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OH
O
O
HO
+ (C 2 H 5 O) 4 Si
4 HO
OH
Si
+ 4 C 2 H 5 OH
HO
O
O
OH
Fi g u re 7. 5:
End linking by a condensation reaction between hydroxyl groups at the ends of a polymer
chain and the alkoxy groups on a tetrafunctional end-linking agent. The number-average
molecular weight M n of the precursor chains becomes the critically important molecular
weight M c between cross links. The distribution of M n also characterizes the distribution
of M c (i.e., network chain lengths).
Because of their known structures, such model elastomers are now the
preferred materials for the quantitative characterization of rubberlike
elasticity. The properties of PDMS networks have been of interest to a va-
riety of groups. 144 -147 Such specific cross-linking reactions are also useful
in the preparation of some of the liquid-crystalline elastomers, 148, 149 dis-
cussed in chapter 3.
7.2.2 Effects of Junction Functionality
Trifunctional and tetrafunctional PDMS networks can be prepared using the
end-linking approach. Such networks have been used to test the molecular
theories of rubber elasticity with regard to the increase in nonaffineness of
the network deformation with increasing elongation. Figure 7.6 shows typical
results. 150 The ratio 2 C 2 /2 C 1 decreases with increased cross-link functionality
because cross links connecting four chains are more constrained than those
connecting three. 151 Junction fluctuations, which lead to nonaffine behavior
at large strain, are reduced for four-functional networks. The decrease in
2 C 2 /2 C 1 with decreasing network chain molecular weight is due to the fact
that there is less configurational interpenetration for short network chains,
which means that cross links are more easily displaced under deformation. As
a result the deformation is nonaffine even at relatively small deformations.
A more thorough investigation of the effects of cross-link functionality
requires more versatile chemical reactions, as illustrated in figure 7.7. Spe-
cifically, vinyl-terminated PDMS chains are end linked using a multifunc-
tional silane. In the study summarized in figure 7.8, 152 this reaction was
used to prepare PDMS model networks having functionalities ranging from
three to eleven, with an unsuccessful attempt to achieve a functionality of
thirty-seven. As shown in the figure, values of 2 C 2 relative to 2 C 1 both de-
crease, for the reasons described in the discussion of figure 7.6.
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