An Introduction of Polymer Solutions

Polymer solutions are normally homogeneous mixtures of polymers and small molecules. Most practically useful polymers are in a certain sort of mixtures, and polymer solutions are the basic prototype to understand the polymer mixture. 

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 coUs. Accordingly, we call such polymer solutions as dilute 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 misimderstood 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 illusive critical overlap concentration C, as illustrated in Fig. 4.2. Then, polymer solutions with the concentrations beyraid C are called concentrated solutions. 

From the dynamic point of view, as illustrated in Fig. 4.3, polymer coUs 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 concentration C C exists, which is of practical importance for characterizing the hydrodynamic property of the polymers in solutimis. 

Polymers are potentially mixed with solvents once the mixing free energy 

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