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X-ray studies of the smectic C˜ phase and transitions between reentrant nematic, smectic A1, AD and C˜
phases in binary mixtures of polar mesogens
T. Lobko, B. Ostrovskii, W. Haase
To cite this version:
T. Lobko, B. Ostrovskii, W. Haase. X-ray studies of the smectic C phase and transitions between˜ reentrant nematic, smectic A1, AD and C phases in binary mixtures of polar mesogens. Journal de˜ Physique II, EDP Sciences, 1992, 2 (5), pp.1195-1213. �10.1051/jp2:1992195�. �jpa-00247701�
J. Phys. II France 2 (1992) l195-1213 MAY 1992, PAGE l195
Classification Physics Abstracts
61.30 64.70M 61.10
X-ray studies of the smectic i~ phase and transitions between
reentrant nematic, smectic Ai, A~ and i~ phases in binary
mixtures of polar mesogens
T. A. Lobko (I), B. I. Ostrovskii (I) and W. Haase (2)
(1) Institute of Crystallography Academy of Sciences of the U-S-S-R-, Leninsky prosp.59, Moscow, 117333, Russia
(2) Institut for Physikalische Chemie, Technische Hochschule Darrnstadt, 6l00Darrnstadt~
Germany
(Received 5 December I99I, accepted 8 January 1992)
Abstract. We report X-ray diffraction measurements in nematic, smectic Al, Ad and
b phases for terminally polar three-ring compounds belonging to 4-[N-(4-n-alkoxysalicylidene)]- 4'-cyanobiphenyl series (nOSACB). A new topology of phase diagram with the reentrant nematic (N~~), monolayer smectic (Ai), overlapped smectic (A~) and commensurate biaxial b phase
was
found in binary mixtures of 40SACB and 90SACB homologous. It includes Aj-b, N~-b and
A~-C phase transition lines, as well as triple N~~Ajb and N~~A~C points. The parameters of the monoclinic two-dimensional © unit cell and tilt angles of molecules have been determined. The
intensity asymmetry and the positions of the off-axis reflections which are characteristic of the
b phase
are discussed on the basis of models with competing order parameters. Our results directly indicate on the strong coupling between incommensurate density modulations of
Ai and A~ types, thus confirming the theoretical description of b phase
as a two-dimensional escape from the incommensurability.
Introduction.
Since the discovery of the first transitions between different smectic A phases [1, 2], considerable efforts have been concentrated on the understanding of the unusual properties
of so-called « frustrated smectics » j3]. The structure of such phases composed of terminally polar mesogenic molecules arises from a competition between two different length scales, namelly, the molecular length L and the length L' of the suitably joined pairs of molecules.
The most unusual features of these objects are the variety of lamellar packing j2, 4, 5], multiple reentrant phenomena [4-8] and the simultaneous existence of incommensurate
density modulations in one and two directions [2, 4, 9, 10].
The variety of nematic and smectic A phases consisting of polar molecules can be characterized unambiguously by X-ray diffraction. The scattering by the nematic phase may
have two diffuse maxima with wavevectors qi = 2 «IL and q~ =
2 «IL' (L~ L'~ 2L)
corresponding to smectic fluctuations with preferred layer spacings for monolayer and dipolar ordering respectively. The monolayer smectic Ai phase shows a Bragg-like peak at qi and possibly a diffuse maximum at q~. In contrast, the partially bilayer (overlapped) A~
phase has a diffuse maximum at qi and a sharp peak at q~. In the incommensurate A~~ phase two collinear modulations of incommensurate wavelength are simultaneously
condensed, producing sharp diffraction peaks at qi and q~, the ratio qi/q~ being irrational. The commensurate antiphases (I, A~~~ and i~)
are identified by the appearance of off-axis reflections, indicative of the additional translational order in the plane of the layers, such that
two vectors q~ sum to form qi.
The topology of the polar smectic A phase diagrams is successfully interpreted within the frame of the phenomenological approach of Prost and Barois [3]. The theory is based on the introduction of the two order parameters $r and ~b, which are characteRstic of the mass-density
p and local polarization P modulations respectively. Depending on the parameters of the
model, one or both order parameters may condense. One of the important terms
incorporated in the model is the coupling term Re ($r * ~b~) which favours commensurate lockin of qi and q~ vectors. In the case when the coupling term dominates in the free energy
density, the commensurate phases are stabilized, allowing the existence either of a bilayer
smectic A2 Phase with two collinear Vectors qi = 2q~, or modulated smectic I, A~~~~,
C phases in which the fundamental Vectors of reciprocal lattice q( and qj' are not collinear with qi (q( + ql'= qi). In the opposite case the incommensurate Ai~ phase may be stable. The
including of the additional mechanisms of one-dimensional melting makes the problem of
smectic Al, and A~ layering coexistence more complicated. For instance, the dislocation loop melting theory predicts different ways in which the Ai-A~ phase boundary may terminate ill ]. In the mean field approximation the theory predicts the existence of a Ai-A~ critical
point. However, when the effect of fluctuations is considered, several topological possibilities appear, including the Ai-A~ termination as a critical point or as a nematic island.
The topology of Ai-A~ phase diagram strongly depends on the qi/q~ ratio (l~
qi/q~~2). For small qi/q~ar I values the phase diagram shows the absence of the phase
transition line, but only a continuous evolution of Al from A~ [2, 4, 5]. Hence, it is possible
to go from Ai to A~ phase by only varying the layer spacing, that is characteristic of upper critical region. For the relatively large qi/q~ a 1.3 values the stability region of the Ai and Ad phases are separated, as a rule, by the nematic gap [2, 4, 7]. In those few cases, when the Al- A~ transition line still exists in the phase diagram, it rapidly terminates at the multicritical
NAIA~ or N~~AIA~ points [2, 4, 12-14], or finishes with an island of the nematic phase [15, 16], or transforms into the line of phase transitions to the i~ phase [2, 4]. It appears that smectic A peRodicity as a common case cannot support two incommensurate competing spacings and prefers to escape frustration by going over to two dimensional phases
(I, A~~~~, i~) rather than a one-dimensional incommensurate phase.
Since the first observations of the antiphase (I) [9] and Rbbon (i~) II?] phase in polar
mesogens the number of X-ray investigations of these objects have been reported [2, 4]. The
high resolution X-ray studies indicate the complicated behaviour of the system in the vicinity
of Ai-A and Ai-i~ phase boundaries. Safinya et al. II 8] had found the intermediate region of
coexisting of incommensurate and i~ fluctuations in Ai phase in vicinity of Ai-A transition for
N° 5 X-RAY STUDIES OF THE SMECTIC C PHASE l197
DB7N02 compound. The careful study of the i~ phase in DB~ON02 compound was carried out by Fontes and coworkers [8]. It was found that the Ai-i~ transition in this mesogen is
preempted by the region of the smectic C phase.
Here we present the X-ray scattering studies of lamellar ordering in binary mixtures of
terminally polar mesogenic compounds belonging to 4-[N-(4-n-alkoxysalicylidene)]-4'-cyano- biphenyl series (nOSACB). A new topology of phase diagram with the reentrant nematic-
smectic i~ transition line and two triple N~AIi~ and N~Aifi points was detected in binary
mixtures of 40SACB and 90SACB homologoues. The cross-sections of phase diagram
corresponding to the A~-i~, Ai-i~ and N~~-i~ phase boundaries are discussed in details. The asymmetry and positions of diffraction peaks are discussed based on models with competing
order parameters. The electrooptical behaviour of i~ phase doped with chiral dipolar
substances (fi phase) is considered parallel with structure investigations.
Experimental technique.
The experiments were carried out using two types of computer controlled diffractometers with linear position-sensitive detectors for data collecting and CUK~ radiation. The first set-up (I) included a focussing horizontal two-circle STOE diffractometer with a curved Ge(lll)
monochromator II 9]. The second set-up (II) utilized a three slit collimation scheme with a Ni
filter or graphite monochromator [20]. The longitudinal resolutions so obtained were
Aqjj =3.2x10~~h~~ (1) and Aqjj =2.2x10~~h~~ (II) full width at half maximum
(FIVHM). The components of the scatteRng wave vector qjj and qi are parallel and
perpendicular to the director n respectively (q = ~ " sin o
=
2 «Id, d is a layer spacing).
A
Thus, measurements of the longitudinal correlation lengths were limited to fjj = 2/Aqjj <
650 h (I) and 900 h (II). The transverse out of plane resolution was determined by the illuminated sample height of 4 mm to be 0.04 h-I (FIVHM). The actual width of profiles in the qi direction was limited by the 1-2° sample mosaic (FIVHM), In our data analysis peak shapes were modeled by simple Lorentzian line shapes. The complicated spectra were
analysed with the least-squares fits by a sum of up to three Lorentzian peaks, yielding peak intensity, position and width.
In order to investigate the off-axis reflections that are characteristic of commensurate modulated phases of the I, fi type,
we used the precision rotation of sample around an axis
orthogonal to the director and the scattering plane (angle w) and the rotation in the plane perpendicular to the incident beam (cradle angle or X). An applied magnetic field of 0.6 T
provided the uniform director orientation in the sample. The mesogens in a thin-walled quartz capillary 2 mm in diameter were placed in an oven, providing the temperature control of
0.01K.
The identification of different liquid crystalline phases were carried out using the
characteristic features of X-ray diffraction pattems. The range of stability of reentrant
nematic phase was proved additionally via optical microscopy and observation of the
Freedericks transition in a planar oRented cell. The threshold of the transition in the N~~ phase was found to be typical of cyanoderivatives with positive dielectric anisotropy,
U~~ =
1.5-2 V.
The intensities profiles in the wide scattering angles region show broad, liquid like peaks
centered at qi~ m 1.5 h~ corresponding to average intermolecular distance of m 5 h in the
smectic planes. The angular width of the profiles corresponds to the interlayer positional
correlations with the length fi S 10h. Thus, the smectic phases under study have to be
referred to smectic A rather a hexatic or lamellar crystalline phases (of the type of smectics B, G, etc.).
Experimental results and interpretation.
In nOSACB homologous series for small values of n S 7 the monolayer AI Phase is stable.
Yet for the large n = 8, 9 values thermodynamically stable are overlapped A~ and a tilted
modulated i~ phase. For example, 90SACB on heating melts directly from crystalline to
A~ phase at 103 °C. The monotropic i~ phase is observed on cooling at temperatures below
98 °C. In a mixture of two homologoues 40SACB and 90SACB having substantially
different lengths of hydrocarbon chains, we have observed nearly the whole set of smectic
phases that are characteristic of frustrated smectics, namely: N, N~, Ai, A~ and i~ (Fig. I). The smectic A~ phase in a mixture mainly consists of 90SACB dipole-dipole pairs
~o~
T°C
~ N A~
300 '~
~_
'~-~
A~
o.7 o.9 x
zoo
~
A~
O O.2 O.4 O.6 O.8 X
40SACB 90SACB
Fig. I. Phase diagrwn for 90SACB-40SACB mixture~ x is the molar fraction of 90SACB. The inset shows the structure of 90SACB and the portion of phase diagrwn with the reentrant nematic -C transition line. The broken curves indicate the melting line on heating and N-I transition line.
N° 5 X-RAY STUDIES OF THE SMECTIC C PHASE l199
with the degree of overlapping d~/L
m I.4 (the stereomodel predicts for a fully extended molecular lengths L
=
30.5 h 90SACB and L
= 24.5 h 40SACB). The regions of the
thermodynamic stability of smectic A~ and C phases diminish as the concentration of a component having a shorter aliphatic chain increases, replacing by the nematic, reentrant nematic and monolayer Ai phase. The smectic A
j and A~ phase prove to be incompatible on
the phase diagram. However, in distinction from the previously reported polar smectics phase diagrams where A
i and A~ phases terminate at the multicfitical N~~AIA~ points [4, 13, 14], our
data reveal the N~~-i~ transition border in between the Aj and A~ phases, yielding the
existence of two N~~AIi~ and N~~A~i~ triple points.
As a function of temperature different cross-sections of the 90SACB-40SACB phase
diagram were studied. Table I summarizes our diffraction data. For x
~ 0.835 (x is the molar
fraction of 90SACB in a mixture) the high temperature smectic A phase was found to be
overlapped A~. The A~ phase is characterized by resolution limited sharp peak at incommensurate position q~
= (0 ; 0 qjj~), qjj~ = 2 «IL' = 0.lsl to 0.144 h-I (L'
=
41.5-43.61), in reciprocal space. The transition to low-temperature smectic phase for powder averaged samples manifest itself by the additional appearance of the sharp Debey rings corresponding to incommensurate wavenumbers ql'
= 2 w/48.5 h
=
0.129 h~ and qi
=
2 w/28.2 h=0.223Ji~~ (Fig. 2). The reciprocal lattice vector q~ corresponding to A~
periodicity varies continuously with decreasing of temperature, transforming without and
jump to one of the fundamental vectors of the low-temperature phase. The mosaic disorder of the samples prohibits a determination of relative orientation of the qi; ql' and q(=
q~ peaks, necessary for understanding of the type of layering in mesogen, which may be either
commensurate modulated fi
or the one-dimensional incommensurate A~~. The
decomposition of the compounds at high temperatures corresponding to nematic phase (t a 220 °C) makes impossible to determine the effective orientation of the director in the
magnetic field. In order to study the well aligned samples, the freely suspended film technique (FSF) [21, 22] has been used. In our experiments the FSF were drawn by simple wiping of the substance across a hole of 4 mm in diameter in a thin brass or beryllium foil. This forms the
spontaneously oriented film in which the molecular planes lie parallel to the film surface. A number of X-ray scattering and reflectivity experiments have been performed on these types of samples [23]. X-ray diffraction from FSF of 90SACB rich mixtures shows sharp resolution
limited peaks indicative of layered structure with the thickness of more than 30 layers. The
Table I. Summary of measured dijfkaction vectors magnitude and positions (h~ for the
four different mixtures studied
;
q~ and qi components of the reciprocal space vectors parallel
and perpendicular to the qi vector ; *-data for the fluctuation ofsmectic density waves. For the 90SACB compound which had a large orientational mosaic, only the magnitude of the q space
vectors are presented. T
= T~ 2 K, T~ = T~~t ; T~ t ; T~~t.
Mixture
, ,, , ,,
~
=
( ) ~l ~2 ~2 ~2 ~2z ~2z ~> " ~i q(
l 0.224 0.144 0.144 0.130
0.79 0.228 0.144* 0.147 0.130 0.126 0.107 0.075 0.019
0.77 0.230 0.144* 0.148 0.131 0.127 0.107 0.075 0.020
0.73 0.233 0.144* 0.150 0.132 0.128 0.108 0.076 0.020
q
,
I-
O.230
~,
~~ ji
2 _
~°° ... .
O.220 j~
O,150 I
~
i q(
o
°°~#'f . ~2
I 0,140
~
<i
~2
q
/ ~ll
2 O,130
.. ~,~q jj
o' °
o '
~ ~
C d
O.05 O.15 o.25
q,i~~ 60 loo 140 180 T°C
a~ b)
Fig. 2. -a) X-ray diffraction profiles for the angular or powder averaged samples of 90SACB demonstrating the simultaneous existence of three fundamental peaks in b phase. b) Magnitudes of the
qj, q~, q( and ql' diffraction vectors as a function of temperature for 90SACB. Filled circles indicate resolution-limited peaks, open circles diffuse maxima.
mosaicity was typically about
m 0.5 to I° FIVHM, that is approximately an order of magnitude
more than was reported for large area films [24]. This effect is most likely caused by the
curvature of the surface of the film near the borders of the hole. With this method the room
temperature phase of 90SACB was identified as crystalline smectic B, due to the presence of
equally strong (001) and (002) reflections corresponding to layer spacing dmL. The FSF
samples studies for x
~ 0.835 mixtures indicate that q( and qj vectors are not collinear in the low temperature smectic phase, thus ruling out the possibility of the existence of the incommensurate Ai~ phase (Fig. 3). Detailed study of the diffraction spectrum of FSF samples
in i~ phase is now in progress.
More informative for the understanding of the structure of i~ phase and the nature of
Ai-i~ and N~~-i~ transitions were the studies of the mixtures having the low temperature N(N~~) phases (x S 0.835) (Fig. I). The nematic phase for x
=
0.73 concentration of mixture
shows two diffuse maxima centered about
qjj~ = 2 «IL
=
0.230h~~ (Lm 27.3 h) and qjj~ = 2 «IL'
= 0.153 Ji~ (L
m 41 h) reciprocal space points. These maxima correspond to
the correlated regions with the translational order of the monomer Ai and dimer
A~ type existing in the vicinity of the N-Ai and N-A~ phase transition boundaries. The
appearance of the Aj phase is signaled by the growth and sharpening at 106°C of a
longitudinal scattering peak at qjjj=0.232h~~ (Fig. 4). Several degrees above the
N° 5 X-RAY STUDIES OF THE SMECTIC C PHASE 1201
~~
©
fi
~
o
400
q~
ib)
zoo
o
o,i o-z q ,I"1
b)
Fig, 3, X-ray diffraction profiles of the q( and qj peaks determined by rotation of free standing film
sample of fi phase around the
w axis as shown on the inset; (a)- w =10°; (b)-w =16°;
x = 0.9R T
= 95 °C.
Ai-C transition the X-ray diffraction in addition to the quasi-Bragg peak at the qj =
(0 ; 0 ; qj ~) and diffuse scattering at the q~ = (0 ; 0 ;
qjj~) points, shows two diffuse rings at
q( = (qi cos w qi sin w
qj(~) and ql'= (qi
~
cos w qi~ sin w qjl'~) in reciprocal space (w is an asimuthal angle, 0 S $r S 2 w) (Fig. 5). At the Ai-fi transition point the condensation of the q( and ql'rings of scattering occurs, the centers of these rings being equally spaced relative to the qi/2 plane (Fig. 6). The intensity of a low q reflex ql'proves to be few times less than
that of q(. Such a behaviour is characteristic of the commensurate two-dimensional periodicity
of the fi type [3, 25].
On passing into the i~ phase the abrupt increasing of mosaicity of the samples was detected
despite starting from a well aligned smectic Ai phase. It was found that cycling through a
transition temperature produced the fi phase with different mosaic distribution. In some cases
a number of domains with the mosaic spread of up to 10° was found. Owing to relatively poor
