Handbook of Solvents - George Wypych - ChemTech - Ventech!

728 Ranieri Urbani and Attilio Cesàro
Figure 12.2.13. Dependence of the intrinsic viscosity [η] of hyaluronic acid (ξ=0.72) and its benzyl derivatives
with decreasing linear charge density, ξ, on the inverse square root of ionic strength, I, at 25°C.
polyion. At infinite ionic strength, the chain dimensions may eventually correspond to the
completely uncharged macromolecule. This is a sort of “ideal state” of the polyelectrolyte;
“ideal” with respect to the long-range electrostatic repulsive interactions only, without relation
to the Θ-conditions.
In the absence of a cooperative conformational transition, for many polysaccharide
polyelectrolytes a linear dependence of [η] upon I 1/2 is observed, with the slope diminishing
with the charge density associated to the polysaccharide chain (Figure 12.2.13). A theory
has been presented for an estimation of the relative stiffness of the molecular chains by
Smidsrød and Haug, 74 which is based on the Fixman’s theory and Mark-Houwink equation.
The chain stiffness parameter is estimated from the normalized slope B of [η] vs. the inverse
square root of the ionic strength:
[]
∂η
−
∂I
= slope = B
( [] η )
12 / 01 .
γ
[12.2.7]
where:
γ has a value between 1.2 and 1.4
The dependence of viscosity on the ionic strength, as given in equation above, has
been increasingly popular in the field of polysaccharides with the purpose of comparing the
chain stiffness of different macromolecules. The derivation is based on the Fixman theory,
which defines the dependence of [η] on the molecular weight through an expansion coefficient
which effectively takes into account the electrostatic interactions in the Debye-Hückel
approximation. The semi-empirical treatment of the hydrodynamic properties of statistical
polyelectrolytes (at sufficiently high values of the ionic strength) is built upon a straightforward
extension of the theory of intermolecular interactions for uncharged polymers, for
3
which a linear relation can be written between the expansion coefficient, α η,
and the square
root of the molecular weight, M. It should also be mentioned 78 that the various theoretical
treatments of the salt dependence of the excluded volume and of the expansion coefficients