Biomedical Engineering Reference
In-Depth Information
3
The sol
-
gel transition
Physical gels exhibit a wide range of properties which determine their use in many
applications. New materials are synthesized for particular industrial requirements and/or
for biomedical applications. Gel characterization requires a large palette of instruments,
techniques and methods, as presented in Chapter 2 . Because of the large number of
systems already known and because new ones are invented every day, there is a need to
understand and predict the behaviour of these systems. It would be ideal if we were able
to understand and map the relations between the (macro)molecular composition of the
initial system and the functional properties (mechanical, swelling, drug delivery and so
on) in the
final gelled state.
However, such an objective is very ambitious and, for the moment, not realizable.
Consequently, we shall concentrate on a particular aspect that still occupies many
chemists and physicists. This is the very special limit when the solution switches from
a liquid state, where polymers are free to diffuse, to a solid-like medium, where the
polymers entrap the solvent. The transition from one state to the other may happen quite
suddenly. Furthermore, despite the large number of theoretical and experimental pub-
lications dealing with the sol
-
gel transition, there is still a debate even on the best way to
determine the
.
In other words, can there really be a unique de
'
gel-point
'
nition of the transition from sol to gel?
Do we have a single method for all systems or could everyone choose the most
convenient way to describe their own particular system (Li and Aoki, 1997 )? In this
chapter we shall try to present the various ways of de
ning the gel point from theoretical
and experimental viewpoints, and put particular stress on both the problems and the
potential resolutions.
3.1
Flory
-
Stockmayer (
'
classical
'
) theory
It was Paul Flory, in work begun in the Carothers group at DuPont in the late 1930s, who
first tried to develop a quantitative theory for the linear end-linking reaction of small
molecular mass species, a typical exemplar being the reaction of adipic acid and
hexamethylenediamine to produce Nylon 66. From this he was able to derive equations
relating number and weight average molecular mass to the
.
For the linear reaction of a single species, for example the self-condensation of a diol,
the weight average degree of polymerization DP w is given by
'
degree of conversion
'
 
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