Frenkel model

The maximum shear strain in engineering units is fb=2/J, which corresponds to the value p(4dc) l in the Frenkel model discussed in Sect. 2.5.1. The relative displacement, xy of adjacent chains shown in Fig. 57 is limited by the maximum value 2/3 for larger displacements the attracting force decreases rapidly and failure is initiated. It is further assumed that A0(tb) [Pg.85]

The release of the trapped carriers may be stimulated by the electric field. In the Pool-Frenkel model the decrease of the potential barrier of the trapped electron by the electric field (AEFp) obeys the formula... 

The main experimental results of charge carrier generation in PVC was explained in the frame of the Pool-Frenkel model [28-30]. The dependence of the recombination time on electric field was due to the change of the mobility in the electric field. Germinate recombination of the electron-hole pairs was investigated by means of luminescence decay characteristics [31]. 

Santos-Lemus and Yartsev (1995) analyzed earlier data on NIPC doped PC by Santos-Lemus (1983) and Santos-Lemus and Hirsch (1986). The temperature dependence was analyzed by a Poole-Frenkel model. From plots of the activation energy versus E /2, zero-field energies were determined for different NIPC concentrations. The values were in the range of 0.60 to 0.73 eV. From a plot of the zero-field activation energy versus p K a value of 0.98 eV was derived for the potential barrier of an isolated NIPC molecule. 

Frenkel Model - A model developed by Russian scientist Frenkel to describe coalescence/sinter-ing of particles of metals and plastics. See the following references for more information Mascia, L., Thermoplastics, Matena/5 Eng., 2 ed., Elsevier Applied Science, New York (1989) and Lontz,J. F., in Fundamental Phenomena in the Material Sciences, Vol. 1 (L. J. Borris and H. H. Hansner, eds.), p. 37, Plenum Press, New York (1964). 

Fig. 4.21 (Color) Relaxed shear stress-strain curves of 22 materials, rescaled such that all have unit slope initially and reach maximum at 1. The renormalized Frenkel model Eq. (4.8) is shown (in heavy black line) for comparison [6]. With kind permission of Dr. Yip...

FIGURE 4.1 Schematic representation of deformation oftwo sequences of atoms according to the Frenkel model. Positions before (a) and after (b) deformation [3],... 

Inconsistency of and values for metals results to a search for another mechanism of yielding realization. At present, it is commonly accepted that this mechanism is the motion of dislocations by sliding planes of the crystal [3]. This implies that interatomic interaction forces, directed transversely to the crystal sliding plane, can be overcome in case of the presence of local displacements number, determined by stresses periodic field in the lattice. This is strictly different from macroscopic shear process, during which all bonds are broken simultaneously (the Frenkel model). It seems obvious that with the help of dislocations total shear strain will be realized at the... 

By substituting reasonable v value, for example, 0.35 [27], and assuming a. = Zj., the following value for x is obtained x = 2 x 10 G. Though for metals this value is higher than the observed x, it is much closer to them than the stress calculated using simple shear model (the Frenkel model. Fig. 4.1). 

The first term is the elastic stress at point x due to the infinitesimal dislocation p(x )dx at point x the second term represents the restoring stress due to the non-linear misfit potential acting across the slip plane. This potential must be a periodic function of u(x) with a period equal to the Burgers vector of the dislocation. As the simplest possible model, we can assume a sinusoidal function for the misfit potential, which is referred to as the Frenkel model [136]. One choice is (see Problem 4 for a different possible choice)... 

Summarizing the results obtained for charge transport in conjugated polymers, the Poole-Frenkel model seems to be a good description [126,127]. This model of transport assumes the existence of two types of carrier movement, one in conductive states (positive polarons) and the other via traps (negative polarons). 

Concerning the Frenkel model for structure in the melt, he has not presented a formalized model nor given any details about the nature of segment-segment contacts which "melt out" at Tn-My concept of his model (shown as Fig. 11) is far simpler than the Pechhold meander model [W-R-Pechhold and H.P. Grossman, Faraday Disc., Chem. Soc., 68,58-77 (1979)]. 

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