Techniques for the characterization of physical gels - Physical Gels from Biological and Synthetic Polymers - page 26

c
c

3
4

c > c : ξ ¼ R g when ð 2 : 11 Þ

In this equation, c * is the so-called overlap concentration, at which the radii of gyration
of the individual polymers start to overlap; in semi-dilute solutions they begin to inter-
penetrate. Equation ( 2.11 ) is valid above c * and the correlation length in semi-dilute
solutions is smaller than the radius of gyration for the isolated macromolecule, because of
the chains interpenetration.)

The intensity scattered by semi-dilute solutions was calculated by de Gennes ( 1979 )
for polymers in good solvents, and has a Lorentzian form:

'

I ð 0 Þ

I ð q Þ¼

2 :

ð 2 : 12 Þ

1 þ q 2 ξ

In principle, the scattering from polymer gels should be similar to that for an entangled
solution, with an additional input from the detailed local structure of junctions. In particular,
at high q vectors (local distances) this would include contributions from the cross-section of
junctions or

fibres. Besides, in many cases gelation is associated with some local hetero-
geneity, which does not seem to be associated with any particular superstructure but with
defects in the colloidal size range (10 20 nm or even larger). In this case an additional

contribution to the scattering intensity is observed at small scattering angles:

-

Ba 0

I ð 0 Þ

I ð q Þ¼

2 þ

q 2 a 0 :

ð 2 : 13 Þ

1 þ

1 þ q 2 ξ

The second term of this equation is an excess scattering contribution, the Debye Bueche

term, in which B is a constant and a 0 is the typical heterogeneity size. Similar excess
scattering was also observed for semi-dilute solutions in both good and

-

Θ -solvents.

2.3 Calorimetric studies

Both chemical and physical gelation routes are usually accompanied by important
enthalpy changes. Calorimetry measures the heat absorbed or generated in a material
when it changes from an initial state to a final state and therefore is a useful method to

follow structural changes during gelation. DSC and micro DSC (μDSC) can be used to
follow a large number of gelation processes such as the conformational changes of
biopolymers, micelle formation in solution, partial crystallization and chemical cross-
linking of macromolecules the latter both in solution and in melts. The enthalpy

changes could occur under isothermal conditions or, for instance, for thermoversible
gels through temperature differences during either heating or cooling stages.
Isothermal Titration Calorimetry (ITC) is another technique, albeit one less known in
gel studies: it allows an independent investigation of the interactions responsible for the
self-association of macromolecules or in complex formation between macromolecules
and other small molecules or ionic species which underlie some gelation mechanisms.

-