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X-ray structural study of the mesophases of some cone-shaped molecules
A.M. Levelut, J. Malthête, A. Collet
To cite this version:
A.M. Levelut, J. Malthête, A. Collet. X-ray structural study of the mesophases of some cone-shaped molecules. Journal de Physique, 1986, 47 (2), pp.351-357. �10.1051/jphys:01986004702035100�. �jpa- 00210212�
X-ray structural study of the mesophases of some cone-shaped molecules
A. M. Levelut (*), J. Malthête (+) and A. Collet (+)
(*) Laboratoire de Physique des Solides (**), Université Paris-Sud, 91405 Orsay Cedex, France (+) Laboratoire de Chimie des Interactions Moléculaires,
Collège de France, 11, place Marcelin Berthelot, 75005 Paris Cedex, France
(Reçu le 10juillet 1985, accepté sous forme définitive le 14 octobre 1985)
Résumé. 2014 Grâce à la diffraction des rayons X, nous avons montré que des molécules coniques peuvent former des mésophases assez ordonnées. Parmi les quatre mésophases étudiées, trois sont classiques puisque les colonnes
forment un réseau régulier plan, tandis que la quatrième est quasi cristalline : seules les chaînes paraffiniques participent à l’ordre tridimensionnel bien qu’elles soient à l’état fondu.
Abstract. 2014 We have established by X-ray diffraction that cone-shaped molecules can form relatively well ordered
columnar mesophases. Four mesophases have been studied. Three of them have the classical two-dimensional
organization in parallel columns while the fourth one shows a quasi-crystalline structure : 3D-ordering takes place at the level of the long paraffinic chains which surround the conical core despite the fact that the chains are
in a « molten state ».
Classification
Physics Abstracts
61.30E
1. Introduction.
Since the 1977 discovery [1] of the first thermotropic mesophase of disc-like molecules, it has been shown that molecules with flat rigid cores surrounded by six
or eight elongated flexible chains can form mesophases
in which the molecules are stacked in columns [2].
The columns are parallel and form a periodic 2D
lattice. The paraffinic medium which surrounds each column is in a molten state and therefore ensures
that there is no correlation across the columns, of the molecular positions along the column axis. It has been shown recently that mesophases can also be obtained
when the flat core is replaced by a conical one [3, 4].
We report here a structural analysis of some of these
new mesophases, and we compare their symmetries
with those of the usual columnar mesophases of disc-
like compounds.
2. Experiments.
We have studied the mesophases of the three hexa- esters of cyclotricatechylene la-c. The transition
temperatures are reported in table I.
Under optical microscope the textures seem cha-
racteristic of columnar mesophases [3, 4], but the
viscosities are very high and the mesophases have a
Table I. - Transition temperatures of the three studied
cyclotricatechylene hexaesters (OC).
waxy appearance. It was possible to obtain regions
with a homogeneous direction of extinction between crossed polarizers when the mesophase was spread
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004702035100
352
out on a glass plate with a spatula. We therefore used
this technique for the obtention of samples for X-ray diffraction experiments. Two kinds of samples were prepared : very thin samples spread on a single crystal
of mica and thicker samples with a lower degree of
orientation which were picked out of a glass plate
with a rasor blade. The X-ray set up is very simple, consisting of a monochromatic beam (CuKa) issued
from a double bent graphite pyrolitic crystal, and a photographic plate collecting the diffracted X-rays.
With the technique described above, we obtained
fibre samples with the fibre axis parallel to the stretch- ing direction. When this axis is perpendicular to the X-ray beam, one obtains a section of the reciprocal
space containing the fibre axis which gives all the
information. We also used a Guinier camera with CuKa radiation in order to have a better accuracy
on the lattice spacing values.
3. Experimental results.
Typically, in a columnar mesophase of disc-like
molecules, a single domain gives a diffraction pattern that consists of one equatorial plane containing all
the Bragg spots and two kinds of diffuse features
lying out this equatorial plane [5]. One part of this diffuse scattering radiation gives an image of the organization of the paraffinic chains since this part
can be compared to the main diffuse ring seen for a
molten paraffin. The other part of the diffuse scat-
tering is localized in a set of reciprocal planes parallel
to the plane containing the Bragg peaks, and per-
pendicular to the column axis. One can relate the
Bragg peaks to the inter-column order, which is a two- dimensional crystalline order, while the diffuse scat-
tering intensity describes the way in which the cores are stacked in a column.
In figure 1, we present X-ray patterns of aligned samples for three of the four studied mesophases (the mesophase of compound la and the low-tem- perature one of compound 16 are isomorphous).
Among these patterns, two fit the general scheme of a
columnar phase (Figs. 1, iv and 1, v); the third one
for compound lc at low temperature is that of an
imperfect 3D crystal (Figs. 1 i to 1, iii). In this last case,
the information about its organization can be deduced
from a semi-quantitative analysis of the pattern.
3.1 MESOPHASES OF lc. - The diffraction patterns of figure 1, i to 1, iii show Bragg spots lying on layer
lines perpendicular to the column axis (Fig. 1 A).
The width of these spots increases with the length
of scattering vector. There are mainly two independent
factors responsible for this broadening : fluctuations of orientation, which spread out the spots on circular
arcs of the same angular width, and an increase of the width parallel to z (fibre axis) with the xy compo- nents of the scattering vector. The layer lines corres- pond to a periodicity along the column axis of 20.96 A.
All the rings observed on the powder pattern cor-
respond to the spots observed for the oriented samples,
and can be indexed on an orthorhombic lattice
a = 47.07 A, b = 31.58 A, c = 20.96 A. In table II
we have listed the measured and calculated lattice
spacing values for the observed spots. It is clear that many Bragg reflections are missing. On each line,
we see one group of a few peaks which are all in the
same range of scattering angles. As the index I increases,
the perpendicular component increases simultane-
ously. Therefore all the 0 0 l reflexions vanish. This fact implies that the projection of the electronic
density along the column axis is uniform. Moreover the extinctions are consistent with the existence of three perpendicular helicoidal two-fold axes i.e. with the space group P 212121.
Besides the major layer lines, we also observed a second set of diffuse lines (B) parallel to the first set.
The line of highest intensity corresponds to a scat- tering vector of (4.82 Å) - 1 while the others show a
modulation of this period (4.82 A) with a wave length
of 20.96 A. A few weak Bragg spots are located on this second set of layer lines. Therefore the structure must be modulated in the column axis direction.
The ratio between the two periods is close to the
rational number 13/3. At last, a broad diffuse scattering ring (C) indicates that paxa,ffinic chains are in a liquid state.
The general description of this diffraction pattern is consistent with a model in which an assembly of
helicoidal columns forms a 3D imperfect crystal.
The pitch of the helices is 20.96 A, and the molecules
forming the column are equidistant with a period
of 4.82 A. This last value is equal to the core-to-core distance in the column of the cyclotriveratrylene crystals [3, 6]. For a more precise description, we can
use our knowledge of the core structure obtained from
different crystalline structures [6, 7]. Unfortunately
we have no information on the external crown formed
by the aliphatic chains, except for the fact that an
important statistical disorder takes place at this level
as is evidenced by the corresponding diffuse scattering
at about 4.5 A. This lack of information concerning
the major part of the compound, together with the problem of the fluctuations of the lattice unit vectors,
precludes a quantitative analysis of the diffraction data. Nevertheless, one can derive some ideas on the organization of the phase from a comparison of the reciprocal image of a helix with our pattern.
Let us give the form factor -% of a helix of pitch P, radius R on which atoms with a scattering factor F
are regularly spaced with a period p in the helix axis
direction. The relation between p and P is 13 p = 3, p = C [8]
where Sz and Sl are the two components of the scat- tering vector S respectively parallel and perpendicular
Fig. 1. 2013 X-ray diffraction patterns of aligned samples of 1 band Ic :
9 (i) and (ii) compound 1c at room temperature on mica, (iii) without substrate. A : Bragg spots, B : diffuse lines, C : broad/
diffuse scattering from melted chains, M : mica Bragg spots;
* (iv) compound 1c at 115 OC, without substrate;
9 (v) compound led at 70 °C on mica.
The column axis (stretching direction) is parallel to the arrows.
354
Table II. - Assignment of Powder rings in the mesophases.
to the helix axis. 1 m n are integers which obey the
relation 1 = 13 m + 3 n and J. is the Bessel function of order n. If we keep in mind the general properties
of Bessel functions, we must assume that a measurable contribution to the intensity comes only from the low orders n and low values of the variable (corresponding
to the first extrema of each Jn). The sum is reduced
to one Bessel function for each value of I. The position
of the visible Bragg spots on the first layer line I = 3 (m = 0, n = 1) corresponds to a helix of mean radius
9 A. Such an helix made of equidistant rigid molecules
will give a measurable intensity in Bragg spots for / = 6, (m = 0, n = 2), / = 7 (m = 1, n = - 2), 1 = 10 (m = 1, n = - 1), 1 = 13 (m = 1, n = 0). The intense diffuse lines for 1 = 13 and I = 10 mask the Bragg spots but for 1 = 7, we observe one Bragg peak lying
the diffuse line. Its position is consistent with the same helix of radius 9 A, and its intensity is weak. According
to this simple model, the two layers 1 = 6 and 1 = 7 (Fig. 2c) should be identical. In fact, the intensity of
the Bragg spots is higher on level 1 = 6 than on level
1 = 7 and the position of the intense visible peaks corresponds to a larger value for S 1. in this level (I = 6). The same problem rises for the comparison
between the layers 1 = 9 and 1 = 4 since Bragg spots
are not unambiguously identified for / = 4.
Nevertheless, the repartition of the intensity on the
two layer lines 1 = 6 and / = 9 is consistent with a
helicoidal structure. As no other lines correspond to
the same period, we must admit that this helix is continuous (Fig. 2b), and that the apparent pitch corresponds to 20.96 A/n. The absence of higher level layer line is probably a consequence of the imper-
fections of the crystal (the Bragg reflexions are only
visible in a limited domain of scattering vector [9]).
If the apparent period is divided by n, the helix
is formed with molecules or part of molecules with a
n-fold symmetry and the structure factor is propor- tional to nJ_(2 nRS 1.) where m is an integer. From
the positions of the maxima of intensity, we deduce
that there are two components to the 3D helicoidal
structure a first one with a two-fold symmetry and a
Fig. 2. - Schematic representation of the diffracted intensity versus the scattering vector
S(I
S I = 2 sin0
for one columnof infinite length with three different structures :
a) Uniaxial stack of discs of radius of gyration R. The distance between two discs is p. The diffracted intensity is proportional
to 6 S.. - ’ j 2(2 1tS 1. R). Sz and S 1. are the two components of the scattering vector respectively parallel and perpendicular
p
to the column axis, m is an integer and Jo the zero order Bessel function.
b) Continuous helix of radius R and pitch P. The diffracted intensity is proportional to b Sz - 1 J’(2 7rS.L R); n is an
integer and Jn the nth order Bessel function.
c) Discontinuous helix of radius R and pitch P with points lying on equidistant planes perpendicular to the column axis
at a distance p. The relation between the period C, the pitch P and p is C = 13, p = 3 P. The intensity is proportional to
b S - c Y- J (2 1tS1. R)J where l, m, n are integers which verify the relation / = 13 m + 3 n. (In fact figures 4a
and 4b are described by these last two relations in which n (respectively m) is equal to zero.)
Notice that we have the first maximum of each Bessel function and neglected the contribution of highest order n > 4. We have plotted 1, m (therefore in figure 2a, n = //13) and the relative value of intensity maxima for each layer line of the top of figures 2b and 2c. The diffraction patterns of different kinds of assemblies of parallel columns derive from these three basic
examples : for a column made of i identical continuous helices obtained by successive rotations of 2 7c/i around their common
axis, the scattered intensity vanishes unless n = 0 modulo i. If the columns form a 2D array, only the zero layer line is dis- continuous, but if we have a 3D lattice, all the layer lines become discontinuous.
d) Schematic representation of the pattern of figure 2a : we have a superposition of figure 2a to which we add a super-
structure of period P, figure 2c, with a large radius R ~ 9 A, and figures 2b in which there are only two layers corresponding
to n = 2, n = 3 with R equal to 4.3 and 4.9 A respectively. The diffuse scattering indication of the molten state of the chain is not shown on this schematic drawing.
356
mean radius of 4.3 A and a second one with a three- fold symmetry and a radius 4.9 A. The existence of a
continuous helix inside a 3D crystal of regularly
stacked molecules can be described as follows : In each column the same equation of a helix gives
the relation between the in-plane coordinate and the
z coordinate of atoms, but in a given column the
values of z are discrete : z = wp + 6 where w is an
integer and 6 is fixed for one given column, but can take all the values between 0 and p. The last feature that we have to take into account is the existence of the diffusive discs. All these discs have the same aspect and correspond to a mean period of 4.82 A (Fig. 2a)
with a modulation of 20.96 A. The modulation only
has a longitudinal component and therefore the helicoidal order has disappeared at this level. The
intensity dependence along these planes agrees with the calculated one for a conical core made of the carbon atoms of the ring (CH2CP)3 using the structural data of references [6] and [7] (Fig. 3). The presence of
a continuous line means that, if the cones are regularly
stacked in columns, no correlation in their positions along the column axis is established between neigh- bouring columns. Let us put all these observations
together in order to have an idea of the molecular
organization : the conical molecules are stacked in columns with a period of 4.82 A. The aliphatic chains
of each molecule are in a disordered state, but the
paraffinic medium is not unformely spread around
the core and is wounded in a helix (Fig. 4).
Parallel helices are correlated along the z direction
with fluctuations of weak amplitude. These fluctuations
are responsible for the width of the large angle Bragg
reflections. Between the helix of paraffmic chains
and the non-helicoidal central part of the column,
the benzoate groups form a continuous helix : the orientation and the axial positions are related in a
column, the orientation at a given level is the same for
two equivalent columns but the location of that part of the molecule is not identical for each column.
Fig. 3. - Form factor of a conical core rotating around its
axis calculated from the crystal structure data [6, 7] at the
level of the first diffuse plane : full line : taking into account only the carbon atoms of the ring (CH2l/»3; dashed line : adding to this ring an external shell including the six
-O-C linkages.
Fig. 4. - Schematic representation of the helical structure of the lc low-temperature mesophase (section perpendicular
to the column axis) : a, tribenzo conical core + the six benzoate groups; b, the paraffmic crown consisting of the
six n-dodecyl chains.
This correlation loss on going from the outside of a
column towards its core may be induced either by
the flexibility of the ester linkages or by the existence
of an orientational disorder of the cones pointing
up or down.
The centre of the column is isotropic around the
column axis. All this description is derived from a
qualitative analysis of the fibre pattern and this analysis does not provide any information about the
phase relationship between the different parts of the helix. We can notice that weak spots seen on the level I = 1 (m = 1, n = - 4) can be due to inter-
mediate zones between the benzoate group (R = 4-5 A)
and 9 A. Unfortunately the number of parameters that one should introduce in a quantitative evaluation
is too high in comparison with the precision of experi-
mental data (the imperfection of the crystal is res- ponsible for the low resolution in wave vector and for the small number of visible reflexions). One important point about the molecular conformation
concerns the orientation of the conical cores. The
proposed space group P 2t 2i 2i implies that the two
columns of the unit cell are polarized in opposite
directions but in fact a space group P 212 21 is not
excluded. In such a case the two possible orientations
are still equally probable. Then the orientation of the cones in one column is probably maintained over a large correlation length, but the orientation inside
a column is independent of the position of the column
in the unit cell. This second space group implies a large longitudinal displacement of the cores relative
to the external part of the columns and probably
is the best choice for the description of this organiza-
tion in which a high degree of disorder coexists with
a rather well defined periodicity. On heating this mesophase, the 3D lattice and the modulation with
a 20.96 A period disappears (Fig. 1, iv) : a diffuse
scattered intensity replaces the 2nd and 3rd layer lines.
The helical structure therefore remains although the
chains are in a less ordered state and the correlation between columns is lost. The 2D columnar lattice is hexagonal and exhibits the same structure as that of the Dbo columnar phase of triphenylene ethers [10].
