Lattice dynamical investigation of the rotator phase of n-paraffins

Abstract

A lattice dynamical investigation was made in order to interpret the thermodynamical behaviors of the first-order solid-state phase transition of n-paraffins from the orthorhombic or monoclinic to the rotator phase. The internal energy, the entropy, and the Helmholtz free energy of the rotator phase were evaluated in variation with chain length, lattice dimension, and temperature, using a model of cooperative rigid rotation accompanied with a small translational fluctuation along the chain axis. The contribution of the molecular vibrations to the thermodynamic functions was estimated by a lattice dynamical calculation in the quasiharmonic approximation from the density of states obtained by the normal coordinate treatment. An orthohexagonal lattice with the dimension of a=31/2 b=8.31 Å was found to exhibit the minimum value of free energy at 300 K, as compared with the measured lattice dimensions of n-C19H40 (a=8.30 Å, b=4.79 Å) at 295.2 K. The calculated linear coefficient of thermal expansion αa (=αb) along the direction perpendicular to the c-axis (the chain axis) is 1.4–1.7×10−4 K−1 which is quite similar to the mean value of αa and αb of the orthorhombic polyethylene (o-PE) lattice at room temperature. The transition temperatures, the heat, and the entropy of transition were evaluated in variation with chain length. The theoretical transition points are 20–30°C higher than the observed ones. The calculated heat and entropy of transition are in good agreement with the experimental values.