Thermodynamic Stability of Polymer Crystals. II. Torsional Vibrations of Chain Molecules

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Abstract
By taking into account the decrease of interchain potential barrier for longitudinal displacement as a consequence of incoherent longitudinal vibration of adjacent chains, the free-energy density exhibits a minimum at a finite number N* of monomer units in the straight section of the macromolecule between the (001) surfaces. Crystals with N* are thermodynamically stabler than those with N≠N*. The agreement with experimental data can be very much improved by considering torsional vibrations. Starting with the known interaction energy between two CH2 groups and considering the influence of the six adjacent polyethylene chains only the lattice force field was derived and the torsional fluctuation amplitude calculated. The resulting N* fits very well with measurements of Fischer and Schmidt on crystals grown at different temperature from dilute xylene and butyl acetate solution when the surface energy is assumed close to 40 erg/cm2. With this value the theory does not predict stable crystals with finite N* above 110°C; thus the growth tendency of polyethylene crystals during annealing has no limits at least until the macromolecules are completely stretched.

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