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C-H stretching regions of both the Raman and i.r. spectra of the extended polymethylene chain have broad secondary maxima. In the case of the Raman spectrum, line shapes are dependent on the environment of the chain, a fact which has been previously exploited in the study of biosystems. We have explained this phenomenon in terms of Fermi resonance interaction between the methylene symmetric C-H stretching mode and appropriate binary combinations involving the methylene bending mode. It is emphasized that appropriate binary states are to be found throughout the Brillouin zone and not just at its center. It is the resulting continuum of binary states which leads to broad secondary bands. The shapes of these bands depend on the dispersion of the bending mode fundamental. For the isolated chain only parallel dispersion is involved, but in the case of the crystal perpendicular dispersion is equally important and leads to the observed dependence on crystal structure. All secondary bands have been accounted for in these terms. The ratio of the Raman intensities of the symmetric C-H stretching fundamentals to the antisymmetric is found to be about 5 and is independent of environment. The relevance of these results to studies on biosystems is briefly discussed.

A vibrational and attendant conformational analysis of the liquid n-paraffins and molten polyethylene is presented. For the purposes of the analysis a valence force field was derived which is applicable to both planar and nonplanar chains. The force field was evaluated from observed frequencies of trans (T) and gauche (G) n-C4H10; TT and GT n-C5H12; TTT, GTT, and TGT n-C6H14; and (T)∞ polyethylene, all of whose infrared spectra were assigned in detail. Infrared spectra of the liquid-n-paraffins n-C4H10 through n-C17H36 were measured at room temperature and n-C4H10 through n-C12H26 also at a temperature just above their melting point. Frequencies and normal coordinates were calculated for the extended forms and for forms having one gauche bond of n-C4H10 through n-C8H18. These quantities were also calculated for the conformations of n-C5H12 through n-C7H16 having two gauche bonds and for the nonplanar but regular conformations (TG)∞ and (G)∞ of polyethylene. Some bands attributable to forms of n-C5H12 and n-C6H14 having two gauche bonds were found. In the case of n-C5H12 the energy difference between the GT and TT states was found to be nearly the same as that between the GG and GT states. Bands in the region 1400–1300 cm−1 were found to be characteristic of specific conformations involving sequences of five or fewer methylenes, such as —GTTG— (1338 cm−1), —GTG (1368 and 1308 cm−1), —GG— (1352 cm−1), and terminal —TG groups (1344 cm−1). All these bands together with two broader ones centered near 1270 and 1080 cm−1 owe their intensity to the wagging of methylenes adjoining gauche bonds. An interpretation of the general features of the C–C-stretching, methylene-rocking, and methylene-scissoring regions is given. Bands associated with molecules or chains having trans sequences involving at least four methylene groups are found. In the region 1300–1150 cm−1 there are chain-length-dependent band progressions resembling those observed for the crystalline n-paraffins. These indicate the presence of molecules with gauche bonds, but these gauche bonds are few in number and are located near the ends of the chains. It is shown that for certain kinds of vibrations, particularly totally symmetric C–C stretching and ∠CCC bending, there is very little change in frequency in going from a fully extended chain to one having one or even two or more gauche bonds. Hence, it is very difficult in the case of the longer n-paraffins to distinguish spectroscopically between fully extended and almost fully extended conformations.

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Solid-solid phase transitions of the odd n-alkanes n-C17H36 through n-C29H60 were studied by using differential scanning calorimetry (DSC) and infrared (IR) spectroscopy. Two phase transitions were found in C25, C27, and C29 in addition to the previously reported highest-temperature solid-solid transition (the so-called "rotator" transition). IR spectra revealed that, as the temperature is raised, the concentration of nonplanar conformers successively increases through each phase transition. Three types of nonplanar defects have been identified in the highest-temperature phase of all the n-alkanes: "end-gauche" (gt...), "kink" (...gtg'...), and "double-gauche" (...gg...). The end-gauche defect was observed in the lower-temperature phases as well. Kink conformers, however, were observed only in the highest-temperature phase while double-gauche defects were found in measurable concentrations only within a few degrees of the melting point. The concentrations of nonplanar conformers in the highest-temperature phases increase with increasing chain length. For example, roughly 70% of C29 molcules are nonplanar prior to melting, in contrast to 5-10% for C17. The relationship between the existence of nonplanar conformers and the various distinct solid phases presents a major puzzle.(1) D. C. Bassett and B. Turner, Nature (London), Phys. Sci., 240, 146 (1972).(2) For example: (a) n-alkylammonium salts, J. Tsau and D. F. R. Gilson,

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The infrared band intensities of crystalline n-alkanes and polyethylene decrease nonlinearly with increasing temperature. For all modes except the C-H stretches, the decrease is large and far exceeds that expected from density and refractive index effects. Similar anomalous decreases occur for the odd n-alkanes at their principal solid-solid (orthorhombic-to-hexagonal) phase transition. Further decreases occur in going to the liquid and gas phase. The intensities of the methylene bending and rocking fundamentals for the gas at 300 K are about I/, those of the crystalline solid at 77 K. A good correlation between the temperature coefficients of the intensity and of the lateral expansion is found for the crystal. This relation suggests that low-frequency modes play an important role in determining the temperature behavior of intensities. A mechanism involving low-frequency modes is proposed that appears to qualitatively explain our experimental results. The sensitivity of intensities to temperature and phase must be taken into account in infrared studies of poly(methy1ene) chain systems and in the transfer of observed and calculated gas-phase intensities to the condensed state. Similar temperature behavior is expected for Raman intensities and for other flexible chain molecules. IntroductionInfrared intensities are defined experimentally by 1(1)where b is the pathlength in the sample, p is the sample density, and A, is the absorbance (to the base e) at frequency v in wavenumbers. The measurement of infrared intensities has been largely confined to small molecules in the gas phase. Large molecules have received relatively little attention and the temperature behavior of their intensities even less. Yet, in an obvious way the temperature behavior of infrared intensities in the condensed state bears directly on the use of infrared spectroscopy for quantitative analysis and structural investigation in cases where temperature is a variable. The present work concerns the poly-(methylene) chain and thus is relevant to studies dealing with how temperature affects the structure of chain-molecule assemblies, such as lipid bilayers, micelles, and hydrocarbon polymers. Such studies have become common by virtue of modern FTIR instrumentation, but the question of how intensities are intrinsically affected by temperature has remained essentially unaddressed.The paucity of experimental studies on solids is probably partly accounted for by the expectation of only a small intrinsic temperature effect. A priori, such an expectation might seem well founded since the Einstein coefficients, which determine the intensity of a spectral line associated with the transition between two isolated energy levels, do not change with temperature. In the near-and mid-infrared regions, small intensity changes with temperature would be expected from the Boltzmann factors and from changes in the density of the sample. However, as we shall show, these factors fall far short of accounting for the large effects that are observed.The present study concern...