Interfacial free energy extended chain

Mendelkem [42] noted that there are three different interfacial free energies that are characteristic of crystallites. One, is for the equilibrium extended chain crystallite, a second one a c represents the mature, but nOTi-eqiulibrium crystallite, and the third one is Uen is the interfacial free energy involved in forming a nucleus. These quantities caimot be identified with one another. Because only portions of the polymeric chains participate in the formations of crystallites, the section or sections of the chains of x length that participate in crystallite formation can be designated as (e and the sections of the chains that remain in disorder and amorphous, as x — Ce -... 

Consideration should also be given to the meaning of the extrapolated value, obtained by measuring melting of folded chain crystallites, when the equilibrium state requires an almost completely extended state [7,8]. The interfacial free energies will be different in the two cases. 

The nucleation theory that has been used in this analysis is based on the inherent properties of chain molecules. The nuclei sizes are very sensitive to chain length in this molecular weight region when reasonable values are assumed for the nucleation interfacial free energy. The demarcation between extended and folded... 

The conclusion that the value of (Te is independent of whether or not lamellar crystalUtes are formed is similar to the conclusion reached in analyzing both the growth and overall crystallization rates of high molecular weight n-alkanes (see Sects. 9.14.1 and 9.14.2). In these instances, as well as with low molecular weight fractions of linear polyethylene, the same interfacial free energy for nucleation is involved, irrespective of whether extended or folded chain crystaUites are formed. It becomes clear that it is not necessary to postulate that a nucleus is composed of regular folded chains in order to form lamellar-Uke crystaUites. 

The dominant contribution to the free energy of lengthy (rubbery) polymer chains is entropy. This is known to accoimt for rubber elasticity, which can be satisfactorily modelled by the entropy of the cross-linked pol3rmer chains alone. A simple illustrative model of copolymer self-assembly can be developed by extending rubber elasticity theory to include bending as well as stretching deformations, to calculate chain entropy as a function of interfacial curvatures in diblock aggregates. 

The chemical nature of the chain, as reflected in the crystal stmcture and in the disordered chain conformation, will strongly influence the interfacial stmcture. At one extreme, we can conceive of a chain for which there is a minimal expenditure of free energy on making a bend. In this case, adjacent re-entry will predominate. For chains whose axes are positioned far from one another in the unit cell, as in the a-helical polypeptides, or have extended conformations in the disordered liquid state, as in cellulose and its derivatives, folding of any type including adjacent re-entry will be minimal. 

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