Memory effects from topological connectivity of nematic liquid - PowerPoint PPT Presentation

Memory effects from topological connectivity of nematic liquid crystals confined in porous materials Takeaki ARAKI a,b) , Marco BUSCAGLIA c) , Tommaso BELLINI c) and Hajime TANAKA a) a) Institute of Industrial Science, University of Tokyo, Japan b) Department of Physics, Kyoto University, Japan c) Department of Chemistry, Biochemistry and Biotecnology, University of Milano, Italy

Liquid crystal Liquid crystals are substances that exhibit a phase of matter that has properties between those of a n-4'-MethoxyBenzylidene-n-ButylAnilin (MBBA) conventional liquid, and those of a solid crystal. smectic isotropic nematic orientational order disorder orientational order and layering (Liquid phase) temperature

Elasticity of nematic phase spray (K 1 ) twist ( K 2 ) bend (K 3 ) Frank elastic energy       1             ˆ ˆ ˆ ˆ ˆ 2 2 2 { ( ) ( ( )) ( ( )) F d r K n K n n K n n   1 2 3   2 n    local director field  (| | 1 ) ( r ) n

Defects in liquid crystals When incommensurate domains contact, defects are formed at the domain boundary Schlieren texture        ( ) ( ) r s r 0  : angular coordinate  : angle of director field  1   defect core energy 2      s : the strength of the defect 2 E d d r s K

Defects in liquid crystals A defect of s interacts with that of s’. Roughly, the strength of the interaction is proportional to ss’ . (+,+) and (-,-) : repulsive (+,-) : attractive A line defect has a tension in 3D. It tend to be shrunken.

Annihilation of defects In bulk, defects of nematic phase are not long-lived A defect of the topological charge s is annihilated with other one of  s 1 1     s s 2 2    1 0 s s Minomura et al. (1997)

Re-organizations of defects 1   s 2 1 1 1       s s s 2 2 2 Energy barrier for a reorganization     3 / 2 1 / 2 ~ E K K :elastic modulus  : chemical potential difference Chuang et al. (1993)

Simulations of nematic ordering Characteristic length R  (Typical separation between defects) 1 / 2 t

Anchoring effect nematic liquid crystal  Director field is aligned at n solid surface with tilt angle   solid wall      90  0 planar homeotropic

Liquid crystal and solid objects The inclusion of solid objects imposes the formation of defect in liquid crystals nematic liquid crystal particles (colloids) porous media

A particle and defect in NLC elastic energy F (a.u.) anchoring strength W (a.u.) K W c   C ( 3 . 5 ) C a H. Stark, Phys. Rep. 351, 387 (2001).

Topology of defect structure Araki and Tanaka (2006) A Saturn-ring defect < Topologically arrested structure

Aggregation of colloids Ravnik et al. (2007) Musevic et al. (2006)

Nematic liquid crystal in porous media Nematic liquid crystal porous media(PM) They show interesting behaviors due to the topological constraints of the defects. And they provide promising properties for optical devices. (Crawford and Zumer (1996)), Bellini et al . (1996,2000,2002).

Nematic liquid crystal in a simple cell E Off On Off The director field can be tuned by external field. Soon after the field is switched off, it will recover the original pattern.

Memory effect of confined nematic liquid crystal Rotunno et al. (2005). Buscaglia (2006) A nematic liquid crystal in a porous medium can efficiently keep its orientational order, even after the field is switched off. The nematic liquid crystal memorizes the orientational field. The aim of this study is to explore the mechanism of the memory effects.

Preparation of random porous media Cahn-Hilliard-Cook equation                2 3 2  t     30 . 7   4 . 6 11 . 8 We can obtain isotropic random porous media with controlled sizes.  : mean pore size

Spatial distributions of Q Red regions represent the porous medium W =0 W =1  bulk 0 . 703 T IN The nematic order grows from the surfaces in a porous medium with finite W .

Defect structure of nematic liquid crystal in porous media Since all the channels do not necessarily have disclination lines running through them, many metastable configurations can be found. The defect configurations are long-lived since the energy barriers connecting them are associated to simultaneous liquid crystal rotation in entire channels, and hence larger than thermal fluctuations. This results in non-ergodic glassy behaviors, defect structures for different analogous to a spin glass. simulations of the same condition The number of the possible configurations is estimated as,    1 / 2 ( 1 ) p  3  6 p average number of arms at nodes, typically p 1      Euler characteristic (topological invariant) dS K 2 ~10 1000000 for 1 mm cell of 1  m pores !

Transformation of defect structure by an external field E =0.3 E =1.0 after the quench under an electric field after the application A strong field melts the defect structure and the topology of defect structure can be changed. The new topology is conserved even after the field is switched off!

Induced and remnant nematic orders   1 3 1     * Q n z n Orientational order along the field z   ( ) 2 3 Q T 0 simulations Q E Q M experiments (5CB in millipore filter (3  m) and silica gel (0.8  m)) E =1.25V/  m

NLC in regular porous materials Bicontinuous cubic (BC) Simple cubic packing (SC) Cylindrical channels (Cyl) The defect structure is also regular in ordered porous media.

Relaxation of memorized order Random porous medium (PPM) Bicontinuous cubic (BC) Q ( t ) Q ( t ) In BC, only a single relaxation mode is observed. After the fast mode, the second slow relaxation appears in RPM. BC: single stretched exponential decay       S ( ) exp( ( / ) ) Q t Q Q t Logarithmic decay for M S superconductor: RPM: stretched exponential decay and logarithmic decay  Anderson (1962) Q        ( ) exp( ( / ) ) L Q t Q Q t Kim et al. (1962)    M S S 1 log( 1 / ) t L

Fast relaxation mode In the both type of porous media, the fast relaxation mode represents the recovery of the elasticity of the nematic phase that is distorted by the external field. In this fast process, the topology of the defect structure does not change. 30 1 0.8 RPM 20 BC  s 0.6  RPM 0.4 10 BC 0.2 0 0 0 10 20 30 40 50 0 10 20 30 40 50   The elastic theory predicts the relaxation time is proportional to l 2 in the limit of the strong anchoring.     1       2     2 F n K dV n W dS n s  2 2       1 F S   K n     t n

T -Dependence of the relaxations RPM BC T =0.1 T =0.01 Q ( t ) Q ( t ) bulk T<T NI T =1.0 bulk T>T NI T =1.0 t (MCC) t (MCC) In BC, the remnant order is almost proportional to the bulk nematic order. bulk , it decays to zero without the slow mode. Above T NI In RPM, the second mode becomes slower with decreasing temperature. What is the mechanism of the second mode in RPM?

The topological change of the defect structure in RPM   43 . 9 At T =0.1 for The second slow mode stems from the reorganizations of topology of the defect structure

The second slow relaxation in RPM  Q        ( ) exp( ( / ) ) L Q t Q Q t    M S S 1 log( 1 / ) t L    12 . 7 Pore size - dependence at T =0.1 Temperature dependence for 10 5 10 4 10 4  L  L 10 3    0 ' exp( / ) b T 10 3 L L    0  exp( ) a L L 10 2 10 2 0 10 20 30 40 0 10 20 30 40 50 60  1 /T    ln / T L In BC, the defect structure reaches the more stable configuration after the fast mode. Then, the second mode is absent.

The topological change of the defect structure in RPM In a subunit of the volume , the elastic 3  energy density is estimated as  1 1 K   2 ( ) ~ e K n 2 2 2  Thus, the stored elastic energy in this small volume is   3   E e K The energy barrier against the topological  change is also scaled as K    exp( / ) cK T L

T and l - dependences of the remnant orders 1 1 Q Q BC: BC: 0.8 0.8 M M   0.6 0.6 Q Q RPM: M L Q   Q Q Q RPM: M L 0.4 0.4 0.2 0.2 Q RPM: M L Q RPM: M L 0 0 10 -2 10 -1 10 0 0 10 20 30 40  T      S  Q ( t ) Q Q exp( ( t / ) ) BC: M S  Q        L Q ( t ) Q Q exp( ( t / ) ) RPM:    M S S 1 log( 1 / ) t L In BC, the remnant order appears to be independent of the pore size. This is consistent with the scaling argument for the strong anchoring case. In RPM, the remnant depends on the mean pore size because of its non- ergodic glassy behavior.