Über die Autorin bzw. den Autor

Gerhard Gompper studied Physics at the Ludwig-Maximilians-Universitaet Muenchen, where he received his Physics Diploma and Ph.D. in Physics in the group of Herbert Wagner. After a postdoctoral stay with Michael Schick at the University of Washington in Seattle, he returned to Munich to earn his habilitation. An assignment as a staff scientist at the Max-Planck-Institute for Colloid- and Interface Science in Berlin-Teltow from 1994 to 1999 preceded his joint appointment as a director at the
Institute for Solid-State Physics at the Research Center Juelich and as a full professor at the University of Cologne. He was recently honored with the Erwin-Schroedinger-Award for interdisciplinary research on the efficiency-boosting effect of amphiphilic polymers in microemulsions.

Michael Schick obtained his Ph.D. in Physics at Stanford University under Felix Bloch. After a post-doctoral position with Paul Zilsel at Case Western Reserve University, he joined the faculty of the University of Washington in 1969. His interests have included phase transitions in lower dimensional systems, wetting phenomena, microemulsions, the phase behavior
of block copolymers and of lipids, and the fusion of biological membranes. He has been honored with Fellowship in the American Physical Society, and a Humboldt Foundation Research Award spent at the Ludwig-Maximilians-Universitaet Muenchen where he worked with Gerhard Gompper. He is married to the scholar of Norwegian Literature, Katherine Hanson, with whom he lives on their floating home in Seattle's Portage Bay. He is an avid, amateur cellist.

Von der hinteren Coverseite

Soft Matter encompasses a wide range of systems of varying components,including synthetic and biological polymers, colloids, and amphiphiles. The distinguishing features of these systems is their characteristic size, which is much larger than that of their atomic counterparts, and their characteristic energy, which is much smaller. Because of their ability to assemble themselves into complex structures, they form the major components of biological systems and technological applications.

"Soft matter" is a unique series of books that strongly stresses the interdisciplinary character of this thriving field of research. The first volume offers a detailed description of the physical aspects of polymers, such as polymer dynamics in melts, and complex structure and
phase behavior of mixtures of homopolymers with block copolymers.
With contributions from highly acclaimed experts, it differs from the very specialized or proceedings-type books currently available.
Aimed at both graduates and researchers, the book is an introduction to soft matter physics as well as a concise reference for those already working in this field.

Aus dem Klappentext

Soft Matter encompasses a wide range of systems of varying components, including synthetic and biological polymers, colloids, and amphiphiles. The distinguishing features of these systems is their characteristic size, which is much larger than that of their atomic counterparts, and their characteristic energy, which is much smaller. Because of their ability to assemble themselves into complex structures, they form the major components of biological systems and technological applications.

Soft matter is a unique series of books that strongly stresses the interdisciplinary character of this thriving field of research. The first volume offers a detailed description of the physical aspects of polymers, such as polymer dynamics in melts, and complex structure and
phase behavior of mixtures of homopolymers with block copolymers.
With contributions from highly acclaimed experts, it differs from the very specialized or proceedings-type books currently available.
Aimed at both graduates and researchers, the book is an introduction to soft matter physics as well as a concise reference for those already working in this field.

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

Soft Matter

Volume 1: Polymer Melts and Mixtures

John Wiley & Sons

Copyright © 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
All right reserved.
ISBN: 978-3-527-30500-1

Chapter One

An Introduction to Soft Matter

Gerhard Gompper and Michael Schick

What Is Soft Matter?

All matter is made of atoms and molecules, and in most common systems, such as water, silicon, or sodium chloride, the size of these building blocks is on a length scale of ngstrms. Such atomic structure cannot be discerned by a microscope with a resolution of tens of nanometers, so that the material looks completely homogeneous. The situation is quite different for a suspension of latex particles, or a mixture of oil, water, and surfactant molecules. Even at a resolution of micrometers, the inhomogeneous structure of these materials is still visible. Figure 1 shows a transmission electron microscopy (TEM) image of a colloidal crystal that clearly shows its structure to be visible on the micrometer scale.

What makes these colloidal systems interesting is that their properties can be quite different from those of liquids or crystals of small molecules. For example, materials that consist of extremely large molecules are usually easily deformable. Hence they are usually referred to as "soft matter". The reason for the softness of such macromolecular materials is readily understood. Let us compare the energies that are needed to deform the surfaces of a common molecular crystal, such as sodium chloride, and of a crystal of spherical colloidal particles with a size of 1 m, a factor of [10.sup.4] larger than ordinary molecules. The resistance of a crystal with respect to external shear forces is characterized by the shear modulus. For a crystal of linear sizes [L.sub.x], [L.sub.y], and [L.sub.x], to which a force F is applied at the top and bottom surfaces in the x and -x directions, respectively (see Fig. 2), the shear modulus, , is defined by

F/[L.sub.x][L.sub.y] = [DELTA][L.sub.x]/[L.sub.y] (1)

where [DELTA][L.sub.x] is the crystal displacement in the top layer. The shear modulus is an intrinsic property of the material, independent of the system size, and has the dimension energy/[(length).sup.3]. We obtain a rough estimate of the shear modulus of a material by inserting the characteristic length and energy scales of the crystal. For a molecular crystal, the energy scale is that of covalent bonds, 10 eV, while for a colloidal crystal the energy scale is not that of some microscopic interaction potential, but rather is on the order of the thermal energy [k.sub.B]T, about (1/40) eV at room temperature. Thus the energy scale is two orders of magnitude smaller in colloidal crystals. The length scale in the colloidal crystal is of the order of its lattice constant, which is four orders of magnitude larger than those of molecular crystals. One therefore estimates that the shear modulus of a colloidal crystal is [10.sup.-2]/[([10.sup.4]).sup.3] = [10.sup.-14] or 14 orders of magnitude smaller than the shear modulus of a molecular crystal. This estimate reproduces quite well experimentally observed values for the shear modulus of colloidal crystals. As the shear modulus is so small, colloidal crystals are extremely soft and can be destroyed by mechanical forces very easily.

The appearance of the thermal energy as the scale of interaction energy is pervasive in soft matter, and reflects the fact that many of the important interactions in these systems are entropic in origin. These effective interactions often arise from microscopic hard-core potentials between the particles themselves, or between the particles and confining walls, or from other constraints. Their net effect is to reduce the allowed configurations of the system and therefore its entropy, and to increase the system's free energy, an increase that can be assigned to an effective interaction. The presence of a factor of [k.sub.B]T in the magnitude of such interactions belies their entropic origin (Israelachvili 1992).

In addition to colloids, there are many other kinds of very large "molecules". Aggregates of polymers and of smaller amphiphilic molecules are the most common building blocks of soft matter. These blocks will be considered in more detail in the next section.

For reasons similar to those sketched above for colloidal crystals, one finds that membranes consisting of amphiphilic molecules are also easily deformable. Such biological membranes enclose red blood cells, shown in Fig. 3, whose size is on the order of micrometers. Due to the flexibility of its enclosure, a red blood cell can penetrate through openings that are ten times smaller than itself.

The Classical Systems

The "classical" soft matter systems, which have been studied since the early 19th century, are dispersion colloids, systems of small amphiphiles, and polymers. We briefly introduce these systems here.

Dispersion Colloids

Colloids are rigid particles that have a size in the range of 1 nm to 10 m. They are usually dispersed in a fluid because, in its absence, the colloidal system behaves as a powder. Such solutions are commonly referred to as dispersions or suspensions. The colloidal particles are small enough to exhibit thermal motion, and therefore behave as "large molecules". Their thermal motion is commonly referred to as Brownian motion, named after the Scottish botanist Robert Brown, who observed thermal motion of pollen grains through a microscope in 1827.

Since colloidal particles typically have a different dielectric constant than the embedding fluid, they attract each other by van der Waals interactions (Mahanty and Ninham 1976; Israelachvili 1992), with the result that they are unstable to coagulation. Two methods are commonly employed to stabilize such systems. The first is to charge the colloidal particles electrically with charges of the same sign to produce an electrical repulsion. The second is to coat the surfaces with a polymer layer, which leads to a steric repulsion.

The lower limit on the size of a colloidal particle of approximately 1 nm assures that the fluid in which the colloidal particles are embedded behaves for the most part as a structureless continuum. Since the typical size of a solvent molecule is 1 , the colloidal particle can usually be regarded as a macroscopic object on the solvent length scale. Moreover, the relaxation times of the degrees of freedom of the solvent molecules are much smaller than those for the colloidal particles. Dynamics and non-equilibrium phenomena can thus be described by equations of motion in which the degrees of freedom of the solvent molecules are integrated out. For both the structure and the dynamics, a colloidal system of identical colloidal particles can therefore be regarded as an effective one-component system. The solvent now appears only via phenomenological parameters, such as the viscosity, and acts as a thermal motor that drives the motion of the colloidal particles.

Colloidal dispersions in some aspects behave much like ordinary condensed matter. Therefore, they provide interesting model systems from which insight can be gained on fundamental processes that apply to molecular systems as well, such as crystallization, critical phenomena, and glass formation. Indeed, as Dogic and Fraden state in their introduction to Chapter 1 of Volume 2, they were originally motivated to study virus suspensions because they thought that they were model systems of simple fluids. They acknowledge in the very same sentence, however, that their colloidal system, like so many others, has its own specific properties that have no counterpart in molecular systems. There are several reasons why colloids exhibit such specific phenomena. One is that the particles can exist in many different shapes, some of which have been examined extensively: for example, spheres, such as in silica suspensions (Manoharan et al. 2003); rigid rods, such as tobacco mosaic virus and double-stranded DNA fragments; and semi-flexible rods, such as the fd virus shown in Fig. 4. The fascinating phase behavior of this bacteriophage is the subject of Chapter 1 of Volume 2 by Dogic and Fraden. As shown there, these colloids self-assemble into various ordered arrays, a property that is shared by other soft matter systems, such as small amphiphiles, and polymers. It is also one of great technological interest, as the periodicity of the structure can often be tuned by varying the constituent particle. The search for a suitable three-dimensional photonic band-gap material has naturally focussed on the above materials (Vos et al. 1996; Pan et al. 1997; Dinsmore et al. 1998). This property of self-assembly, particularly into ordered arrays, is another recurrent theme in soft matter.

Another reason for the particular behavior of colloids is their very slow dynamics. The microstructural arrangement of colloidal particles typically relaxes in a time range of seconds. This results, for example, in a nonlinear response of colloidal systems, like those of rigid rods, to a shear field, a subject treated authoritatively in Chapter 3 of Volume 2 by Dhont and Briels. For molecular systems, such nonlinear response would occur at unrealistically high shear rates and frequencies. In general, the subject of the hydrodynamic behavior of colloidal fluids is one of significant technological, as well as intrinsic, interest.

Colloids are treated extensively in many texts, such as Russel (1987), Russel et al. (1989), van de Ven (1989), Hunter (1989), Evans and Wennerstrm (1994), Dhont (1996), and Dhont et al. (2002).

Self-Assembling Amphiphilic Systems

Amphiphilic molecules usually consist of a hydrophilic head-group and a hydrophobic tail. The latter typically consists of one or two hydrocarbon chains, which can be totally saturated or partially unsaturated with one or more double bonds. The hydrophilic part consists of either a polar group, whose dipole moment interacts strongly with those of water, or an ionizable group, such as COOH, which dissociates, leaving a residual charge that interacts even more strongly with the solvent dipoles. Such an ionic amphiphile with a tail of a single chain, sodium dodecyl sulfonate, is shown in Fig. 5. An example of a non-ionic, two-chain biological lipid, phosphatidyl choline, is shown in Fig. 6. Note that one chain is saturated, while the other has a sole double bond half-way down the chain. This is a common lipid motif. Molecules such as these have several names: "amphiphilic" from the Greek for "loving both", or "amphipathic", a name favored in the biological community, or "surfactant", a contraction of "surface-active", because these molecules absorb preferentially at interfaces of water with oil or with air and reduce the surface tension.

The basis for the hydrophobic interaction between the tails and water is once again entropic. The tails break up the extensive hydrogen-bonding network of the water, thus reducing its entropy, which can again be viewed as an effective repulsion. The head-groups also disturb this network, but they more than make up for the entropy reduction by means of their favorable interaction with the water dipoles. Due to these interactions, amphiphiles placed in water will self-assemble and form arrays such that the hydrophilic head-groups are exposed to water while the tails are sequestered from it. The simplest such array is that of a bilayer, shown in Fig. 7, which is a very common structure. Indeed, the basis of all biological membranes is the lipid bilayer. If the amount of amphiphile is increased, the number of bilayers formed is increased, and the system will arrange itself into an ordered lamellar phase. Under various conditions, such as a change in the water content, or a change in the architecture of the amphiphile, several other ordered phases can be formed. Among these are: the cylindrical phase, in which the amphiphiles form single sheets that close into cylinders and are packed in a hexagonal array with the water on the outside and the tails hidden on the inside; a body-centered cubic (bcc) phase, in which the sheets form spheres that pack into a bcc array with water on the outside; and, perhaps most bizarre of all, a "gyroid" phase, in which a bilayer membrane divides space into two identical, sample-spanning, volumes. Because of this, the phase is often denoted "bicontinuous". It is a perfectly good cubic phase (space group Ia]bar.3]d), and was first identified in small amphiphilic systems by Luzzati and Spegt (1967). Later it was observed in systems of block copolymer (Hadjuk et al. 1994). While not uncommonly exhibited by soft materials, it is not a space group ever found in molecular crystals, probably because the structure would consist of atoms in sites of three-fold coordination creating a rather low-density structure not favored by the strong atomic interactions. A disordered and therefore liquid analog of such a bicontinuous phase is observed in these binary (water and amphiphile) systems, and has been denoted a "sponge" phase (Cates et al. 1988). When water is removed from these systems, inverted phases may form in which the reduced amount of water is on the inside of the arrays, and the tails are on the outside (Seddon and Templer 1993).

In addition to the ordered phases at relatively high concentration of amphiphile, there is also a fluid phase at low amphiphile concentration in which these molecules form small, usually spherical, aggregates, called micelles. The head-groups face the water and the tails are again sequestered within.

If a third, oil-like, component is added to these systems, it will swell the regions in which the tails reside, as shown in Fig. 7. Thus one finds exactly the same phases as in the binary system but with at least one new possibility. If the concentration of amphiphile is low in a system in which the solvent is oil, the fluid will contain micelles that are inverted, with the heads in and tails out. As one changes the composition of the solvent from mostly water, containing normal micelles with heads out, to mostly oil, containing inverted micelles, the fluid must pass through a region in which the amphiphiles assemble in some intermediate way. In fact, the system can pass through a composition region in which the oil and water are separated by disordered sheets of amphiphiles, again forming a bicontinuous fluid. Such a phase, which still retains much structure, is denoted a microemulsion. In addition to the intrinsic interest of describing a fluid with significant structure, microemulsions have been of technological use, as they can contain in one fluid phase a large amount of two components, here oil and water, which would phase-separate in the absence of the amphiphile.

Self-assembling amphiphilic systems are discussed in the texts by Israelachvili (1992), Gelbart et al. (1994), Gompper and Schick (1994), Safran (1994), Jnsson et al. (1998), and Dhont et al. (2002). Texts devoted to the physics of membranes are Lipowsky and Sackmann (1995), Boal (2002), and Nelson et al. (2004).

Polymers

Polymers are essentially giant molecules, or macromolecules, consisting of an extremely large number of basic units chemically joined together to form one entity. They are ubiquitous. Polyethylene, the practically endless repetition of a simple H-C-H group, forms most of the plastics found in the home, whether in containers, shopping bags, or toys. Polystyrene is the basis for Styrofoam, and also forms the plastic in light switches and the plates surrounding them. Poly(methyl methacrylate) forms the clear plastics Lucite and Plexiglass. Not all polymers, however, are of the technical variety; DNA and RNA are biological polymers consisting of only four distinct monomers, while proteins are also polymers built out of 20 different monomers, the amino acids.

The fact that polymers are ubiquitous should not blind one to the difficulty of accepting the concept of a giant molecule. It is not now, nor was earlier, an obvious one. It was in 1922 that the German organic chemist, Hermann Staudinger, who coined the term "macromolecule", published a theory that rubber was made of a natural polymer, and that it was the entropic properties of such chains that were the source of the elasticity of the material. A long 21 years passed before these insights were recognized by the award of a Nobel Prize in chemistry.

(Continues...)

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