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Smectic a1 ↔ a2 transition of n_c-60.8 : a
two-dimensional phase separation of the molecular endgroups
H. Fadel, D. Guillon, A. Skoulios, F. Barbarin, M. Dugay
To cite this version:
H. Fadel, D. Guillon, A. Skoulios, F. Barbarin, M. Dugay. Smectic a1 ↔ a2 transition of n_c-60.8 : a two-dimensional phase separation of the molecular endgroups. Journal de Physique, 1989, 50 (3), pp.375-385. �10.1051/jphys:01989005003037500�. �jpa-00210922�
Smectic A1 ~ A2 transition of NC=60-8 : a two-dimensional
phase separation of the molecular endgroups
H. Fadel (1,2), D. Guillon (1,2), A. Skoulios (1,2), F. Barbarin (3) and M. Dugay (3) (1) Groupe des Matériaux Organiques, Institut Charles Sadron (CRM-EAHP), ULP-CNRS, 6
rue Boussingault, 67083 Strasbourg Cedex, France
(2) Institut de Physique et Chimie des Matériaux de Strasbourg, UM 380046 CNRS-ULP- EHICS, 67083 Strasbourg Cedex, France
(3) Laboratoire d’Electronique, UA 830, Université Blaise Pascal, 24 Avenue des Landais, 63170 Aubière, France
(Reçu le 30 mai 1988, révisé le 7 octobre 1988, accepté le Il octobre 1988)
Résumé. 2014 On a étudié par diffraction des rayons X la transition de phase smectique A1 ~ smectique A2 d’un système mésomorphe unaire. Le smectogène considéré, polaire mais symétrique, était le 4-cyanohexyloxybenzylidène-4’-octylaniline. Les intensités des réflexions de
Bragg ont été mesurées en fonction de la température. Les données expérimentales ont été analysées selon un modèle structural précisant la localisation des groupes cyano et méthyle
terminaux à la surface des couches smectiques. La transition A1 ~ A2 a été ensuite interprétée en
termes d’une séparation de phases bidimensionnelle des groupes terminaux.
Abstract. 2014 The smectic A1 ~ A2 phase transition of a one-component liquid crystalline system
was studied with X-ray diffraction. The smectogen used was a polar but symmetrical smectogen, namely the 4-cyanohexyloxybenzylidene-4’-octylaniline. The intensities of the Bragg reflections
were measured as a function of temperature. The experimental data were analysed according to a
structural model describing the location of the cyano and methyl endgroups of the molecules at the surface of the smectic layers. The A1 ~ A2 transition was then interpreted in terms of a two-
dimensional phase separation of the endgroups.
Classification
Physics Abstracts
61.30 - 64.70 - 64.90
Introduction.
Three types of smectic layering have been described in the literature so far : the monomolecular (such as Al), the bimolecular (such as A2), and the sesquimolecular (such as Ad) layering [1]. They characterize smectic phases which are well defined from a ther- modynamic point of view and which are involved in first- or second-order phase transitions [2- 9]. Experimentally, they are differentiated from one another by their stacking period,
determined by X-ray diffraction : the monomolecular layering is characterized by a period comparable to one molecular length, the bimolecular layering by a period comparable to two
molecular lengths, and, finally, the sesquimolecular layering by a period intermediate between one and two molecular lengths [1].
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01989005003037500
The A, +-* A2 phase transition has been studied by high resolution X-ray diffraction on
macroscopically oriented samples. The systems used were binary mixtures of two smectogens,
one being symmetrical, the other highly polar and dissymetrical [8]. Analyzed from a phenomenological point of view, the transition was found to be first or second order
according to the composition of the mixture. For the critical smectic A2 fluctuations near the second order transition, the temperature dependence of the susceptibility and correlation
lengths was found to be in agreement with heat-capacity measurements [6], but in disagreement with current theoretical expectations [7]. Clearly, further experimental and
theoretical work, especially with one-component systems, is still needed to provide a better understanding of the phase transition and to bring out the essential factors that actually
govern it.
Now, the A, --> A2 transition was recently found to occur as a function of temperature also
with a pure smectogen, namely the N==C201360.8 [9]. This compound belongs to a novel class
of polar but symmetrical cyano mesogens - the 4-cyanoalkoxybenzylidene-4’-alkylanilines (abbreviated in the following to N==C-nO.m) :
In contrast with the polar dissymetrical smectogens quoted above, the molecules here are symmetrical and are formed of a central aromatic core and of two terminal aliphatic chains.
The cyano endgroup is not carried directly by the aromatic core, but instead is attached to the free end of one of the aliphatic chains ; it is thus mechanically and electrically decoupled from
the aromatic moiety.
The essential characteristic of the N-C-nO.m mesogens lies in the fact that, in spite of
their clear dipolar structure, the molecules are highly symmetrical from the standpoint of their global chemical architecture. As a result, the smectic layers are necessarily single layers of
molecules. Due to the amphiphilic character [10], the aromatic cores and the aliphatic chains
of the molecules are segregated in space. In lateral register with one another, the aromatic
cores form fairly well defined sublayers covered on both faces by the disordered aliphatic
chains (see Figs. 3 and 4 in Ref. [11]). Depending upon the exact chemical nature of the mesogen and the experimental temperature conditions, the monomolecular smectic layers pile up over one another in two different ways, so as to produce either single- (A,) or double-layered (A2 ) smectic systems. The point of difference between the two structures is simply connected with the specific location of the cyano endgroups with respect
to the molecular layers. Located at the surface of the monolayers, the polar groups are either
equally distributed on both faces of each monolayer, leading to the formation of
AI phases - or else, significantly accumulated on only one face, inducing an antiparallel stacking of the monolayers and giving rise to A2 phases (see Figs. 3 and 4 in Ref. [11]).
The case of N---C--60.8 is of especial interest to consider here as, to our knowledge, it
offers the first example of a phase transition between Ai and A2 that occurs with a pure
compound [9], and also as it rules out the formation of sesquimolecular Ad phases because of
its symmetrical architecture :
The X-ray diffraction pattems registered for this product above 64 °C contain a single Bragg
reflection at 30.6 A corresponding to the thickness of a single-layered smectic structure ; on the other hand, the X-ray pattems registered below 64 °C contain two Bragg reflections at 61.1 and 30.6 A corresponding to the thickness of a double-layered structure. The 61.1 À
reflection fades out rapidly upon heating within a narrow temperature range, indicating a
rather abrupt and reversible transition between the two smectic structures. Differential
scanning calorimetry measurements, performed with various heating rates (from 0.5 to
6 K/mn), show that the Az +-+ Ai transition is hardly but unambiguously detectable (Fig. 1) ;
the value of the enthalpy involved is indeed very small (0.12-0.14 kJ/mol) in consideration of the experimental precision (Mettler FP85). Regarding now the phase detected below 47.7 °C,
its double-layered smectic B2 nature is ascertained by experiments of total miscibility with
N--C-40.8 [9, 11] ; indeed, as also reported previously [9], a direct identification of
B2 by X-ray diffraction is very difficult, for the N---C--60.8 smectic B phase is monotropic in
nature and hence metastable.
The present paper is intended to describe as thoroughly as possible the A, +-+ A2 phase
transition of N-C-b0.8 using X-ray diffraction. However, because N==C-60.8 does not display a nematic phase, the preparation in a magnetic field of macroscopically and uniformly
oriented samples of smectic liquid crystals - as required, in principle, for a clear detection of
any smectic fluctuations - was difficult to achieve. This prevented us from carrying out a systematic X-ray investigation of the transition, with emphasis on the smectic fluctuations,
similar to that mentioned above [8]. Instead, we took care of measuring the relative intensities of the Bragg reflections corresponding to spacings of one and two molecular lengths, of discussing the experimental observations in detail, and of giving a molecular interpretation of
the phenomena involved.
Experimental.
X-ray diffraction data were collected using a vacuum small-angle camera equipped with a bent gold-plated glass mirror (nickel filtered K a copper radiation from a GX20 Eliott rotating
anode X-ray generator) and a CEA-LETI linear position-sensitive detector. Samples were
contained in 1 mm thick Lindemann capillaries, and heated in a custom-made electrical oven
whose temperature was controlled by a TP25 Haake thermal regulator with an accuracy of about 0.1 °C. In order to get the homogeneous X-ray patterns needed in this work for an easy and meaningful measurement of the relative intensities of the Bragg smectic reflections
corresponding to the single- and double-layered structures, carefully selected powder samples
were used. Examples of diffraction patterns registered are illustrated in figure 2 ; they clearly
show the Bragg peaks corresponding to the single- and double-layered smectic structures of
Fig. 1. - Differential scanning calorimetry diagram of N=C-60.8 registered at 4 K/mn. Arrow shows the A2 H A1 transition.
Fig. 2. - Small-angle X-ray diffraction patterns of smectic N=C-60.8, registered with a linear position sensitive detector at three temperatures, in 30 min. Maximum intensity measured was of about
40 000 counts ; shown reciprocal spacings were explored in 40 steps ; reflection II is the fundamental
Bragg harmonic of the A2 smectic structure, while reflection 1 is either the second harmonic of the
A2 or the fundamental harmonic of the Ai structure ; the substracted baselines were estimated by a least-square polynomial regression method, from intensity data outside Bragg peaks.
N---C---60.8, along with the progressive disappearance of the bilayer signal as a function of
increasing temperature.
Diffraction measurements were carried out every 0.2 °C, both by heating and cooling in the
range from about 59 °C up to the transition temperature at 64.2 °C. In agreement with the previous observations [9], the thickness of the smectic layers proved to be independent off temperature. For a measurement of the intensities ln and II of the II and 1 Bragg reflections,
the baselines were estimated by a least-square polynomial regression method (from intensity
data outside the Bragg peaks), then substracted from the measured intensity distributions.
Experimental results were not corrected for the effect of beam height, nor for the effect of the
powder texture of the samples ; they are shown in figure 3 where (the non corrected, and hence overestimated) IIIII, I is plotted as a function of temperature. Clearly, the A2 H Ai transition is abrupt as already reported [9], the III/II, intensity ratio decreasing dramatically upon heating within less than 2 °C. In addition, it strongly resembles a second
order phase transition, since III/II varies with temperature in a continuous way, falling down
to zero at 64.2 °C with a slope which apparently is infinite. Because of the experimental uncertainty, it is not possible to rule out the presence of discontinuous drop of the ln intensity near the transition temperature, indicative of a weak first order phase transition.
This interpretation is supported by the observation of an extremely weak, but real differential
calorimetry signal at 64 °C.
Fig. 3. Temperature dependence of III/II. The full line was drawn as a guide for the eyes.
Structural model.
To interpret the above experimental observations, it is useful to come back to the structural model presented previously in reference [9] (Fig. 4a). This model takes into account the fact that the presence of a Bragg reflection corresponding to double layers does not necessarily imply perfect double-layering of the molecules, with complete segregation of the cyano and the methyl endgroups into distinct planes altemately piled up in space. In reality, it only says that the molecules inside each monolayer (half of the double layer) are oriented predomi- nantly, but not necessarily completely, in a same up or down direction, in a sort of a ferroelectric intralamellar arrangement, and that the so « polarized » monolayers are stacked
over one another in an antiferroelectric manner.
Fig. 4. - Structural model : a) ferroelectric intralamellar ordering of the molecules with antiferroelec- tric interlamellar stacking of monolayers ; b) electron density distribution of a fully extended molecule
along its elongational axis ; c) schematic view of the molecular arrangement in a bilayer with an
intralamellar ferroelectric order parameter 1 - 2 XI.
Proper use of the structural model in a quantitative analysis of the thermal dependence of
III/II requires, of course, preliminary definition of two order parameters - one describing
the ferroelectric intralamellar arrangement of the molecules, the other describing the
antiferroelectric stacking of the « polarized » monolayers. In addition, it must allow the order
parameters to fluctuate, at least to some extent. It is out of the question for us to undertake
here such a detailed study, because of the obvious inherent difficulties of the theoretical
thermodynamic calculations implied, the coupling of the two order parameters being as yet
impossible to handle correctly from a statistical thermodynamic point of view. We decided, therefore, to only consider the simple case where the antiferroelectric stacking of the
« polarized » monolayers is complete and where the ferroelectric intralamellar arrangement
of the molecules is temperature dependent, without fluctuations from layer to layer.
The antiferroelectric stacking of the « polarized » monolayers being complete seems quite a
reasonable assumption, since it is mainly due to the antiparallel association of the cyano
endgroups of adjacent layers. Indeed, the electrical coupling energy of two antiparallel cyano
dipoles (dipole moment: g = 3.5 Debye units [12]) standing at a lateral distance
r = 3.5 A [13] (corresponding to the van der Waals diameter of a cyano group) is very high :
J.L2/4 7TEO r3 = 0.179 eV = 2 075 K. This high energy allows for only a very small amount of
unpaired cyano groups, of the order of 0.2 % at about 60 °C. The amount of unpaired cyano groups should in fact be somewhat larger because of the dilution effect due to the location of the cyano groups at the surface of the monolayers among the methyl terminal groups of the molecules. Finally, it must be noted that the cyano endgroups are not associated perma-
nently ; it is beyond all question that they must come together and continuously separate from
one another in a dynamical way.
With these assumptions, the structural model that can be described is the following. Let X
and 1 - X be the mole fractions of the molecules oriented respectively up and down. The net
polarization of each monolayer is hence : |l - 2 X|. With p (x ) being the electron density
distribution of a fully extended molecule along the layer normal (Fig. 4b), the electron density
distribution of a monolayer will be : X p (x ) + (1 - X) p (- x ). For a double layer made up of
two « polarized » monolayers superposed in an antiferroelectric way (Fig. 4c), the electron
density distribution may be written [14] as :
where L is the length of a fully extended molecule and where the symbol + stands for a
convolution operation. The structure factor F (h ) - that is, the amplitude of the X-ray beam
scattered at a Bragg angle defined by the reciprocal spacing h = 2 sin 0/,k - is given by the
Fourier transform of the electron density distribution :
(
where f (h ) = a (h ) + ib (h ) is the Fourier transform of p (x ) and f*(h) = a (h ) - ib(h) is
the complex conjugate of f(h). Knowing that the intensity of the X-ray beam scattered at a
reciprocal spacing h is 1 (h) = 1 F (h ) 12, it is easy to calculate :
This expression does not take into account the Debye-Waller effect due the thermal agitation
of the molecules along the layer normal ; however, it can easily be seen that the corresponding attenuation of I (h = 1 IL) with respect to 1 (h = 1/2 L ) is negligible (of the
order of only a few percent for L = 30 Â and for an amplitude of thermal agitation of 5 Â).
It is of interest to analyse now the experimental data of this work (Fig. 3) with the
molecular model just described. As C is a constant whose value is determined by the longitudinal electron density distribution of the molecules, it is clear that any thermal variation of IIIII, = I(h = 1/2 L)II(H = 1/L) reflects the variation of the ferroelectric intralamellar order parameter Il - 2 XI | alone. In order to calculate the temperature
dependence of the order parameter, it is necessary to get an estimate of C before anything
else. This is easy to achieve from the knowledge of the number of electrons contained in the various parts of the molecule (13 for N-C-, 56 for -(CH2)60-, 56 for -(CH2)7-’ 94 for
-lP-CH N-lP-, and 9 for -CH3), and from the knowledge of the lengths along the layer
normal of their electron clouds as estimated from CPK molecular models (1.15, 8.1, 11, 8.1
and 2.3 Â, respectively). The corresponding linear electron density profile is shown in
figure 5. With such a profile, the constant C is found to be equal to 0.74. The thermal
variation of the (overestimated) order parameter i - 2 X | deduced from the (non corrected) experimental data using this value of C is represented in figure 6.
Fig. 5. - Longitudinal electron density distribution of a fully extended N=C-60.8 molecule.
Fig. 6. Temperature dependence of the ferroelectric intralamellar order parameter around A2 H Ai phase transition.
The question reasonably arises now of how much the value of C, and hence that of the order parameter, may depend upon the exact electron density profile chosen for the system.
Actually, this profile is characteristic of the chemical architecture of the molecules and, therefore, cannot really be modified very much. Nevertheless, attempts to calculate C by changing the lengths of the various constituent parts of the molecules by as much as 10 % have
been performed resulting in values of C included in the range from 0.6 to 0.9. The impact of
such an overestimated dispersion of the values of C on the value of the order parameter is, however, very small. For example, at about 62 °C where the order parameter is the highest,
values found for | - 2 XI | are in the range from 0.7 to 0.9. (Real values, from corrected intensity measures of the Bragg reflections, must in fact be somewhat smaller.)
As a conclusion, the results shown in figure 6 regarding the thermal dependence of the
ferroelectric intralamellar order parameter are little affected by small changes of the electron
density profile chosen. In addition, the numerical values found, and particularly those found for the maximum order parameter at 62 °C, are perfectly plausible. In spite of its simplicity,
the structural model used in the present work turns out to be remarkably realistic.
Molecular interpretation.
Up to this point, the analysis of the experimental data was carried out only from a structural point of view, in terms of an order parameter describing the orientational arrangement of the molecules inside the smectic layers. It is time now to try to understand the structural behavior observed, on a molecular level, especially around the A2 +-+ Ai transition.
As stated above, the up and down orientation of the molecules within the layers determines
the exact location of the cyano and methyl endgroups at the surface of the monolayers (Fig. 4). By ignoring the bulk of the molécules, and by only taking into account the cyano and
methyl endgroups, the smectic structures under consideration may be described as the
stacking of two types of planes, A and B, altemately superposed, A being the median plane of
the bilayers, and B their external surfaces (Fig. 7). The fraction X of the molecules oriented
upwards in the monolayers is in fact the fraction of molecules having their cyano endgroup in
the median plane of each bilayer and their methyl endgroup in the planes corresponding to
the external surfaces of the bilayers. From the experimental values of the order parameter
Il - 2 X (T) | = P (T) (Fig. 6) it is easy to determine the relationship between the tempera-
ture and the cyano concentration in the median planes of the bilayers (Fig. 7a) : X(T) = 1/2:t P (T)/2. With P ( T ) in the range from 0 to 1, the branch X(T) =
1/2 + P (T)/2 gives values of the cyano concentration in the median planes, varying from 1/2
to 1 ; and the branch X (T ) = 1/2 - P (T )/2 gives values from 0 to 1/2. The selection of the
one or the other branch is totally conventional : it simply depends on whether or not the
formation of the bilayers is considered as being an enrichment of the median planes in cyano
endgroups. In the following, only the branch X ( T ) = 1/2 + P ( T )/2 will, arbitrarily, be taken
into account. Thus, depending upon the value of P (T), the cyano concentration in the median planes can vary from 1/2 to 1, while it varies from 0 to 1/2 at the external surfaces of the bilayers.
Quite interestingly, figure 7a closely resembles a phase diagram for a binary liquid mixture presenting a miscibility gap at temperatures lower than an upper critical solubility
temperature (see Fig. 7b left). The curve gives the composition of the two coexisting phases as
a function of temperature. By analogy, the transition from Ai to A2 may, formally, be interpreted as a phase separation of the cyano and the methyl endgroups in binary mixture [15]. The two coexisting phases may then be taken as being the median planes of the bilayers
on one hand, and the external surfaces of the bilayers on the other. The weakly first-order
A, *-+ A2 phase transition observed would correspond to the appearance of a phase separation
