phase separation behaviors of polymer solutions, releasing the first stage of cohesive
energy of crystalline molecules by puttingwell-separated molecules into neighbors.
In parallel, the crystallization process of the single component from liquid to
solid resembles to polymer crystallization, releasing the second stage of cohesive
energy of crystalline molecules by assembling nearby molecules into crystalline
order. Such an analogue implies that, we need two energy parameters to describe the
molecular driving forces for phase separation and crystallization, respectively.
Free energy change is the deterministic factor to the behavior of phase transitions.
In this chapter, we first introduce the classic Flory-Huggins lattice statistical thermo-
dynamic theory of polymer solutions, mainly focusing on the calculation of free
energy change upon the mixing process. In the next chapter, i.e. Chap. 9 ,wewill
introduce phase separation. The corresponding molecular driving force for phase
separation is the mixing interactionBbetween two species. After that, in Chap. 10 ,
we will introduce polymer crystallization. The corresponding molecular driving force
for crystallization is the parallel packing interactionEp. Adjusting the contributions of
these two kinds of molecular interactions to the total free energy, we can control
the thermodynamic conditions for both phase separation and crystallization, and
furthermore control the kinetics of phase transitions, for the designed morphology
and assembly structures of polymers. In the last chapter of this book, we will introduce
the interplay of phase transitions in the polymer-based miscible systems.
8.2 Flory-Huggins Lattice Theory of Polymer Solutions
8.2.1 Advantages of the Lattice Model
From the condensed matter physics of liquid states, the volume repulsive
interactions of molecules dominate the microscopic structure of the liquid, and
the attractive interactions just play a role of local perturbation (Rowlinson 1970 ).
The lattice model treats the distribution of molecules as “one hole for one radish”
Fig. 8.2 Illustration of basic
phase diagrams of gas, liquid
and solid of the single
component system separately
according to temperature
versus pressure (left) and
temperature versus density
(right)
8.2 Flory-Huggins Lattice Theory of Polymer Solutions 149