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OCR for page 206
10
Polymers
INTRODUCTION
Polymers are macromolecules made up of long sequences (thou-
sands) of small chemical units repetitively attached by strong chemical
bonds to form chains or other structures. Differences from one type of
polymer to another are due not only to the chemical nature of their
constituents but also to their physical arrangement. Small structural
differences, such as branching or cross-linking, can produce profound
differences in properties.
Research in the field of polymer science is a massive endeavor in the
United States and abroad. Polymers possess a range of properties,
often unique, that have proved to be adaptable to a wide variety of
uses. The production of polymers in this country as measured by
volume exceeds that of steel.
The investigation of polymers is diverse, requiring interdisciplinary
efforts of physicists, chemists, materials scientists, biochemists and
biophysicists, and chemical and mechanical engineers. Research in the
field is currently vigorous. In the past 10 or 15 years new instrumental
developments, e.g., small-angle neutron scattering; Fourier transform
infrared spectroscopy; solid-state nuclear magnetic resonance (NMR);
light, x-ray, and electron scattering; electron microscopy; new surface
probes; computerized instrumentation; and computer simulation, have
had a large impact. Paralleling this have been theoretical breakthroughs
206
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POL YMERS 207
in problem areas central to the field, e.g., polymer disentanglement, the
excluded volume problem, "elation, and nonlinear mechanics. Another
factor enlivening the field is the uncovering of new materials and
properties. Examples are semiconducting and conducting polymers,
piezoelectrics, liquid crystals, block copolymers, high-strength ex-
truded materials, immobilized enzymes, and polymeric membranes.
RESEARCH PROBLEMS
Amorphous State Solutions and Melts
The dilute-solution state is one in which attention can be focused on
the behavior of individual macromolecules. For the most part polymer
chains form loose coils, and it has been useful to draw an analogy
between the path of such a chain and the path a walker might follow
wandering randomly through space. However, there is an important
difference. The walker can freely recross his path, but the polymer
chain cannot cross parts of its path already occupied. This is referred
to as the excluded volume, or self-avoiding walk, problem. A coiled
molecule expands, on average, to decrease regions of overlap.
Whereas the average end-to-end distance of a random walk of N steps
goes like N'/9, that of a self-avoiding walk goes like No with v ~ 0.6.
The appearance of a characteristic exponent is reminiscent of critical
phenomena, reviewed elsewhere in this report (see Chapter 31. In that
chapter there is a discussion of magnetic models and their differences
according to the dimensionality of the spin. Formally it is found that
the polymer problem is in the same universality class as a magnet of
zero-spin dimensionality This may make no physical sense for mag-
nets, but it illustrates the importance in modern theory of limits defined
only mathematically.
Once the theory of critical phenomena was applied to polymer
problems it proved capable of describing a vast array of observations,
both static and dynamic. This includes the description of a state unique
to polymers, semidilute solutions. Dilute solutions are those in which
the units are widely separated. For polystyrene of molecular weight 106
g/mol (about 10,000 styrene monomers per molecule) a solution of
about 0.1 percent polymer has monomer units widely separated, but
the polymer molecules as a whole are beginning to overlap each other,
i.e., are not dilute. In this semidilute condition, a screening of the
excluded volume interactions between monomers on the same chain
develops. Screening is another critical phenomena concept (cf. Chap-
ter 31. From an experimental point of view, common polymers may not
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208 A DECADE OF CONDENSED-MATTER PHYSICS
be long enough for the semidilute theory to apply fully over a large
range of concentrations; i.e., they may always be in what is termed a
crossover region between dilute and semidilute. It is hoped that
progress in handling such crossover effects will soon be made. Poly-
mers provide many other manifestations of crossovers that may help to
delineate the effects.
An extremely valuable advance in investigating polymers occurred
some 10 years ago with the development of small-angle neutron
scattering. It opened up the possibility for studying the properties of
single-polymer molecules in condensed states, when they are perme-
ated by other molecules of the same kind. This is done by labeling some
of the molecules through replacement of hydrogen atoms with deute-
rium. It was quickly confirmed that, in the melt, random-walk statistics
apply to single-polymer chains. Since then many other results, some
quite surprising, have been obtained (see below).
The flow properties (rheology) of polymers are rather unusual,
exhibiting long-term memory, viscoelastic effects, and nonlinearities.
These are due to the fact that polymer systems, melt or semidilute, are
entangled masses. When a strain is induced in a polymer melt the
individual molecules are distorted and continue to exert a force (stress)
resisting that strain, until the molecules have moved out of the
strained, entangled mass and have relaxed to an equilibrium entangled
condition. The quantitative description of the dynamic entanglement
problem has recently been achieved in a marvelously simple way.
Consider a single, long-chain molecule. The molecules surrounding it
can be considered, effectively, to form a tube. Think of a snake in a
tube as long as itself. If the tube is distorted these distortions are
transferred to the snake. That distortion is experienced on some part of
the snake as it moves out of the tube until it has fully escaped. Of
course, escape is only possible by moving along the tube, lateral
motions being prevented. Because of this analogy the proposal is called
the reptation theory. It has been successfully applied to describe
diffusion, rheology, relaxation of rubbers, healing of cracks, crystalli-
zation from the melt, and phase-separation dynamics. There is much
experimental activity aimed at testing the applicability and limits of the
theory and at developing new refinements, extensions, and uses.
To this point we have discussed problems involving properties of
systems where the most important aspect is the chain character of the
molecule, and the detailed structure and motions on the atomic scale
(nanometers) are of peripheral importance. There are many character-
istics of structure, packing, and dynamics on the smaller scale that
affect polymer properties. Modern tools have advanced the science
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POL YMER5 209
enormously in a decade. These include NMR, fluorescence spectros-
copy, Raman and infrared spectroscopy (especially Fourier transform
infrared spectroscopy, or FTIR), wide-angle neutron scattering, neu-
tron spin-echo spectroscopy, and computer simulation. Traditional
methods have been important, too. Light has been shed on how the
small units of the molecule pack and manage to move, given that they
are restricted by being only pieces of a larger molecule. Structure and
properties have been correlated as a step toward a fuller understanding
of their relationship. An aim, actually achieved to some extent' is to
tailor-make materials with desired physical properties by controlling
the molecular or physical structure.
Glass
The glassy state is extremely common in polymeric materials. The
usual glassy brittleness has been circumvented by blending and grafting
glassy polymers with rubbery particles in complex ways that are not
fully understood. Let us concentrate here on the pure glasses. In
general one can say that the theoretical foundations for describing the
glass are primitive compared with other physical states of matter.
There is substantial, but indirect, evidence that the explanation for
some properties involves atom-sized bits of free volume in the glass
and that motion is only possible in association with this free volume.
What is a glass? It is a disordered material in which the times are long
for relaxation back to equilibrium following a change of physical
conditions (e.g., temperature or stress). These times may be seconds or
centuries. It was once hoped that a description could be achieved in
terms of only one extra fundamental parameter that had not relaxed.
Recent evidence is that this is not so. However, there seems to be a
universal function that the slow relaxations obey. If the system is
driven (or normally fluctuates) out of equilibrium, it returns according
to the formula expE-(t/~l, where t is the time and ~ and ,8 are
parameters. Unfortunately this is not a mathematical expression that is
frequently encountered in physics, so little idea exists of what the
underlying mechanisms are.
Elastomers, Gels, Cross-linked Networks
One of the outstanding, early achievements of polymer physics was
the development of a working picture for rubber elasticity. A rubber
(gel, elastomer) is formed from a nonglassy, amorphous polymer when
the molecules are tied together by a few cross-links per molecule.
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210 A DECADE OF CONDENSED-MATTER PHYSICS
Basically, macroscopic deformation of the specimen is reflected in a
distortion in the positions of the cross-link points. This, in turn,
decreases the number of ways the chains between the cross-links can
arrange themselves (technically speaking, decreases the entropy).
Decreasing entropy takes work, just as increasing energy does (as in
stretching a spring), hence the resisting force of a stretched rubber. It
was long ago realized that idealized calculations of the elastic force
were imperfect, but difficulties in preparing well-characterized samples
inhibited (and still do) the test of refined models, for instance those that
attempt to account for entanglement. Neutron scattering provides a
powerful tool for probing this problem, but the early results do not
agree with any of the theories. Explanations may involve a deeper
analysis of the topology of the network and its reaction to strain (e.g.,
the unfolding of three-dimensional pleats).
In the course of the process whereby a collection of single molecules
is transformed into a totally connected network by progressive cross-
linking, there is one critical amount of cross-linking that leads to the
first appearance of a cluster spanning the sample. This is the gel point.
The properties of systems near this condition are well described as crit-
ical phenomena. Ramifications of this description are being pursued.
Polymer Crystals
Looked at on the scale of atomic spacings (nanometers), polymer
crystals exhibit the regular characteristic of small-molecule crystals.
Looked at on larger scales, the differences are legion. Each crystal that
forms tends to be surrounded by amorphous material. Fractional
crystallinity might typically be in the 20 to 70 percent range. The
crystals are commonly lamellar (plateletlike) in shape, with a thickness
of lO to 20 nm and much larger in other directions. The molecules
stretch back and forth between the lamellar faces. The polymer chains
form high-energy folds at each face and usually re-enter the crystal
either adjacently or in nearby positions. The crystal would be more
stable if it were thicker (fewer folds per molecule), so this is not the
equilibrium state. The crystals form this way for kinetic reasons. To
form a more stable crystal would take so long that it does not occur
ordinarily. Thus one is faced with the challenge of deciphering the
details of the nucleation bottlenecks to growth in order to understand
and predict properties of the crystal. The number of proposed growth
processes applicable under various conditions has recently increased.
After a period of quiescence this problem has received considerable
attention of late because of unexpected results that emerged when the
state of individual molecules was examined with neutron scattering.
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POF YMERS 21 1
Viewed on a still larger scale, the lamellae frequently arrange
themselves in a spherulitic pattern of bifurcating, radial fibrils, often
twisting as they grow. Note that the presence of a twist implies a
handedness, which is not inherent to the symmetry of the molecule.
Recently, attention has focused on how that broken symmetry is
introduced and propagated.
There are other varieties of crystal morphology, such as fibers
formed on drawing or the forms observed when growth is in contact
with certain surfaces. Also it appears possible to grow extended chain
crystals under pressure, which may be related to liquid-crystallike
ordering.
Electrical Properties
Traditionally, attention has focused on many polymers because of
their properties as electrical insulators. Recently, however, the atten-
tion of numerous physicists, many new to the field, has turned to
macromolecules because of the discovery of interesting electrical
properties in certain polymers. An example is polyacetylene, which
when pure is a semiconductor but can be doped into the range of
metallic conduction. The polymer consists of a chain of carbon atoms
with hydrogen atoms attached to each. In a small ring of this nature all
the carbon-carbon bonds would be equivalent, and a half-filled metallic
band would be formed. In a large ring or a long chain, however, the
polymer lowers its energy by displacing atoms to create alternating
single and double bonds between carbon atoms, which gives rise to
insulating electronic bands. There are two degenerate structures
formed by this d~mer~zat~on, each formed from the other by the
interchange of the double bonds. Thus either bonds 1, 3, 5, . . . or 2, 4,
6, . . . can be double. Occasionally one gets transitions between the odd
and the even patterns. The resulting walls that separate domains of the
two degenerate structures are mobile, and are associated with excited
electronic states that spread over some 15 atoms. They are called
topological solitons. The dopant modifies the electronic state of the
soliton, creating charge donors and acceptors. One of the most
remarkable properties of these solitons is that the relation between
their spin and charge is reversed from the usual situation; i.e., a soliton
with charge 0 has spin 1/2, while a soliton with charge +e has spin 0.
These appear to be the actual stable states for mobile neutral defects
and charges in polyacetylene. Extensions of this idea to other cases has
shown that the charge partitioning can be even more pathological,
yielding net fractional charges on solitons that can be rational or
irrational. These electronic states can be investigated by various
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212 A DECADE OF CONDENSED-MATTER PHYSICS
spectroscopic.techniques. Recently efforts have been made to look at
the properties of polyacetylene in a way that integrates physical,
structural, and chemical (bond arrangements and transitions) aspects.
Another material with interesting electrical properties is polyvinyli-
dene fluoride, which is ferroelectric, piezoelectric, and pyroelectric.
Microscopically these important materials properties arise from di-
poles (on the monomer unit) that can be oriented by subjecting the
polymer films to high electric fields at elevated temperatures (well
above the glass transition). The possibility of building regular dipoles
into polymer structures and creating a wider class of such materials is
certainly an exciting direction for the future. The combination of the
mechanical properties of polymers combined with piezoelectric and
other physical properties offers the promise of a variety of technolog-
ical applications.
Other Polymer Properties
There are other types of polymers, and properties of polymers, no
less interesting and important than those just described, that space
does not permit us to discuss in any detail.
1. Some polymers form liquid crystalline phases as an outgrowth of
the rigidity of the backbone or substituent groups attached to the chain.
This ordering leads to some high-strength materials.
2. Commonly polymers are blended to form useful materials that are
either true mixtures or intimately associated microphases.
3. Block copolymers are made up of two or more chains attached in
the same molecule. Phase separation may occur, but only microdo-
mains can form because of the chemical connection between the
separated units.
4. Some polymers contain ionizable groups. Their structure, in
solution or bulk, is strongly influenced by Coulomb forces.
5. The surface is the face a polymeric phase presents to the world.
This surface may be the natural one or one modified deliberately or
through aging. Tremendous progress in surface science has been
utilized by polymer researchers.
6. Last, but by no means least, mention should be made of some of
the problems associated with bipolymers: organization, kinetics, func-
tion, compatibility, mechanical properties, and transitions.
The excitement of the polymer field is an outgrowth of the diversity
of properties that these materials exhibit, a list of properties that keeps
growing by discovery or design.
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POL YMER5 213
OPPORTUNITIES
The following list highlights several important areas of polymer
physics in which significant progress may be expected (or at least
hoped for) in the next few years. It is intended to be representative and
not comprehensive:
1. Experimental and theoretical efforts that contribute to a funda-
mental understanding and/or phenomenological description of glasses,
including polymeric ones. The nature of relaxational motions and how
these relate to ultimate strength.
2. Understanding of crazes formed during failure and application of
that knowledge to the toughening of glasses. (Crazes are microcracks
caused by environment and/or mechanical working.)
3. A broader development of the reptation idea to the description of
processes influenced by entanglements. A better connection between a
fundamental description of entanglements and the effective tube de-
scription. Attack on a few persistent disagreements between theory
and experiments.
4. Characterization of polymer properties under conditions corre-
sponding to crossovers between asymptotic regimes, such as solution
concentrations between dilute and semidilute.
5. Development and utilization of molecular tags that can be
attached to macromolecules. These tags should have properties, such
as spectra, fluorescence, or scattering cross section, that make them
easier to observe than the polymers themselves. They should reflect
the polymer's phase structure or dynamics. The question of the de-
gree to which these properties are modified by the tags should be
clarified.
6. Transport of low-molecular-weight molecules through polymers.
Use of low-molecular-weight molecules as probes of polymer proper
ties.
7. Various studies of polymer dynamics employing high fluxes of
synchrotron radiation or pulsed neutrons.
8. Definitive characterization of the polymer-fold surface of crys-
talline lamellae.
9. Description of the various polymer crystal nucleation, growth,
and aging processes, to explain such observations as curved crystals,
spherulitic growth of twisted fibrils, and thickening of lamellae during
annealing.
10. Rheology of liquid crystalline polymers. Ordering effects of
flows and electrical fields on these materials.
11. Mechanisms of charge conduction along and between conduct
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214 A DECADE OF CONDENSED-MATTER PHYSICS
ing macromolecules of various types. The role of dopants. Control of
the nonelectrical properties (e.g., solubility, morphology, strength,
degradation) of these materials.
12. Rheology of polymer blends (those that are fine dispersions),
composites (polymer matrices with particulate or fibrous inclusions),
thin films, and block copolymers.
13. Modification of polymer surfaces so that their chemical and
physical properties (e.g., adhesion, biocompatibility, catalysis, reac-
tivity) differ from those of the bulk.
14. Kinetics of phase separation.
15. Understanding of the forces and factors governing polymer
miscibility.
16. The role of entanglements in rubber elasticity.
17. Development of an understanding of the physical factors gov-
erning the three-dimensional ordering of bipolymers, sufficient to make
quantitative predictions of that ordering in viva, and disruption of order
by solvents, heat, and other agents. Description of how the ordering
influences biological function, especially with respect to complex
processes such as enzymatic action and membrane transport. Structure
and function of membranes and their protein inclusions.
Representative terms from entire chapter:
critical phenomena
