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9 Liquid-State Physics CLASSICAL LIQUIDS Whereas a crystalline solid is invariant against displacement through a lattice constant along each of the three principal coordinate axes, a liquid is invariant against an arbitrary displacement in space. A liquid also differs from a crystalline solid in its orientational symmetry. In a crystal the bonds or lines joining nearest neighbor atoms are oriented along specific directions in space. In a liquid, however, the lines joining pairs of nearest neighbor atoms will point with equal probability in all directions of space. There also exist in nature various liquid-crystal phases, which exhibit a broken orientational symmetry, like a crystal, but possess the translational invariance of a liquid. In this chapter we survey recent advances in our understanding of classical liquids and of liquid crystals, and point to areas of liquid-state physics in which progress can be expected in the next few years. Introduction In terms of everyday experience, liquids are certainly as common as solids. The study of liquids has a renowned classical tradition centering largely on the great disciplines of hydrodynamics and hydraulics. However, there is a more atomistic aspect of the study of liquids that has paralleled some of the developments in the statistical mechanics of 190

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L/QU/D-S TA TF: PH YS/~S 191 solids, though it has progressed more slowly. Research is focused on the microscopic description of liquids, which in the last decade has seen noticeable advances both in theory and in experiment. In partic- ular, the whole notion of experiment has broadened to include certain Monte Carlo and molecular-dynamical computer simulations noted below. The intent of the microscopic view of fluids is to try to understand the static and dynamic properties of fluids, typically in the classical regime (where quantum effects are unimportant), starting from the basic principles of classical statistical mechanics and a knowledge of the fundamental interactions in the system. These interactions repre- sent the basic forces between the atoms or molecules of the liquid and change according to the type of system being discussed (e.g., liquid argon, liquid metals, and molten salts). On the scale of thermal energies the interactions in the above examples are strong, and even simple liquids of monatomic molecules, which have spherically symmetric interactions, are highly correlated systems. To treat this classical many-body problem, the common starting point is to assume the atoms interact by means of pair forces alone. This is only an approximation (though often a good one) because it is known that the influence of one atom on a second is often modified by the presence of a third. Moreover, full details of the exact pair interactions between most real molecules are not yet known precisely. It is partly for this reason that computer experiments in the past decade have become so valuable a source of information. With these tech- niques it is now possible to simulate the experimental properties of model pair-potential fluids that are immediately pertinent to the micro- scopic theories that attempt to explain them. In such hypothetical fluids, only pair interactions are considered and the forces between pairs of particles are unambiguously defined. A small class of repre- sentative models (no one of which is intended to mimic any particular fluid exactly) have been studied exhaustively enough to yield reliable benchmark results. With Monte Carlo and molecular-dynamics tech- niques it has been possible to get accurate data both on the structure of these model fluids and on the major functions that describe their thermodynamic properties. Static Properties Liquids, by their very nature, are disordered systems whose physical attributes must be described in statistical terms. More particularly, the structural properties of the liquid are represented in terms of distribu

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192 A DECADE OF CONDENSED-MATTER PHYSICS tion functions that give the probabilities of finding given numbers of atoms (one, two, three, . . .) at certain locations. The most prominent of these functions is the pair-distribution function (see Figure 9.1), which gives the probability of finding an atom at a distance r from a given atom. In real fluids, the pair-distribution function is actually deter- mined by the scattering of x rays or neutrons but is also, however, directly obtainable from simulation methods. One of the main tasks of the theory of classical fluids is to determine these distribution functions starting only with the interactions between particles (generally the pair potentials), the mean density of particles, and the temperature and to deduce the thermodynamic properties of the corresponding fluids from them. Over the past decade a whole range of methods for finding the pair-distribution function and associated thermodynamics has reached maturity. No longer do workers in the field seek one unique way of predicting liquid properties; instead there is a hierarchy of techniques to choose from in which increasing quantitative accuracy can be had for the price of decreasing analytic simplicity and increasing compu- tational labor. These techniques include thermodynamic perturbation theory and its variants, as well as the use of integral equations for finding approximate pair-distribution functions. The integral equations range from those that can be solved in terms of closed-form expres- sions (the so-called mean spherical approximation and generalizations thereof) to somewhat more complex equations that must be handled numerically but often yield approximations of even higher accuracy 2 o ; I IAN I I ~ LOW-DENSITY LIMIT ,IQUID 1 1 1 1 1 1 2~ 3< Lennard-Jones Rod ia I Distri button Function 0 ~ FIGURE 9.1 Pair-distribution functions for triple-point and low-density fluids. The density of particles. relative to the mean density. is plotted as a function of the particle separation. The distance ~ corresponds to the collision diameter for the 6-12 Lennard- Jones pair potential. (Courtesy of W. G. Hoover.)

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LI Q UlD-S TA TE PH YSI CS 1 93 (e.g., the exponential and renormalized hypernetted chain approxima- tions). Both the computer simulation and the theoretical methods, first applied to simple classical models of monatomic fluids and idealized models of ionic and polar fluids, are now being extended to cope with the presence of intrinsic e-particle forces for n-3 as well as with the related but distinct problem of computing e-particle distribution func- tions for n - 3 for model pair-potential fluids. Perhaps even more important, over the past 5 years enormous progress has been made on a number of fundamental extensions of the above work. To give some examples: (i) The treatment of nonsimple fluids consisting of polyatomic molecules has yielded to both computer-simulation and integral-equation techniques (often applied to the key probability of simultaneously locating two atoms on different molecules). (ii) Variants of the theories that we have discussed above are also being applied with success to colloidal suspensions and other liquids containing macromolecular particles. (iii) Analytically viable path-integral ap- proaches have been developed to deal with intrinsic quantum effects in the liquid state (e.g., the polarizability of liquids), and, at the same time, powerful computer-simulation methods have been used to solve the Schrodinger equation exactly for many-particle systems under various liquid-state conditions. (iv) The effects of the liquid-state environment on chemical reactions and on conformation changes have begun to be studied in depth using statistical-mechanical models and formulations. (v) Several other technologically important areas of liquid research are also rapidly beginning to reach maturity. The formal theory of inhomogenous fluids was already well developed several decades ago, but the surfaces of liquids and the boundary regions of liquids in contact with solids, which give rise to the wetting problem, are only now being studied intensely, with the promise of reliable predictions for the first time. (vi) For many years, observed liquid- mixture phase diagrams included types that sometimes eluded theoret- ical realization with Hamiltonian models, even for two-component mixtures. The binary-mixture types all appear to be reproducible theoretically now, although full understanding in this area is far from complete. Mixtures that become unstable and separate under increase in temperature are especially challenging in this connection. Dynamical Properties of Classical Liquids The determination of properties associated with molecular motion in condensed phases consists of three approaches: ~ I ~ direct experimental measurement of spectral lineshapes, transport coefficients, and relax

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1 94 A DECA DE OF CONDENSED-MA TTER PH YSI CS ation times; (2) analytical or simple model-based theory; and (3) computer simulation of realistic models for fluids. The experimental techniques used to study fluid dynamics can be divided into two categories: those that probe single-particle dynamics and those that probe collective (many-body) motions. Within each category there are numerous techniques that often provide comple- mentary information and that provide probes of dynamics over a wide range of time (or frequency) and wavelength scales. Nuclear magnetic resonance (NMR), electron spin resonance (ESR), infrared and Raman spectroscopy, and a host of relatively new nonlinear optical techniques fall within the first category. Using these methods one can obtain relaxation times associated with phenomena such as molecular rota- tion, vibrational relaxation and dephasing, and intramolecular rear- rangements. To elucidate the physics that determines these time scales, one makes measurements over a range of physical conditions, for instance over a range of temperatures. Recent experiments employ- ing pressure or density as an external variable have had particular impact. For example, ESR studies have shown that simple free volume corrections to the Debye-Stokes relation for rotational diffusion times, which seem to work well in describing the temperature dependence, may not be valid over a wide range of pressures. Studies of vibrational lineshapes as functions of temperature and density have provided information that has stimulated the development of the first compre- hensive theory grounded in a fundamental treatment of intermolecular forces and time scales. NMR studies of the pressure or density dependence of intramolecular rearrangement rates in small alkanes have provided the first experimental evidence that such rates decrease at low densities, a result in marked contrast to the predictions of transition rate theory but in accord with recent theoretical predictions based on the premise that reactions in fluids are friction controlled and require energy dissipation. The advent of picosecond and subpicosec- ond laser techniques has also led to advances in the understanding of dynamics in fluids, allowing fast processes to be studied directly in the time domain. Such studies have allowed at least partial separation of fast and slow, or homogeneous and inhomogeneous, contributions to vibrational relaxation, information that cannot be obtained directly in the frequency domain but that is of fundamental importance to a theoretical understanding of such relaxation. Recent picosecond stud- ies of intramolecular rearrangement times have shown deviations from simple diffusionlike behavior that may be due to viscoelasticity. These techniques should continue to provide new information, particularly as they move from the developmental stage to the point where they can be

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LIQUID-STATE PHYSICS 195 more readily applied to a wide variety of systems over a range of physical conditions. Experimental techniques that probe collective dynamics in liquids include dielectric relaxation, ultrasound and viscoelasticity measure- ments, light scattering, flow and acoustic birefringence, and neutron scattering. Much of the current work using these techniques is aimed at studying collective motions on time scales where macroscopic hydro- dynamics no longer applies; here the details of the intermolecular forces and collisional dynamics become more important. Such studies are the result of technical advances that have enabled measurements to be taken at higher frequencies or shorter times, and the extension of measurements to lower temperatures and higher viscosities, where the characteristic relaxation times are slower, bringing faster processes into experimentally accessible regions. In particular, it has been found that, in contrast to the situation at higher temperatures and lower viscosities, many of the collective relaxation processes in viscous fluids are highly nonexponential, a phenomenon for which there is still no convincing theoretical interpretation. Since generalized hydrody- namics provides a theoretical framework in which data obtained using different techniques can be analyzed in a consistent fashion, it is especially important that data be obtained over a wide range of physical conditions using complementary techniques, for instance, light scattering and acoustic measurements. Technical developments will continue to provide new and better information. For example, new advances in time-domain dielectric relaxation have extended the applicability of this technique to shorter times or higher frequencies. Nonlinear optical techniques should be of benefit in studies of collec- tive as well as single-particle properties. Newly developed optically induced transient grating experiments (laser-induced phonons) allow for the generation and study of very-high-frequency ultrasonic waves. The low-frequency analogue of Raman gain spectroscopy could pro- vide an attractive alternative to Fabry-Perot interferometry for the study of dynamic light-scattering spectra of viscous fluids, since the inherent frequency resolution is much higher, enabling the study of slower processes and more viscous fluids. There are many ways to model the physics of a liquid in order to obtain predictions of its dynamical behavior. One important approach used today is kinetic theory. Here one follows sequences of molecular collisions and determines spectra and transport coefficients as a direct consequence of the collisional history of the molecule. The unified collision-based theory of fluids began with Boltzmann's classic treat- ment of gases (1873) and was extended to dense gases by Enskog

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196 A DECADE OF CONDENSED-MATTER PHYSICS (1922~. Recently, Enskog's approach has been systematically general- ized so that it can now be used to treat systems approaching liquid densities. In the liquid regime, Enskog's picture of uncorrelated molecular collisions is simply inadequate. Several workers have made significant revisions in the basic framework of the Enskog theory in order to accommodate the effects of correlated sequences of collisions. The cage effect in liquids, for example, arises when molecules, say 1 and 2, are forced by molecule 3 to collide. Thus, molecule 3 cages molecules 1 and 2. The consequences of such recollisions are pro- found, even going so far as to undermine the usual density expansion approaches used to calculate transport coefficients. Most of the em- phasis in liquid-state kinetic theory has been on smooth, hard sphere systems. For nonspherical molecules (basically all molecules in nature except the inert gases, liquid metals, and a few other exceptions), the state of kinetic theory is much more primitive. Only recently has the Engskog theory of nonspherical particles been applied to condensed- matter dynamics, and there it yields unsatisfactory and inaccurate predictions of the transport coefficients owing, perhaps, to the omis- sion of correlated recollisions. The understanding of the properties of rigid nonspherical molecules is just in its infancy. Our discussion up to this point has centered on rigid molecules whose dynamics can be treated using kinetic theory. The study of the dynamics of small, flexible molecules, such as the alkanes, is also interesting. The intramolecular rearrangements that take place in such molecules are primitive models for chemical reactions, and there has been renewed interest in determining the rates at which flexible molecules change shape and how such changes in shape affect prop- erties involving overall rotation and translation. Historically, there has always been an interest in small-alkane dynamics, but earlier ap- proaches dictated the motions by fiat, and thus provided few funda- mental insights into molecular conformational dynamics. Today, one derives the equations of motion from Newton's laws, and then follows the time evolution of the system in order to determine how energy is transported through the molecule, the temperature of individual bonds, and in general how the molecule moves as a result of collisions with the solvent. Molecular dynamics (MD) computer simulations have, since the 1950s, continued to point out interesting phenomena in liquids and, sometimes, even hints at their explanation. Perhaps the most important developments in the past 5 years involve the applications of MD to (1) nonlinear phenomena, as seen through nonequilibrium molecular dy- namics (NEMD) and (2) the dynamics of polyatomic molecules. In the

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LIQUID-STATE PHYSICS 197 NEMD technique, one applies an external disturbance to a collection of, say, 500 molecules in a box. The disturbance might be a shear gradient. One then observes the induced momentum flux in the fluid as a consequence of the shear; the proportionality between the flux and shear gradient defines the shear viscosity. This technique provides a calculation of the shear viscosity and other transport coefficients that is more efficient than direct MD. Shear NEMD calculations have dem- onstrated that the shear viscosity has a square-root dependence on the magnitude of the shear gradient and on the frequency of shear (Figure 9.2), observations that raise important conceptual questions in the theory of fluids. Computer simulations of fluids composed of nonspheri- cal molecules have played a similar role by providing details of molecular dynamics inaccessible to experiment. For example, it has been observed that a characteristic feature of rotational dynamics in condensed phases is an oscillation in the angular-velocity time- correlation function. Experimental transport coefficients, which are 1\U cat 2 b d5 - o LENNARD-JONES TRIPLE - POINT VISCOSITIES - ;~ = 0.8442 T*= 0.722 :108) - <~v(54) ~TAI L - - - ! ~ .. . . . 8 12 0 4 In) ViTim FIGURE 9.2 Shear (upper) and bulk (lower) viscosities for triple-point Lennard-Jones fluids as functions of a dimensionless strain rate. The experimental viscosities for liquid argon are indicated by horizontal arrows. The typical square-root behavior of these viscosities is responsible for the cusp in the Newtonian zero-strain-rate limit. [From W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980).]

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198 A DECADE OF CONDENSED-MATTER PHYSICS given by the time integral of the correlation function, do not readily see this feature. This oscillation indicates that the backscattering or caging mentioned in connection with molecular translation is also crucial to the understanding of the dynamics of molecular rotation in a liquid. In other words, correlated sequences of collisions must be understood in order to predict liquid properties. Colloidal System~Soap Solutions Solutions of soap in water are a familiar part of our everyday life; they also account for several multibillion-dollar industries involving detergent action, drug delivery, and oil recovery. Nevertheless, little is understood on a fundamental level about the many different ways in which soap molecules are aggregated in aqueous solvents. Sometimes they go into solution by means of the formation of spherical clusters of molecules; other times these aggregates-or micelles are distinctly nonspherical, e.g., rodlike or disklike in shape. At high enough concentrations suspensions of these rods and disks are observed to transform themselves into stacks of infinite cylinders and lamellar sheets. In many instances, particularly on the addition of salt or alcohol or another soap species, intermediate phases appear in which the rods and disks remain small but tend to align along a single direction. In each of these various states, of course, the solution of aggregates displays markedly different mechanical, flow, and solubility properties. To explain these features it is not sufficient to apply the usual theories of colloidal suspensions. This is because-unlike the cases of metal grains or biological macromolecules, say the interacting parti- cles in soap solutions are aggregates of molecules that do not maintain their integrity. instead, any change in thermodynamic parameters such as temperature or concentration results in a reorganization of the clusters into a new distribution of sizes and shapes. Furthermore, since the particles themselves undergo change, so do the forces between them. Accordingly, a statistical-mechanical treatment of the bulk properties of concentrated soap solutions must necessarily confront explicitly the coupling between micellar growth and interactions. Similarly, the experimental study of these systems is also more problematic than that of ordinary colloidal suspensions. During the past decade, much progress has been made in developing the theoretical concepts necessary for understanding micellization in aqueous soap solutions. Particular emphasis has been on accounting for the various preferred curvatures assumed by different aggregates, relating these different geometries to molecular shapes, degree of

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LIQU/D-STA TE PHYSICS 199 ionization, and overall soap concentration. Just as importantly there have been dramatic advances in the resolution of neutron, x-ray, and light-scattering experiments relevant to determining the microscopic structures of these systems. Furthermore, much effort has been devoted to the microemulsions that form on addition of oil to micellized solutions of soap in water. In most cases a cosurfactant (e.g., another soap molecule or an alcohol) is necessary to stabilize these oil/water dispersions. Thus one is dealing in general with at least a four- component, concentrated solution that shows a dramatically rich polymorphism at room temperature. These phases are also often characterized by extremely low interracial tensions (~lo-3 dyne/cm), making them of great interest for enhanced oil solubilization as well as for studies of fundamental thermodynamics and critical phenomena. It appears that the new and diverse phenomena displayed by these systems will continue to provide many fruitful challenges to our current ideas concerning the effects of dimensionality and symmetry on phase transitions and equilibrium structures. LIQUID CRYSTALS What Are Liquid Crystals? The name liquid crystals covers a broad category of materials exhibiting molecular organization and macroscopic symmetry interme- diate between the total disorder of an isotropic liquid and the order of perfect crystals: Nematic phases are ones in which the centers of the molecules making up the material are more or less randomly arranged as in an ordinary liquid, while the orientation of the molecules exhibits long- range order. For instance, rodlike molecules are oriented with their long axes parallel to one another or disklike molecules with their plane surfaces parallel. These phases flow like ordinary liquids but exhibit the anisotropic optical, electrical, and magnetic properties usually associated with crystals. Smectic phases are layered systems, so that they resemble crystals in having periodic order in one direction (the layers), while retaining some degree of disorder within the layers. There are many subtle variations on this theme, the simplest of which is the smectic A phase with liquidlike disorder in each layer. Within these two general classes of partially ordered materials there are several subclasses, which is one source of richness in the field.

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200 A DECADE OF CONDENSED-MATTER PHYSICS Another source of richness is the tremendous variety of materials that exhibit these kinds of ordering: Small organic molecules containing roughly 40-100 atoms are com- monly the rodlike units that make up nematic phases. Equally often these same materials exhibit smectic phases with the rods packed into layers, the rod axes being either perpendicular to the layers (smectic A) or at an oblique angle to the layers (smectic C). Amphiphilic systems, based on molecules in which one end is oil soluble and the other end is water soluble, usually organize themselves into basically layered structures with the oil-soluble parts in one plane of the layer and the water-soluble parts in another plane. By simply stacking up the layers one can build smectic phases, but more complex structures can be achieved too. For instance, the amphiphilic layer can be rolled into a cylinder, and arrays of these cylinders suspended in water or oil can form a nematic phase. Colloidal systems of objects larger than single molecules, for in- stance virus particles suspended in water, can form liquid crystals. Several viruses are rodlike in shape and make nematic phases. Polymers consisting of rodlike molecular units strung together end to end, or attached like the teeth of a comb to a flexible molecular string, often exhibit nematic ordering. As one might expect, the mechanical properties of these systems are different from those of liquid crystals made of small molecules. Biological sc~bcellul`'r structures such as cell membranes exhibit molecular organization and other properties similar to various liquid- crystal phases. In some cases these are really liquid crystals, while in other cases the structural complexity of the biological systems exceeds that of a liquid crystal, so using the terminology of liquid-crystal physics to describe the biological system is more an aid to thinking than a real physical description. Why Are Liquid Crystals Interesting? Although liquid crystals have been known since 1888, it is not unfair to say that the last decade has brought a surge of interest in their physical properties. Clearly one source of the fascination with liquid crystals is the variety of substances that exhibit these phases. That stimulates one to look for the unifying principles responsible for the similarity of behavior of widely differing systems. At the same time, the variety of different liquid-crystal phases exhibited by similar small molecules leads one to try to understand the subtle differences in

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FlQUlD-5TA TE PHYSICS 20 1 molecular properties that lead to different kinds of ordering (smectic versus nematic, for instance). This has led to both fundamental theoretical research on molecular ordering and interactions and the development of new materials, in a kind of molecular engineering to achieve systems with specific properties. A second source of fascination is the large number of unusual macroscopic phenomena found uniquely in liquid-crystal phases. These include dramatic changes in the macroscopic structure of a sample induced by a magnetic or electric field or by flow. For instance, in an initially undistorted single crystal of a nematic, an applied field may produce a periodic stripelike structure. This rather complex response to a simple applied force is striking. Without going into the detailed analysis of any of the myriad of cases in which something like this occurs, one can say that it results from the anisotropic nature of the coupling of the applied field to the liquid crystal. As soon as the liquid crystal begins to respond to the field, which usually involves a change in orientation of the molecules, the change of orientation results in a change of the strength of the coupling of the liquid crystal to the external field. This is an example of a nonlinear response that often leads to complex structural changes in a sample submitted to rather simple external forces. These phenomena have proved challenging and stimulating in a number of ways. Understanding them and learning to produce and control them has led both to a deeper understanding of liquid crystals and nonlinear phenomena and to some interesting applications of these materials. Most of these macroscopic phenomena involve changes in the optical properties of the sample, much larger changes than are ever observed in ordinary crystals or liquids. As a result, most of the applications of liquid crystals to date are to various display devices, such as the digital readout of a wrist watch or a calculator; applications to television-type displays are in the near future. Finally the changes of state exhibited by liquid-crystal-forming materials have been interesting. These include changes between, an ordinary liquid or solution and a liquid crystal, as well as changes between various liquid-crystal phases. A number of these changes of state fall in the category of continuous phase transitions, which may exhibit critical phenomena owing to fluctuation effects. In addition, the rich variety of phase changes offered by these materials in films as thin as two monolayers has presented unique challenges in the fields of two-dimensional melting and the ordering of defects. These phenom- ena have been the subject of intensive research in recent years, and liquid crystals have provided a rich testing ground for theoretical ideas

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202 A DECADE OF CONDENSED-MATTER PHYSICS as well as a challenging array of phenomena to stimulate new ideas. In fact, one of the most common liquid-crystal phase changes, from the nematic to the smectic A phase, has still not been completely under- stood. Major Advances Liquid-crystal displays have become the dominant form of display in applications requiring low power, portability, or operation in a wide range of lighting conditions but are limited to cases in which only a small to moderate amount of information has to be displayed. Thus, they are widely used in wrist watches and calculators but not to replace cathode-ray tubes in computer terminals or television sets. This achievement of research in liquid crystals has resulted from a combination of important contributions from various sources. First, the liquid-crystal displays now used are based on the twisted nematic polarization switch effect, an electric-field effect in which the internal orientational structure of the liquid crystal sample is changed in a way that rotates the polarization of light passing through it. Understanding the macroscopic phenomenology of this effect and making it reliable for practical application involved correct preparation of sample surfaces, development of ways to prevent the formation of defects during device operation, understanding the dynamics of the liquid crystal's response to electric fields, and understanding the rather complex optics of the device. Second, new materials with the properties necessary to make these devices practical had to be developed. These materials had to combine properties such as a wide nematic temperature range around room temperature, chemical stability for a long life, as well as ideal optical, electrical, elastic, and viscous properties. The development of success- ful materials for this application has been a major achievement resulting from close collaboration between physicists and chemists. In addition, a number of related technological developments were needed, including sample sealing methods, surface treatment tech- niques, and electrical signal-handling techniques. This is a specific example of an aspect of liquid-crystal science that has been essential to the field the interdisciplinary nature of the subject. A second major achievement of the field has been the understanding and development of a number of new states of molecular organization and ordering. Again, this has required close cooperation between chemists and physicists and the interplay of theory and experiments.

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LIQU/D-5TA TO PH YS/cS 203 The variety of partially ordered states of matter that can properly be called liquid crystals is remarkable. This subject has attracted some of the brightest researchers and is in a state of intense development now. There are numerous other outstanding achievements in this field, some of which would require detailed technical discussion to be described meaningfully. These include the development of ultra-high- strength fibers spun from liquid-crystal materials and the discovery of ferroelectric liquid crystals that have a spontaneous electrical polar- ization. OPPORTUNITIES FOR FUTURE WORK One of the major areas of the physics of the liquid state where little real understanding exists is that of fluids away from, and especially far away from, equilibrium. Although some partial and fragmentary knowledge is available, neither the average properties of such fluids (such as the flow and density fields) nor the fluctuation phenomena about the average and their correlations are well understood. There are two aspects to this: 1. A fundamental microscopic theory of dense fluids not in equilib- rium is not available. Since progress on this problem is slow, it is not a fashionable topic, which does not mean, of course, that it is not important. So far, only an approximate theory for a fluid of hard spheres has been developed, and some modest attempts are under way to generalize this theory to more realistic fluids. However, we are still far from any detailed microscopic understanding of the nonequilibrium properties of real fluids. New approaches, both theoretical and exper- imental, for dealing with this problem are being developed, and this development should be encouraged. Among the new possibilities for the experimental study of liquids out of equilibrium one should mention laser spectroscopy, improved neutron spectroscopy with the new spallation sources (such as the Los Alamos Neutron Scattering Cen- ter), and synchrotron radiation. The use of synchrotron radiation could also help in clarifying the behavior of chemically reacting mixtures, about which more basic knowledge, both theoretical and experimental, would be highly desirable. 2. A fundamental macroscopic understanding of the behavior of fluids far from equilibrium based on the nonlinear equations of hydro- dynamics, such as the approach to chaos or turbulence, will certainly remain an important and fashionable topic for research in the future. There is an interesting connection here with the behavior of some ':

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204 A DECADE OF CONDENSED-MATTER PHYSICS chemically reacting fluid mixtures, in which diffusion also occurs (as, for example, in the Belousov-Zabotinskii reaction), and clarification of the relevant basic equations, aided by recent advances in our under- standing of critical phenomena, will be of great theoretical and practi- cal importance. An understanding of non-Newtonian fluids (e.g., their theological properties) from a more physical rather than from an abstract mathe- matical point of view is being gained. However, a real, basic under- standing of such fluids, sometimes necessary for shrewd practical applications, is still lacking. The properties of liquid crystals, glasses, polymers, and gels, for example, are being studied from various points of view. All this work should be encouraged and supported. However, there is a great need for a unification of the various approaches. In polymer science, for example, the theoretical-physics approach and the chemical-engineering approach are not at all compatible, and this slows progress in the field. For both transport and equilibrium properties, and for the inclusion of three- and higher-particle effects into these calculations, a more concentrated effort is needed in the future. A particularly interesting opportunity is the further development of models for polyatomic fluids, and the development of theories of nonuniform fluids, in the context of which liquid against solid interfaces provide an important example. In view of the strong connection between the liquid-interface problem and large-scale commercial chemical-engineering processes (including, for example, catalytic processes) it seems clear that more emphasis and greater support should be devoted to experimental measurements as well as to the microscopic understanding of liquids and their mixtures, both uniform and nonuniform. Liquid-crystal research is at an interesting point in its evolution. There has been sustained activity in the field on a number of fronts for the last 15 years. In spite of the advances made, it is still clear that the number of new questions being encountered outweighs the number of problems solved. In the area of liquid-crystal displays, which has served as a funda- mental motivating force for much research, there is the potential for major new developments. The currently successful twisted nematic displays are capable of practical application only to situations requiring display of a relatively small amount of data. This is because the display must constantly be refreshed: it has no internal memory. Much effort is being devoted to the development of a display with intrinsic memory in addition to all the desirable features of the twisted nematic displays.

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FIQUlD-STA TE PHYSICS 205 Another issue is speed: the current displays can be updated only relatively slowly. The combination of greater speed and intrinsic memory would make television applications of liquid crystals espe- cially feasible. Some of the most promising research in this area now concerns the use of ferroelectric liquid crystals, one of the striking discoveries of the last decade that has not yet been fully developed. As with the twisted nematics, success in this area will depend on the cooperation of physicists and chemists and on the development of knowledge in a number of areas that are currently not well understood, such as the interaction of smectic liquid crystals with surfaces. There is currently rapid development in the understanding of new kinds of molecular ordering and phase transitions. Much of this has been associated with high-resolution x-ray studies of the various smectic phases, in combination with other studies such as optical and NMR experiments. The availability of national synchrotron-radiation facilities has played an important role in this development. Whereas in the recent past most of the emphasis has been placed on the study of liquid crystals based on small organic molecules, now considerably more effort by physicists is being devoted to liquid crystals formed by amphiphilic systems, polymers, colloidal suspen- sions, and biological substructures. This broadening of interests is leading to a number of new discoveries. As in any rapidly developing field, of course, there are many interesting questions encountered that go unanswered as a particular area of the subject is explored. In this sense, even within the generally well-studied aspects of liquid crystals, there are still many opportuni- ties for productive research.