The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 93

consequence of spinodal decomposition ( Chapter 10 ). Moreover, the whole system is
known to be under kinetic control. One aspect of interest here is that there is very little
concentration dependence of the modulus, even close to the phase transition; some of the
Miller data, for example, suggests that G ~ c 0.2 . On this evidence alone it is reasonable to
af gel percolation process.

Later work included that by Cohen and co-workers (Cohen and Talmon, 1987 ), who
suggested that micro

rm that these ' gels ' are not the result of a sol -

c cluster aggregation
process, and by Donald and co-workers (Hill and Donald, 1989 ; Horton and Donald,
1991 ), who examined the systems by hot stage microscopy and concluded that the gel
consisted of a weak network of solid PBLG crystals dispersed among the original chains.
Shukla and co-workers (Shukla and Muthukumar, 1988 ) examined a range of concen-
trations and also established part of the phase diagram. Although the synthesis of PBLG-
like derivatives and their exploitation in complex

brillar structures are formed by a non-speci

such as the formation of
nanotubes and channel cavities is still an active area of research, more fundamental work
is somewhat scarce. Indeed, the most complete recent study appears to be that by Tadmor
and co-workers (Tadmor et al., 2002 ), who used SAXS and SANS. Their time-resolved
measurements showed characteristics of a nucleation and growth process with an
incubation period which was extremely dependent on the gelation temperature. They
suggest that the structure is formed by homogeneous nucleation and one-dimensional
growth of

' applications '

fibrils that then merge or branch to form the network structure.
To conclude, helical PBLG is an interesting physicochemical system, but of more
general interest and applicability is the Flory type phase behaviour, and it is this that has
been examined for other systems, and is discussed in later chapters.

3.10 Conclusions

Theoretical models for determining the gel point are based on the concept of connectivity
between the polymer chains in the sol state or monomers undergoing polymerization. For a
chemical gel it is possible to control the cross-linking reactions and unambiguously identify
the moment when the network becomes insoluble. Provided the samples are handled with
great care to avoid breakage, light scattering, size exclusion chromatography and intrinsic
viscosity measurements can be performed on samples which have been diluted before the
gel point is reached, or where the reaction has been stopped chemically. All types of
rheological experiments can also be performed in situ, ensuring that, as far as can be
determined, measurements remain in the linear regime. The only limitation comes from the
instrumental precision and range of sensitivities.
When dealing with physical gelation, many more dif culties appear. The links are not

point-like junctions, but contain local structures with many different characteristics,
including local crystallization in synthetic polymers, multiple strand structures in bio-
polymers and micelle formation in copolymer solutions. The first question is whether

these cross-links can be assumed equivalent to permanent links, i.e. whether the lifetime
of any junction is long enough that the gel exhibits a permanent modulus, which does not
relax during the time of observation; some physical gels can ful

l this requirement. The