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Interaction and self-organization of inclusions in two-dimensional free-standing smectic films

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Pages 1-29 | Received 31 Jan 2019, Accepted 21 Feb 2019, Published online: 05 Apr 2019

References

  • Poulin P, Stark H, Lubensky TC, et al. Novel colloidal interactions in anisotropic fluids. Science. 1997;275:1770–1773.
  • Poulin P, Weitz DA. Inverted and multiple nematic emulsions. Phys Rev E. 1998;57:626–637.
  • Lubensky TC, Pettey D, Currier N, et al. Topological defects and interactions in nematic emulsions. Phys Rev E. 1998;57:610–625.
  • Senyuk B, Aplinc J, Ravnik M, et al. High-order elastic multipoles as colloidal atoms. arXiv:1811.03901 [cond-mat.soft].
  • Nelson DR. Toward a tetravalent chemistry of colloids. Nano Lett. 2002;2:1125–1129.
  • Stark H. Physics of colloidal dispersions in nematic liquid crystals. Phys Rep. 2001;35:281–389.
  • Fukuda J-i. Liquid crystal colloids: a novel composite material based on liquid crystals. J Phys Soc Jpn. 2009;78:041003.
  • Blanc C, Coursault D, Lacaze E. Ordering nano- and microparticles assemblies with liquid crystals. Liq Cryst Rev. 2013;1:83–109.
  • Muševič I. Solid microparticles in bulk liquid crystals. In: Lagerwal JPF, Scalia G, editors. Liquid crystals with nano and microparticles. Singapore: World Scientific; 2017. p. 323–360.
  • Smalyukh II. Liquid crystal colloids. Annu Rev Condens Matter Phys. 2018;9:207–226.
  • Brochard F, de Gennes P-G. Theory of magnetic suspensions in liquid crystals. J Physique. 1970;31(7):691–708.
  • Cladis PE, Kleman M, Pieranski P. Sur une Nouvelle Methode de Decoration de la Phase Mesomorphe du MBBA. CRAS (Paris). 1971;B273:275–277.
  • Meyer RB. Point disclinations at a nematic-isotropic liquid interface. Mol Cryst Liq Cryst. 1972;16:355–369.
  • Frank FC. I. Liquid crystals. On the theory of liquid crystals. Discuss Faraday Soc. 1958;25:19–28.
  • Pettey D, Lubensky TC, Link DR. Topological inclusions in 2D smectic C films. Liq Cryst. 1998;25:579–587.
  • Muševič I, Škarabot M, Tkalec U, et al. Two-dimensional nematic colloidal crystals self-assembled by topological defects. Science. 2006;313:954–958.
  • Poulin P, Cabuil V, Weitz DA. Direct measurement of colloidal forces in an anisotropic solvent. Phys Rev Lett. 1997;79:4862–4865.
  • Fukuda J-i, Yokoyama H. Separation-independent attractive force between like particles mediated by nematic-liquid-crystal distortions. Phys Rev Lett. 2005;94:148301-1–148301-4.
  • Kotar J, Vilfan M, Osterman N, et al. Interparticle potential and drag coefficient in nematic colloids. Phys Rev Lett. 2006;96:207801-1–207801-4.
  • Vilfan M, Osterman N, Čopič M, et al. Confinement effect on interparticle potential in nematic colloids. Phys Rev Lett. 2008;101:237801-1–237801-4.
  • Smalyukh II, Lavrentovich OD, Kuzmin AN, et al. Elasticity-mediated self-organization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal. Phys Rev Lett. 2005;95:157801.
  • Takahashi K, Ichikawa M, Kimura Y. Direct measurement of force between colloidal particles in a nematic liquid crystal. J Phys Cond Mat. 2008;20:075106-1–075106-5.
  • Rasi M, Zuhail KP, Roy A, et al. N-SmA-SmC phase transitions probed by a pair of elastically bound colloids. Phys Rev E. 2018;97:032701-1–032701-6.
  • Terentjev EM. Disclination loops, standing alone and around solid particles, in nematic liquid crystals. Phys Rev E. 1995;51:1330–1337.
  • Ruhwandl RW, Terentjev EM. Monte Carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle. Phys Rev E. 1997;56:5561–5565.
  • Ruhwandl RW, Terentjev EM. Long-range forces and aggregation of colloid particles in a nematic liquid crystal. Phys Rev E. 1997;55:2958–2961.
  • Stark H. Director field configurations around a spherical particle in a nematic liquid crystal. Eur Phys J E. 1999;10:311–321.
  • Andrienko D, Germano G, Allen MP. Computer simulation of topological defects around a colloidal particle or droplet dispersed in a nematic host. Phys Rev E. 2001;63:041701-1–041701-7.
  • Andrienko D, Allen MP, Skacej G, et al. Defect structures and torque on an elongated colloidal particle immersed in a liquid crystal host. Phys Rev E. 2002;65:041702-1–041702-7.
  • Loudet J-C, Poulin P. Application of an electric field to colloidal particles suspended in a liquid-crystal solvent. Phys Rev Lett. 2001;87:165503-1–165503-4.
  • Loudet J-C, Mondain-Monval O, Poulin P. Line defect dynamics around a colloidal particle. Eur Phys J E. 2002;7:205–208.
  • Fukuda J, Yokoyama H. Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field. Eur Phys J E. 2006;21:341–347.
  • Grollau S, Abbott NL, de Pablo JJ. Spherical particle immersed in a nematic liquid crystal: effects of confinement on the director field configuration. Phys Rev E. 2003;67:011702-1–011702-10.
  • Völtz C, Maeda Y, Tabe Y, et al. Director-configurational transitions around microbubbles of hydrostatically regulated size in liquid crystals. Phys Rev Lett. 2006;97:227801-1–227801-4.
  • Khullar S, Zhou C, Feng JJ. Dynamic evolution of topological defects around drops and bubbles rising in a nematic liquid crystal. Phys Rev Lett. 2007;99:237802-1–237802-4.
  • Ravnik M, Škarabot M, Žumer S, et al. Entangled nematic colloidal dimers and wires. Phys Rev Lett. 2007;99:247801.
  • Tkalec U, Ravnik M, Čopar S, et al. Reconfigurable knots and links in chiral nematic colloids. Science. 2011;333:62–65.
  • Araki T, Tanaka H. Colloidal aggregation in a nematic liquid crystal: topological arrest of particles by a single-stroke disclination line. Phys Rev Lett. 2006;97:127801.
  • Jampani VSR, Škarabot M, Čopar S, et al. Chirality screening and metastable states in chiral nematic colloids. Phys Rev Lett. 2013;110:177801.
  • Trivedi RP, Tasinkevych M, Smalyukh II. Nonsingular defects and self-assembly of colloidal particles in cholesteric liquid crystals. Phys Rev E. 2016;94:062703.
  • Hijnen N, Wood TA, Wilson D, et al. Self-organization of particles with planar surface anchoring in a cholesteric liquid crystal. Langmuir. 2010;26:13502–13510.
  • Škarabot M, Ravnik M, Žumer S, et al. Hierarchical self-assembly of nematic colloidal superstructures. Phys Rev E. 2008;77:061706-1–061706-4.
  • Muševič I, Škarabot M. Self-assembly of nematic colloids. Soft Matter. 2008;4:195–199.
  • Škarabot M, Ravnik M, Žumer S, et al. Two-dimensional dipolar nematic colloidal crystals. Phys Rev E. 2007;76:051406.
  • Zuhail KP, Sathyanarayana P, Seč D, et al. Topological defect transformation and structural transition of two-dimensional colloidal crystals across the nematic to smectic-A phase transition. Phys Rev E. 2015;91:030501(R).
  • Ognysta U, Nych A, Nazarenko V, et al. 2D interactions and binary crystals of dipolar and quadrupolar nematic colloids. Phys Rev Lett. 2008;100:217803-1–217803-4.
  • Ognysta U, Nych A, Uzunova VA, et al. Square colloidal lattices and pair interactions in a binary system of quadrupolar nematic colloids. Phys Rev E. 2011;83:041709.
  • Nych A, Ognysta U, Škarabot M, et al. Assembly and control of 3D nematic dipolar colloidal crystals. Nat Commun. 2013;4:1489.
  • Nazarenko VG, Nych AB, Lev BI. Crystal structure in nematic emulsion. Phys Rev Lett. 2001;87:075504-1–075504-4.
  • Lev B, Nych A, Ognysta U, et al. Nematic emulsion in a magnetic field. JETP Lett. 2002;75:322–325.
  • Smalykh II, Chernyshuk S, Lev BI, et al. Ordered droplet structures at the liquid crystal surface and elastic-capillary colloidal interactions. Phys Rev Lett. 2004;93:117801-1–117801-4.
  • Nych AB, Ognysta UM, Pergamenshchik VM, et al. Coexistence of two colloidal crystals at the nematic-liquid-crystal-air interface. Phys Rev Lett. 2007;98:057801-1–057801-4.
  • Paek S-I, Kim S-J, Kim J-H. Magnetic-field-induced structural change of a two-dimensional colloid of glycerol droplets on a nematic liquid-crystal surface. Phys Rev E. 2013;87:032505.
  • Gharbi MA, Nobili M, In M, et al. Behavior of colloidal particles at a nematic liquid crystal interface. Soft Matter. 2011;7:1467–1471.
  • Humar M, Skarabot M, Ravnik M, et al. Electrically tunable diffraction of light from 2D nematic colloidal crystals. Eur Phys J E. 2008;27:73–79.
  • Pieranski P, Beliard L, Tournellec JP, et al. Physics of smectic membranes. Physica A. 1993;194:364–389.
  • de Jeu WH, Ostrovskii BI, Shalaginov AN. Structure and fluctuations of smectic membranes. Rev Mod Phys. 2003;75:181–235.
  • Nguyen ZH, Park CS, Pang J, et al. Surface energetics of freely suspended fluid molecular monolayer and multilayer smectic liquid crystal films. PNAS. 2012;109:12873–12877.
  • Geminard JC, Holyst R, Oswald P. Meniscus and dislocations in free-standing films of smectic-A liquid crystals. Phys Rev Lett. 1997;78:1924–1927.
  • Kleman M, Lavrentovich OD. Soft matter physics: an introduction. New York: Springer; 2003.
  • Dolganov PV, Dolganov VK, Cluzeau P. The effect of spontaneous polarization on two-dimensional elasticity of smectic liquid crystals. JETP. 2013;145:1209–1216.
  • Stannarius R, Harth K. Defect interactions in anisotropic two-dimensional fluids. Phys Rev Lett. 2016;117:157801.
  • Stannarius R, Harth K. Inclusions in freely suspended smectic films. In: Lagerwal JPF, Scalia G, editors. Liquid crystals with nano and microparticles. Singapore: World Scientific; 2017. p. 361–414.
  • Dolle S, Harth K, John T, et al. Impact and embedding of picoliter droplets into freely suspended smectic films. Langmuir. 2014;30:12712–12720.
  • Qi Z, Park CS, Glaser MA, et al. Experimental realization of an incompressible Newtonian fluid in two dimensions. Phys Rev E. 2016;93:012706.
  • Schuring H, Stannarius R. Isotropic droplets in thin free standing smectic films. Langmuir. 2002;18:9735–9743.
  • Dolganov PV, Cluzeau P, Joly G, et al. Interaction of surfaces in smectic membranes and their instability near thinning transitions. Phys Rev E. 2005;72:031713.
  • Bohley C, Stannarius R. Inclusions in free standing smectic liquid crystal films. Soft Matter. 2008;4:683–702.
  • Harth K, Stannarius R. Corona patterns around inclusions in freely suspended smectic films. Eur Phys J E. 2009;28:265–272.
  • Dolganov PV, Dolganov VK, Kats EI. Anomalies of a meniscus of microinclusions in freely suspended smectic films. JETP Lett. 2015;102:242–247.
  • Lee JB, Konovalov D, Meyer RB. Textural transformation of islands on free standing Smectic-C* liquid crystal films. Phys Rev E. 2006;73:051705.
  • Bougrioua F, Cluzeau P, Dolganov P, et al. Light-induced layer by layer thickening in photosensitive liquid crystal membranes. Phys Rev Lett. 2005;95:027802.
  • de Jeu WH, Fera A, Ostrovskii BI. Thickening of a smectic membrane in an evanescent X-ray beam. Eur Phys J E. 2004;15:61–64.
  • Clark NA, Eremin A, Glaser MA, et al. Realization of hydrodynamic experiments on quasi-2D liquid crystal films in microgravity. Adv Space Res. 2017;60:737–751.
  • Radzihovsky SP, Cranfill C, Nguyen Z, et al. Two-dimensional island emulsions in ultrathin, freely suspended liquid crystal films. Soft Matter. 2017;13:6314–6321.
  • Stoebe T, Mach P, Huang CC. Unusual layer-thinning transition observed near the smectic-A-isotropic transition in free-standing liquid-crystal films. Phys Rev Lett. 1994;73:1384–1387.
  • Demikhov EI, Dolganov VK, Meletov KP. Step-by-step thinning of free-standing films above the smectic-A-nematic phase transition. Phys Rev E. 1995;52:R1285–R1287.
  • Pikina SE, Ostrovskii BI. Nucleation and growth of droplets in the overheated free-standing smectic films. Eur Phys J E. 2017;40:24–40.
  • Dolganov PV, Demikhov EI, Dolganov VK, et al. Collective behaviour of light-induced droplets in smectic membranes. Eur Phys J E. 2003;12:593–597.
  • de Gennes PG, Prost J. The physics of liquid crystals. 2nd ed. Cambridge: Clarendon Press; 1994.
  • Dolganov PV, Nguyen HT, Joly G, et al. Different mechanisms of nucleation and self-organization of droplets in ferroelectric smectic membranes. Eur Phys J E. 2008;25:31–37.
  • Link DR, Natale G, Shao R, et al. Spontaneous formation of macroscopic chiral domains in a fluid smectic phase of achiral molecules. Science. 1997;278:1924–1927.
  • Dolganov PV, Kats EI, Cluzeau P. Stepwise transition of a topological defect from the smectic film to the boundary of a dipolar inclusion. Phys Rev E. 2010;81:031709-1–031709-6.
  • Korolev KS, Nelson DR. Defect-mediated emulsification in two dimensions. Phys Rev E. 2008;77:051702-1–051702-11.
  • Cluzeau P, Poulin P, Joly G, et al. Interactions between colloidal inclusions in two-dimensional smectic-C* films. Phys Rev E. 2001;63:031702–1031702-4.
  • Cluzeau P, Dolganov V, Poulin P, et al. Droplets nucleation in smectic-C* free-standing films. Mol Cryst Liq Cryst. 2001;364:381–393.
  • Najjar R, Galerne Y. Two-dimensional liquid crystal dispersions in free standing films of tilted smectics. Mol Cryst Liq Cryst. 2001;367:475–485.
  • Lejcek L. Inclusions with finite surface anchoring energies in smectic C and chiral smectic C* free-standing films. Ferroelectrics. 2016;495:116–128.
  • Zhou C, Yue P, Feng JJ. The rise of Newtonian drops in a nematic liquid crystal. J Fluid Mech. 2007;593:385–404.
  • Mondain-Monval O, Dedieu JC, Gulik-Krzywicki T, et al. Weak surface energy in nematic dispersions: saturn ring defects and quadrupolar interactions. Eur Phys J B. 1999;12:167–170.
  • Cluzeau P, Bonnand V, Joly G, et al. Self-organization of N* inclusions in SmC* free-standing films. Eur Phys J E. 2003;10:231–240.
  • Dolganov PV, Cluzeau P. Manipulation of interaction and self-organization of inclusions in free-standing smectic films). Abstracts of 36th German topical meeting on liquid crystals; 2008 Mar 19–21; Magdeburg, Germany.
  • Vőltz C, Stannarius R. Self-organization of isotropic droplets in smectic-C free-standing films. Phys Rev E. 2004;70:061702–1061702-9.
  • Vőltz C, Stannarius R. Buckling instability of droplet chains in freely suspended smectic films. Phys Rev E. 2005;72:011705.
  • Stannarius R, Vőltz C. Spontaneous buckling of compressible droplet chains in free standing smectic-C films. Phys Rev E. 2005;72:032701.
  • Pattanaporkratana A, Park CS, Maclennan JE, et al. Manipulation of disk-shaped islands on freely suspended smectic films and bubbles using optical tweezers. Ferroelectrics. 2004;310:131–135.
  • Conradi M. Light-controlled movement of isotropic droplets in smectic films. Liq Cryst. 2010;37:1215–1220.
  • Pattanaporkratana A, Park CS, Maclennan JE, et al. Direct measurement of interaction forces between islands on freely suspended smectic C films using multiple optical tweezers. Ferroelectrics. 2006;344:71–80.
  • Lee J-B, Pelcovits RA, Meyer RB. Role of electrostatics in the texture of islands in free-standing ferroelectric liquid crystal films. Phys Rev E. 2007;75:051701-1–051701-5.
  • Dolganov PV, Dolganov VK. Director configuration and self-organization of inclusions in two-dimensional smectic membranes. Phys Rev E. 2006;73:041706-1–041706-10.
  • Tasinkevych M, Silvestre NM, Patricio P, et al. Colloidal interactions in two-dimensional nematics. Eur Phys J E. 2002;9:341–347.
  • Patricio P, Tasinkevych M, Telo da Gama MM. Colloidal dipolar interactions in 2D smectic-C films. Eur Phys J E. 2002;7:117–120.
  • Cluzeau P, Joly G, Nguyen HT, et al. Two-dimensional ordering of inclusions in smectic C phase. JETP Lett. 2002;75:482–486.
  • Cluzeau P, Joly G, Nguyen HT, et al. Formation of two-dimensional crystal-like structures from inclusions in smectic C films. JETP Lett. 2002;76:351–354.
  • Dolganov PV, Nguyen HT, Joly G, et al. Ferroelectricity-induced effects in interaction and self-organization of inclusions in smectic membranes. Europhys Lett. 2006;76:250–256.
  • Dolganov PV, Shuravin NS, Dolganov VK, et al. Chain structures and clusters of particles with the mixed dipole-quadrupole interaction in smectic freely suspended nanofilms. JETP Lett. 2016;104:263–268.
  • Tasinkevych M, Silvestre NM, Telo da Gama MM. Liquid crystal boojum-colloids. New J Phys. 2012;14:073030.
  • Dolganov PV, Nguyen HT, Joly G, et al. Shape of nematic droplets in smectic membranes. Europhys Lett. 2007;78:66001-p1–66001-p5.
  • Burylov SV, Raikher YL. Orientation of a solid particle embedded in a monodomain nematic liquid crystal. Phys Rev E. 1994;50:358–367.
  • Bohley C, Stannarius R. Energetics of 2D colloids in free-standing smectic-C films. Eur Phys J E. 2006;20:299–308.
  • Silvestre NM, Patrício P, Telo da Gama MM. Interactions between circular inclusions in smectic-C films with planar anchoring. Mol Cryst Liq Cryst. 2008;495:266/[618]–273/[625].
  • Fukuda J, Yokoyama H. Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle: numerical analysis using adaptive grids. Eur Phys J E. 2001;4:389–396.
  • Bohley C, Stannarius R. Colloidal inclusions in smectic films with spontaneous bend. Eur Phys J E. 2007;23:25–30.
  • Fukuda J. Configuration of a chiral smectic-C film with a circular inclusion. Eur Phys J E. 2007;24:91–98.
  • Dolganov PV, Cluzeau P. Influence of chirality on director configuration and droplet interaction in ferroelectric free-standing films. Phys Rev E. 2008;78:021701-1–021701-4.
  • Dolganov PV, Nguyen HT, Kats EI, et al. Rearrangement of topological defects and anchoring on the inclusion boundary in ferroelectric smectic membranes. Phys Rev E. 2007;75:031706-1–031706-8.
  • Silvestre NM, Patricio P, Telo da Gama MM, et al. Modeling dipolar and quadrupolar defect structures generated by chiral islands in freely suspended liquid crystal films. Phys Rev E. 2009;80:041708–1041708-8.
  • Dolganov PV, Kats EI, Dolganov VK, et al. Dimer structures formed in smectic films by inclusions with parallel and antiparallel topological dipole moments. JETP Lett. 2009;90:382–386.
  • Dolganov PV, Dolganov VK, Cluzeau P. Behavior of inclusions with different value and orientation of topological dipoles in ferroelectric smectic films. JETP. 2009;109:169–175.
  • Dolganov PV, Shuravin NS, Dolganov VK, et al. Smectic Islands in antiferroelectric nanofilms. JETP. 2017;125:709–713.
  • Tang X, Selinger JV. Orientation of topological defects in 2D nematic liquid crystals. Soft Matter. 2017;13:5481–5490.
  • Dolganov PV, Shuravin NS, Fukuda A. Two-dimensional hexagonal smectic structure formed by topological defects. Phys Rev E. 2016;93:032704-1–032704-4.
  • Kamien RD, Selinger JV. Order and frustration in chiral liquid crystals. J Phys Condens Matter. 2001;13:R1–R22.
  • Meyer RB, Pelcovits RA. Electroclinic effect and modulated phases in smectic liquid crystals. Phys Rev E. 2002;65:061704.
  • Link DR, Maclennan JE, Clark NA. Simultaneous observation of electric field coupling to longitudinal and transverse ferroelectricity in a chiral liquid crystal. Phys Rev Lett. 1996;77:2237–2240.
  • Dolganov PV. Response of structures formed by individual and self-organized inclusions to electric field in ferroelectric smectic nanofilms. J Mol Liq. 2018;267:249–252.
  • Caillier F, Oswald P. Collapse dynamics of smectic-A bubbles. Eur Phys J E. 2006;20:159–172.
  • Dahmlow P, Trittel T, May K, et al. Surface reduction of freely floating smectic bubbles. Liq Cryst. 2018;45:993–1003.
  • May K, Harth K, Trittel T, et al. Dynamics of freely floating smectic bubbles. EPL. 2012;100:16003.
  • Noruzifar E, Camley BA, Brown FLH. Calculating hydrodynamic interactions for membrane-embedded objects. J Chem Phys. 2014;141:124711.
  • Saffman PG, Delbrück M. Brownian motion in biological membranes. Proc Natl Acad Sci USA. 1975;72:3111–3113.
  • Nguyen ZH, Atkinson M, Park CS, et al. Crossover between 2D and 3D fluid dynamics in the diffusion of islands in Ultrathin Freely Suspended smectic films. Phys Rev Lett. 2010;105:268304.
  • Eremin A, Baumgarten S, Harth K, et al. Two-dimensional microrheology of freely suspended liquid crystal films. Phys Rev Lett. 2011;107:268301.
  • Qi Z, Nguyen ZH, Park CS, et al. Mutual diffusion of inclusions in freely suspended liquid crystal films. Phys Rev Lett. 2014;113:128304-1–1283045.
  • Kuriabova T, Powers TR, Qi Z, et al. Hydrodynamic interactions in freely suspended liquid crystal films. Phys Rev E. 2016;94:052701-1–052701-14.
  • Klopp C, Stannarius R, Eremin A. Brownian dynamics of elongated particles in a quasi-two-dimensional isotropic liquid. Phys Rev Fluids. 2017;2:124202.
  • Turner MS, Sens P. Interactions between particulate inclusions in a smectic-A liquid crystal. Phys Rev E. 1997;55:R1275–R1278.
  • de Oliveira IN, Pereira MSS, Lyra ML, et al. Long-range elastic-mediated interactions between nanoparticles adsorbed on free-standing smectic films. Phys Rev E. 2009;80:042702.
  • Pereira MSS, Lyra ML, de Oliveira IN. Elastic mediated force between nanoparticles adsorbed on smectic films under an external field. Phys Rev E. 2013;87:022502-1–022502-7.
  • Conradi M, Ziherl P, Sarlah A, et al. Colloids on free-standing smectic films. Eur Phys J E. 2006;20:231–236.
  • Meienberg K, Malinina T, Nguyen Z, et al. Nanoparticle aggregation and fractal growth in fluid smectic membranes. Mol Cryst Liq Cryst. 2015;611:14–20.
  • Gharbi AM, Beller DA, Sharifi-Mood N, et al. Elastocapillary driven assembly of particles at free-standing smectic-A films. Langmuir. 2018;34:2006–2013.

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