THE EXPLANATION OF POLYMORPHISM, AND THE RELATION BETWEEN
ENANTIOMORPHISM AND OPTICAL ACTIVITY.
_Polymorphism._ It has been shown in Chapter VII. that Mitscherlich had
in several instances proved the possibility of the occurrence of the
same substance in two different forms, notably sodium dihydrogen
phosphate NaH_{2}PO_{4}.H_{2}O, calcium carbonate CaCO_{3} (as calcite
and aragonite), the metallic sulphates known as vitriols, and the
chemical element sulphur, and that he gave to the phenomenon the name
“dimorphism.” Since that time large numbers of dimorphous substances
have been discovered, and several which occur in three forms and even a
few in no less than four totally distinct forms. Until the establishment
of the geometrical theory of crystal structure, as expounded in Chapter
IX., this phenomenon of polymorphism gave rise to endless fruitless
discussion. It was most generally attributed to the different nature of
the so-called “physical molecule,” which was supposed to be an aggregate
of chemical molecules and the unit of the space-lattice determining the
crystal system; the different polymorphous varieties were supposed to be
built up of structural units or physical molecules consisting of an
aggregation of a different number of chemical molecules. Several
attempts were made by various investigators, notably by Muthmann and by
Fock, to determine the number of chemical molecules constituting the
physical molecule.
All these efforts, however, ended unsatisfactorily, and in the year 1896
the author showed, in a memoir[11] on “The Nature of the Structural
Unit,” that in general the physical molecule is a myth, and that the
chemical molecule is the only structural unit possessing the full
chemical composition of the substance in question; and that its centre
of gravity, or better, any representative point within it, such as a
particular atom, is the unit point of the Bravais space-lattice of the
crystal structure, while the atoms of which the chemical molecule are
composed, arranged stereometrically identically similarly in all the
molecules, are the points of the individual point-systems which make up
the combined point-system. This does not imply a necessarily parallel
and identically orientated arrangement of all the molecules, as at first
postulated by Sohncke and which is a fact for his sixty-five
point-systems; for in accordance with the conclusions of Schönflies, von
Fedorow, and Barlow discussed in Chapter IX., cases are possible in
which alternate molecules may be arranged as each other’s mirror images.
Such are the cases of external molecular compensation or molecular
combination, two oppositely enantiomorphous sets of molecules balancing
each other within the structure, but by exterior compensation as regards
the molecule itself. Moreover, the principle of mirror-image symmetry
enters, as stated in Chapter IX, altogether into the constitution of no
less than 165 of the 230 types of homogeneous structure possible to
crystals.
Hence the conception of a physical molecule is totally unnecessary and,
moreover, erroneous. The alkali sulphates and selenates exhibit
dimorphism, one member of the series, ammonium selenate, having only
hitherto been observed in the pure state in the second, monoclinic,
form, and never in the ordinary rhombic form; and the author has
conclusively proved for these salts, and also for the double salts which
they form with the sulphates and selenates of magnesium, zinc, iron,
nickel, cobalt, manganese, copper, and cadmium, that the chemical
molecule is the only kind of molecule present, and that its
representative points are, as just stated, the nodes of the Bravais
space-lattice of the crystal structure, determining both the system of
the crystal and its obedience to the law of rational indices.
The explanation of polymorphism thus proves, in the light of the results
which have now been laid before the reader, to be a remarkably simple
one. Special pains were taken in explaining those results to show that
the temperature had a great deal to do with the conditions of
equilibrium of the crystal structure, for it determines the
intermolecular distances, that is, the amount of separation of the
molecules, and thus controls their possibility of movement with respect
to one another. Now the behaviour of the chemical molecules on the
advent of crystallisation is undoubtedly largely influenced by the
stereometric arrangement of the atoms composing them, and it is possible
for the latter to be such that the molecules may take up several
different parallel or enantiomorphously related positions; or as we have
just seen, a regular alternation within the crystal structure of such
mirror-image positions may be taken up. These different arrangements,
whether parallel or enantiomorphously opposite, may be, and probably
will be, of different degrees of stability, each of these different
forms finding its maximum stability of equilibrium at some particular
temperature, which is different for the different varieties. Hence, at a
series of ascending or descending temperatures, assuming the pressure to
remain the ordinary atmospheric, these different types of homogeneous
crystal structures will be most liable to be produced, each at its own
particular temperature, for which stable equilibrium of that crystal
structure occurs.
These different assemblages are as a rule quite dissimilar, certainly in
the crystal elements, often in class and not infrequently in system.
Generally two such different crystalline forms are all that are possible
within the life-range of temperature of the substance. But occasionally
three or even as many as four such different forms are found to be
capable of existence within the temperature life-limits of the
substance.
Polymorphism is thus completely and simply explained as a direct result
of the establishment of the geometrical theory of crystal structure as
laid down in Chapter IX. The equilibrium of the homogeneous structure is
a function of the temperature, and the stereometric arrangement of the
atoms in the chemical molecule of a substance may be such as permits of
two or more homogeneous arrangements of the molecules in assemblages of
varying degrees of stability, but each of which has a maximum stability
at a particular temperature. Hence, within any given range of
temperature such a substance will assume that type of homogeneous
arrangement of its molecules in a crystal which corresponds to the
stablest equilibrium within these temperature limits, assuming the
pressure constant within the bounds of the usual atmospheric variations.
Employing the language of physical chemistry, such a substance will thus
present two or more different solid “phases,” each characterised by its
specific crystalline form, the elementary parallelepipedon of which is
quite a distinct one. Each phase possesses also its own specific optical
and other physical properties, such as melting point, solubility,
thermal expansion, and elasticity.
It would appear as if the element sulphur is also polymorphous in this
sense, for the monoclinic prismatic form (Fig. 2, Plate I.)—the best
known and most easily prepared, from the state of fusion, of all the
forms other than the common rhombic form, in which sulphur is found in
the neighbourhood of volcanoes and in which it is also deposited from
solution in carbon bisulphide—is of distinctly lower stability, the
crystals passing in a few days into powder composed of minute crystals
of the stable rhombic variety. But in the case of carbon, with its
totally different and apparently at ordinary temperatures equally stable
varieties of octahedral-cubic diamond (Fig. 82, Plate XVI.) and
hexagonal graphite, there is some doubt; for although the diamond is
converted into graphite at a red heat in the electric arc, it is
doubtful whether we are not in the presence of a case of chemical
polymerism or allotropy, like the case of ozone, where three atoms of
oxygen compose the molecule, instead of the two atoms in the molecule of
ordinary oxygen. The fact that the negatively electrified electronic
corpuscles of the Crookes tube cause the same conversion of diamond into
graphite, producing according to Parsons and Swinton a temperature of
4,890° C. in the act, is evidence in favour of allotropy, as the charged
corpuscles are a very likely agent for breaking down such atomic
combinations. Moreover, diamond is volatilised out of contact with air
at 3,600° C. without liquefaction, and the vapour when cold condenses as
graphite. But there is reason to believe, from experiments by Sir Andrew
Noble and Sir William Crookes, that under great pressure carbon does
liquefy at 3,600° C., and that the liquid drops on cooling crystallise
as diamond.
The yellow and red varieties of phosphorus may also be due to a similar
cause, the yellow variety, which forms excellent crystals, corresponding
to P_{4}, while the red variety may correspond to a molecule composed of
a different number of atoms than four.
Another view of the nature of polymorphism has lately been brought
forward by Lehmann, as the result of his remarkable experimental
discovery of “liquid crystals,” to which fuller reference will be made
in Chapter XVI. This new view is, however, but an amplification of the
foregoing explanation of polymorphism, indicating the possible mode in
which the stereometric position of the atoms in the molecule does
actually influence and even determine the particular homogeneous
structure which shall be erected, and explains why the temperature plays
such an important rôle. Lehmann’s theory is that any one definitely
stereometrically constituted chemical molecule can only display one
particular homogeneous structure and form of crystal, and that when at a
particular temperature the system or class of symmetry is altered, this
occurs because the stereometric arrangement of the atoms within the
molecule is altered, that is, a new form of molecule is produced, which
naturally gives rise to a new form of crystal. As far as the author
understands it, this does not mean an isomeric change from the chemical
point of view, the chemical compound remaining the same, but that the
stereometric positions of the atoms have been changed, without altering
their chemical attachments, but sufficiently to change the nature of the
point-system which they produce. A significant fact in support of this
view is that the molecules of the substances forming liquid crystals are
usually very complicated and extended ones, comprising a large number of
atoms, the molecules, in fact, corresponding in length with the long
names of the organic substances of which they are generally composed.
Lehmann’s work has certainly proved that the molecule is endowed
with more individuality than has hitherto been ascribed to it, and
he even shows that there is some ground for believing that his
liquid crystals are such because this directive orientative force
resident in the molecules themselves maintains them in their
mutually crystallographically orientated positions even in the
liquid state, which may be and sometimes is as mobile as water. It
thus appears that any general acceptance of Lehmann’s ideas will
only tend to amplify and further explain the nature of polymorphism
on the lines here laid down, the temperature of conversion of one
form into another being merely that at which either a different
homogeneous packing is possible, or that at which the stereometric
relations of the atoms in the molecule are so altered as to produce
a new form of point-system without forming a new chemical compound.
_Enantiomorphism of Crystalline Form and Optical Activity._ It has
already been stated that two supplementary forms which are similar but
not identical, the one being the inverse or mirror-image reflection of
the other, as a right-hand glove is to a left-hand one, are termed
“enantiomorphous.” Also it has been shown that all those crystal forms
which have no plane of symmetry, either of simple symmetry or
alternating symmetry (which is equivalent to saying that no centre of
symmetry is present in addition to no plane of symmetry), are
enantiomorphous, and that such forms belong to eleven specific classes.
It has further been shown that the introduction of this principle of
mirror-image symmetry or enantiomorphism into the conditions already
laid down by Bravais and Sohncke for a homogeneous structure, by von
Fedorow, Schönflies, and Barlow, enabled those investigators to derive
the remaining 165 of the 230 possible types of homogeneous structures
compatible with crystal structure, over and above the 65 already
established by Bravais and Sohncke, and thus to complete the geometry of
crystal structure, when the units of such structure are represented by
points. Sohncke subsequently accepted the new principle, and modified
his own theory so as to bring it into line with it. He exhibited some
disinclination, however, at first, to accept the idea—which is a part of
the assumption of the other three authors just referred to, and which
appears to be absolutely necessary to explain one or two of the most
complicated of the crystal classes—of the possibility of two
enantiomorphous kinds of molecule being present in the crystal of the
same single substance, the balancing of the two sets having the effect
of producing mirror-image symmetry of the whole crystal, that is, the
development of a plane of symmetry.
Now the whole subject is of deep interest, both physical and chemical as
well as crystallographical, inasmuch as it is precisely such substances
as show enantiomorphism,—and can thus exist in two forms, one of which
is the mirror-image of the other and not its identical counterpart, the
two being like a pair of gloves,—which are found to possess the property
of rotating the plane of polarised light and which are therefore said to
be “optically active.” Moreover, the property may be displayed by both
the crystals and their respective solutions, or by the crystals only.
If, therefore, two optical antipodes of the same substance are known,
one rotating the plane of polarisation to the right and the other
rotating it to the same extent to the left, their crystals invariably
exhibit mirror-image symmetry with respect to each other. The converse
does not necessarily hold good, however, that a crystal possessing the
symmetry of one of these eleven classes will always exhibit optical
activity.
Pasteur[12] was the first to recognise this important relation between
enantiomorphous crystalline form and optical activity, in the case of
tartaric acid, which has the empirical formula C_{4}H_{6}O_{6} and the
constitution:
COOH
|
CHOH
|
CHOH
|
COOH
Tartaric acid was isolated by Scheele in 1769, and its discovery was
described in the very first memoir of that distinguished chemist.
Another very similar acid, as regards some of its more apparent
properties, was afterwards, in 1819, described by John of Berlin, and
investigated by Gay-Lussac in 1826; the latter obtained it from the
grape juice deposits of the wine manufactory of Kestner at Thann in the
Vosges. It was still more fully investigated by Gmelin in 1829, who
called it racemic acid (Traubensäure). But it needed the genius of
Berzelius to prove that it really had the same composition as tartaric
acid, although so different to that acid in some of its properties.
We have here as a matter of fact, the first instance brought to light
involving the principle of isomerism, the existence of two or more
distinct compounds having the same chemical composition as regards the
numbers of atoms of the same elements present, but differing in chemical
or physical properties, or both, owing to the different arrangement of
those atoms within the molecule. The “isomers” may be chemical or purely
physical; the latter involves no alteration of the linking of the atoms,
but merely of their disposition in space, and is the kind met with in
the case of the tartaric acids.
Biot, so noted for his optical researches, showed afterwards that
tartaric and racemic acids behave optically differently in solution, an
aqueous solution of the former rotating the plane of polarisation to the
right whilst that of racemic acid is optically inactive, not rotating
the plane of polarisation at all. That is, if the dark field be produced
in the polariscope, by crossing the polarising and analysing Nicol
prisms at right angles, tartaric acid solution will restore the light
again, and the analyser will have to be rotated to the right in order to
reproduce darkness. In the case of tartaric acid, the crystals
themselves also rotate the plane of polarisation, the amount being as
much as 11°.4 in sodium fight for a plate of the crystal one millimetre
thick. On the other hand, neither the solution nor the crystals of
racemic acid rotate the plane of polarisation at all.
Pasteur’s discovery, made in the year 1848, consisted in finding that
racemic acid is really a molecular compound of two physical “isomers,”
namely, of ordinary tartaric acid, which, as we have seen, rotates the
plane of polarisation to the right, and of another variety of tartaric
acid which rotates the beam of polarised fight to the same extent to the
left. The latter and ordinary tartaric acid he therefore distinguished
as lævo tartaric acid and dextro-tartaric acid respectively. Pasteur
went even further than this, in discovering yet a fourth variety of
tartaric acid, which is optically inactive like racemic acid, but which
cannot be split up into two optically active antipodes.
Indeed, it has since been shown that there are three varieties of this
truly inactive tartaric acid; they are cases of isomerism of the
chemical molecule itself, that is, the stereometric arrangement of the
atoms in the molecule is different in the three cases. For the molecule
of tartaric acid—in common with the molecules of all carbon compounds
the solutions of which, or which themselves in the liquid state, rotate
the plane of polarisation—possesses an asymmetric carbon atom, an atom
of carbon which is linked by its four valency attachments to four
different kinds of atoms or radicle groups; indeed, the molecule of
tartaric acid contains two such asymmetric carbon atoms, namely, the two
in the pair of CHOH groups. For each of these carbon atoms is linked by
one attachment to the carbon atom of the outer COOH group, by another to
an atom of hydrogen, by a third to the oxygen of the group OH, and by
its fourth attachment to the carbon atom of the other group CHOH, which
carries the rest of the molecule, that is, this attachment is to the
other half-molecule CHOH.COOH. Hence, it is quite obvious that there can
be two different dispositions of the atoms in space, one of which would
be the mirror-image of the other, while leaving the arrangement of the
atoms about the two asymmetric carbon atoms dissimilar and not
symmetrical in mirror-image fashion. That is, the two dispositions would
render the molecules in the two cases enantiomorphous with respect to
each other, and these two would be the arrangements respectively in the
two optically active varieties. That this is the correct explanation of
the ordinary dextro variety and the lævo variety of tartaric acid can
now admit of no doubt.
But if the groups round the two asymmetric carbon atoms are symmetrical
in mirror-image fashion, there will be compensation within the molecule
itself, and the substance will be optically inactive from internal
reasons. This is the explanation of the optically inactive variety which
is unresolvable into any components. The different varieties of this
inactive form are doubtless due to the different possibilities of
arrangement of the atoms in each half, while leaving the two halves
round each asymmetric carbon atom symmetrical to each other.
We now know that the decomposable inactive variety, racemic acid, may
be readily obtained by· dissolving equal weights of the ordinary
dextro and lævo varieties in water and crystallising the solution by
slow evaporation at the ordinary temperature. For further
investigation has fully borne out the conclusion of Pasteur, that
racemic acid simply consists of a molecular compound of the two active
varieties. It is thus itself inactive because it is externally
compensated, the two kinds of enantiomorphous molecules being
alternately regularly distributed throughout the whole crystal
structure, the very case which von Fedorow, Schönflies, and Barlow
assumed to be possible, and which Sohncke only tardily admitted. The
crystalline form of racemic acid is, as was to be expected, quite
different from the monoclinic form of the active tartaric acids, being
triclinic; and indeed it is not crystallographically comparable with
the active form, inasmuch as the crystals of racemic acid contain a
molecule of water of crystallisation, whereas the active varieties
crystallise anhydrous.
Ordinary dextro and lævo tartaric acids crystallise in identical forms
of the sphenoidal or monoclinic-hemimorphic class of the monoclinic
system, the class which is only symmetrical about a digonal axis, the
unique symmetry plane of the monoclinic system, which also operates when
full monoclinic symmetry is developed, being absent in this class. Hence
the interfacial crystal angles, the monoclinic axial angle, and the
axial ratios are identical for the two varieties. But the crystals are
hemimorphic, owing to the absence of the symmetry plane, and
complementarily so, the dextro variety being distinguished by the
presence of only the right clino-prism {011}, while the lævo variety is
characterised by the presence only of the left-clino-prism {0̄11}, these
two complementary forms, each composed of only two faces and which on a
holohedral crystal exhibiting the full symmetry of the monoclinic system
would both be present as a single form of four faces, being never both
developed on the same optically active crystal.
This hemimorphism of the two kinds of crystals will be rendered clear by
Figs. 63 and 64, representing typical crystals of dextro and lævo
tartaric acids which are obviously the mirror images of each other.
[Illustration:
FIG. 63.
]
[Illustration:
FIG. 64.
Crystals of Dextro and Lævo Tartaric Acids.
]
A remarkable discovery was made by Pasteur in connection with one
of the salts of racemic acid, sodium ammonium racemate,
Na(NH_{4})C_{4}H_{4}O_{6}, or
COONH_{4}
|
CHOH
|
CHOH
|
COONa
which is obtained by adding ammonia to the readily procurable salt
hydrogen sodium racemate. Sodium ammonium racemate was found by Pasteur
to be decomposable into the salts of dextro and lævo tartaric acids, on
crystallisation of a solution saturated at 28° C. by inoculation with a
crystal of either of those active salts. The solution on cooling being
in the state of slight supersaturation, which we now know from the work
of Ostwald and of Miers as the metastable condition, corresponding to
the interval between the solubility and supersolubility curves (see Fig.
98), if a crystal say of sodium ammonium lævo-tartrate be introduced,
this variety crystallises out first and can be separated from the
residual dextro-salt, which can then be subsequently crystallised.
Moreover, in certain direct crystallisations of sodium ammonium racemate
without such specialised inoculation, Pasteur found all the crystals
hemimorphic, some right-handed and some left-handed, and he was actually
able to isolate from each other crystals of the two varieties. On
separate recrystallisation of these two sets of crystals, he found them
to retain permanently their right or left-handed character, indicating
that the molecules themselves composing these crystals were
enantiomorphous. Their solutions correspondingly rotated the plane of
polarisation of light in opposite directions. Pasteur afterwards
obtained from the dextro-salt pure ordinary (dextro) tartaric acid, and
from the lævo-salt the lævo-acid, by converting them first into the lead
salts and then precipitating the lead as sulphide by sulphuretted
hydrogen.
In the case of lævo tartaric acid, this was its first isolation, as it
had hitherto been unknown. Gernez afterwards independently found that a
saturated solution of sodium ammonium racemate affords crystals of the
lævo-salt just as readily as of the dextro-salt; if a crystal of either
salt be introduced, crystals corresponding to that variety are produced.
Another most fruitful observation of Pasteur, the principle of which has
since been the means of isolating one of the two constituents of many
racemic compounds, was that when the spores of _Penicillium glaucum_ are
added to a solution of racemic acid containing traces of phosphates the
ordinary dextro component is destroyed by the organism, while the lævo
component is unattacked so long as any dextro remains; hence, if the
fermentation operation be stopped in time the lævo-acid may be isolated
and crystallised. Why a living organism thus eats up by preference one
variety only, possessing a particular right or left-handed screw
structure, of a compound containing the same elementary constituents
chemically united in the same manner, remains a most interesting
biological mystery.
The crystals of both dextro and lævo tartaric acids prove to be
pyro-electric, that is, develop electric excitation when slightly
heated. The end which exhibits the development of the clinodome develops
positive electricity in each case, when the crystal is allowed to cool
after warming, so that the two varieties are oppositely pyro-electric,
just as they are oppositely optically active. The most convenient method
of demonstrating the fact is to dust a little of Kundt’s powder, a
mixture of finely powdered red lead and sulphur, through a fine muslin
sieve on to the crystal as it cools. The sulphur becomes negatively
electrified and the red lead positively by mutual friction of the
particles in the sifting, and the sulphur thus attaches itself to the
positively electrified part of the crystal and the red lead to the
negatively electrified end. This phenomenon of the development by the
two varieties of an optically active substance of opposite electrical
polarity has since been shown to be a general one.
Finally, on mixing concentrated solutions containing equivalent weights
of dextro and lævo tartaric acid Pasteur observed that heat was evolved,
a sign of chemical combination, and the solution afterwards deposited on
cooling crystals of racemic acid. Hence, the only conclusion possible is
that racemic acid must be a molecular compound of the two oppositely
optically active tartaric acids. It thus partakes of the character of a
double salt, analogous to potassium magnesium sulphate for instance.
Consequently the crystal structure is one in which alternating molecules
of the two acids are uniformly distributed, and the case is actually
presented of two oppositely enantiomorphous sets of molecules producing
a homogeneous structure.
This interesting pioneer case of tartaric acid has been the cause of
the term “racemic” being applied to the inactive form of a substance
when it is decomposable into two oppositely optically active
enantiomorphous varieties of the substance. No well authenticated
exception has been found, in all the many instances which have been
observed of the phenomenon since Pasteur’s time, to the fact that
optically active substances exhibit what was formerly termed
hemihedrism; that is, expressing the case in accordance with our later
more accurate ideas of crystal structure as elucidated in previous
chapters, such substances invariably belong to classes of symmetry
possessing less than the full number of elements of symmetry possible
to the system to which the class belongs. These classes are eleven in
number, those possessing no plane of symmetry; they are, namely, the
asymmetric class of the triclinic system, the sphenoidal class of the
monoclinic system (to which the two tartaric acids, dextro and lævo,
belong), the bisphenoidal class of the rhombic system, the pyramidal
and trapezohedral classes of the trigonal, tetragonal, and hexagonal
systems, and the tetrahedral-pentagonal-dodecahedral and
pentagonal-icositetrahedral classes of the cubic system.
The optical activity has been proved by Le Bel and Van t’Hoff to be due
in most cases to enantiomorphism of the chemical molecules, that is, to
the enantiomorphous stereometric arrangement of the atoms in the
molecules, and therefore also,—as we have just seen, in accordance with
the geometrical theory of crystal structure,—of the combined
point-system in the case of each of the two varieties.
The point-systems are probably of a spiral screw-like character, either
right-handed or left-handed, as has been shown by Sohncke to be the case
for the two varieties of quartz, which crystallises in the trapezohedral
class of the trigonal system, one of the eleven classes just enumerated.
The example afforded by quartz will be developed fully in the next two
chapters, as this beautifully crystallised mineral enables us to study
and to demonstrate the phenomena of optical activity in a unique manner
and on the large scale.
The solutions as well as the crystals are usually optically active in
the cases where, as in the instance of the tartaric acids, the
substances are soluble in water or other solvent. Occasionally, however,
the optical activity is lost by dissolving in a solvent, and in such
cases it is the point-system only, and not the molecules themselves,
which is enantiomorphous. Sodium chlorate, NaClO_{3}, is an instance of
this kind. Moreover, a crystal can belong, as already mentioned, to one
of the eleven above enumerated classes of symmetry without displaying
optical activity, as all the point-systems possessing the symmetry of
these eleven classes do not exhibit screw-coincidence movements. Barium
nitrate, Ba(NO_{3})_{2}, is such a case.
The two “optical antipodes,” as the dextro and lævo varieties are
conveniently termed, of an optically active substance thus possess an
enantiomorphous crystal structure; but they are alike in their physical
properties such as density, melting point, optical refraction and optic
axial angle, cleavage, and elasticity. The crystal angles are identical
for the forms which are developed in common by them, and which are
usually those which the particular low class of symmetry possesses in
common with the holohedral class of the system. The crystallographic
difference between the two varieties comes in with respect to the
specific forms characteristic of the particular class of lower than full
systematic symmetry, and these forms are never displayed in common by
the two varieties, this being the essence of the enantiomorphism. When
the crystals are not rich in faces, however, it frequently happens that
only the common forms of higher symmetry just referred to are developed
on the crystals, and the two varieties are then indistinguishable in
exterior configuration; it is only on testing their rotatory power,
either by means of a section-plate of the crystal or by means of a
solution, or their pyro-electric properties, or, lastly, their
etch-figures afforded by a trace of a solvent (which etchings on the
crystal faces are enantiomorphous and an excellent indication of the
true symmetry), that their real character can be ascertained. Many
mistakes have been made in the past, and crystals assigned to a higher
than their true class of symmetry, owing to the investigation of only a
single crop of crystals fortuitously poor in the number of forms
displayed.
In the racemic form, if one should be deposited from the mixed solutions
of the two optical antipodes as a molecular compound of the latter, we
have an occurrence akin to polymerism, that is, the combination into a
single whole entity of a number of molecules, essentially two in the
case of racemism. Just as polymeric varieties of organic substances are
always found to have quite different crystalline forms, so an optically
inactive racemic form of a substance is generally quite different
crystallographically to the dextro and lævo varieties. But there is
usually some similarity along specific zones of the crystals, a kind of
isogonism or morphotropy being developed, such as has been shown to
occur, for instance, by Armstrong and Pope in the case of the substance
sobrerol.[13]
Besides the true racemic form it is often observed that under certain
conditions crystals are obtained which appear to combine the characters
of both the dextro and lævo varieties, exhibiting both series of
distinguishing hemimorphic or hemihedral forms on the same crystal; that
is, they show the full, holohedral, symmetry of the system. This has
been shown by Kipping and Pope[14] to be due to repeated twinning, thin
layers of the right and left-handed varieties being alternated, just, in
fact, as in the interesting form of quartz known as amethyst, to which
reference with experimental demonstration will be made in Chapter XIV.;
the whole structure assumes in consequence the simulated higher symmetry
which usually accompanies laminated twinning. Such forms have been
termed “pseudo-racemic.” In their memoir (_loc. cit._, p. 993) Kipping
and Pope summarise a large amount of highly interesting work on this
chemico-crystallographic subject which has been carried out by them, and
it may be useful to quote their precise definition of the relationship
between racemic and pseudo-racemic substances. They say:
“We define a pseudo-racemic substance as an intercalation of an equal,
or approximately equal, proportion of two enantiomorphously related
components, each of which preserves its characteristic type of
crystalline structure, but is so intercalated with the other as to form
a crystalline individual of non-homogeneous structure. A solid racemic
compound, on the other hand, may be defined as a crystalline substance
of homogeneous structure which contains an equal proportion of two
enantiomorphously related isomerides.
“The relations holding between a mere mixture of optical antipodes, a
pseudo-racemic substance, and a racemic compound, are closely parallel
to those existing between a crystalline mixture, an isomorphous mixture,
and a double salt. The crystallographic methods, by which a double salt
can be distinguished from an isomorphous mixture, may be directly
applied to distinguish between racemic and pseudo-racemic substances.
Thus, according as the crystalline substance obtained from a mixture of
two salts resembles or differs from either of its components
crystallographically, it is regarded either as an isomorphous mixture or
a double salt; similarly, an inactive externally compensated substance,
which closely resembles its active isomerides crystallographically, is
to be considered as pseudo-racemic, whereas when the contrary is true,
it is to be regarded as racemic.”
The work of Kipping and Pope may be regarded as having finally
vindicated and substantiated the law of Pasteur, that substances of
enantiomorphous molecular configuration develop enantiomorphous
crystalline structures, and that the crystal structures assumed by
enantiomorphously related molecular configurations are themselves
enantiomorphously related.
This subject, the main results and principles of which have now been
elucidated, may well be closed with a reference to an interesting case
of enantiomorphism and optical activity which the author has himself
investigated,[15] and which is very similar to the case of the tartaric
acids. It had been previously shown[16] by P. F. Frankland and W. Frew,
that when calcium glycerate was submitted to the fermenting action of
the _Bacillus ethaceticus_ one-half only of the glyceric acid was
destroyed, and that the remaining half was optically active, rotating
the plane of polarisation to the right.
Now glyceric acid,
CH_{2}.OH
|
CH.OH,
|
COOH
has manifestly one so-called asymmetric carbon atom (that is, a carbon
atom the four valencies of which are satisfied by attachment to four
different monad elements or groups), that belonging to the CHOH group.
There are consequently two possible arrangements of the molecule in
space, probably corresponding to the two optically active varieties,
namely, those represented, as far as is possible in one plane, as below,
the asymmetric carbon atom (not shown in the graphic representation)
being supposed to be at the centre of the tetrahedron, which is usually
taken to represent a carbon atom with its four valencies.
[Illustration]
Dextro-glyceric acid itself proved to be an uncrystallisable syrup, but
the calcium salt, Ca(C_{3}H_{5}O_{4})_{2}.2H_{2}O, was obtained in
crystals sufficiently well-formed to permit of a complete
crystallographic investigation, which the author undertook by friendly
arrangement with Prof. Frankland. Although the acid itself is
dextro-rotatory, aqueous solutions of the calcium salt are lævo-rotatory
to the extent of –12.09 units of “specific rotation” for sodium light.
The crystals were colourless well-formed prisms which proved to be of
monoclinic symmetry, the best individuals being formed by very slow
evaporation of the aqueous solution. They were terminated at both ends
by pyramid and dome faces, and sometimes grew to the length of a
centimetre. The actual crystal elements found after a full series of
measurements were as under:—
CALCIUM DEXTRO-GLYCERATE.
_Crystal system_: monoclinic.
_Class of Monoclinic System_: sphenoidal or monoclinic-hemimorphic.
_Habit_: prismatic.
_Monoclinic axial angle_: β=69° 6′.
_Ratio of axes_: _a_ : _b_ : _c_ = 1.4469 : 1 : 0.6694.
_Forms observed_:
_a_ = {100}, _c_ = {001}, _r′_ = {̄201}, _p_ = {110},
_m_ = {011}, _o_ = {111} _s_ = {̄1̄11}, _n_ = {̄2̄11}.
It will thus be seen that the system and the class are precisely those
of the two active tartaric acids, which renders the case the more
interesting. The usual appearance of the crystals is shown in Fig. 65,
and the stereographic projection is given in Fig. 66, which will
elucidate the symmetry more clearly, the plane of projection being the
plane of symmetry The latter, however, in this class is inoperative, the
two ends of the digonal symmetry axis, which runs perpendicularly to the
plane of the paper, being differently terminated, as in the tartaric
acids. The faces of the forms _o_ = {111} and _m_ = {011} were never
found developed on the left side of the symmetry plane, that is, on the
left side of the crystal as drawn in Fig. 65, the symmetry plane running
perpendicularly to the paper vertically from front to back; they were
only present on the right. Conversely, the faces of _s_ = {̄1̄11} and
_n_ = {̄2̄11} were never found developed on the right, but only on the
left of the plane of possible symmetry.
Moreover, it was frequently observed that the right-hand faces (110) and
(̄110) of the primary prismform _p_ were much more brilliant and truly
plane than those on the left hand, (1̄10) and (̄1̄10), which were
usually dull and often curved, as were also frequently the faces of the
left-hand forms _s_ and _n_. The right-hand distinguishing forms _m_ and
_o_, on the contrary, were generally most brilliant and gave admirable
reflections of the goniometer signal-slit.
[Illustration:
FIG. 65.—Crystal of Calcium Dextro-Glycerate.
]
[Illustration:
FIG. 66.—Stereographic Projection of Calcium Dextro-Glycerate.
]
The following table represents the results of the angular measurements,
twelve different well-formed individual crystals having been employed.
The angles marked with an asterisk were the important angles the mean
observed values of which were accepted as correct, being the best
measured angles, and which were therefore used as the basis of the
calculations.
_Table of Interfacial Angles of Calcium Glycerate._
Angle measured. No. of Limits. Mean Calculated.
measurements. observed.
{_ap_ = 100 : 110 42 52° 32′ − 54° 16′ 53° 29′ *
{_pp_ = 110 : ̄110 20 72 7 − 73 33 73 4 73° 2′
{_ac_ = 100 : 001 13 68 22 − 69 42 69 3 69 6
{_cr′_ = 001 : ̄201 13 52 4 − 52 31 52 13 *
{_r′a_ = ̄201 : ̄100 13 58 35 − 58 46 58 41 *
_cm_ = 001 : 011 10 31 47 − 32 19 32 3 32 2
_r′n_ = ̄201 : ̄2̄11 2 29 43 − 29 48 29 45 29 47
{_ao_ = 100 : 111 7 53 59 − 54 10 54 3 53 54
{_om_ = 111 : 011 7 18 20 − 18 35 18 26 18 29
{_ma_ = 011 : ̄100 13 107 22 − 108 24 107 41 107 37
{_an_ = ̄100 : ̄2̄11 11 62 32 − 63 44 63 6 63 10
{_ns_ = ̄2̄11 : ̄1̄11 1 − 21 35 21 27
{_sa_ = ̄1̄11 : 100 3 94 49 − 95 34 95 18 95 23
{_po_ = 110 : 111 9 43 51 − 44 44 44 35 44 38
{_oc_ = 111 : 001 9 32 56 − 33 15 33 7 33 7
{_cs_ = 001 : ̄1̄11 7 41 32 − 43 2 42 10 42 17
{_sp_ = ̄1̄11 : ̄1̄10 7 59 15 − 60 54 59 59 59 58
{_pc_ = ̄1̄10 : 00̄1 14 77 2 − 78 21 77 42 77 45
{_cp_ = 00̄1 : 110 16 101 39 − 103 36 102 16 102 15
{_pm_ = 110 : 011 9 52 15 − 53 25 52 42 52 41
{_mn_ = 011 : ̄2̄11 5 79 5 − 79 26 79 15 79 12
{_np_ = ̄2̄11 : ̄1̄10 5 47 41 − 48 23 48 4 48 7
{_pr′_ = 110 : ̄201 14 106 35 − 108 42 108 5 108 1
{_r′p_ = ̄201 : ̄1̄10 26 70 54 − 73 32 71 55 71 59
{_ps_ = ̄1̄10 : 1̄1̄1 5 66 42 − 67 17 67 4 67 5
{_sr′_ = 1̄1̄1 : 20̄1 6 40 36 − 41 29 41 5 40 56
_pm_ = ̄110 : 011 3 75 5 − 76 21 75 37 75 45
There is a moderately good cleavage parallel to the basal plane _c_ =
{001}.
The optical properties afford conclusive proof of the monoclinic nature
of the symmetry. The plane of the optic axes is perpendicular to the
possible symmetry plane, _b_ = {010}, and the first median line makes an
angle of 23° with the vertical axis c, emerging consequently nearly
normal to the basal plane _c_ = {001}, so that a section-plate parallel
to the _c_-faces, or a tabular crystal or cleavage plate parallel to
_c_, shows the optic axial rings and brushes well. The values of the
apparent optic axial angle in air, 2E, and of the true optic axial angle
within the crystal, 2V_{a}, the latter measured with the aid of a pair
of accurately ground section-plates perpendicular to the first and
second median lines and immersed in oil, are given in the next table.
2E 2V_{a}
For lithium light 51° 35′ 34° 56′
„ sodium „ 52° 30′ 35° 28′
„ thallium „ 53° 50′ 36° 16′
The intermediate refractive index β was found to be as under—
For red lithium light 1.4496
„ yellow sodium „ 1.4521
„ green thallium „ 1.4545
The double refraction was also determined and found to be of positive
sign.
The optical properties of calcium dextro-glycerate thus confirm
absolutely the monoclinic nature of the symmetry, as regards the crystal
system. And it was conclusively demonstrated by the goniometrical part
of the investigation that the exterior symmetry was not such as agreed
with holohedral monoclinic symmetry, but with that of the sphenoidal
class, in which the only one of the two elements of monoclinic symmetry
(the plane of symmetry and the digonal axis of symmetry) in operation is
the digonal axis, thus leaving the two terminations of that axis, at
opposite sides, right and left, of the possible symmetry plane,
unsymmetrical. And this is precisely the symmetry which is
characteristic of an enantiomorphous optically active substance.
Unfortunately, the corresponding lævo-salt has not yet been obtained in
measurable crystals, but there can be no doubt that whenever such are
forthcoming they will display enantiomorphism in the precisely opposite
and complementary sense, the facial forms characteristic in this
dextro-salt of the right termination of the digonal axis being absent on
that side of the systematic symmetry plane but developed on the left
side instead, and _vice versa_, and that the two enantiomorphous forms
will together make up the whole of the faces required by the full
symmetry of the monoclinic system.
A concrete instance like this, worked out practically in the laboratory,
brings home the precise nature of this interesting relationship, between
crystallographic and molecular enantiomorphism on the one hand and
optical activity on the other hand, in a particularly clear and forcible
manner. It is hoped that this brief account of it will also consequently
have been of assistance to the reader, in more clearly appreciating the
main points of this chapter.