Linear macromolecules, heat capacity

Wunderlich, B. and Baur, H. Heat Capacities of Linear High Polymers. Vol. 7, pp. 151-368. Wunderlich, B. and Grebowic2, JThermotropic Mesophases and Mesophase Transitions of Linear, Flexible Macromolecules. Vol. 60/61, pp. 1-60. 

U. Gaur and B. Wunderlich, Additivity of the heat capacities of linear macromolecules in the molten state. Polymer Div. Am. Chem. Soc. Preprints 20, 429 (1979)... 

Varna-Nair M and Wunderlich B, "Heat Capacity and other Thermodynamic Properties of Linear Macromolecules", X-Update of the ATHAS (i.e. Advanced Thermal Analysis) Data Bank, a computerized version of the data bank of heat capacities. 

Heat capacity theory permits a correlation with the chemical structure of the repeating unit (U). In the solid state, only vibrational contributions need to be considered (skeletal and group vibrations). For an approximate discussion of the skeletal vibrations, the molecule is considered to be a string of structureless beads of the given formula weight. For linear macromolecules with similar backbones, the geometry and force constants are similar so that intramolecular skeletal vibrations are fixed by the mass of the structureless bead. The inter-molecular vibrations of linear macromolecules have quite low... 

Loufakis K, Wunderlich B (1986) Heat capacities of linear macromolecules containing chlorine and fluorine. Polymer, 27 563... 

Gaur U, Lau S-F, Wunderlich B (1983) Heat capacities and other thermodynamic properties of linear macromolecules IX. Aromatic and Inorganic polymers. J. Phys. Chem. Ref. Data, 12 91... 

Heat capacity is the basic quantity derived from calorimetric measurements, as presented in Sects. 4.2-4A, and is used in the description of thermodynamics, as shown in Sects. 2.1 and 2.2. For a full description of a system, heat capacity information is combined with heats of transition, reaction, etc. hi the present section the measurement and the theory of heat capacity are discussed, leading to a description of the Advanced THermal Analysis System, ATHAS. This system was developed over the last 30 years to increase the precision of thermal analysis of linear macromolecules. 

Several steps are necessary before heat capacity can be linked to its various molecular origins. First, one finds that linear macromolecules do not normally crystallize completely, they are semicrystaUine. The restriction to partial crystallization is caused by kinetic hindrance to full extension of the molecular chains which, in the amorphous phase, are randomly coiled and entangled. Furthermore, in cases where the molecular structure is not sufficiently regular, the crystallinity may be further reduced, or even completely absent so that the molecules remain amorphous at all temperatures. 

The next step in the ATHAS analysis is to assess the skeletal heat capacity. The skeletal vibrations are coupled in such a way that their distributions stretch toward zero frequency where the acoustical vibrations of 20-20,000 Hz can be found, hi the lowest-frequency region one must, in addition, consider that the vibrations couple intermolecularly because the wavelengths of the vibrations become larger than the molecular anisotropy caused by the chain structure. As a result, the detailed molecular arrangement is of little consequence at these lowest frequencies. A three-dimensional Debye function, derived for an isotropic solid as shown in Figs. 2.37 and 38 should apply in this frequency region. To approximate the skeletal vibrations of linear macromolecules, one should thus start out at low frequency with a three-dimensional Debye function and then switch to a one-dimensional Debye function. 

The Advanced THermal Analysis System was developed in the 1980 s to be able to interpret the heat capacities of linear macromolecules more precisely. In the solid state, the heat capacity is described by contributions from the vibrations of an approximate spectrum. Any deviation is a sign of additional processes, usually conformational disordering or motion. In the liquid state extensive addition schemes based on group contributions have been developed to judge heat of fusion baselines and increases in heat capacity on devitrification at Tg. 

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. 

The main advantage of adiabatic calorimetry is the high precision. The cost for such precision is a high investment in time. For the measurement of heat capacities of linear macromolecules, care must be taken that the sample is reproducible enough to warrant such high precision. Both chemical purity and the metastable initial state must be defined so that useful data can be recorded. 

R. Pan, Heat Capacities of Linear Macromolecules , PhD Thesis, Dept, of Chem., Rensselaer Polytechnic Inst., Troy, NY, 1987. 

V. V. Tarassov, On a Theory of Low Temperature Heat Capacity of Linear Macromolecules , Comptes Rendus (Doklady) of the Academy of Sciences USSR 4h, 20 (1945). 

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