One may imagine that, when the concentration of the polymers is extremely low,
polymer coils disperse in an ocean of solvent molecules, and form individually
isolated single-chain systems like jellyfishes. A further dilution of the polymer
solutions only increases the average distance between the isolated coils, without
changing the internal structures of coils. Accordingly, we call such polymer
solutions asdilute solutions.
The territory of an expanded single coil is much larger than the volume the
monomers actually occupy. Therefore, in comparison to the collisions of small
molecules, the probability of mutual collisions between two coils is significantly
enhanced. When such fluffy coils diffuse, the mutual friction yields a solution with
a high viscosity. In the early history of polymer science, the high viscous polymer
solution was misunderstood as a colloidal gel. However, polymer solutions are
actually the molecular dispersions of long chains in the solvent molecules. With the
increase of the polymer concentration, the coils start to interpenetrate into each
other. We can define an illusivecritical overlap concentrationC, as illustrated in
Fig.4.2. Then, polymer solutions with the concentrations beyond C are called
concentrated solutions.
From the dynamic point of view, as illustrated in Fig.4.3, polymer coils are
rather ellipsoids with their anisotropy depending upon chain semi-flexibility, and
their hydrodynamic radii are usually larger than their radii of gyration. Thus, a
dynamic overlap concentrationC’<C*exists, which is of practical importance for
characterizing the hydrodynamic property of the polymers in solutions.
The dissolution process of a solid linear polymer dissolves into a solvent is often
slow. With the continuous permeation of the solvent, the polymer first swells, and
then completely dissolves in the solution. Commonly, a semi-crystalline polymer
requires an extra heating up to its melting point, to accelerate the dissolution. This
process is generally an analogous to the cooking of rice. The rice grains first swell in
hot water. The addition of more water leads to a complete disappearance of the rice
grains, forming a transparent porridge consisted of amyloid solutions. Similarly,
heating of the polymer drives the swelling of chains towards a homogeneous solution.
A thin film of rice gel could be dried at the top surface of the hot porridge. The
formation of such a gel state, also known asthermoreversible gel,is crucial in some
polymer materials. For instance, PVC gel containing 30 % volume of plasticizers can
Fig. 4.2 Illustration of different concentrations of polymer solutions with respect to the critical
overlap concentration C: the dilute solutions (C<C,left) and the concentrated solutions
(C>C*,right)
4.2 Single-Chain Conformation in Polymer Solutions 45