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All matter, from the simplest fluid such as gaseous helium to the most complex system like a biological cell, is made of electrons and nuclei. Electric potentials tend to glue the nuclei together, while kinetic energy, connected to atomic (nuclear) masses moving with given velocities, tends to pull them apart. It is this eternal struggle between electricity and temperature that ultimately gives rise to the entire world as we see it, with its properties and its changes. This chapter focuses on the analysis and simulation of the phase equilibria, phase changes, and mesophases of molecules using a variety of methods such as light scattering, calorimetry, chemical spectroscopy, X-ray scattering and diffraction, electron micrography and atomic force microscopy, and evolutionary molecular simulation. The basic thermodynamic functions are discussed, along with melting, solid–liquid equilibrium and nucleation from the melt, vapor–liquid and vapor–solid equilibrium, glasses, liquid crystals, nucleation and growth from solution, crystal growth and morphology, and prediction of crystal faces, attachments, energies, and morphology.

This chapter is concerned with harmonic maps from a polyhedron to the unit two-sphere, which provide a model of nematic liquid crystals in bistable displays. This chapter looks at the Dirichlet energy of homo-topy classes of such harmonic maps, subject to tangent boundary conditions, and investigate lower and upper bounds for this Dirichlet energy on each homotopy class; local minimisers of this energy correspond to equilibrium and metastable configurations. A lower bound for the infimum Dirichlet energy for a given homotopy class is obtained as a sum of minimal connections between fractional defects at the vertices. In certain cases, this lower bound can be improved. For a rectangular prism, upper bounds are obtained from locally conformal solutions of the Euler-Lagrange equations, with the ratio of the upper and lower bounds bounded independently of homotopy type.

This chapter describes the origins of the liquid crystal display project at the David Sarnoff Research Center (DSRC). The discussion focuses on two members of RCA’s technical staff: physical chemist Richard Williams and electrical engineer George Heilmeier. In 1962, Williams demonstrated that certain liquid crystals could modulate light when subjected to an electric field. He composed a patent describing how this behavior might be utilized in displays before setting the idea aside to pursue other investigations. Two years later, Heilmeier expanded on Williams’ research and observed several electro-optical effects in liquid crystals. Heilmeier convinced the DSRC’s leadership to organize the interdisciplinary team that ultimately transformed one of these phenomena, known as “dynamic scattering,” into the basis for the first LCD prototypes. Examining how Williams and Heilmeier approached the development of liquid crystal displays illustrates the importance of individual research styles even in the supposedly impersonal confines of a corporate laboratory.

This chapter describes the molecules and the molecular interactions associated with the self-assembling phenomena leading to the existence of lyotropic polymorphism. It includes the description of a step-by-step procedure to produce a lyotropic liquid crystal. An introductory example, based on one of the most studied lyotropic systems, is discussed in detail. The lyotropic mesophases are presented and discussed through many experimental results. Nematic, cholesteric, lamellar, two-dimensionally, and three-dimensionally ordered phases are presented. Experimental results coming from X-ray and neutron scattering and diffraction, nuclear magnetic resonance, linear and nonlinear optical techniques, are presented and discussed to establish the phase diagrams and the properties of these systems. Some technological and industrial applications of lyotropic-like systems are presented, in particular in cosmetics, surfactant industry and oil recovery. The interface between biology and the physics of lyotropic mesophases is also discussed.

A liquid crystal is a compound that exhibits simultaneously both solid and fluid properties. This unusual behavior confers unique optical and electrical properties, which are exploited in many applications, most notably the multi-billion dollar liquid crystal display (LCD) industry. Liquid crystallinity results from the presence of a mesogenic structure, with anisotropy of shape or polarity. There are two types of liquid crystal polymers, those formed of rigid monomer units and those with mesogenic groups grafted to the chain backbone. This chapter focuses on the dynamics of liquid crystals—how it is related to structure and its behavior near thermodynamic phase transitions.

The parallel alignment of dipoles in a ferroelectric is due primarily to a relatively strong long-range interaction along the polar c-axis and a weaker shorter-range interaction normal to the axis. Physically this comes about because for electric dipolar forces the parallel alignment is energetically favourable for an isolated pair of c-axis dipoles but not for an isolated pair of dipoles normal to the polar axis. Theoretical and experimental estimates can be made of a correlation range, or distance over which near-neighbour-cell polar displacements are strongly correlated in some sense. This chapter deals with ferroelectric thin films and ceramics such as semiconducting ceramics, optical ceramics, and semiconducting ceramics, the grain boundaries of ceramics, effect of impurities on ceramics, and metastable polarization in ferroelectric materials such as electrets, liquid crystals, and pyroelectric polymers.

Contrary to the optimistic predictions presented at its 1968 press conference, RCA’s dynamic scattering LCD prototypes were not ready for the marketplace. Liquid crystal display fabrication remained a haphazard affair, and it was unclear what applications would benefit from the company’s new invention. Personnel at the David Sarnoff Research Center (DSRC) attempted to address these issues, most notably through a collaboration with RCA’s semiconductor division to organize the first LCD assembly line. Nevertheless, this chapter confirms that there were limits to their agency. RCA’s management viewed LCDs as a distraction from the company’s ongoing campaign to become a major player in the computer industry and resisted the DSRC’s efforts to commercialize liquid crystals. While George Heilmeier and his colleagues later criticized those actions as short-sighted, their growing recognition of dynamic scattering’s limitations also contributed to the LCD’s marginalization and its eventual characterization as a disruptive technology.

In September 1971, Robert Sarnoff—David Sarnoff’s son and successor as chairman of RCA—announced plans to divest his company’s commercial computing operation. The resulting staff and budget cuts left RCA’s liquid crystal program in flux just as new competitors and display technologies were beginning to emerge. This chapter contrasts the gradual decline of liquid crystal research at RCA with the rapid growth of Optel, the first major LCD spinoff. Founded by Zoltan Kiss, a physicist previously employed at the David Sarnoff Research Center, Optel embraced a flexible attitude toward innovation reminiscent of Silicon Valley startups. This approach enabled it to assemble the first wristwatch with a liquid crystal readout and quickly make the transition from dynamic scattering displays to the “twisted nematic” models that came to dominate the market. In the end, neither firm established itself as a lasting presence in the LCD industry, but their respective downfalls showcase the strategic challenges confronting scientists in different types of research organizations as they struggle to commercialize disruptive technologies.

The origin of ferroelectricity in liquid crystals and the basic physical properties of the systems are briefly discussed. Special attention is paid to elementary excitations in ferroelectric liquid crystals, i.e. the symmetry recovering Goldstone mode, the amplitudon mode and the symmetry‐breaking soft mode. The phase diagram of ferroelectric liquid crystals in magnetic and electric fields is presented and the field‐induced Lifshitz point is discussed. The difference in the soliton structure in electric and magnetic fields is presented. The properties of freely suspended smectic thin films are shown as a function of the number of smectic layers involved. This represents an example of the cross‐over from the 3D to 2D universality class.

Less than a decade after introducing the world to the LCD, RCA sold its liquid crystal operation to Timex. Today the company no longer exists, and its contributions to the flat-panel display industry are largely forgotten. As this concluding chapter argues, however, the collapse of RCA’s liquid crystal display program did not spell the end of its influence on consumer electronics. Through their inventions, publications, and direct consultation, RCA scientists and engineers remained involved in LCD production, first in the United States and later in Europe and Asia. The proliferation of liquid crystal displays in our televisions, calculators, wristwatches, and smartphones hinged upon the actions of these pioneering researchers.

Soft matter is inherently nonlinear stuff, this is partly because of the pre-eminent role played by the hydrogen bond and the hydrophobic interaction in the processes involving soft materials. The hydrophobic interaction is an appropriately weak interaction, and even small changes of pH or concentration can invoke large changes in the structure and dynamics of soft systems. This chapter introduces the vocabulary of soft matter. It begins by describing the hydrophobic interaction. This is followed by a description of colloids and polymers. Cellular, piezoelectric, conducting, and shape-memory polymers are introduced. Polymer gels are described, as well as liquid crystals and ferrofluids. Smart structures of the future will certainly have a crucial role for soft matter.

When plane-polarized light enters a crystal it divides into right- and lefthanded circularly polarized waves. If the crystal possesses handedness, the two waves travel with different speeds, and are soon out of phase. On leaving the crystal, the circularly polarized waves recombine to form a plane polarized wave, but with the plane of polarization rotated through an angle αt. The crystal thickness t is in mm, and α is the optical activity coefficient expressed in degrees/mm. The polarization vector of the combined wave can be visualized as a helix, turning α ◦/mm path length in the optically-active medium. Because of the low symmetry of a helix, optical activity is not observed in many high symmetry crystals. Point groups possessing a center of symmetry are inactive. In relating α to crystal chemistry it is convenient to divide optically-active materials into two categories: Those which retain optical activity in liquid form, and those which do not. It has long been known that optically-active solutions crystallize to give optically-active solids. This follows from the fact that molecules lacking mirror or inversion symmetry can never crystallize in a pattern containing such symmetry elements. Thus one way of obtaining optically-active materials is to begin with optically-active molecules, as in Rochelle salt, tartaric acid and cane sugar. Few of these crystals are very stable, however, and the optical activity coefficients are usually small, typically 2◦/mm. The same is true of many inorganic solids, though they are seldom optically active in the liquid state. For NaClO3 and MgSO4·7H2O, α is about 3◦/mm. Quartz and selenium, however, have coefficients an order of magnitude larger, showing the importance of helical structures to optical activity. Both compounds crystallize as right- and left-handed forms in space groups P312 and P322, with helices spiraling around the trigonal screw axes. Quartz contains nearly regular SiO4 tetrahedra with Si–O distances of 1.61 Å. Levorotatory quartz belongs to space group P312 and contains right-handed helices; enantiomorphic dextrorotatory quartz crystallizes in P322. Trigonal selenium also contains helical chains.

Polymers have connectivity between (usually) identical monomer units, and this connectivity gives rise to a rich physics, without even considering electronic properties. This chapter covers the essentials of the physics of polymers. Here the length of polymer chains is presented, so that the size of a polymer is understood. Crystallinity is treated next. Electronic polymers are generally stiff materials, prone to forming liquid crystalline and semicrystalline phases, and so these are discussed. In amorphous states, polymers have an associated glass transition, and this is also treated. Of considerable importance to the treatment and processing of polymers is that in solution and in mixtures (blends), polymers have an associated phase diagram, and can mix or demix depending on concentration and temperature. The physics of these phenomena are generally tractable, and so the mathematics of polymer phase behaviour is presented. Finally, block copolymers, and their phase behaviour, are briefly discussed.

Chapter 1 introduces material which is developed in later chapters as the main substance of the book. It includes discussions of the atomic nature of matter, states of matter, crystalline and amorphous solids, isomorphism and polymorphism, solid-state transitions and liquid crystals. An outline of bonding in covalent, molecular, ionic, metallic and hydrogen-bonded solids is provided, together with a classification of solids in terms of these sub-divisions.

Surfactants form micelles in aqueous solution above the critical micelle concentration (cmc); micelles are dynamic structures. Micellization is driven by the transfer of surfactant chains from water to the micelle core. There is an optimum size (aggregation number) and shape for micelles (dependent on surfactant molecular shape and packing within micelles) for which the standard free energy of micellization, Δ‎_micμ‎^o, is minimum. Inert electrolyte influences the degree of dissociation (α‎) of ionic micelles and hence micellar shape and aggregation number. Micellization in mixed surfactant solutions, and in mixed polymer + surfactant systems is also discussed. Micelles can dissolve (solubilize) other amphiphilic materials and nonpolar oils, which changes the cmc. If sufficient oil is solubilized, microemulsion droplets result (see Chapter 10). As the concentration of micelles in solution rises, intermicellar interactions lead to the formation of a variety of lyotropic liquid crystalline phases (mesophases).

This book begins at the 1968 press conference where the Radio Corporation of America (RCA) announced the creation of the first liquid crystal displays and provided the earliest description of that technology’s history. The company’s predictions of flat-panel televisions and electronic windows that switched from clear to opaque at the push of a button captivated everyone in attendance. Newspaper articles echoed the discovery narrative set forth by RCA vice-president James Hillier. While many details in Hillier’s account of the invention of the LCD were accurate, they were not derived from first-hand experience. Instead he relied upon members of RCA’s technical staff to distill the complexities of industrial research into a streamlined summary for public consumption. Through the selective inclusion and omission of information, these scientists and engineers molded popular understandings of the LCD’s origins and commercial potential, just as they had shaped the corporation’s R&D strategy since 1951, when RCA launched its earliest flat-panel display projects.

Soft matter includes a large variety of materials, typically composed of polymers, colloids, surfactants, liquid crystals, and other mesoscopic constituents. This chapter addresses the question of why these materials are grouped together and called soft matter. It first introduces typical soft matter (polymers, colloids, surfactants, and liquid crystals), and then discusses the common features of these materials and the physics that gives such features to soft matter.

This chapter discusses methods for converting the many body problem in interacting polymer fluids to a statistical field theory. Auxiliary field transforms are introduced, that decouple interactions among polymer species and reduce the problem to that of individual polymers interacting with one or more fluctuating fields — the subject of Chapter 3. Examples of models for a variety of systems are enumerated, including polymer solutions, blends, block and graft copolymers, polyelectrolytes, liquid crystalline polymers, and polymer brushes.