Pressure and temperature effects on the vibrational frequencies of crystalline polymethylenes. II. Lattice anharmonicity and the equation of state

The lattice anharmonicity of crystalline polymethylene is interpreted from the observed pressure and temperature dependence of Raman active interchain lattice frequencies of the n-paraffins C₂₃H₄₈ and C₄₄H₉₀. The temperature dependence of the L_c′ interchain lattice frequency is separated into quasiharmonic and self-energy shifts. The former is due to the volume dependence of the force constant of the oscillator. The latter is due to the anharmonicity of the dynamic potential, and is obtained as a function of volume and phonon population. The setting angle of the carbon skeleton is predicted to be temperature-sensitive. While the potential surface of the crystal is asymmetric along the L_c′ normal coordinate, it is essentially symmetrical along the T_b′ coordinate. The well-known Mie–Gruneisen equation of state is generalized to include anharmonicities of oscillators through the temperature dependence of their vibrational frequencies.