still maintain reasonable mechanical properties. If the polymer chains are slightly
cross-linked, they will only swell without dissolution. Such a state is normally
referred asgel. Proteins are viable to form hydro-gels in water, and one simple
example is human skin. The gel cannot swell unlimitedly, because the polymer
chains between the cross-linking points could not be stretched in too much extent.
The thermodynamic driving force of dissolution is actually balanced by the entropy
penalty of chain conformations, reaching a so-calledequilibrium swelling state.
Section8.3.1will introduce the detailed theoretical treatment of equilibrium swelling.
In a solid of high cross-link density, polymer chains are rather short to release little
conformational entropy. Therefore, solvents cannot permeate such a solid, and no
swelling occurs.
Polymers are potentially mixed with solvents once the mixing free energy
DFmix¼DHmixTDSmix< 0 (4.3)Conventionally,DSmix<0. According to (4.3), the dissolution of polymers is
mainly determined by the temperature and the mixing enthalpy. In the microscopic
level, the latter mainly originates from the change of inter-molecular interactions.
Of course, the practical dissolution is determined by the critical condition of
thermodynamic equilibrium between two solution phases, as introduced in Sect.9.1.
The inter-molecular interactions in the polymers include the overlapping repulsion
between atoms, the ion-ion interactions, ion-induced-dipole interactions, dipole-
dipole interactions, polar-nonpolar interactions, and nonpolar-nonpolar interactions,
etc. For the van der Waals interactions between the nonpolar polymers, about 70 % of
the attractive interactions are sourced from the dispersion forces, which are instant
dipole-dipole interactions induced by the vibration of the substituted groups in the
chains. The frequency of vibration influences the refractivity, so the forces are named
with dispersion forces. The dispersion forces within a pair of neighboring groups can
be expressed as
B 12 ¼
3
2
I 1 I 2
I 1 þI 2a 1 a 2
R^6(4.4)
Fig. 4.3 Illustration of the
anisotropic polymer coils,
whose dynamic size is much
larger than the size of the
statically occupied coil
46 4 Scaling Analysis of Real-Chain Conformations