Slide 1Slide 2Slide 3Slide 4Slide 5Granular versus ColloidalSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Introductory remarksLiquid crystals as quintessential soft matter.Simultaneously transmit torques (solid) and flow (liquid).NOT a soft solid, like a gel, but a true solid and a true fluid.Contrast with glasses – transmits torque for “high” frequencies while flows for “low” frequencies.Very soft. kT is very important.What is responsible for this remarkable behavior?Introductory remarksClassification of liquid crystals by symmetry, structure and description of their macroscopic properties.Classification of liquid crystals by materials, length scale, geometry, molecular complexity.Continuum description of elasticity and hydrodynamics.Phase behavior.Interaction with external fields.Characteristic defects.Introductory remarksHow does the field of liquid crystal research fit into into soft matter?Historically, liquid crystals, colloids, polymers were studied by chemists.1960’s French physicists (around deGennes) revived liquid crystal research.1m 10-2 -10-4 m10-5 -10-8 m10-9 -10-10 m “macro”Colloidsliquid crystals“quantum”gh(h)kTmgh-e)( hThermal motion prevents sedimentationyetstrongly couple to external fieldsIntroductory remarksRecognition that energy, length and time scales are similar for colloids, polymers, liquid crystals, emulsions, gels, membranes.Consequently, same theoretical description.http://www.elsie.brandeis.edu/Feb 1984: Pieranski: Colloidal Crystals, Les Houches Chaikin, Clark, Pieranski, Ackerson, Maret, Klein, JP Hansen, Charvolin, Dubois-Violette, Pansu, …..Personal history: irreversible aggregation of colloids w. G.B. Benedek in 1979, x-ray diffraction of virus with D.L.D. Caspar in 1980, 2D colloids and liquid crystals for thesis w. R.B. Meyer 1981-86.Granular versus Colloidal 100 nm TMV 10,000,000 nmhttp://www.uio.no/studier/emner/matnat/kjemi/KJM3100/v06/undervisningsmateriale/kjm3100_liquid_crystals_f.pdfChemistry of materials: Paul Norby, Kjemisk Institutt, Norwayhttp://www.uio.no/studier/emner/matnat/kjemi/KJM3100/v06/http://fig.if.usp.br/~school06/palfy_1.pdfhttp://fig.if.usp.br/~school06/http://www.maths.strath.ac.uk/research/seminars/LClectures/http://bly.colorado.edu/lcphysics/textures/http://boulder.research.yale.edu/Boulder-2002/notes.htmlhttp://dept.kent.edu/spie/liquidcrystals/index.htmlBooksCambridge University PressphenomenologyLCD flat panel: $50B in 2005(1889)Fliessende Kristalle: “flowing crystals”Otto Lehmann:Über fliessende Kristalle, Zeitschrift fur Physikalische Chemie, 1889.If one trusts the interpretation of the experimental observations, this is so far the only case whan a crystalline substance, showing considerable birefringence, has such a weak mechanical strengththat it can hardly resist the action of its own weight.Forty years of debates between view that liquid crystals were chemically and physically homogeneous phases vs. view that optical turbidity was a result of either demixing impure substances or incomplete melting of the crystalline phase.George Friedel (1922): “mesomorphic states”. States are intermediary (meso-morphic) between those of crystals and liquids.230 space groups allowing for the classification of all possible crystalline structuresin 3D.The same substance can display crystalline polymorphism dependingon temperature and pressure (ice IX, etc.).Analogously mesomorphic polymorphism is a characteristic of liquid crystalsModern definition of mesophases; Broken symmetries; short- and long-distance order.Symmetry of a system of particles can be lower than that of the interaction Hamiltonian.In a homogeneous and isotropic space the hamiltonian must be invariant with respect to3SOtG t – the group of 3D translationskzjyixtˆˆˆSO3 – the group of space rotationsIn a gas or liquid there is no symmetry breaking, but in a crystal both translational and orientational symmetries are broken.iqroqr e)()(In a crystal, density is only invarient with respect to the elements of one of the 230 possible space groups.Symmetry breaking is less important in mesophases than in 3D crystals: liquid crystals are intermediaries between 3D crystals and the liquid isotropic phase.Hybrid molecular form and molecular frustrationBlock co-polymersliquid crystalline block copolyersself-assembling amphiphillics88 Ccrystalcrystalcrystal-91 C isotropic liquid+98 C gas8CB: octane +