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Instability of the lattice structure of crystalline liquids near the BPI-BPII phse transition
V. Dolganov, O. Lourie
To cite this version:
V. Dolganov, O. Lourie. Instability of the lattice structure of crystalline liquids near the BPI-BPII phse transition. Journal de Physique II, EDP Sciences, 1992, 2 (7), pp.1383-1387. �10.1051/jp2:1992206�.
�jpa-00247735�
Classification Physics Abstracts 61.30
Short Communication
Instability of the lattice structure of crystalline liquids near the BPI-BPII phase transition
V-K- Dolganov and O-R- Lourie
Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow distr., Russia
(Received 16 April 1992) Accepted 19 May 1992)
Abstract. Essential change of the splitting between reflections (200) and (i10) with tem-
perature in the Blue Phase I (BPI) transmission spectrum in an electric field has been observed.
The electrostriction coefficient ruin in BPI increases anomalously, while approaching the BPI- BPII phase transition temperature. These results show that the phase transition is connected with lattice instability with increasing temperature.
In crystalline liquids BPI and BPII iii the local orientational ordering of molecules forms a 3D periodic structure with the symmetries of the cubic lattices (O~ ando~). BPIII has no
periodic structure, since it exhibits only a broad, weak selective reflection [2, 3]. It has been shown theoretically by Keyes [4] that the cubic lattices of BPI and BPII can be unstable with respect to fluctuations of the lattice, and, as a result, the phase transition will occur either to an isotropic liquid (I), or to BPIII. In the present paper the lattice instability has been shown
to be the reason of the phase transition between the 3D ordered phases, BPI and BPII.
The BPI-BPII transition is a very weak first-order phase transition. The latent heat of transition is 1-2 orders less than that under the BPI phase transition [5-8], which is also a weak first order transition. For the weak first-order transitions, such as N-I, SA-N, Sc SA and others, the absolute instability temperature of the low temperature phase is near Tc, the order parameter and the corresponding physical characteristics varying es8entially in the
vicinity of Tc. Observation of an anomalous behaviour of physical quantities near the BPI-BPII phase transition could make it possible to describe this transition in more detail and show the
cause, responsible for the blue phase structure transformation.
The paper presents measurements of the temperature dependence of the electrostriction in the region of the BPI-BPII phase transition. Measurements were made on samples containing
a chiral-nematic mixture with the chiral component ll#X-16 (81.I wt.p.c., Vilnius University, Lithuania) and a nematic liquid crystal 16S0D (18.9 wt.p.c.). The mixture exhibits negative
dielectric anisotropy. The BPI-BPII phase transition temperature is 38.025 °C. The samples
1384 JOURNAL DE PHYSIQUE II N°7
were placed between two parallel glass plates coated with transparent electrodes. The tem-
perature stability was ~ 0.005°C. The samples were 17 pm thick. The diffraction lines were measured in the transmission spectrum. Alternate voltage at a frequency of 4 kHz was used.
The BPI transmission spectrum for orientation [100] ii E outside the sample absorption region is presented by a band in the range of I ci 435 4Sl nm. The band consists of reflection
(200) and four reflections (l10), coinciding in wavelength, of a b-c-c- lattice O~ (1200
= dnsinR,
~ " 90°, ~l10 " 2~/~dnsIn$, $
= 4$°, ~200 " ~l10)
In an electric field the band splits (Fig. I). For the substances with negative dielectric
anisotropy the lattice at E 1 [100] is extended along the field direction [9], which results in the long-wave shift of reflection (200) and in the short-wave shift of reflection (l10) in
the transmission spectrum. Figure 2 depicts the temperature dependence of splitting A
=
~200 ~l10.
f-o
A
I/I~
I
B
c
0.
o.50
~~° ~~°
&~
,
(mm) ~~°
Fig. i. Transmission spectrum of BPI in an electric field: a) T
=
37.90° C, b) T
= 37.96°C, c) T = 38.02°C, U
= 45V.
A most interesting feature of tbe data obtained is
a drastic increase in the splitting upon approaching the phase transition temperature. The deformation of the cubic structure is
caused by electrostriction. It was shown earlier [10] that the quadratic dependence of the diffraction band shift on the field strength is fulfilled adequately up to the field values, at which phase transitions take place. In an electric field the relation A200 ~z -2Aiio is fulfilled to a good precision for the shifts of diffraction bands 1200 and Ii
lo- The relation is valid when deformation of an elementary cell occurs with a constant volume of the unit cell. The last fact permits evaluating the electrostriction coefficient ii
ii i = §jiooj using the magnitude of the total splitting iyooj = 2A/31E~ (Fig. 3).
Dependence §jiooj(T) can be described by the function §pooj(T) = A (T T*)~
,
T* being in close vicinity to the phase transition temperature (Fig.3). Upon phase transition the absolute value of §pooj decreases essentially (Fig. 3) and exhibits only a weak temperature dependence
in BPII. Therefore, a sharp increase offjiooj in BPI is not associated with the general change
of temperature and shows a pretransitional behaviour for the BPI-BPII transition. The shift of the diffraction band in the substance with
a larger cholesteric helix, observed in ii Ii, is likely
to be due to change of the electrostriction.
loo
6 ~
(nm)
o o o
50 BPI
~ BPII
I
° n
o u
u u
u
To
37.9 38.0 T,rC)
Fig. 2. Temperature dependence of splitting A between reflections (200) and (i10) of BPI phase.
(Q) U = 35V, (o) U
= 45V.
QN 0 fN
~ l~
m Oo
D j
u
~
~ ~
~~ ~ _«
,
~~~
o
~~~~ (
~ '~
~o 10 , ', ~ _~>~~o
,.K,o D
8 ';
D , ~Q
~ ,»
D ~,
» ,
Tc',», ,
0 , 0
37.9 38.0 T,rC)
Fig. 3. Temperature dependence of electrostriction coefficient (iii> (Ll o) BPI phase, (o) BPII phase, (.) ~~~
The electrostriction tensor is expressed through macroscopic characteristics of the blue phase, 7iknp " SikimPnpim, here the tensor Sikim is reciprocal to the elastic constant tensor
ljnmp,Pnpim being8~r the elasto-optic tensor [12]. An increase in 71111 can be directly associated with a decrease in the modulus of elasticity hill. In this case with increasing temperature, the structure O~ (BPII) becomes unstable with respect to spontaneous deformation of the lattice, and, as a result, a transition to structure O~ (BPII) with a larger elasticity modu-
lus occurs. Since upon deformation the elementary cell volume remains unchanged, of the
three electrostriction tensor components there, only t,vo are independent: 71111
" ijiooj and
1386 JOURNAL DE PHYSIQUE II N°7
72323 " ijiooj ~ijiooj 71122
" ~71111 (9]. In the BPI phase fjiooj * -3.9 x 10~~~m~V~~
4 2
and has a slight temperature
pendenc~.
Hence, 72323 has a weaker temperature dependence
than 71111, and it may be supposed that the instability of lattice, relative to shear deformations, should take place at higher temperatures.
The root-mean-squared fluctuations of the cubic lattice are f = (u~)~~~Id = (kT/~rld~)~~~
[4], here dis a unit cell length, I is an effective elastic constant in an assumption of the elastically isotropic lattice. Under high elastic anisotropy the effective elastic constant is proportional
to the smaller one of the two (hill,12323) A comparison of 72323 with the results of the shear modulus measurements [7] shows that the essential part of the temperature dependence
§jiooj(T) is connected with an alteration of I. According to the Lindemann criterion [13]
the melting occurs when fo is of the order 0.2. If f is evaluated using the data obtained by Kleiman, Bishop, Pindac and Taborec [7] for 12323 and elastic constants are considered to be inversely proportional to the corresponding electrostriction coefficients, then we get the value of
~- 0.05 for f in the vicinity of the BPI-BPII transition. Since in our case in the transition there arises an ordered phase, the BPI lattice instability with respect to the transition to the BPII structure can occur at f < fo. The estimates of quantity f are thus in agreement with
our interpretation of the cause of the BPI-BPII phase transition.
It should be noted in conclusion that the anomalous temperature dependence of I can be displayed, for instance, as a strong (~- Ill [14]) increase of the diffusion scattering near reflections, and as a decrease of the structural relaxation times [IS, 16] on approaching the phase
transition temperature. The results obtained suggest a possibility of using the elastic constant tensor or the lattice spontaneous deformation
as the order parameter [17-19] for describing the elastic instability transition between blue phases in the framework of the Landau theory.
Acknowledgements.
We are grateful to Prof. E-I- I(atz for helpful discussions.
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