A raman spectroscopic determination of the interlamellar forces in crystalline <i>n</i>‐alkanes and of the limiting elastic modulus <i>E</i>_c of polyethylene

Abstract

Abstract A simple treatment based on continuum mechanics shows that weak interlamellar forces in crystalline n ‐alkanes should result in a characteristic upward shift of the frequencies of the longitudinal acoustical (LA) modes, which is independent of the chain length and decreases inversely with the mode order. A raman spectroscopic determination of the LA mode frequencies of a series of different n ‐alkanes confirms the theoretical conclusion and permits a derivation of a force constant characteristic of the interlamellar forces. The discussion results in a new formula valid for the LA mode frequencies of the orthorhombic n ‐alkanes in the acoustical limit and yields a new determination of the limiting elastic modulus E c of crystalline polyethylene. The value obtained, E c = 2.9 × 10 12 dyne/cm 2 , is markedly smaller than the value derived by Schaufele and Shimanouchi neglecting the influence of the interlamellar forces on the LA mode frequencies.