CHAIN DIRECTION ELASTIC-MODULUS OF PE CRYSTAL AND INTERLAMELLAR FORCE-CONSTANT OF N-ALKANE CRYSTALS FROM RAMAN MEASUREMENTS

Spectroscopic data can deliver force constants only if the exact chain conformation is known. For the longitudinal acoustic modes (LAM), how ever, simple linear chain models can be used to yield the effective lo ngitudinal 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 a nd the heavier endmasses shift the LAM branches to higher and lower fr equencies, respectively. There exists a value xo depending on the mass es and force constants, where the branches cut the dispersion curve of the infinite molecule. For s/N greater than or equal to x(0) the effe ct of endmasses dominates. Low-frequency RAMAN spectra of n-alkanes (N = 20,..., 40 C atoms) were recorded and analyzed. The LAM1 branch run s clearly above a smooth fit through all other LAM data and the origin . This fit approximates to first order the dispersion curve of the inf inite PE molecule in an ideal crystal. Its curvature exceeds that of t he dispersion curve of the simple linear chain, but is somewhat smalle r than that of the dispersion curve of the planar zig-zag chain with r igid bonds. The slope at the origin yields the limiting elastic modulu s E(c) = 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 va lue f(l) = 2.5 N/m. This value decreases with increasing chain length. The relevance and applicability of the model is discussed. (C) 1997 J ohn Wiley & Sons, Inc.