Thermophysics of Polymers I: Theoryhere, Herbert Baur provides a simple description of the theory of thermophysics of polymers. In order to illustrate the theoretical skeleton, he only treats the simple, easily comprehensible problems of polymer physics, yet, in detail. The main points covered are: thermally excited conformation isomery of polymers; phonon gas of ideal polymer crystals; the dissipative thermo-mechanical behaviour of polymers, new aspects of viscoelastic behavior, glass transistion, and crystallization. |
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Page 123
... group velocity must , in general , be distinguished from the phase velocity ( 6.132 ) ( Fig . 6.10B ) . Due to the dependence of the group velocity on the wave number , a signal composed of waves with different wave numbers eventu- ally ...
... group velocity must , in general , be distinguished from the phase velocity ( 6.132 ) ( Fig . 6.10B ) . Due to the dependence of the group velocity on the wave number , a signal composed of waves with different wave numbers eventu- ally ...
Page 142
... velocity ce [ compare ( 6.192 ) with ( 6.142 ) ] . The group velocity vanishes at 2 = 1 , μ , μ + 1 , i . e . , at the boundaries of the first Brillouin zone , and in the case of the optical branch also for k = 0 ( N2 = μ + 1 , w = @o ...
... velocity ce [ compare ( 6.192 ) with ( 6.142 ) ] . The group velocity vanishes at 2 = 1 , μ , μ + 1 , i . e . , at the boundaries of the first Brillouin zone , and in the case of the optical branch also for k = 0 ( N2 = μ + 1 , w = @o ...
Page 179
... group velocity becomes constant and equal to the phase velocity , as is required by Debye's T3 - law ( Sect . 6.5.2 ) . The group velocity of the bending waves , however , only depends on the intermolecular interaction para- meters ( in ...
... group velocity becomes constant and equal to the phase velocity , as is required by Debye's T3 - law ( Sect . 6.5.2 ) . The group velocity of the bending waves , however , only depends on the intermolecular interaction para- meters ( in ...
Contents
Equilibrium and Stability Conditions | 20 |
Homogeneous Mixtures | 27 |
2 | 33 |
Copyright | |
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according arrested equilibrium bending modes branch Bravais lattice Brillouin zone chain molecules chemical potentials coefficient of thermal conformational isomers const constant corresponding crystalline curve Debye Debye relaxation degrees of freedom density dependent differential dispersion relation elastic enthalpy entropy equilibrium position equilibrium thermodynamics extensive quantities free energy free enthalpy frequency G-representation gauche-bonds Gibbs function Gibbs fundamental equation group velocity heat capacity Hence homogeneous interaction intermolecular internal energy internal equilibrium internal variable lamella lattice units leads linear chain liquid M₁ mass points mechanical melting mixture modulus mole number molecular N₁ N₂ non-equilibrium obtains perturbation phase phonons polymer crystal pressure processes quantities quasi-elastic relaxation relevant internal degrees respect response functions Sect segment so-called stretching modes T₁ temperature thermal expansion tion v₁ valid vector vibrations volume wave number x₁ Σ Σ ат др эт