Universality parameter, polymer glass

Williams, Landel and Ferry (1955) have given an empirical expression for a T)y applicable to a wide variety of polymeric materials, for temperatures not too different from the glass transition temperature Tg of the polymer. Their expression contains material-dependent parameters. In its simplest form, there is only one such parameter, the glass transition temperature Tg. This approximate universal expression is given by... 

Classification of composites by the phase inclusion size bears a philosophical aspect how small should a component in the matrix be not to make the term composite material so universal as to include in fact all materials Interatomic distances in molecules and crystals are of 1.5 10 m dimensionality, distances between iterative elements of the crystalline structure are 10 —10 m, while the size of the smallest intermolecular voids in polymers is 10 m. Note that mean nanoparticle size (plastic pigments are 10-8-10 m in size, the diameter of monocrystalline fibers or whiskers is 10 —10 m, glass microspheres are 10 —10 m) is commensurate with parameters of monolithic simple materials. This means that in the totality of engineering materials, nanocomposites occupy a place at the boundary between composite and simple materials. 

The study of the frequency dependence of the AC conductivity obtain information about electronic states and transport mechanism of disordered solids. In numerous disordered solids (amorphous and doped semiconductors, semiconductor glasses, polymers, granular materials, etc.), the AC conductivity in a wide frequency range (up to GHz range) can be described by a fractional power dependence a(m ) = AcT, where A is a constant and the parameter 5 lies in the range 0 < 5 < I (universality, see reviews [1, 2]). 

In [5] parameter Jg correlates with uncondied space part at stmcture glass transition temperature of polymer, but how it was shown by unconnected with polymer relaxation properties studies of unconChed space, does not it. It was proved empirically that it is average valne for linear, branched and rarely cross-linked polymers is universal and equal to 0.025. On the ground of made transformations it may be drawn a conclusion, that this value preserves for thick mesh polymers, too. 

Equations [7] and [9] are mathematically equivalent. TRef is a reference temperature and v(TRef) the value of the relaxation rate at this temperature. Ci and C2 = TRef 7o are so-called WLF parameters. It was argued that these parameters should have universal values that are independent of the polymer investigated if the glass transition temperature Tg is chosen as reference temperature However, it was found that these... 

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