DISCUSSION OF THE INTENSITIES OF SOME VIBRATIONAL BANDS OF CRYSTALLINE POLYETHYLENE
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Date
1956
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Ohio State University
Abstract
The integrated absorption coefficients (in $10^{13}$ $sec^{-1}$) of the five infrared-active factor group fundamentals of long straight polymethylene chains are approximately: $O(CH_{2}$ wagging), $2(CH_{2}$ rocking), $5(CH_{2}$ deformation), 20(sym, CH stretching), and 41 (asym. CH stretching). These results are incompatible with the usual bond moment theory according to which the rocking and wagging fundamentals should have almost equal intensities proportional to the square of the permanent dipole moment $^{\mu}CH$ of the CH bond. A modification of the theory consistent with the observed intensities has been developed on the assumption that the dipole moment of the CH bond is directed along the bond axis even when the latter is displaced from its equilibrium position. Taking into account also the symmetry of the polymethylene chain, one obtains from the observed infrared intensities the following numerical values: |^{\mu}{CH}|\cong{O}(\partial|^{\mu}{CH}|/\partial\gamma)/(\partial|^{\mu}{CH}|/\partial_{t})\cong 2.1 \mbox{ and }\partial|^{\mu}{CH}|/\partial{x}={O} Here x, y, z are the components of the displacement of the hydrogen atom, the x-axis being parallel to the chain and the z-axis being perpendicular to the plane of the carbon skeleton. The bond moment obtained in this manner is smaller than previous estimates. The Raman spectrum of long polymethylene chains contains three lines assigned to $CH_{2}$ rocking ($1168 cm^{-1}$), twisting ($1295 cm^{-1}$) and wagging ($1415 cm^{-1}$). These assignments have been supported by intensity calculations based on the bond polarizability theory and the symmetry of the chain. The following calculated intensity ratios were obtained $I_{twisting}$: $I_{wagging}$: $I_{rocking}$ = 6:3:1 in qualitative agreement with the observed intensities.
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Author Institution: Department of Physics, University of Oklahoma