Soft and Biological Matter

Transcription

1 Soft and Biological Matter Series editors Roberto Piazza, Milan, Italy Peter Schall, Amsterdam, The Netherlands Roland Netz, Berlin, Germany Wenbing Hu, Nanjing, People s Republic of China Gerard Wong, Los Angeles, USA Patrick Spicer, Sydney, Australia David Andelman, Tel Aviv, Israel Shigeyuki Komura, Tokyo, Japan

2 Soft and Biological Matter is a series of authoritative books covering established and emergent areas in the realm of soft matter science, including biological systems spanning from the molecular to the mesoscale. It aims to serve a broad interdisciplinary community of students and researchers in physics, chemistry, biophysics and materials science. Pure research monographs in the series as well as those of more pedagogical nature, will emphasize topics in fundamental physics, synthesis and design, characterization and new prospective applications of soft and biological matter systems. The series will encompass experimental, theoretical and computational approaches. Both authored and edited volumes will be considered. More information about this series at

3 Igor Muševič Liquid Crystal Colloids 123

4 Igor Muševič Jožef Stefan Institute University of Ljubljana Ljubljana Slovenia ISSN ISSN (electronic) Soft and Biological Matter ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 For Maja, Sašo and Nataša

6 Preface I started the work on liquid crystal colloids around the year 2000 as a continuation of our experiments on forces between surfaces in liquid crystals. We were using the atomic force microscope (AFM) as a tool to measure structural forces in the nematic and smectic liquid crystals. In those experiments, liquid crystal was confined to a very narrow gap, between 1 and 100 nanometres, typically between a perfectly smooth crystalline surface of mica and the micrometre diameter glass microsphere attached to the cantilever of the AFM. We were looking for the fluctuation forces, also called the Casimir force, of the nematic director field confined to the thin gap between the mica and the microsphere. We never observed the Casimir force, simply because it was to tricky to separate it from the much stronger mean-field forces, which were caused by the gradient of the order parameter in that gap. These mean-field forces between the two surfaces at the nanometre separation were indeed strong, and I was questioning myself whether similar forces between the surfaces of the particles in the nematic liquid crystal exist at a much larger separation, of the order of a micron or so. At the same time, two articles came along my desk: one was the Science paper by Poulin, Stark, Lubensky and Wietz, showing beautiful images of the attraction of water droplets in nematics. The other was a paper on photonic crystals by Yablonovitch and Gmitter, published in Physical Review Letters in When reading these papers, I asked myself whether it is possible to build photonic crystals by putting small colloidal particles into nematic liquid crystals, combining the essence the above-mentioned both papers. This was around the year At that time, the experiments with colloidal particles in nematics were practically a kind of science fiction, since no tool was available for grabbing individual micrometre diameter particles inside the measuring cell and moving them to an arbitrary position. However, we were lucky that in that period laser tweezers started to emerge as very powerful non-contact tweezers, which use light to trap and manipulate the particles even when they are floating in the nematic liquid crystal sandwiched between two rather thick glass plates. As mentioned before, we started the experiments with laser tweezers by good luck, using low refractive glass beads, putting them in the nematic liquid crystal and vii

7 viii Preface trying to see whether the tweezers are able to grab such a particle and move it. It came as a big surprise to the three of us, Miha Škarabot, Igor Poberaj and myself, when we saw that glass beads could nicely be trapped in the nematic liquid crystal, although the refractive index of glass is lower than the refractive indices of both nematic liquid crystal used in the experiments. I explained this anomalous trapping by noting that polarisation of the laser tweezers is an important parameter and that the second important phenomenon is the action of the strong electric field of the laser tweezers on the nematic liquid crystal itself. We could soon explain this anomalous trapping on a general grounds by considering elastic deformation of nematic liquid crystal by light and the polarisation of light, which selectively grabs the nematic director along the direction of larger polarizibility and moves the particle together with the field. After the work on this anomalous trapping of colloids by optical tweezers was published, there was a lot of excitement and new ideas on what physics experiments could be done with the laser tweezers. This result opened the exciting pathway to the assembly of the first 2D nematic colloidal crystal in Another milestone occurred in the same year 2006, when Miha Ravnik proposed to use local quench of the nematic liquid crystal colloids from the isotropic phase to the nematic phase and entangle two colloidal particles. This was soon realised in the experiment by using the absorption of the laser tweezers in the nematic liquid crystal colloids to melt the nematic and then quench it. The result was colloidal entanglement, where colloidal particles could be entangled by topological defect loops. The entanglement later provided the most complex colloidal binding in the nematic liquid crystals, i.e. knotting and linking of colloids, which was observed by Uroš Tkalec and myself in Linking and knotting of the nematic liquid crystal opened the doors to the experimental topology in liquid crystals and what followed were several years of very creative and exciting exploration of this complex phenomenon by many different groups all over the world. Along the work on nematic colloids, I began in 2007 with Matjaž Humar a parallel work on an entirely new line of research with the aim of using the nematic dispersions for microphotonics. There was only a slight hint at that time that liquid crystals could provide a beautiful setting for the realisation of tiny photonic elements, such as optical microcavities, microlasers and photonic microfibers. Indeed, all this was found latter in the dispersions of nematic or cholesteric liquid crystals in other immiscible fluids, such as water. This led me to consider whether one could use the structural forces for binding and entangling colloidal particles in the nematics together with the photonic properties of nematic dispersions. The aim is to create a soft matter analogue to the solid state microphotonic circuits, where instead of silicon, a soft matter is used to self-assemble into a topological photonic soft matter. At present, we have clear proof that such technology based on soft matter self-assembly is indeed possible. This work is written as a kind of retrospective of all the mentioned studies and it follows, more or less chronologically, the experimental work performed in the last decade, starting from the year It turns out that telling the story in a chronological order is the best way to present the development of ideas from simple

8 Preface ix beginnings to very complex issues. Most of the work in this book was performed in my laboratory at the J. Stefan Institute; however, the book would be far from complete without including the work of other researchers from very different laboratories around the world. I did my best to include all relevant work in this field and I hope that I have not missed any important references. Ljubljana, Slovenia December 2016 Igor Muševič

9 Acknowledgements I owe many thanks to a number of colleagues and friends with whom I have been working in all these years. In the first place, I would like to mention Miha Škarabot, with whom I started the experiments on nematic colloids around the year Several years before, Klemen Kočevar and myself performed the first Atomic Force Microscopy experiments of measuring forces between the particles in the nematic liquid crystals. At the same time, Giovanni Carbone collaborated with me and developed a new force measuring technique for detecting presmectic forces in the nematics. I also owe thanks to Igor Poberaj and Dušan Babič for enabling our work with their laser tweezers, which were later on used in so many fascinating experiments. One of the most demanding and exciting experiments was performed by Uroš Tkalec, who noticed strange knotting and linking of colloidal particles in chiral nematic cells. I still vividly remember many hours of discussion we had on this phenomenon, and how long it took for us to understand what was really happening in knotting and linking colloidal experiments. I owe many thanks to Ulyana Ognysta, Andriy Nych, Christian Bahr, Giorgio Mirri and Surajit Dhara. This work would not be possible without collaboration with my colleagues from the physics theory of liquid crystals, first Slobodan Žumer, then Miha Ravnik and Simon Čopar, with whom I spent countless hours of vivid discussions, analysis of the experiments, comparisons of experimental findings and theoretical predictions, etc. Without this synergy between the experiments and the theory, much less would be achieved in this field. I owe special thanks to Matjaž Humar, who was brave enough to start an entirely new line of research on the microphotonics of liquid crystals. A lot of this work was done by my Ph.D. students and post-docs, who visited my lab, and I would like to thank Venkata Subba Rao Jampani, Marjetka Conradi, Anna Ryzhkova, Maryam Nikkhou, Karthik Peddireddy, Gregor Posnjak, Maruša Mur and Uroš Jagodič. Igor Muševič xi

10 Contents 1 Introduction Molecular Order in Nematic Liquid Crystals Landau-de Gennes Theory of the Nematic-Isotropic Phase Transition Elastic Distortions of Nematic Liquid Crystals Interactions of Liquid Crystals with Surfaces Optical Properties of Nematic Liquid Crystals Topological Defects in Nematic Liquid Crystals Winding Number and Topological Charge Euler Characteristic and Genus of Colloids Elastic Energy of Topological Defects Dipolar and Quadrupolar Nematic Colloids Dipolar Nematic Colloids: Elastic Dipoles with Hedgehogs Quadrupolar Nematic Colloids and Saturn Rings Forces Between Spherical Colloidal Particles in Nematic Liquid Crystals Forces Between Spherical Dipolar Colloidal Particles in Nematics Forces Between Spherical Quadrupolar Colloidal Particles in Nematics Mixed Interaction: Dipolar Spherical Particles Interact with Quadrupolar Particles in Nematic Forces Between Micro-rods in a Nematic Liquid Crystal Janus Colloids and Platelets in Nematic Liquid Crystals Nanoparticles in a Nematic Liquid Crystal Self-diffusion and Pair Interaction of Nanocolloids in the Nematic Liquid Crystal Interaction of Nanocolloids with Topological Defects Vortices and Nematic Colloids xiii

11 xiv Contents 2.8 Ferromagnetism in Dispersions of Magnetic Platelets in Nematic Liquid Crystals Forces Between Particles in Chiral Nematic Liquid Crystals Optical Trapping and Manipulation of Nematic Colloids Optical Tweezing of Particles in Isotropic Media Trapping and Manipulation of Particles in Nematic Liquid Crystals Measuring Forces Between Nematic Colloids by Video-Microscopy and Particle Tracking D and 3D Colloidal Crystals and Superstructures Photonic Crystals Two-Dimensional Dipolar Colloidal Crystals in Nematic Liquid Crystals Two-Dimensional Quadrupolar Colloidal Crystals in Nematic Liquid Crystals Numerical Simulations of Two-Dimensional Quadrupolar Colloidal Crystals in Nematic Liquid Crystals Binary Colloidal Crystals in Nematic Liquid Crystal: Mixture of Dipoles and Quadrupoles Three-Dimensional Nematic Colloidal Crystals Hierarchical Assembly of Nematic Colloids Entanglement of Nematic Colloids Entanglement of Colloidal Particles in a Homogeneous Nematic Knots and Links in Chiral Nematic Colloids Charge Production and Entanglement on a Fibre in a Nematic Liquid Crystal Elastic Interactions and Entaglement of Microspheres and Fibres in a Nematic Liquid Crystal Colloidal Particles of Complex Topology in Nematics Topology of Colloidal Particles Is Important Colloidal Handlebodies in Nematics Knot- and Link-Shaped Microparticles in Nematics Möbius Strips and Non-orientable Surfaces in Chiral Nematics Koch Stars Colloids in Nematics Spiraling Rods, Flat Spirals and Ribbed Rods in Nematics Nematic Microdroplets, Shells and Handlebodies Structure and Topology of Nematic Microdroplets Structure and Topology of Chiral Nematic Microdroplets with Parallel Surface Anchoring Structure and Topology of Chiral Nematic Microdroplets with Perpendicular Surface Anchoring

12 Contents xv 7.4 Skyrmions and Torons in Chiral Nematic Microdroplets Toroidal Nematics and Handlebodies Nematic Shells Topological Particle-Like Structures in Chiral Nematics Strange Imperfections and Self-formed Structures in Chiral Nematic Liquid Crystals Skyrmions in 2D Chiral Nematics Torons in 2D Chiral Nematics Photonic Properties of Nematic Microdroplets Photonics from Liquid Crystals Whispering Gallery Mode Resonances in Nematic Microdroplets Nematic Microdroplets as WGM Microlasers D Microlasers from Cholesteric Liquid Crystal Droplets Wave Guiding and Lasing in Smectic a Liquid Crystal Fibres References Index