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BIPHASES, BLUE PHASES, AND SHAPES OF NUCLEATION
J. Gilli, M. Kamaye, P. Sixou
To cite this version:
J. Gilli, M. Kamaye, P. Sixou. BIPHASES, BLUE PHASES, AND SHAPES OF NUCLEATION.
Journal de Physique Colloques, 1990, 51 (C7), pp.C7-183-C7-188. �10.1051/jphyscol:1990718�. �jpa- 00231117�
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C 0 1 1 0 q ~ e C 7 , suppl6rnent au n023, T o m e 51, ler decembre 1990
BIPHASES, BLUE PHASES, AND SHAPES OF NUCLEATION
J . M . G I L L I , M . KAMAYE and P . SIXOU
Laboratoire de Physique de la Matidre CondensBe, CNRS UA-190, Faculte des Sciences de Nice, parc Valrose, F-06034 Nice Cedex, France
RClsumC- Nous avons BtudiC les phases bleues obtenues avec un oligomire mksomorphe polydisperse a chaines l a t e r a l e s e t nous pensons qu'elle peuvent b t r e decrites a p a r t i r d'un modhle de t y p e
"microCmulsion": la tendance connue de c e genre d e matbriau impur a former une biphase conduit probalement ici a la segregation des deux composantes isotrope e t anisotrope en deux sous-reseaux imbriquks. Ce t y p e de modhle conduit
6
s e poser le probl6me plus gkneral de la forme de nuclbation de la phase cholestCrique: dans Ie c a s de c e mGme materiau chiral en solution, c e t t e derniere s'ophre p a r I'intermCdiaire d'une tres g r a n d e v a r i e t e de f o r m e s gComBtriques.A b s t r a c t - We have studied blue p h a s e s w i t h a s i d e chain polydisperse c h o l e s t e r i c oligomer and w e think t h e y can be described by a "microemulsion" model: the known tendency of this kind of impure material to form a biphase brings probably here to the s e p a r a t i o n of the isotropic and anisotropic phases in two associated n e t w o r k s . This kind of model is related to the m o r e general problem of the cholesteric shape of nucleation: in the c a s e of a solution of this s a m e material, t h e nucleation i s operated with a g r e a t number of different geometrical shapes.
Many r e c e n t experimental w o r k s have described the blue phases behaviours of small molecules liquid c r y s t a l s , in a n a r r o w t e m p e r a t u r e range, between the small pitch cholesteric and isotropic phase.
For a strong enough chirality, t h r e e different blue phases, BP Ill, 11 and l a r e successively observed when t e m p e r a t u r e i s decreased f r o m the isotropic phase. Microcalorimetric measurements have shown (1) four peaks in t h i s c a s e , demonstrating the thermodynamic s t a b i l i t y of t h e s e five different phases, s e p a r a t e d by f i r s t order transitions. The observation of Kossel lines associated to convergent light diffraction in the visible domain 12) allows the identification of the Cl8 and
o2
cubic s y m m e t r i e s of the BP1 and BP11 l o w e s t t e m p e r a t u r e blue phases. Concerning BP I l l (blue fog) observed a s a strongly light diffusing fog beetween microscope slides, no s a t i s f a c t o r y description exists a t t h e p r e s e n t time.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990718
Theoritical model
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F r o m a theoretical p o i n t o f view, a Landau-Ginzburg approach allows the prediction o f t h i s kind o f tridimensional phases w i t h o u t being able t o describe t h e i r favoured s y m m e t r i e s and t h e i r sequence w i t h temperature.
A m o r e geometrical approach, points out the double t w i s t tube a s an alternative to the classical f r u s t r a t e d cholesteric s t r u c t u r e (3): a cylinder of t h i s kind allows an elastic energy gain if i t s radial extent does not overstep a c r i t i c a l value o f the order o f the h a l f cholesteric pitch. The geometrical stacking o f these tubes needs the presence o f elasticaly distorted connecting domains and above all, o f singular lines w i t h undefined d i r e c t o r orientations (3).
These t w o models are consistent i f w e associate these connecting unfavourable regions w i t h a decrease t o zero o f the local order parameter i n the c o r e o f disclinations. But, and w e think this p a r t i c u l a r l y pertinent i n the case o f polydisperse p o l y m e r i c material, a discontinuous c o r e singular line model brings u s t o p r e f e r a microemulsion model, f o r blue phase constituted b y polydisperse compounds. In t h i s model, t w o phase separated b y a sharp interface, i n a thermodynamic equilibrium, are coexisting i n a temperature dependent proportion.
It i s w e l l known i n the case o f mesomorphic p o l y m e r i c m a t e r i a l s generaly c o n s t i t u t e d o f coexisting s l i g h t l y d i f f e r e n t molecular species associated t o d i f f e r e n t t r a n s i t i o n temperatures, t h a t anisotropic-isotropic f i r s t o r d e r t r a n s i t i o n s a r e p e r f o r m e d by t h e i n t e r m e d i a t e o f l a r g e temperature extent biphases (4). The f i r s t anisotropic component i s enriched i n hight transition temperature (Tc) species, the isotropic one i s enriched i n l o w Tc species (we can note here t h a t the same kind o f process i s unvolved i n the case o f v e r y pure components i n solutions)..
Cooling down f r o m the homogenous phase, the occurence o f the physical s t r u c t u r e o f t h i s kind o f biphase i s generaly operated throught a classical process o f nucleation, g r o w t h and coalescence associated t o the possibility o f minimising total f r e e energy o f the s y s t e m b y a decrease o f the r a t i o o f i n t e r f a c e e x t e n t t o anisotropic volume: t h i s brings t o the macroscopic separation o f the t w o components. In some p a r t i c u l a r cases, however, the nucleating objects can undergo the necessity o f l i m i t t i n g t h e i r g r o w t h t o a c r i t i c a l size, t h i s being associated t o a complex volume and surface topological s t r u c t u r e . (this i s t h e case f o r the radial extent o f a double t w i s t tube), This k i n d o f situation i s probably able t o describe the l a r g e temperature blue phase domain obtained b y u s (5) w i t h a side chain c h o l e s t e r i c o l i g o m e r and i n p a r t i c u l a r o f BP Ill: as developed i n t h e following, this model allows the understanding o f the transition f r o m the
o2
simple cubic s y m m e t r y t o t h e
o8
centered cubic (BP 11- BPI) w i t h the decrease o f temperature.The s h a ~ e of the nucleatina obiect~
In the case of liquid crystal mediums, energetical contributions arise from the topological necessity of volume andlor surface defects or distortions and the nucleation problem is hugely more complex than the simple liquid one (case of smectics): a very thin energetic equilibrium exist here, between volume and surface contributions.
Two different extreme hypothesis have been proposed (6) to define the shape of the anisotropic objects constituting the first appearance of the first order transition isotropic- BP Ill.
-
a spherical or quasi spherical form favourable by its lowered surface extent.-
an elongated one, as the double twist cylinder, whose volume elastic energy is now favourable.Concerning the second hypothesis, it is necessary to limitate the tube longitudinal extent and to introduce point singular andlor curvature defects constituting connexion locus with other tubes by anihilation. The radial calibration phenomena is here clearly understandable but we don't think that nucleation of tubes of uncorrelated spacial orientations can easily give rise to a regular cubic network (an hexagonal or quadratic one being more probable).
The first hypothesis of globular objects is for us a better candidate and we can try to built such an object from a limited number of 3D oriented tubes along various symmetries axes (fig. 1). In this case the surface defects connectivity becomes tridimentional and able to bring to the BP I1 and I organisations (see fig. 2). The temperature dependent calibration is simply explained here by the constituting tube properties.
FIGUREI: the nucleating quasispherical objects are built as an association of a limitted number of double twist tubes. (a): association of three cylinders, analogue of an 0* node. (b and c): two different drawings of a possible dodecaedral node model for the BPlll nucleation.
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FIGURE2: a naive geometrical model for BPll (a), and BP1 (b), showing the possible relation between sphere and cylinders organisations: surface singular point defects being the possible connection locus between nucleating calibrated objects. The tube higher cornpacity network is constituted of tubes nodes that are the topological analogue of the nucleatig globules.
TABLE 1
Table 1 gives the optimal compacities (% of tube volume/total volume) obtained with both hypothetical objects and seems to strongly suggest the observed phase behaviour: blue fog constituted of isolated "quasi spherical" globules, followed, for a 52% ratio, by a simple cubic network of spheres, the connexion of defects allowing now the 58% ratio for the sc cylindrical structure. The following sc-cc transformation BPII-BP1 is obtained through the occurence of new diagonal defect connections between the cubic network nodes (- 68%). We can also see that the validity of the spherical model decreases as the cholesteric phase is approached and it seems to predict more compact quadratic (78%) and hexagonal (90%) bidimentional tubes packing: it is interesting to remark that experimental observations of the first birefringent texture obtained from BP I seem to reveal an hexagonal character ( see photo. a).
We give here briefly a few experimental results related from our point of view, to this "nucleation shape" problem :
volume ratio aniso/iso
S P H E R E S volume ratio
aniso/iso
simple cubic 02
58%
non compact hexagonal
60%
centered cubic 05
52%
cubic 02
52%
centered cubic 08
68%
centered cubic 08
68%
quadratic hexagonal bidimensional
78%
face centered cubic
74%
90%
compact hexagonal
74%
-
We think that the progressive disapearance of blue phase when chirality decreases is probably associated to the geometrical and topological shape change of the nucleating objects.-In the thermotropic main chain polymers case, the splay exclusion predicted by some authors (7) possibly favour a double twist tube nucleation and this is a possible explanation of the absence of blue phase behaviour in this case even when the cholesteric pitch is low enought.
-It is also known in some cases of diluted chiral polymeric main chain systems (probably able to undergo more easily splay distortions), that a physical gel can be obtained in the neighbouring of Ch
-
iso transitions (cf biological systems as cellulosic derivatives (8) ). We observed a comparable behaviour with an oligometric side chain polymer diluted in different particular solvents: few corresponding textures observed with a polarising microscope are associated here, with an elongated nucleation and the entanglements of these disordered tubes probably induce the anomalous viscosity and the strong optical diffusion observed.-The use of this same diluted material with variable cooling kinetics, concentrations, etc, allowed us to observe a large variety of macroscopic nucleation shapes and the objects (see photomicrographies) are more or less calibrated.
PHOTOMICROGRAPHIES: Gr=700, taken with a polarising microscope in transmission for a,b,c,d,e and in reflexion for f. (a): an "hexagonal" texture obtained after 12 hours annealing of BPII.
(b,c,d,e): elongated, disc like, torus like, and helicoidal shapped nucleating objects obtained with variable temperature kinetics, and concentration, of a side chain cholesteric polymer in solution, cooling down from the homogenous isotropic phase. (f): at a higher polymer concentration, star shapped Bragg reflecting objects are obtained.
Conclusion:
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The unlarged observation o f blue phase t e m p e r a t u r e domain w i t h polydisperse polymers, solutions, and more generaly w i t h cholesteric impure m a t e r i a l have brought u s t o describe blue phases i n t e r m o f t w o phase microemulsion equilibrium. This kind o f approach put f o r w a r d the general opened question o f the chiral nematic shape o f nucleation and the problem o f surface/volume topology o f f i n i t e c h i r a l objects.
F r o m another p o i n t o f view, these r e f l e x i o n s associated t o the p o s s i b i l i t y o f supercooling tridimensional organisations under th.e glass t r a n s i t i o n o f o u r p o l y m e r i c m a t e r i a l s t r o n g l y suggest d i f f r a c t i o n experiments able to reveal the exact features o f the repeat units o f the blue phase "crystals".
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