Chain direction elastic modulus of PE crystal and interlamellar force constant of n-alkane crystals from RAMAN measurements
✍ Scribed by M. Pietralla; R. Hotz; T. Engst; R. Siems
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 205 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0887-6266
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✦ Synopsis
Spectroscopic data can deliver force constants only if the exact chain conformation is known. For the longitudinal acoustic modes (LAM), however, simple linear chain models can be used to yield the effective longitudinal chain modulus from spectroscopic data of oligomer crystals. The model of p-coupled linear chain molecules with N masses and only nearest neighbor interactions was used to investigate the longitudinal acoustic modes with s nodes. The frequencies plotted versus s/N fall onto different branches for different s. The intermolecular coupling and the heavier endmasses shift the LAM branches to higher and lower frequencies, respectively. There exists a value x 0 depending on the masses and force constants, where the branches cut the dispersion curve of the infinite molecule. For s/N ¢ x 0 the effect of endmasses dominates. Lowfrequency RAMAN spectra of n-alkanes (N Å 20, . . . , 40 C atoms) were recorded and analyzed. The LAM1 branch runs clearly above a smooth fit through all other LAM data and the origin. This fit approximates to first order the dispersion curve of the infinite PE molecule in an ideal crystal. Its curvature exceeds that of the dispersion curve of the simple linear chain, but is somewhat smaller than that of the dispersion curve of the planar zig-zag chain with rigid bonds. The slope at the origin yields the limiting elastic modulus E c Å 315 GPa in chain direction of crystalline polyethylene. From our measurements on n-alkanes we obtained the frequency shift of LAM1 due to the interlayer coupling and the heavier endmasses. Calculation of the intermolecular coupling constant of the model of a long row of linear chain molecules with the same frequency shift yield the mean value f l Å 2.5 N/m. This value decreases with increasing chain length. The relevance and applicability of the model is discussed.