Debye stiffness

For covalent crystals temperature has little effect on hardness (except for the relatively small effect of decreasing the elastic shear stiffness) until the Debye temperature is reached (Gilman, 1995). Then the hardness begins to decrease exponentially (Figure 5.14). Since the Debye temperature is related to the shear stiffness (Ledbetter, 1982) this softening temperature is proportional to C44 (Feltham and Banerjee, 1992). 

Random Systems The scattering from random two-phase systems was considered by Debye(13,14) and other accounts are available (15,16) These formulations have been applied to gels of a fairly stiff polymer by Goebel, Berry and Tanner (17,18) If the system is spatially isotropic then ... 

In pure polyelectrolyte solutions a decreasing polyelectrolyte concentration cp is followed by an increase of the Debye length 1D and an increase in chain stiffness. Applying scaling concepts [109] and considering an electrostatic contribution to the persistence length Lp [110-113] various concentration regimes could be identified for polyelectrolyte solutions. Odijk derived different critical con-... 

Before doing that, however, it is useful to understand qualitatively the anticipated behavior of the susceptibilities. Let us consider the Debye-type expression Eq. (4.107) for the linear susceptibility. The drastic change of the exponential factor reduces all the limiting behavior to just two cases. The first is oytjo 1, specifically, the system is rather cold and stiff. Thus the response is close to zero. The second case is oar [Pg.457]

For a solution of stiff-chain macromolecules (for example, PBLG), with p 3 x 103 Debye [153], the corresponding estimation shifts to Eq > 4 kV/cm but still remains within the experimentally feasible range. 

Analysis of the electron scattering by the T1F dimer suggests a value for the instantaneous dipole moment of several debye.606 This is not consistent with a stiff, symmetric, linear structure for the dimer. 

It was shown that with increasing internal chain stiffness the effective exponent y for Le — crosses over from a value of one toward two as the internal stiffness of a chain increases. The quadratic dependence of the electrostatic persistence length on the Debye radius for the discrete Kratky Porod model of the polyelectrolyte chain was recently obtained in [65]. It seems that the concept of electrostatic persistence length works better for intrinsically stiff chains rather than for flexible ones. Further computer simulations are required to exactly pinpoint the reason for its failure for weakly charged flexible polyelectrolytes. 

Fig. 3.16 Debye temperature as a function of e/a ratio for binary alloys of the Ti-Mo-Re sequence. Particularly noteworthy are that (1) an e/a of 6 guarantees a maxmum in the stiffness of the bcc alloys (2) at sufficiently low e/a values, the occurrence 0) phase be-gins to stiffen the bcc lattice and (3) at sufficiently high e la values, the lattire is stiffened by a transfotmation to a phase [Col73].

Recently Barrat and Joanny have addressed one of the criticisms of the OSF theory. They have used variational methods to allow the chain to be flexible instead of locally stiff. A new expression for the persistence length is obtained scaling as the Debye length or which agrees with experi-... 

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