Tobolsky Eisenberg theory

These results provide qualitative support for the validity of the ring-chain structural model for vitreous selenium implied by the Tobolsky-Eisenberg theory (1,2) of equilibrium polymerization. The establishment... 

The Tobolsky-Eisenberg polymerization theory was considered potentially useful for predicting molecular structure in vitreous materials. In principle, the copolymerization form of the theory described by Tobolsky and Owen (3) provides a way to calculate the concentrations of the various species present in equilibrium in the liquid phase. As a first approximation, the molecular constitution of the liquid phase at the M.P. is the structure retained in the vitreous phase upon rapid quenching to room temperature. A slight modification of the Tobolsky-Owen theory... 

Gee s theory was unified by Toboesky and Eisenberg (31) and further improved by Tobolsky et al. (52) who removed the original restriction demanding an multiple numbers of 8 S atoms in each chain. This theory demands the existence of a transition (floor) temperature and excellently accounts for its sharpness as determined from Gee s results. A similar situation is observed in liquid selenium (32). 

However, this model also predicts a continuous increase in the polymer content with temperature resulting in 48% at 250 °C and 68% at 350 °C while the best analytical data show that the maximum value for Sqo in high-purity sulfur melts is 40% [93]. In addition, the equilibrium reactions between rings other than Ss and the polymer as well as the substantial polymer content at temperatures below 157 °C are neglected in this model. Therefore, the polymerization theory by Tobolsky and Eisenberg as well as its slightly modified versions [42, 69, 130-132] are also unsatisfactory. 

Laser Raman spectroscopy has been used as a tool to elucidate the molecular structure of crystals, liquids, and amorphous alloys in the As-S-Se-Te system. Characteristic monomer and polymer structures have been identified, and their relative abundances have been estimated as a function of temperature and atomic composition. These spectroscopic estimates are supported by calculations based on the equilibrium polymerization theories of Tobolsky and Eisenberg (1,2) and of Tobolsky and Owen (3). Correlations between the molecular structure of the amorphous alloys and physicochemical properties such as the electron drift mobility and the glass transition temperature are presented. 

Fig. 5.12. Average degree of polymerization (atoms per chain) as a function of temperature for liquid selenium (Warren and Dupree, 1980). Full curves, Nchain from resonance shift analysis tmd Eq. (5.7) assuming /. = 0 dashed curve, Nc am from magnetic susceptibility broken curve (ET), calculated from theory of ring-chain equilibrium by Eisenberg and Tobolsky (1960).

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