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In document on Liquid Crystal Colloids (сторінка 83-104)

on Liquid Crystal Colloids

Emergent Phenomena and Functional Materials

Shapes of macromolecules in porous environments: field theoretical renormalization group approach V. Blavatska,a C. von Ferberb,c and Yu. Holovatcha

aInstitute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine

bApplied Mathematics Research Centre, Coventry University, CV1 5FB Coventry, UK

cTheoretische Polymerphysik, Freiburg University, 79104 Freiburg, Germany

We apply the method of field theoretical renormalization group to analyze universal shape properties of long polymer chains in porous environments. So far such analytical calculations have primarily focused on the scaling exponents that govern conformational properties of polymer macromolecules. However, there are other observables that along with the scaling exponents are universal (i.e. independent of the chemical structure of macromolecules and of the solvent) and may be analyzed within the renormalization group approach. Here, we address the question of shapes acquired by long flexible polymer macromolecules when immersed in a solvent in the presence of a porous environment. This question is of relevance for understanding of the behavior of macromolecules in colloidal solutions, near microporous membranes, and in biological environments. To this end, we consider a previously suggested model [1] of polymers in d dimensions in an environment with structural obstacles, characterized by a pair correlation function h(r), that decays with distance r according to a power law: h(r) ∼ r−a. We apply the field-theoretical renormalization group approach and estimate the size ratioRe2/R2G and the asphericity ratio Ad up to the first order of a double ε= 4−d, δ = 4−a expansion.

References

[1] V. Blavats’ka, C. von Ferber, Yu. Holovatch. Phys. Rev. E 64, (2001) 041102 [2] V. Blavatska, C. von Ferber, Yu. Holovatch. Phys. Lett. A 374, 2861 (2010).

[3] V. Blavatska, C. von Ferber, Yu. Holovatch. Condens. Matter Phys., (2011), to appear.

P 2 Posters Photo induced anchoring on chalcogenide surface

N. Boyarchuk,a Y. Kurioz,a M. Klebanov,b V. Lyubin,b K. Slyusarenkoa and Y. Reznikova

aInstitute of Physics, National Academy of Sciences of Ukraine, Pr.Nauky 46, Kyiv, 03028 Ukraine

bDepartment of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

We present basic characteristics and model of photoinduced anchoring of liquid crystals (LCs) on a chalcogenide surface. It was found that characteristics of the alignment strongly depend on the LC material for the same chalcogenide glass. The photoalignment is partially reversible and can be controlled by changing the polarization of light. The proposed model is based on suggestion of the existence of dicroicunits on the chalcogenide surface.It is assumed that the LC molecules are adsorbed on these units in correlation with their anisotropic axes.The energy of the polarized light, which is adsorbed mainly by the dichroic unitsis transferred to the neighboring LC molecules that causes their desorption. The resulted anisotropic angular distribution of the adsorbed molecules produces the light-induced easy orientation axis of a LC.

84

Magnetic twist Frederiks transition in a rectangular nematic cell S. Burylov

Institute of Transport Systems and Technologies, Ukrainian Nat. Acad. of Sci., Pisarzhevskogo St. 5, 49005 Dnepropetrovsk, Ukraine

The magnetically induced Frederiks transition in a rectangular nematic cell is considered. In the initial state a nematic director orientation is uniform in the cross section of the cell. An applying magnetic field H is normal to this section. The magnetic Frederiks transition threshold HF for the rectangular cell is determined, an analytical description of a director orientation profile for fields H > HF is obtained and dependences of a profile shape upon the applying magnetic field and values of the twist elastic module K22 are investigated.

P 4 Posters Necessary conditions of the modulated structure formation in the filled nematics

Andrii Kleshchonok,a Victor Reshetnyaka and Valentin Tatarenkob

aPhysics Faculty, Kyiv National Taras Shevchenko University, Prospekt Glushkova 2, Building 1, Kyiv, Ukraine

bDepartment of Solid State Theory, G. V. Kurdyumov Institute for Metal Physics, N.A.S.U., 36 Academician Vernadsky Blvd., UA-03142 Kyiv, Ukraine

We propose the theoretical model of instability of the nematic liquid crystals filled with spherical micro- and nanoparticles against formation of the modulated structures. We analyze the condition, when the mod- ulated structures may arise. This condition allows to estimate temperature of the stability loss, anchoring energy, necessary for the modulated structure formation, and wave vector of the spatial modulation. There is a long-range effective interaction between the particles, which can lead to the formation of superstruc- tures. In general, this interaction includes several contributions: van der Waals-type direct interaction and indirect interaction via the director field distortions. The latter depends on the temperature of the sample, the coupling energy between a colloidal particle and a nematic host, and the particle concentration. This effective interaction controls the spatial structure and the kinetic properties of the system. The positions of the minimum Fourier components of the effective impurityimpurity- interaction energies as well as the corresponding period do have a crucial dependence on the value of the anchoring energy. The magnitude of the anchoring on the impurity particle surface determines the temperature of the stability loss, which should belong to the rather narrow temperature interval of the nematic phase existence.

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Synthesis and characterization of H-shaped liquid crystals

Milena Kołpaczyńska,a Józef Mieczkowski,a,b Damian Pociechaa and Ewa Góreckaa

aDepartment of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland

bInstitute of Chemistry, Military University of Technology, Kaliskiego 2, 00-908 Warsaw, Poland

Molecular organization of novel liquid-crystalline compounds is an attractive field of materials science.

The driving force of mesophase formation is a fundamental topic for molecular assembly systems. A primary factor in the thermotropic liquid crystal phases is the gross molecular shape of a compound. The liquid crystal dimers in which conventional mesogenic units are pre-organized in a classical shape can produce unusual phase structures and unique physical properties. The vast majority of liquid crystalline dimers reported in the literature consist of two identical rod-like units that are linked at terminal positions via n-alkyl chain [1, 2]. Such twins often exhibit dramatic dependence of their clearing/melting temperatures and transition enthalpies on the length and parity of the n-alkyl spacer, linking the mesogenic units [3, 4].

In our work we focused on H - shaped dimers and understanding the relationship between their molecu- lar structure and phase properties. New series of dimeric molecules built of mesogenic units linked laterally by the n-alkyl (n=1, 3 - 6) spacer were synthesized and studied.

O

O O (CH2)n

O

O O

OCH2

O O

C2H5

OCH2

O O

C2H5 H25C12O

H25C12O

C5H11

C5H11 H

H R

O (CH2)n

O O

O CH3

COOC2H5 H

O

O CH3

COOC2H5 H O

O O

O

O

O C

H3 C H3

1. An odd - even effect of the central polymethylene spacer on the phase tran- sition temperatures and enthalpies has been observed

2. Insignificant dependence of the layer spacing on the parity of carbon atoms in lateral linkage suggests that the spacer must be in folded rather than all-trans conformation (for both odd and even atom spacers molecules mesogenic cores adopt nearly parallel ar- rangement). With elongation of an alky spacer, the layer spacing decreases, that is related to increasing of end groups in- terdigitation between layers.

3. For chiral compounds, the electric polarisation was found to be much lower for dimers than for related monomers, which was explained by partial compensation of intramolecular dipole moments.

P 6 Posters Maier-Saupe nematic fluid: integral equation and field theory approaches

I. Kravtsiv,a M. Holovko,a and D. di Capriob

aInstitute for Condensed Matter Physics, NAS of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine.

bÉcole normale supérieure de chimie de Paris, Case 39, 4, Pl. Jussieu, 75005 Paris, France.

We apply the integral equation and the field theory approaches to describe the structure and ther- modynamics of two model nematic systems. Both of these methods take into account fluctuations thus allowing to go beyond the mean field approximation.

First we consider a spatially homogeneous fluid of point particles interacting with the potential ν(r12,Ω12) = A

r12e−αr12P2(cosθ12),

wherer12denotes the distance between two particles,Ω = (θ, φ)are particle orientations, andP2(cosθ12) = (3 cos2θ12−1)/2is the second order Legendre polynomial of relative molecule orientations.

For such a system in the mean field approximation we retrieve the standard Maier-Saupe theory for liquid crystals. In the Gaussian approximation we obtain new results for the pair correlation function, the free energy, and the pressure. From the Ward symmetry identity we derive a simple condition for the correlation functions and calculate the elasticity constant.

Next we present results for a fluid confined by a hard wall with the potential of inter-particle interaction ν(r12,Ω12) = A0

r12e−αr12+ A2

r12e−αr12P2(cosθ12).

From the inhomogeneous Ornstein-Zernike equation we obtain analytical expressions for the pair corre- lation function. Based on this result we calculate expressions for the density profile, the order parameter profile, and the adsorption coefficient.

88

Polarization diffraction gratings in liquid crystals cells with chalcogenide glassy surface Yu. Kurioz,a N. Boyarchuk,a M. Trunovb and Yu. Reznikova

aInstitute of Physics of NAS of Ukraine, Prosp. Nauky 46, Kyiv 03680, Ukraine

bUzhgorod National University, Pidhirna Str., 46 Uzhgorod 88000, Ukraine

We report on recording of permanent electrically-controlled polarization gratings in a cell with liquid crystals (LCs) 5CB or E7 and chalcogenide As20Se80 as a command surface. The gratings were recorded due to formation of the easy orientation axis on the chalcogenide surface upon irradiation of the filled cell with a polarized light in the absorption band of the chalcogenide glass [1]. To record the gratings, two laser beams withλ = 532 nm with opposite circular polarizations were intersected in the plane of the cells. The spatial distribution of the resulted easy axis led to the corresponding modulation of the optical axis in the LC bulk and recording of the grating. Application of the electric field caused reorientation of the LC and change of the phase retardation modulation in the cell. It allowed effective control of the diffraction efficiency of the grating, η, which maximum value achieved ≈ 30%.

High sensitivity and thermal stability of the grating in LC cells with chalcogenide layers together with effective electrically driven control of the gratings characteristics makes them very attractive for potential optical and photonics applications.

References

[1] Yu. Kurioz et al. Mol. Cryst. Liq.Cryst, 2008, 489, 94[420]

P 8 Posters The influence of light beam’s narrowness on the hysteresis of Freedericksz transition in a nematic cell M. Ledney and O. Tarnavskyy

Faculty of Physics, Kyiv National Taras Shevchenko University, prosp. Glushkova, 4, Kyiv, Ukraine The influence of incident light beam’s narrowness and intensity distribution along beam’s transverse dimension on the hysteresis of light induced Freedericksz transition in a homeotropic nematic liquid crystal cell has been considered. Cases of one- and two-dimensional confined beams have been investigated. In the case of one-dimensional confined beam several different distributions of the light intensity have been used for calculations. Threshold values of orientational instability and values of maximal director’s jumps for increasing and decreasing of the incident light intensity have been found numerically as functions of beam’s transverse size. Conditions for the maximal width of the hysteresis loop have been obtained. It has been demonstrated also that the range of admissible elastic Frank constants’ ratios(K3−K1)/K3 and K2/K3 becomes wider with increasing of the transverse size of one-dimensional confined light beam.

90

The spatial-periodic threshold structure of director in a nematic cell with periodic anchoring energy M. Ledney and O. Tarnavskyy

Faculty of Physics, Kyiv National Taras Shevchenko University, prosp. Glushkova, 4, Kyiv, Ukraine The threshold reorientation of director under the influence of static external electric field in a planar nematic cell with a periodic surface anchoring energy has been investigated theoretically. The value of transition’s threshold and spatial distribution of director above the threshold have been found as functions of the period and anchoring energy value. It has been shown that the threshold of the transition depends non-monotonically on the number of anchoring energy periods s that could be located along the cell length. The distribution of director above transition’s threshold in the case of integers traces the periodic changes of anchoring energy. The amplitude of periodic director’s deviations grows while the ratio of the cell thickness to the anchoring energy period decreases.

P 10 Posters Helical twisting in nematic-cholesteric systems with photoactive components

M. Serbina, N. Kasian and L. Lisetski

Institute for Scintillation Materials of NAS of Ukraine, 60 Lenin Ave., Kharkiv, Ukraine

For cholesteric liquid crystalline systems containing photosensitive nematic ZhK-440 and a mixture of cholesterol derivatives, changes in helical twisting induced by UV irradiation were studied. The UV- induced shift of the selective reflection maximum λmax was shown to depend upon concentration of the nematic component. At low concentration of ZhK-440λmax increases, which correlates with corresponding temperature-induced changes. At higher concentrations of azoxy nematic,λmax decreased regardless of the temperature behavior of the system. To explain the experimental data, a theoretical description is proposed on the basis of development of molecular models of helical twisting. Good agreement was obtained between calculated and measured values of UV-induced shift∆λmaxas function of the azoxy nematic concentration, with two extrema and an inversion point. This description is claimed to be unparalleled by other existing theories of helical twisting. The extra twisting emerging in the system due to formation of non-mesogenic and non-chiral cis-isomers can be presumably assigned to ordered orientation of short molecular axes of cis-molecules, with resulting contribution to helical twisting determined by the sense of the helix that had been already formed in the cholesteric system.

The above-discussed phenomenon of extra twisting is compared to a presumably similar behavior caused by introduction of banana-shaped molecules into a cholesteric matrix, with analysis of frequently cited data given by Thisayukta, Takezoe e.a [1] and of more recent data on banana-shaped dopants in helically twisted matrices. Essential differences are noted between the molecular mechanisms involved in both cases.

References

[1] J.Thisayukta, H.Niwano, H.Takezoe J.Watanabe, J.Am.Chem.Soc., 124, 3354 (2002).

92

Elasticity in homeotropically aligned lyotropic chromonic liquid crystal studied with magnetic field Freedericksz transition

Yu. Nastishin,a,b O. Boiko,c V. Nazarenko,c L. Tortoraa and O. Lavrentovicha

aLiquid Crystal Institute and Chemical Physics Interdisciplinary Program, Kent State University, Kent, OH 44242.

bInstitute of Physical Optics, 23 Dragomanov str., Lviv, 79005, Ukraine.

cInstitute of Physics, prospect Nauky 46, Kiev-39, 03039, Ukraine

Using the magnetic field Freedericksz transition technique, we measure the temperature- and concentration- dependent bend K3 and splay K1 elastic moduli of the nematic phase in a self-assembled lyotropic chromonic liquid crystal. The ratioK3/K1 increases sharply with temperature and decreases with the con- centration; we attribute this to the shortening/elongation of the aggregates as temperature/concentration increases.

Acknowledgments: The work was supported by NSF MWN grant DMR076290, STCU project #5258.

P 12 Posters Modelling smectic layers in confined domains

Mykhailo Pevnyi and Jonathan Selinger

Kent State University, Liquid Crystal Institute, Kent, Ohio, USA

The influence of the surface on smectic liquid crystal configuration in a bulk has been a subject of intense investigation for many years. The results of experimental research on liquid crystal colloids were published recently, reporting the layered structures of liquid crystals in colloidal particles [1].

This inspired us to develop an approach for modelling smectic layers in confined nanoscale domains. We have done this calculation by simulating the nematic – smectic A phase transition. The standard approach to describe the nematic – smectic A transition was suggested by P.-G. de Gennes [2]

and is applicable for small director deviations from homogeneous alignment.

The complex smectic order parameter is introduced there. According to that theory the free energy functional is

FN A= Z

d3x{r|ψ|2+ u

2|ψ|4+C|(∇ −iqnδn)ψ|2+felastic} (1) An intuitive way to extend that theory for the case of an inhomogeneous director field would be to use the following free energy functional.

F = Z

d3x{r|ψ|2+ u

2|ψ|4 +C|(∇ −iqn)ψ|2+felastic} (2) Although this model gives a good approxination for a nearly homoge- neous director it has one significant limitation: the model gives a free energy difference between the director -n and n, whereas the real physical system has a symmetry between n and -n. Thus, this model is appropriate for a

transition between the polar nematic and polar smectic phases, but not for the conventional nonpolar nematic – smectic transition. To preserve the symmetry of the nematic and smectic phases we suggest using the real density modulationδρ as the smectic order parameter. The coupling term in the free energy must then be[(∂ij +q2ninj)δρ]2, which is independent of the sign of n. The free energy functional now takes the form.

F = Z

d3x{aδρ2+bδρ3+cδρ4 +B[(∂ij+q2ninj)δρ]2+felastic} (3) For the special case of homogeneous director alignment, this model leads to a sinusoidal density wave, as in the de Gennes theory. However, the advantage of this model is that it can be used for an arbitrary nematic director configuration as well. In this work, we use the two theoretical approaches to model the nematic – smectic transition in simple two-dimensional domains. We numerically minimize the free energy of Eqs. (2) and (3) subject to boundary conditions of different types, and determine the configuration of the smectic layers. We compare the theoretical results with experiments on smectic liquid crystals in nano-colloidal particles.

Acknowledgments: We would like to thank B. R. Ratna for helpful discussions. This work was supported by NSF Grant DMR-0605889.

References

[1] C. M. Spillmann et al., Langmuir 25, 2419-2426 (2009).

[2] P. G. de Gennes and J. Prost The Physics of Liquid Crystals, Oxford University Press, 1993.

94

Rod-like mesogens containing thiophene unit

Zita Puterová, Jerzy Romiszewski, Jozef Mieczkowski and Ewa Gorecka

Laboratory of Physicochemistry of Dielectrics and Magnetism Faculty of Chemistry, University of Warsaw, Žwirki i Wigury 101,02-089 Warszawa, Poland

S O

O NH O

O R1O

R2 N

R1O

R1O

O i

ii, iii N COOCH3

iii

R1O

S NH2 H3COOC

O

O R2

P

COOCH3 Br

iv

OR2 H3COOC

v

O R2 ClOC

vi

DST

New rod-like mesogens containing diphenyl-thiophene rigid core and pro- mesogenic styryl tail with alkyl chains on both ends were synthesized (see fig- ure). These liquid crystals exhibit pre- dominantly thermotropic smectic A and nematic phases. Several applications of these compounds have been proposed, for example as materials in non-linear optics [1] or generations of fast switch- ing displays [2]. However, the high tran- sition temperatures of such mesogens often inhibit practical applications [3].

The influence of increasing alkyl chain lenght to phase behaviour and transition temperatures on a series of thiophene based rod-like mesogens (DTS) was in- vestigated. In addition, thiophene based rod-like molecules could be of interest on their own, because of their interest- ing fluorescent properties.

Compounds were investigated us- ing polarized optical microscopy (POM, Zeiss Axio Imager 2.m), differential scan- ning calorimetry (DSC TA Q 200) and X-Ray diffraction of powder samples.

Acknowledgments: This research is supported by Polish Foundation of Sci- ence under Team Programme No. TEAM 2010-5/4 and within the Foundation for

P 14 Posters Dynamics of the interior molecular structure AFLC with partly fluorinated tail

Marcin Sufin and Antoni Kocot

University of Silesia, Katowice, Poland, Institute of Physics

Dynamics of the interior molecular structure was investigated with using IR spectroscopy and optical methods. Widely known problem of differences between the tilt angles estimated from layer thickness (X-ray) and obtained using optical methods (Gleeson et. al. 2004) inspired as to engaged different (IR) method to evaluate molecular tilt angle. Investigations ware conducted on AFLC samples with fluorinated alkyl chain and in additional with large optical tilt angle∼45 deg [1]. Such structures with different length of alkyl chain (9, 11, 13 and 15 fluorine atoms per chain) are source of different dynamic of alkyl chain with comparison to the hydrogen chain equivalent. It also has influence on dynamic of others interior parts of molecule as well dynamic of molecule as one complex. IR measurements extremely significant shows that molecular tilt angle taken for mesogen (BPh-Ph at freq. ∼1605 cm−1) is not zero and suggest that molecules in SmA phase are tilted. It is very spectacular but really possible if we assume that hcos2θi0.5 from IR and hcosθi from optical measurements are similar in low temperature and start differ when temperature increase until SmA phase is reached. We suggest that in SmA phase director is still tilted but because of molecular whirl or vanished correlation between the tilt directions in neighboring layers, director is perpendicular to the plane of smectic layer. Nonzero tilt angle in SmA phase is nothing new. It is also known experimentally as a de Vries phase [2]. We also notice that behavior of alkyl chain and CH2

group differ from behavior of mesogen in different temperatures. Summation of all molecular sublayers (mesogen + alkyl chain + CH2 group) gives quite accurate estimation of the layer thickness obtained by X-ray methods [3].

References

[1] J. Gasowska, R.Dabrowski, W. Drzewinski, M. Filipowicz, J. Przedmojski, K. Kenig, Ferroelectrics, 309, 83-93 (2004).

[2] U. Manna, J. K. Song, Y. P. Panarin, A. Fukuda, J. K. Vij, Phys. Rev. E 77, 041707 (2008).

[3] H. F. Gleeson, Y. Wnag, S. Watson, D. Sahagun-Sanchez, J. W. Goodby, M. Hird, A. Petrenko, M. A.

Osipov, J.Mater.Chem., 14, 1480 (2004).

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In document on Liquid Crystal Colloids (сторінка 83-104)