Stepto theory

In the Stepto theory, the free energy of the network is given by... 

Einstein A (1905) Uber die von der molekiilarkinetischen Theorie der Warme geforderte Bewegung von in ruhenden Fliissigkeiten suspendierten Teilchen. Ann Phys 17 549-560 Jenkins AD, Kratochvil P, Stepto RFT, Suter UW (1996) Glossary of basic terms in polymer science. Pure Appl Chem 68 2287-2311... 

Stepto, R. F. T. Cail, J. Taylor, D. J. R., Formation, Structure and Elastomeric Properties of Polymer Networks Theory and Modehng. Macromol. Chem. 

Cail, J. I. Stepto, R. F. T., The Gel Point and Network Formation Including Poly(dimehylsiloxane) Polymerizations Theory and Experiment. In Science and Technology of Silicones and Silicone-Modified Materials, Clarson, S. J. Fitzgerald, J. J. Owen, M. J. Smith, S. D. Van Dyke, M. E., Eds. American Chemical Society Washington, DC, 2007 Vol. 964, pp 190-202. 

The phenomenological theories following the approach of Rivlin and others were based on empirically developed strain energy functions. These have been overtaken by molecular network models notably by Edwards and colleagues, Boyce and colleagues and Stepto and colleagues. 

Within the limits of small fluctuations one can take into account cyclization in graph theory and estimations for the gel point can be predicted, for example Ahmad and Stepto derived, based on Kilb s result... 

The work of Stepto et al. [26-28] included two aspects, namely, the aforementioned experimental work and the theoretical work based on the so-called rate theory [27, 28]. The rate theory involves a set of kinetic differential equations, which are based on the time dependence of the concentrations of monomers and reaction products. In Stepto s approach the time dependence is converted into a dependence on the conversion. At first, the rate theory was elaborated for three-dimensional polycondensations excluding a significant influence of cyclization, and later, extended to two-dimensional polycondensations including cyclization. A detailed description of the complex equations is beyond the scope of this chapter, which is focused on the discussion of the consequences of Stepto s work. Three results are particularly important ... 

In a second version of the reference model the exactly calculated rings were limited to V = 3 and this version was termed Limited Number of Rings model (LNR) The third version called hybride model the first three or four rings were exactly calculated, and an approximation to calculate the larger rings was added. The most important aspect of the work of Valles et al. is the comparison of the reference model (first version) with the spanning tree model and with the rate theory . For this comparison the mathematical evaluation of those models was simplified by the recursive method, but the results were identical with those obtained by Gordon et al. [24, 25] or by Stepto et al. [28]. All comparisons were illustrated in two ways ... 

---