Functional groups free energy

The shortcomings of the phantom network concepts have stimulated a number of attempts to find theoretically a more satisfactory elastic free energy function to describe the properties of elastomers at different states of deformation. The efforts to explain the real network behaviour by a special non-topological mechanism can be divided into four types. The first group considered intra- and intermolecular effects los-ni) wjtii these assumptions it is hard to explain values of the Mooney-Rivlin parameter which are of the order of the corresponding Cj parameter. 

The absence of thermal data as a function of composition for all but one of the carbide systems makes an estimation technique desirable. An examination of the various free energy function values, listed in the text, reveals some convenient patterns between the stoichiometric compositions of the MC compounds. Above 1500°K, the fef vs. Tcurves of Groups 4 and 5 are nearly parallel and the adjacent carbides, TiC-VC and ZrC-NbC, have values which are very close at corresponding temperatures. A comparison between HfC and TaC is less satisfactory, but within 5%. If this trend is followed by the defect compositions, values for the other Group 4 and 5 carbides can be estimated from the measurements in the NbC system. 

Among these variants, the white bear version developed by Roth et al. (2002) or equivalently the modified FMT (MFMT) by Yu and Wu (2002) is most reputed. Although both modifications are developed by two individual research groups at almost the same time, they are completely equivalent (Roland, 2010). The basic idea in these modifications is that more accurate EOS for bulk HS system can be incorporated into the free energy functional. 

Use of a Monte Carlo or a cluster (Hybrid) algorithm to calculate ionization constants of the titratable groups, net average charges, and electrostatic free energies as functions of pH. 

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