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## Über dieses Buch

Modern polymer materials are designed by applying principles of correlation between chemical structure, physical macrostructure and technological properties. Fundamentals of polymer physics are explained in this book without excessive use of calculations. Four main sections treat relaxation of polymers, melting and crystallization, the mechanism of deformation in thermoplastics, elastomers and multiphase systems, and thermodynamics of mixing and swelling of polymers and polymer networks. The book presents the theoretical models of polymer physics in a comprehensive style and relates their applicability to real polymer systems in terms of the available experimental observations.

## Inhaltsverzeichnis

### 1. Object and Aims of Polymer Physics

Abstract
The substitution not only of metals but also of glass, wood, paper and leather by high-quality, high-performance synthetic materials is gathering momentum. The continuation of this substitution process has been further assured by the introduction of blend technology, in particular the blending of thermoplastics, which has led to the development of “High-Tech” polymeric materials. It is doubtful whether these material developments could have been made without the fundamental information derived by a consideration of polymer physics. One of the most important tasks of polymer physics involves, from investigation of molecular mobility and deformation, phase transitions, molecular interactions and the resulting supra-molecular structures, the development of an understanding, from a molecular standpoint, of the physical and technological properties of polymeric materials. Such an understanding is a prerequisite for any systematic modification or optimization, in terms of the continually increasing industrial requirements of existing materials and, indeed, for a programmed development of new materials. Such developments require a continuous feed-back between the polymer physicist and, not only, the synthetic and analytical chemists and the development technologists, but also between the physicist and the manufacturing and process technologists and the constructors and designers of plastic articles.
Ulrich Eisele

### 2. Mechanical Relaxation in Polymers

Abstract
The state of an ideal elastic body under stress and strain due to the influence of a load can be described by corresponding tensors. The components of the strain tensor en and 7ik determine the relative change in the dimensions and angles of a small, cubic volume element. Such an element is imagined to be extracted from within the body under load. In a similar manner, the components of the stress tensor σii and τik can be used to determine the forces operating on the surfaces of the imaginary cube. The usual matrix formulation for tensors leads to the following expressions:
$$\varepsilon=\begin{pmatrix} \varepsilon_{11}& \gamma_{12}& \gamma_{13}\\ \gamma_{21}& \varepsilon_{22}& \gamma_{23}\\ \gamma_{31}& \gamma_{32}& \varepsilon_{33}\\ \end{pmatrix} \,\,\, \sigma=\begin{pmatrix} \sigma_{11}& \tau_{12}& \tau_{13}\\ \tau_{21}& \sigma_{22}& \tau_{23}\\ \tau_{31}& \tau_{32}& \sigma_{33}\\ \end{pmatrix}$$
Ulrich Eisele

### 3. Simple Phenomenological Models [4, 8]

Abstract
Many attempts have been made to describe the creep and relaxation behaviour of polymers in terms of simple models based on elastic springs and viscous damping elements.
Ulrich Eisele

### 4. Molecular Models of Relaxation Behavior

Abstract
Polymer relaxation phenomena result from thermally activated jump processes involving individual molecules or molecular segments. A useful model for a simple change of site process is the Snoek effect observed in C-doped α-iron. The C-atoms are foreign elements in the cubic space-centered Fe-lattice and occupy sites half-way along the edges of the elementary cell (see Fig. 20).
Ulrich Eisele

### 5. Glass Transition [14–47]

Abstract
The glass transition is a phenomenon which not only affects the modulus of polymeric materials; it also affects the specific volume, the enthalpy, the entropy, the specific heat, the refractive index, the dielectric constant etc., of such materials.
Ulrich Eisele

### 6. Flow and Rubber Elasticity in Polymer Melts [4,45, 46, 48–57]

Abstract
In addition to those relaxation processes which have been discussed up to now (γ- process, glass transition) there is an additional process, which occurs in all uncrosslinked polymers: the flow relaxation process. By this process the polymer melt exhibits a recoverable strain if the stress is released. In dynamic mechanical investigations, this corresponds to a paraelastic relaxation process taking place over the same frequency range as that where J=l/ωη. This process occurs on the temperature scale above the glass transition, whereas on a frequency scale it occurs below this transition. Figure 47 shows, as an example, the frequency dependent master curves of the dynamic shear compliance and the shear modulus for polyisobutylene at a reference temperature, T0 = 273K, obtained using the frequency-temperature superposition principle. In this graph one can see (from left to right): flow, the rubber plateau, the glass transition and the modulus and compliance plateaus of the glassy, frozen solid. From a comparison of the two curves it is obvious that the maximum loss modulus at the glass transition occurs at a frequency some six orders of magnitude greater than that of the loss compliance.
Ulrich Eisele

### 7. Crystallization Behavior [58–75]

Abstract
Single polymer crystals were first recognized in 1953 (Schlesinger and Leeper). Such crystals grow preferably from dilute solution to form rhombic platelets several μm in diameter and approx. l0 nm thick.
Ulrich Eisele

### 8. Melting Behavior [76–84]

Abstract
The melting of polymers is, in principle, a first order transition. Nevertheless, it is not possible to describe all the experimental observations, which have been made for polymer melts, in terms of equilibrium thermodynamics. Due to the limited mobility of the long polymer chains, they do not reach their equilibrium conformation within a finite time. Thus, in order to completely describe the state of a system, not only the usual variables of state but also inner ordering parameters, which reflect the thermal history of the system, are required.
Ulrich Eisele

### 9. Mechanism of Deformation of Thermoplastics and Multi-component Systems [85–97]

Abstract
The deformation of polymers in the non-linear region is exceedingly complex. Even in the simple, uniaxial stress-strain experiment there is a considerable variety of possible phenomena. Figure 93 shows stress-strain curves for a selection of thermoplastics and elastomers.
Ulrich Eisele

### 10. Rubber Elasticity of Covalently Crosslinked Elastomers [98–129]

Abstract
Since rubber elastic deformation behavior results, to a first approximation, from reversible change of site processes of chain segments, the first law of thermodynamics can be used as a starting point for a consideration of this phenomenon: The internal energy U of a system can be increased by introducing energy from outside the system, either in the form of thermal energy or as a result of mechanical or electrical work:
$${\text{dU}} = {\text{dQ}}+ {\text{dA}}$$
(183)
In order to thermodynamically describe equilibria, variables of state are introduced. An isothermal, isobaric system will tend towards a minimum Gibbs free energy G:
$${\text G} = {\text{U-TS}} + {\text{pV}}$$
(184)
$${\text{dG }} = {\text{0 with T and p constant at thermal equilibrium }}$$
(185)
An isothermal, isochoral system tends towards a minimum Helmholtz energy F:
$${\text F} = {\text {U-TS}}$$
(186)
$${\text{dF}} = {\text{0 with T and V constant at thermal quilibrium }}$$
(187)
Thus, all processes in an isothermal, isochoral system tend to a minimum internal energy and a maximum entropy.
Ulrich Eisele

### 11. Tear Formation and Propagation in Elastomers [130–144]

Abstract
During cyclical deformations of an elastomer small cracks appear on the surface of the sample even though the maximum theoretical stress at peak deformation is much smaller than the tensile strength of the material. Crack growth, the speed of which usually increases with increasing crack length, is often the limiting factor for the useful life of a rubber article. At a defined end of usefulness one speaks of fatigue life. Crack propagation and fatigue life result from stress concentrations at the tips of cracks on the surfaces of rubber articles. These stress concentrations build up at naturally occuring, microscopic surface flaws, extraneous inclusions or inhomogeneities.
Ulrich Eisele

### 12. Deformation Behavior of Thermoplastic Elastomers [145–157]

Abstract
Entropy elastic deformation of polymers requires that the molecular chains cannot dissipate an applied strain via plastic flow. This state is achieved in covalently crosslinked elastomers by statistically bonding neighboring chains together, for example, via S-bridges. An alternative way of hindering plastic flow is to introduce moieties which form strong physical bonds between the chains into the network. The two principal types of network are shown schematically in Fig. 130. In the physical network the parts of the molecules which are enclosed by the rings shown in Fig. 130 are held together by non-covalent interactions so that these regions form effective, large volume crosslinks. These regions, together with the entropy elastic chains outside these physical crosslinks, allow such materials to exhibit considerable elasticity.
Ulrich Eisele

### 13. Compatibility of Polymers [158–190]

Abstract
Mixtures of polymers do not, generally, form thermodynamically stable singlephase systems. Complete miscibility in a mixture of two polymers requires that the free energy of mixing is negative:
$$\Delta G_m = \Delta H_m - T\Delta S_m < 0$$
(326)
Ulrich Eisele

### 14. Network Swelling [98, 188, 189]

Abstract
The swelling of crosslinked polymers can also be theoretically described with the aid of the Flory-Huggins theory. To this end, the first step is to take account of the contribution to the free energy from the elastic deformation of the network due to the infusion of liquid molecules. The molar free energy of the swollen network is given by:
$$\Delta {\text g_m}= \Delta {\text g_{ml}}+ \Delta {\text g_{m2}}355$$
(355)
Ulrich Eisele

### 15. Environmental Stress Cracking of Polymeric Materials [190]

Abstract
Gases and liquids act on thermoplastics to produce an effect known as Environmental Stress Cracking (ESC). An essential characteristic of ESC is that, with an appropriate medium, damage only occurs under mechanical stress, the amount of which may be considerably less than the nominal limiting load for a given material. Even high impact thermoplastics, such as polycarbonates, behave as brittle materials under relatively low stress in the presense of some solvents (e.g. for polycarbonates: Toluene or toluene/isooctane mixtures).
Ulrich Eisele

### Backmatter

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