adjacent sub-chains are the same whether the two belong to the same
molecule or not. For distances>x, i.e., at longer time scales, behavior is
different; the diffusivity of a whole polymer molecule is greatly reduced.
Generally, macroscopic properties of the solution do not depend on the
radius of gyration of the polymer, but on the correlation length. The
osmotic pressure, for instance, is now approximately given bykT=x^3. This
means that every ‘‘blob’’ in the system behaves as if it were one molecule,
insofar as the colligative properties are considered. Notice that Eq. (6.11) is
not valid outside the dilute regime.
In theconcentrated regime, the concentration of the polymer is fairly
even. Nevertheless, a correlation length can be defined, and it is
proportional to 1=j. For most food polymers, this regime will be reached
at fairly high polymer concentrations, say above 3%, unlessbis very small.
Forpolyelectrolytes, the stiffnessðb/LÞis mostly larger than for the
same polymer uncharged. This would mean that the correlation length is
larger under most conditions. However, the relations determining the
boundaries in the state diagram and the correlation length in the various
regimes have not been well established. For charged food polysaccharides in
the nondilute regimes, the correlation length will probably increase with
increasing charge and decreasing ionic strength.
FIGURE6.14 Explanation of the concept of correlation lengthxin a semidilute or
concentrated polymer solution. (From P. G. de Gennes. Scaling Concepts in Polymer
Physics. Cornell Univ. Press, 1979.)