Equation Tarasov

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. 

Pfadenhauer and McCain (179) and Tarasov and Buslaev (180) studied the hexafluoroscandate ion in terms of two dynamic processes affecting the line-shape of the resonance, namely chemical exchange involving fluoride ions on the one hand and " Sc relaxation on the other hand. The latter two authors tackled the problem by solving the Kubo-Sack master equation for chemical exchange using... 

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 number of skeletal vibrational modes used in the Tarasov equation with the theta temperatures of the previous two columns. Values of theta temperatures in parentheses are estimates based on data from polymers of similar backbone structure. The group vibration frequencies are usually tabulated in the listed references. 

Fig. 1. Cumulative vibrational spectrum of the skeletal vibrations of polyoxymethylene (POM). , Experimental crystalline POM , calculated with the Tarasov equation (N = 2).

The N in equations 1-4 refers to the appropriate number of vibrators and x stands for hvIkT = 6 IT. The sum of all is three times the number of atoms in a repeating unit, the number of degrees of freedom. Tarasov proposed a special combination of equations 2 and 4 for the skeletal vibrations of a linear chain (62)... 

A. Tarasov, K. Titov. (2013) On the use of the Cole-Cole equations in spectral induced polarization. Geophysical Journal International, vol. 195, pp. 352-356. 

C value are calculated from the Tarasov equation (Data Bank, 1982)... 

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