Polymer Nucleation Energetics PDF

18. Polymer nucleation energetics Overview: Polymer crystals usually are thin and lamellar when crystallized from both dilute solution and the melt. A unique dependence is found between the lamellar thickness and crystallization temperature and, in particular, the lamellar thickness...

18. Polymer nucleation energetics Overview: Polymer crystals usually are thin and lamellar when crystallized from both dilute solution and the melt. A unique dependence is found between the lamellar thickness and crystallization temperature and, in particular, the lamellar thickness is found to be proportional to 1/ΔT. Chain folding is known to occur during crystallization from dilute solution and occurs to a certain extent during melt crystallization. The growth rates of polymer crystals are found to be highly dependent upon the crystallization temperature and molar mass of the polymer. It is envisaged that in the primary nucleation step, a few molecules pack side by side to form a small cylindrical crystalline embryo. This process involves a change in free energy since the creation of a crystal surface, that has a surface energy, will tend to cause G to increase whereas incorporation of molecules in a crystal causes a reduction in G that will depend upon the crystal volume. The result of these two competing effects upon ΔG is illustrated schematically as a function of crystal size. The theories of crystallization envisage the growth of the polymer crystals as taking place by a process of secondary nucleation on a pre-existing crystal surface. This process is similar to primary nucleation but differs somewhat because less new surface per unit volume of crystal is created than in primary nucleation and so the activation energy barrier is lower. 1 The basic energetics of the crystallization process can be developed if it is assumed that the polymer lamellae have a fold surface energy of γe, a lateral surface energy of γs and that the free- energy change on crystallization is ΔGV per unit volume. ΔGn(surface) = 2blγs + 2nabγe A reduction in free energy in a crystal that will be given by ΔGn(crystal) = -nabl ΔGV Overall, ΔGn= 2blγs + 2nabγe -nablΔGV It is assumed that polymer crystals have an equilibrium melting temperature Tmo, which is the temperature at which a crystal without any surface would melt. where ΔHV and ΔSV are the enthalpies and entropies of fusion per unit volume, respectively. However, at Tom, there is no change in free energy for the idealized boundaryless crystal since melting and crystallization are equally probable and so ΔGV=0 at this temperature, which means that For crystallization below this temperature, ΔGV will be finite and it is envisaged that ΔSV and ΔHV will not be very temperature dependent and so at a temperature T (