature will be such that the middle position is occupied by that curve (or its metastable prolongation) which represents the two phases of most widely differing specific volume.
Now, although these rules admit of a considerable variety of possible arrangements of curves around the triple point,[101]only two of these have been experimentally obtained in the case of the triple point solid—liquid—vapour. At present, therefore, we shall consider only these two cases (Figs. 13 and 14).