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108 Ralf Steudel 3.6 Polymerization Theories for Liquid Sulfur The polymerization reaction of liquid sulfur above 157 C, often termed as “Sl-Sm transition” or simply “l-transition”, cannot be considered as a phase transformation in the normal sense but is a kinetically controlled equilibri- um reaction. In fact, over the whole temperature range there is an equilibri- um between small cyclic monomer molecules and polymeric sulfur mole- cules of differing molecular sizes and types (rings and chains). Thus, there is no spontaneous and complete polymerization reaction at a defined tem- perature but only an additional polymer formation on rising the temperature above 157 C! This temperature follows from the temperature dependence of the heat capacity [14] and of the polymer concentration [124]. Neutron dif- fraction measurements on liquid sulfur support this view [125]. Since the equilibrium is established only slowly owing to the high activation energy the polymerization reaction is considerably heating-rate dependent. Several authors have tried to simulate the mechanism of the reactions in liquid sulfur by molecular dynamics (MD) calculations. The starting reac- tion, that is the opening of the S8 ring by homolytic bond dissociation, was achieved either thermally [126] or photochemically [116, 127]. The thermal treatment of a theoretical system initially consisting of 125 S8 rings resulted in mixtures of diradical-chains of various sizes together with some medium sized rings like S12 besides S8. However, the rather simple potential function used and the restriction of the density to a fixed value are probably respon- sible for the fact that the molecular composition of this system shows hardly any similarity to the real sulfur melt [126]. The same kind of criticism has to be applied to a MD calculation based on density functional theory in which only nine S8 molecules placed in a cubic box were heated or photoexcited followed by quenching [128]. As expected the rings turned into chains of different lengths but no rings other than S8 were produced. A more realistic treatment is the simulation of a ring opening polymeriza- tion by Ballone and Jones [129]. These authors investigated the behavior of 10,000 cyclic particles in a periodically squared (cubic) simulation box. To start the reaction one molecule of an initiator was added, and the develop- ment of the system as a function of temperature, density and “reaction time” was studied. At low densities the initially present cyclic tetramers turned into a mixture of smaller and larger rings while at higher densities one huge chain-like polymer molecule resulted together with a “background” of medi- um sized rings consisting of up to several thousand monomers (since the initiator molecule is incorporated into the polymer only one such molecule can form in such a simulation). The formation of these species is entropy- driven since the reaction enthalpy was assumed to be zero. The larger num- ber of possible configurations in the polymer as well as in the medium sized rings results in a positive reaction entropy. In addition, the fact that a “living polymer” is formed which is able to undergo bond interchange reactions also adds to the entropy gain. Although sulfur was not considered specifical-PDF Image | Topics in Current Chemistry
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