The sol–gel transition - Physical Gels from Biological and Synthetic Polymers - page 87

a particular concentration and temperature once helices start to build. These experiments
do not take into account the mechanism of gelation. Gelatin gelation is reported in detail
in Chapter 7 .

3.6 Eldridge-Ferry method

One of the longest-established ways of characterizing the behaviour of thermorever-
sible gels is due to Eldridge and Ferry ( 1954 ), who made a series of careful measure-
ments of the melting temperature of gelatin gels as a function of polymer concentration
and molecular mass. It should be made clear at the outset that the approach has been
criticized by some theorists, but it is nevertheless still widely used, as are a number
of variations and improvements. These are discussed in detail in the review by te
Nijenhuis ( 1997 ).
Eldridge and Ferry (EF) decided to treat gel ' melting ' as a first-order phase transition,

in a manner similar to Flory s original treatment for crystalline melting of polymers. They

had observed that a plot of ln c versus 1/T m , where T m is the gel melting temperature (K),
was linear, as was a corresponding plot of ln (gelatin primary chain molecular mass)
versus 1/T m . This suggests that a van

'

'

t Hoff law of the form

M w ¼ D

H m 0
RT m 2 ;

d ln c
dT m

ð 3 : 29 Þ

where H m is the melting enthalpy, could be applied. The method assumes an equili-

brium between

Δ

2 cross-linking sites , 1 cross-link ;

although the nature of the equilibrium (in particular the relative rate of the back reaction)
does not actually alter the tenets of the model. Here the sites are assumed to be tetrafunc-
tional, but te Nijenhuis ( 1997 ) has generalized the model to the case of cross-link
functionality f to give

M w ¼

H m 0

d ln c
dT m

D

RT m 2 :

ð 3 : 30 Þ

ð 1 f = 2 Þ

The limitations of this method are several. First, it assumes that the number of elastically
active cross-links is a function of concentration but not of temperature, so it neglects
wastage (which will increase at lower concentrations). Second, it requires that the
number of unused junctions is also proportional to concentration, which only applies,
for example for gelatin, if the ageing process has not proceeded very far. It also neglects
the possibility of a critical gel concentration, which suggests that the plot cannot always
be linear at lower concentrations. Despite all of these points, the method has great
practical use, and is still widely applied in studies of thermoreversible gels, especially
including work on PVA and gelatin. Much of this work has concentrated on evaluating