General properties of polymer networks - Physical Gels from Biological and Synthetic Polymers - page 111

Network made of polymer chains with sticky end groups. Figure 4.6

A schematic view of the network structure is shown in Figure 4.6 . A small number of
end-chains associate in micelles with an aggregation number of the order of 10 or less.
This association mechanism is reversible, but the chains form viscoelastic solutions
because the binding energy of a hydrophobe in a micelle is small enough that it can
disentangle itself randomly, and at a finite rate. This is a reversible, non-permanent or

transient network.
The

first systematic study on reversible networks was carried out in 1946 by Green and
Tobolsky ( 1946 ), in which the stress relaxation in rubber-like polymer networks was
treated by the kinetic theory of rubber elasticity, extended to allow for the creation and
annihilation of junctions during network deformation. The theory predicts a high-
frequency storage modulus given by

G ∞ ¼ ν e k B T ; ð 4 : 9 Þ

where ν e is again a number density of elastically active chains. The resultant Newtonian

(shear-rate

- independent) shear viscosity is

ðγÞ¼ð 0 Þ¼τ 0 G ∞ ; ð 4 : 10 Þ

where, in the present context, the relaxation time τ 0 is the reciprocal of the chain-end

disentanglement rate. This model does not predict the shear thinning or shear thickening
effects observed with HEUR solutions; to include such effects, an additional assumption
is introduced to relate the disentanglement rate to the shear rate.