Handbook of Solvents - George Wypych - ChemTech - Ventech!

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Figure 12.2.11. Characteristic ratio, correlation function
and persistent length as a function of the degree of polymerization,
n, for [α-D-(1-3)-glc] n (pseudonigeran) and
(b) the [β-D-(1-3)-glc] n (curdlan) calculated on the in
vacuo energy maps.
C
∞
2
r 6 R
= lim =
n→∞
2
nL nL
where R g is the average square radius of gyration
experimentally accessible. This relation
is considered extremely important in
the sense that any conformational perturbation
is amplified by a factor n in the final
value of C ∞ (or of ), and therefore represents
a highly demanding test for the appropriateness
of the conformational
calculations and at the same time a discriminating
factor for conformation-dependent
solution properties (e.g., viscosity).
An alternative measure of chain extension
is the persistent length, P n, which
behaves in a similar asymptotic dependence
on n as observed for C n, in Figure
12.2.11. It is meant as the capacity of the
chain to preserve the direction of the first
residue (vector) of the chain. Therefore, as
the directional persistence dissipates with
increasing chain length and the direction of
the terminal residue vector L n loses correlation
with that of the initial vector L 1,P napproaches
an asymptotic limit for
sufficiently long chains. Both the C n and P n
functions in Figure 12.2.11 reveal the
[α-D-(1-3)-glc] n chain to be much more extended than that of [β-D-(1-3)-glc] n.
The directional correlations are also well characterized by the correlation function F n
of equations [12.2.6], which measures the average projection of a unit vector aligned with
each virtual bond of the chain onto the unit vector relative to the first residue. The strongly
oscillating character of F n for [β-D-(1-3)-glc] n, which is also observed at low n in both the C n
and P n functions, reflects the pseudo-helical persistence of the backbone trajectory which
becomes uncorrelated (i.e., F n declines to zero) as the molecular weight increases. It is noteworthy
that the oscillations in F n retain approximately the pseudo-helical periodicity present
in the crystalline forms of that polysaccharide (Figure 12.2.2). The monotonic decline of F n
(a) for [α-D-(1-3)-glc] n, on the other hand, shows that this polymer possess a stronger directional
correlation due to the different glycosidic linkage which has a dramatic effect on the
character of the chain trajectory.
The chain properties illustrated above are often described with terms such as “stiffness”
and “flexibility”. It is important to clarify that stiffness and structural rigidity may not
necessarily be alternative to flexibility and structural disorder, since two different concepts
enter into the above definitions: one is concerned with the number of different accessible
conformations, the other with the (average) direction of the sequential bonds, i.e., with the
chain topology.
2
g
2