Topics in the Theories of Elasticity and of Liquid Crystals

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

TECHNICAL SUMMARY: This proposal supports theoretical research and education in three distinct areas: isoststatic and nearly isostatic materials, imprinted liquid crystal elastomers, and the interplay between line (disclination) and point (hedgehog) defects in nematic liquid crystals. A major part of this research studies the many peculiar and fascinating properties of periodic isostatic lattices, like the simple square and cubic lattices, and their nearly isostatic forms created by adding rigidity-by including additional springs like the cross beams on a bridge. These systems offer insight into general isostatic systems in a context that is not complicated by the off-lattice randomness inherent in more studied ?jammed" systems. Using modern synthetic and photo chemistry, it is now possible to create spatially varying patterns of anisotropy characterized by the director in polymer or related nematics and to freeze in those patterns via a chemical cross linking process. For example, one might create a thin-film elastomer whose director, restricted to the plane of the film, rotates by 90 degrees between the film's top and bottom surfaces. This imprinting makes the top and bottom surfaces different and causes them to respond differently to changes in temperature, pH, or light intensity and, thereby, to produce shape changes in the film. These films are thus ideal candidates for mechano sensors of various sorts. A major research effort focuses on calculating the elastic and other properties of elastomer films and narrow tubes imprinted with various director patterns. Colloidal particles can now be dispersed in a controlled way into liquid crystals to create particle lattices entangled with arrays of topological defect lines called disclinations. Closed loops of these lines produce director patterns equivalent to those of point defects called hedgehogs. In a third research thrust, the PI aims to formulate ways of characterizing the amount of hedgehog charge a line defect carries for each unit of its length. The goal will be to provide a mathematical characterization of this charge density and to use it to help understand networks of disclinations like those in colloidal dispersions. The broader impact of the proposal is expanding the experience, education and training of students and post-docs in the interdisciplinary field of soft-matter physics. Bringing these new interdisciplinary aspects of research to the larger community, the PI plans to write a major review article on nonlinear elasticity and to begin the process of updating his popular text book, "Principles of Condensed Matter Physics." The PI is Chair of his department and encourages Department outreach programs, one of which brings in several hundred local high school students each year to see captivating demonstrations of physics. NON-TECHNICAL SUMMARY: This proposal supports theoretical research and education in areas of soft condensed-matter physics. The program builds on the PI's previous experience in liquid crystals, elasticity, and phase transitions. Liquid crystals, a class of materials widely known because of liquid crystal display (LCD) application, are materials that have a rich variety of internal structures with molecules in spatial arrangements less organized than solid crystals but with directional patterns formed the orientation of the constituent molecules. With molecular orientation an added variable to the spatial organization, researchers have found that the internal structure of liquid crystals, polymers and other soft matter systems can be extraordinarily complex, but very logically patterned. Patters and structure are connected with strength and stability. It is well known that engineers do not build bridges with a motif of only horizontal and vertical struts in a square or rectangular pattern; rather they put in diagonal cross beams to increase structural stability. In fact, a square or cubic lattice with nearest neighbor vertices frictionlessly connected by springs that can only support loads directed along their axes are inherently unstable. These lattices represent a general category of what are called isostatic systems that have almost, but not quite, enough constraints to make them stable. There are many systems in nature, including piles of sand, spherical beads compacted until they become jammed, and even glasses, that are nearly isostatic. A major part of this research is to study the many peculiar and fascinating properties of periodic isostatic lattices, like the simple square and cubic lattices, and their nearly isostatic forms created by adding rigidity-increasing springs like the cross beams on a bridge. These systems offer insight into general isostatic systems in a fashion that is free from many complications that appear in systems that are traditionally studied. Liquid crystal elastomers are fascinating materials that combine the orientational properties of liquid crystals with the remarkable stretching properties of rubber. Liquid crystalline elastomers are formed by chemically binding together (cross linking) long-chain molecules (polymers) with liquid-crystal forming molecular subunits to create a liquid crystalline network that can withstand stretching. Using modern synthetic and photo chemistry, it is now possible to create and ?freeze in? spatially varying patterns of orientational order. For example, one might create a thin-film elastomer in which the orientation of the long-chain molecules twists smoothly from one orientation at the top surface to another at the bottom. This imprinting makes the top and bottom surfaces different and causes them to respond differently to changes in temperature, pH, or light intensity and, thereby, to produce shape changes in the film. These imprinted films and other imprinted geometries such as tubular elastomers are ideal candidates for mechano sensors of various sorts. The PI aims to calculate the properties of imprinted films and tubes. The broader impact of the proposal is primarily the education and training of students and post-docs in the interdisciplinary field of soft-matter physics. Bringing these new interdisciplinary aspects of research to the larger community, the PI plans to write a major review article on nonlinear elasticity and to begin the process of updating his popular text book, "Principles of Condensed Matter Physics." The PI is Chair of his department and encourages Department outreach programs one which brings in several hundred local high school students each year to see captivating demonstrations of simple physics.