Heat capacities of linear macromolecules

Adiabatic and differential scanning calorimetry can both make important contributions to the measurement of heat capacities. All heat capacities of linear macromolecules have been collected, computer stored and evaluated. Together with information on glass transitions and equilibrium melting data, the heat capacities are used to derive an overall understanding of the thermal property. Prediction schemes of solid and liquid heat capacities, the increase of heat capacities at the glass transition temperature, and the temperatures of melting are analyzed. I N T RU DU CT I 0 N Heat capacities are reasonably well understood . In the solid state, only vibrational contributions need to be considered. For linear macromolecules, it is sufficient to use the harmonic oscillator approximation. All linear macromolecules have, furthermore, a similar backbone structure, permitting easy analysis of the vibrational frequency spectrum in terms of chemical structure. For such discussion, the overall frequency spectrum is divided into skeletal vibrations and group vibrations. For an approximate discussion of the skeletal vibrations , the molecule is considered to consist of a chain of structureless beads of the given formula weight. The intramolecular vibrations of the skeleton can now easily be estimated. For many carbon backbone macromolecules, geometry and force constants are the same. A change in mass is the only remaining variable. It changes the vibrational frequency proportional to 1//hiass. The intermolecular skeletal vibrations, in turn, are usually few and affect heat capacities only up to about 50 K. Often it is possible to approximate the intermolecular skeletal vibrations with a three-dimensional Debye function  and the higher frequency intramolecular skeletal vibrations can be averaged into a one-dimensional Debye function as suggested by Tarasov . The group vibratlons spread usually over narrow frequency ranges and their heat capacity contribution can be approximated by Einstein functions [4] at average frequencies. In this way all but the contributions of the intermolecular skeletal vibrations to the heat capacity are additive according to the chemical structure. An earlier suggested additivity scheme  is to be tested with new data and extended to other backbones. Additivity of the heat capacity of liquids is more difficult to assess. The major additional contribution to the vibrational heat capacity is the potential energy, describable by a hole theory [6]. Such contributions are only partially based on intramolecular effects and as a result, additivity of liquid heat capacities is still a subject of discussion. It will be shown that the old "bead model" needs extension for different size "beads". For many years heat capacity data of high precision were almost exclusively measured by adiabatic clorimetry [7]. A precision of 0.1% or better could routinely be achieved, but measurement was involved and data generation was slow. When the first larger survey of such data for linear macromolecules was made  we found that due to sample difficulties, overall agreement between data of different laboratories was in many cases not better than 3%. Such accuracy could also be achieved with the newly developed scanning calorimeters . Furthermore, computerization of data collection could improve this accuracy even further , 50 that now differential scanning calorimetry is the method of choice for large volume heat capacity measurement on linear macromolecules. Some examples and comparisons of differential scanning and adiabatic calorimetry will be given.

Field of study: Chemistry