Polymer Nucleation Energetics

Polymer Nucleation Energetics

• Polymer crystals are typically thin and lamellar when formed from dilute solutions or melts.
• Lamellar thickness is inversely proportional to the crystallization temperature change (∆T).
• Chain folding occurs during crystallization from dilute solutions and to some extent during melt crystallization.
• Crystal growth rates strongly depend on crystallization temperature and polymer molar mass.

Primary Nucleation

• Primary nucleation involves a few molecules packing together to form a small cylindrical crystalline embryo.
• This process involves a change in free energy.
• Formation of a crystal surface increases free energy (G), while incorporation of molecules into the crystal decreases free energy, depending on crystal volume.
• The interplay of these two factors is illustrated schematically as a function of crystal size.

Secondary Nucleation

• Polymer crystal growth occurs via secondary nucleation on existing crystal surfaces.
• This process is similar to primary nucleation, but less new surface area is created per unit crystal volume.
• This results in a lower activation energy barrier compared to primary nucleation.

Crystallization Energetics

• Polymer lamellae have fold surface energy (ye) and lateral surface energy (ys).
• Free energy change on crystallization (AGv) is dependent on these surface energies and the volume of the crystal.
• A reduction in free energy within a crystal is given by ∆Gn(crystal) = -nabl AGv.
• The overall free energy change (AG) is the sum of surface energy components and the volume-dependent free energy change.

Equilibrium Melting Temperature

• Polymer crystals have an equilibrium melting temperature (Tm°).
• This is the temperature at which a crystal without surface effects would melt.
• At Tm°, there is no change in free energy (∆Gy=0) between melting and crystallization.

Temperature Dependence of Crystallization

• Below the equilibrium melting temperature (T < Tm°), crystal growth will have a finite free energy change.
• The free energy change is approximately proportional to the latent heat of fusion (∆H) and the temperature difference from the equilibrium melting point (∆T).