General properties of polymer networks - Physical Gels from Biological and Synthetic Polymers - page 115

0.8

M = 35000 g mol − 1

0.6

0.4

0.2

0

0 2 4 6

c (wt %)

8 10 12

Comparison between theory and experiment for the fraction of elastically active chains, assuming
an end-capping efficiency of 70% (dashed line) or 100% (continuous line) for C 16 end-cap chains
and a molecular mass of 35 000 g mol − 1 . Adapted fromAnnable et al. (1993) with permission of the
American Institute of Physics for The Society of Rheology.

Figure 4.9

statistical mechanical model. It is seen that G ∞ /(nk B T) does not reach the limit 1 even at
high concentration, but is close to that found in experiments.

4.4.2 Flowers connected by bridges (SJK model)

The topology of associating polymer solutions with end-capped associative groups was
further analysed theoretically by Semenov et al.( 1995 ; SJK model), who explored various
regimes. They pointed out other important features related to micelle formation in the
associative polymers. Telechelic polymers form micelles which consist of a compact
hydrophobic core, surrounded by a corona of the long, soluble parts of the chains that
form loops. This structure is similar to block copolymer micelles. The aggregation number
(or number of chains per micelle) N agg , determined experimentally, is in general between
5 and 50. This number is rather insensitive to concentration, the molecular mass of the
soluble parts and other parameters. The inner structure of a micelle is similar to that of a star
polymer, and the authors consider that the properties of star polymers in solution in good
solvents also apply to the micelles. While star polymers in good solvents always repel each
other, the important difference with telechelic polymers is the possibility of bridging that
gives rise to attraction between micelles. The attraction between micelles can be large
enough that the micelles phase separate and form a macro-phase of densely packed
' '

, where neighbouring micelles are connected by bridges. A temporary, reversible
network is formed by the connected

owers

flowers, as shown in Figure 4.10 .

4.4.2.1 Elastic properties of the network of flowers (SJK model)

The elastic properties of the network of

flowers are interpreted in the SJK model by

analogy with grafted polymer layers on flat surfaces, in good solvents - the so-called

' brushes ' . When two brushes come into contact the chains are less and less stretched