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Liquid Sulfur 111 SR8 Ð SC8 K11⁄4 cSC8 =cSR8 ð18Þ SCi þSR8 Ð SCiþ8 K2 1⁄4 cSCiþ8 =cSR8 cSCi ð19Þ The diradical chain S8C obtained by ring opening of a cyclic S8 molecule is assumed to act as an initiator in the following stepwise ring addition poly- merization shown in Eq. (19). It was assumed that the equilibrium constant K2=c(Si+8C)/c(S8R)·c(SiC) is independent of the chain-length i. The number average chain length P is then given by Eq. (20): M01⁄4ðP1Þ=PK2 þK1 PðP1Þ=K2 ð20Þ M0=3.90 mol kg1 is the total concentration of pure sulfur. Using crude literature data for the polymer content and for P at various temperatures (as estimated before by Gee), the following thermodynamic data were derived from plots of log K vs 1/T: – DHo(18)=137 kJ mol1, DSo(18)=96 J mol1 K1 – DHo(19)=13.3 kJ mol1, DSo(19)=19.4 J mol1 K1 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 S1 in high-purity sulfur melts is 40% [93]. In addition, the equilibrium reactions between rings other than S8 and the polymer as well as the substantial polymer con- tent at temperatures below 157 C are neglected in this model. Therefore, the polymerization theory by Tobolsky and Eisenberg as well as its slightly mod- ified versions [42, 69, 130–132] are also unsatisfactory. In 1963 Gee [133] published a modified version of his polymerization the- ory which in principle allows for the incorporation of small rings other than S8. The general description of a ring addition reaction (Eq. 21) is given by Eq. (22) if no solvent is present: SCi þSRn Ð SCj ðj1⁄4iþnÞ ð21Þ Rlnð1 FÞ1⁄4DS0 DH0=T ð22Þ This assumption is approximately valid in the case of liquid S8 which is always the majority ring species in sulfur melts below 170 C. For S7, the sec- ond most abundant ring in liquid sulfur, the term R·ln c must be added to Eq. (22) (c is the fraction of that ring in the mixture of S8 and dissolved poly- mer): Rlnð1FÞ1⁄4DSDH=TþRlnc ð23Þ In the case of S8 the ring addition reaction is endothermic and endentrop- ic (DS>0). This results in a “floor temperature” for the polymerization and Eq. (23) can be simplified to the form Eq. (16) given above [133]. No poly-PDF Image | Topics in Current Chemistry
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