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OCR for page 190
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
OCR for page 191
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
OCR for page 192
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.)
OCR for page 193
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
OCR for page 194
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
OCR for page 195
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
OCR for page 196
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
OCR for page 197
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).]
OCR for page 198
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
OCR for page 199
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.
OCR for page 200
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
OCR for page 201
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
OCR for page 202
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.
OCR for page 203
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
':
OCR for page 204
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.
Representative terms from entire chapter:
transport coefficients
