chain overlap, but the relations between properties of the solution and
polymer characteristics are different. In the domain labeled phase
separation, the polymer is not fully soluble: see Section 6.5.1.
Two of the boundaries between the regimes are roughly given by
b¼+j: see Figure 6.13. The critical point for phase separation is
approximately
jcr¼1
1 þq^0 :^5ð 6 :12aÞbcr¼ 1 ð 1 þq^0 :^5 Þ^2 ð 6 :12bÞwhereq¼the net volume of a polymer molecule divided by the volume of a
solvent molecule. It follows that q is proportional ton, and for most
polysaccharides in waterq& 0 : 04 M, which mostly is 500–10^5. Some results
are given in Table 6.4. Ifnis high,bcris seen to be very close to zero andjcr
is quite small.jcralso marks the boundary between the dilute and the
concentrated regime, but the range inbover which this boundary extends,
i.e., about frombcrtobcr, is very small for largeq: see Table 6.4. Many
food polymers in water haveb-values above 0.01, which means that they
would pass from the dilute to the ‘‘semidilute’’ to the concentrated regime,
when increasing their concentrationðjÞ.
Actually, we have used the term ‘‘semidilute’’ in a loose sense here
(hence the quotation marks); it denotes neither dilute, nor concentrated.
Polymer scientists distinguish a semidilute and a marginal regime. Scaling
FIGURE6.12 Schematic examples of well soluble polymer molecules in solution at
increasing concentrations. (Modified from P. G. de Gennes. Scaling Concepts in
Polymer Physics. Cornell Univ. Press, 1979.)