Intrinsic Debye length

Erom the summary of the theoretical results presented above, it follows that the intramolecular volume of a star-branched PE, with a sufficiently large number of arms, is essentially electroneutral. That is, the bare charge of a star polymer is neutralized by mobile counterions. These counterions are predominantly retained inside the macroion volume, even if the star is immersed in a dilute salt-free solution. Moreover, if the intrinsic Debye length associated with the intramolecular concentration of entrapped counterions, = l paNis used as an upper estimate for the intramolecular electrostatic screening length, one finds that in the osmotic PE star, p a), the electrostatic interactions are screened at... 

Table 5.2-25 Intrinsic Debye lengths for various semiconductors...

Intrinsic Debye length (cm) 2.9x10-3 7.0x10-3 2.0x10-1 2.7x10-2 8.6xl0- 2.4x10- ... 

Note that when the concentration of added salt is very low, Debye length needs to be modified by including the charge contribution of the dissociating counterions from the polyelectrolytes. Because the equilibrium interaction is used, their theory predicts that the intrinsic viscosity is independent of ion species at constant ionic strength. At very high ionic strength, the intrachain electrostatic interaction is nearly screened out, and the chains behave as neutral polymers. Aside from the tertiary effect, the intrinsic viscosity will indeed be affected by the ionic cloud distortion and thus cannot be accurately predicted by their theory. 

The effect of salt on the conformations of a many-arm (osmotic) PE star becomes important when the salt-controlled bulk Debye screening length, given by (33), becomes smaller than the intrinsic screening length, in a salt-free osmotic PE star. This is also true, equivalently, when the concentration of added salt exceeds the intramolecular concentration of counterions in the osmotic star. Clearly, the local electroneutrality in this case is ensured, and the LEA is applicable for analysis of the PE star conformations on a length scale larger than td. 

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. 

Therefore, the macroscopically measurable B and Aco connect directly to the bond length and energy of the specimen and their response to the intrinsic coordination imperfection and the applied stimuli through the BOLS correlation and the LBA approach. Exercises lead to derived information of the cohesive energy and Debye temperature, energy density, compressibility, the bulk modulus and their first-order derivatives, and the analytical correlation between the B and Aco. 

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