Handbook of Solvents - George Wypych - ChemTech - Ventech!

12.2 Chain conformations of polysaccharides 731
tween states i and f of a polyelectrolyte, characterized by a set of ξ i and ξ f(i.e., b i and b f) values,
polyelectrolyte theory predicts a simple relationship 82 between the values of the
melting temperatures (T M, the temperature of transition midpoint) and the logarithm of the
ionic strength, I:
−1
( M )
dT
d I
( log )
()
9. 575F
ξ
=−
Δ H
M
where ΔMH is the value of the enthalpy of transition (in J per mole of charged groups) determined
calorimetrically. This linearity implies, indeed, that the enthalpy change is essentially
due to non-ionic contributions and largely independent of I. The function F(ξ) depends
on the charge density of both the final state (subscript f) and the initial state (subscript i),
within the common condition that ξf < ξi, that is the final state is characterized by a smaller
value of the charge density. The value of F(ξ) is given in the literature.
This relation has been successfully applied first to the transition processes of DNA, 83
polynucleotides, 84 but also to many ionic polysaccharides (carrageenans, 85 xanthan, 86
succinoglycan, 87 ) of great industrial interest. Accurate determination of the TM values of the
polysaccharide as a function of the ionic strength is necessary.
12.2.6.4 Conformational calculations of charged polysaccharides
The major problem for conformational calculations of ionic polysaccharides arises from the
correct evaluation of the electrostatic potential energy due to the charged groups along the
chain and to the all other ions in solutions. The interaction between the polyion charges and
the counterions is formally non-conformational but it largely affects the distribution of the
conformational states. Ionic polymers are often simplistically treated either in the approximation
of full screening of the charged groups or in the approximation of rigid
conformational states (regular rod-like polyelectrolyte models).
A combination of the molecular polyelectrolyte theory 82,83 with the methods of statistical
mechanics can be used at least for the description of the chain expansion due to charges
along the polysaccharide chain. The physical process of the proton dissociation of a (weak)
polyacid is a good way to assess the conformational role of the polyelectrolytic interactions,
since it is possible of tuning polyelectrolyte charge density on an otherwise constant chemical
structure. An amylose chain, selectively oxidized on carbon 6 to produce a carboxylic
(uronic) group, has proved to be a good example to test theoretical results. 81
If the real semi-flexible chain of infinite length is replaced by a sequence of segments,
the average end-to-end distance of each segment defines the average distance between
charges:
b
r
= [12.2.8]
N
where N is the number of charges in the segment. The distance between charges fluctuates
within the limits of the conformational flexibility of the chain, as calculated by the proper
non-bonding inter-residue interactions.
The probability function W�(r) of the end-to-end displacement r of a charged segment
can be obtained by multiplying its a priori (non-ionic) probability W(r) with the Boltzmann