THE vibrations of an infinitely long chain of CH2-groups have been calculated using a valence and angle force potential. It is assumed that the carbon atoms form a zigzag line in the x,y-plane, from which the two C—H linkages branch off symmetrically with respect to this plane, with the x-axis as molecular axis. This array can be considered as a crystal lattice the elementary cell of which consists of two CH2-groups (six particles in the cell) resulting in eighteen vibrations of the elementary cell. The potential function V has the form : where li is stretching of Ci–Ci+1 linkages; li and li are stretching of two C—H linkages attached to Ci; Î»i is change of the angle Ci1—Ci—Ci+1; αi is change of the angle Hi—Ci–Hi; Î´i, Î´iâ are changes of the angle Ci1—Ci—Hi; ϵi and ϵi are changes of the angle Hi—Ci—Ci+1; Îi is angle of twist of C—C linkages produced by a rotation of the two CH2-groups at the ends of the bond around it; a is the equilibrium distance of the carbon atoms, b of the C–H linkages and Î¸ the tetrahedral angle; fC, fH, etc., are the force constants associated with these movements.
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KELLNER, L. Vibrations of an Infinitely Long Chain of CH2-Groups and the Infra-red Spectrum of Polythene. Nature 163, 877 (1949). https://doi.org/10.1038/163877a0
The Journal of Chemical Physics (1951)
Analytical Chemistry (1950)