Skeletal vibrations, polymer heat capacity

Details for the ATHAS calculations are given in Pyda M, Bartkowiak M, Wunderlich B (1998) Computation of Heat Capacities of Solids Using a General Tarasov Equation. J. Thermal Anal Calorimetry 52 631-656. Zhang G, Wunderlich B (1996) A New Method to Eit Approximate Vibrational Spectra to the Heat Capacity of Solids with Tarasov Eunctions. J Thermal Anal 47 899-911. Noid DW, Varma-Nair M, Wunderlich B, Darsey JA (1991) Neural Network Inversion of the T arasov Eunction Used for the Computation of Polymer Heat Capacities. J Thermal Anal 37 2295-2300. Pan R, Varma-Nair M, Wunderlich B (1990) A Computation Scheme to Evaluate Debye and Tarasov Equations for Heat Capacity Computation without Numerical Integration. J Thermal Anal 36 145-169. Lau S-F, Wunderlich B (1983) Calculation of the Heat Capacity of Linear Macromolecules from -Temperatures and Group Vibrations. J Thermal Anal 28 59-85. Cheban YuV, Lau SF, Wunderlich B (1982) Analysis of the Contribution of Skeletal Vibrations to the Heat Capacity of Linear Macromolecules. Colloid Polymer Sd 260 9-19. 

Pyda and co-workers [49, 60] measured the reversible and irreversible PTT heat capacity, Cp, using adiabatic calorimetry, DSC and temperature-modulated DSC (TMDSC), and compared the experimental Cp values to those calculated from the Tarasov equation by using polymer chain skeletal vibration contributions (Figure 11.7). The measured and calculated heat capacities agreed with each other to within < 3 % standard deviation. The A Cp values for fully crystalline and amorphous PTT are 88.8 and 94J/Kmol, respectively. 

More refined models of the heat capacities of polymers can be obtained by deconvoluting the "skeletal vibrations" of chain molecules from their set of discrete "atomistic group vibrations", and by further deconvoluting the "intramolecular" component of the skeletal vibrations from the "intermolecular" (i.e., interchain) component. The major portion of the heat capacity at temperatures of practical interest (i.e., temperatures which are not too low) is accounted for by the atomistic group vibrations. The remaining portion of the heat capacity arises from skeletal modes. Detailed discussion of these issues is beyond the scope of this chapter. The reader is referred to the reviews provided by references [1-3] for further details and lists of the original publications. 

The strict additivity of the heat capacity contributions of the group vibrations, and the continuous change in 1 with chemical composition, led to the development of addition schemes for heat capacities. As long as the contribution which corresponds to the backbone grouping of a polymer is known empirically, it is possible to estimate heat capacities of such polymers and copolymers. The just completed discussion of the Tarasov analysis indicates that, indeed, the group vibrations are additive, but that for the low-temperature heat capacities deviations are to be expected as long as the intermolecular skeletal vibrations are not fuUy excited. In this case it is possible to estimate 3 from similar substances for an improved estimate. 

The heat capacities up to 160° K are little different from those of polyethylene recalculated to four moles of CH. The planar trans potymer has up to 50° K the heat capacity of a partially crystalline polyethylene, while the helical cis polymer shows a somewhat higher heat capacity tlian amorphous polyethylene. The skeletal vibrations are thus more affected by the change in chain conformation than by the introduction of a double bond. The loss of two H-atoms and the larger force constant for the C=C-bond is evident in the 5 to 10% lower heat capacity of polybutadiene from 70 to 160° K. 

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