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868 Macromolecules, Structure

FIGURE 8 Several experiments illustrating the differences between a Newtonian fluid and a polymer fluid. (a) The
surface of a Newtonian fluid is depressed near a rotating rod, whereas a polymeric fluid tries to climb the rod. (b)
When two spheres are dropped one after the other into a Newtonian liquid, the second sphere always catches up and
collides with the first one. In the polymeric liquid, if we wait a critical length of time between dropping the spheres, the
spheres tend to move apart. (c) The two fluids are being pumped into circular tubes. The figure shows successive
snapshots. The pump is turned off after the fourth frame. The Newtonian fluid comes to rest, whereas the polymeric
liquid recoils, illustrating a “memory effect.” (d) When flowing in a trough, the surface of the Newtonian fluid is flat,
except for a meniscus effect, whereas the polymeric liquid has a slightly convex surface. [From Bird, R. D., and
Curtiss, C. F. (1984). Phys. Today 37, 36–43.]

2
2
¯ r = 6¯ s . (14) solvent and solute. In this approach, the solution of sol-
vent and macromolecule is treated as a lattice (Fig. 9).
The radius of gyration is particularly important since it
The number of distinguishable ways of arranging the N 1
can be measured experimentally by light scattering and
solvent molecules of volume fraction v 1 and N 2 poly-
other techniques.
mer molecules of volume fraction v 2 are then counted.
2. Polymer Solution Thermodynamics
As a consequence of their macromolecular size, polymers
in solution exhibit large deviations from ideal behavior.
(Ideal behavior is described by Raoult’s law, which states
that the partial vapor pressure of a component in solution
is proportional to the concentration of that species.) Poly-
mers have very small entropies of mixing, which accounts
for their large deviations from ideal behavior. The small
entropy of mixing arises because of the size and intercon-
nected nature of macromolecular chains. Whereas a small
molecule can be distributed among solvent molecules in
a great number of ways, there are fewer ways in which a
polymer can be arranged.
The Flory–Huggins theory, developed in 1942 by P. J.
Flory and M. L. Huggins, accounts for the restrictions FIGURE 9 Lattice representation of a macromolecule (intercon-
that chain connectivity imposes on the arrangement of nected dots) in a solvent matrix. The x’s represent the solvent.