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 126
... Brillouin zone ( 6.134 ) , and if we assume an even - numbered N , & is restricted to the values = 0 , 1 , 2 ... Brillouin zone . These states are identically repeated in the subsequent zones ( with | k | > πία ) . The wave numbers are ...
... Brillouin zone ( 6.134 ) , and if we assume an even - numbered N , & is restricted to the values = 0 , 1 , 2 ... Brillouin zone . These states are identically repeated in the subsequent zones ( with | k | > πία ) . The wave numbers are ...
Page 136
... Brillouin zone , but the resultant momentum must then , in order to maintain the unambiguity of the description , be brought back to the first Brillouin zone [ see the comments on Eq . ( 6.133 ) ] . In general , one must point out here ...
... Brillouin zone , but the resultant momentum must then , in order to maintain the unambiguity of the description , be brought back to the first Brillouin zone [ see the comments on Eq . ( 6.133 ) ] . In general , one must point out here ...
Page 139
... Brillouin zone , we obtain according to ( 6.183 ) w2 = β MA [ ( μ + 1 ) + ( μ − 1 ) ] , with the two solutions W = WA , max = 26 MA 1/2 > 1/2 20 2p W = @ 0 , min μ = MA MB / Over the total range of the first Brillouin zone , the ...
... Brillouin zone , we obtain according to ( 6.183 ) w2 = β MA [ ( μ + 1 ) + ( μ − 1 ) ] , with the two solutions W = WA , max = 26 MA 1/2 > 1/2 20 2p W = @ 0 , min μ = MA MB / Over the total range of the first Brillouin zone , the ...
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