Frequency Spectrum of Polymers
The frequency spectrum of a polymer can be separated into skeletal and group vibrations. For polyethylene (PE) and most other polymers one can clearly distinguish between these two vibrations.The skeletal vibrations reach from zero to approximately 2x1013 Hz. Polyethylene shows two degrees of freedom (N) in this frequency range. They can be visualized as torsional and accordion-like motions of the CH2-backbone. The torsional motions involve mainly bond rotation, and the accordion like motion bending of the C-C-C bonds. These vibrations contribute mainly to the increase in heat capacity from 0 to 200 K.
The group vibrations are activated at somewhat higher frequencies (temperatures).2 The gap in the frequency distribution is responsible for the levelling of the heat capacity between 200 and 300 K. The first set of group vibrations originate from relatively isolated C-H-bending and C- C-stretching motions in the backbone chain. It reaches from 2 to approximately 5x1013 Hz, that is, both the stretching vibration of the C-C-bond and the C-H-bending fall into the same frequency range. They are responsible for the noticeable increase of the heat capacity starting at about 300 K.
The CH2-groups have two more group vibrations of very high frequency (8x1013 Hz). They originate from the C-H-stretching motion. They are so high that their contribution to the heat capacity can be neglected below 400 K. In total, nine vibrations are possible for the three CH2-groups when fully excited. However, even at the melting point only half of all vibrations are excited. The total heat capacity at constant volume (Cv) is about 38 J/(K mol), whereas a fully excited polyethylene has a heat capacity of about 75 J/(K mol).
References and Notes
- B. Wunderlich, Pure & Appl. Chem., Vol. 67, No. 6, pp. 1019-1026 (1995)
The collective vibrations in periodic, elastic arrangements of atoms or molecules in condensed matter are also known as phonons. Each phonon represents a quantizied excited state of many possible modes of vibrations in the elastic structure of interacting particles.