Elastic network bond-bending

Arbabi, S Sahimi, M, Elastic Properties of Three-Dimensional Percolation Networks with Stretching and Bond-Bending Eorces, Physical Review B 38, 7173, 1988. 

Central force elastic percolation If one considers an elastic network of springs, which can provide only the central force, and not the bond-bending force considered earlier, then the elastic energy of such a random bond network can be expressed by the same energy function H in (1.11) with... 

Accurate numerical studies, using this self-consistent strain calculation method for various elastic networks, with central and bond-bending forces, by Sahimi and Arbabi (1993) gave Tf = 2.42 0.14 and = 2.64 0.3 in d = 2 and 3 respectively. These estimates again compare well with the experimental results of Benguigui et al (1987) ind = 2, and fall within the above-mentioned theoretical bounds (given by (3.14)). 

They considered both central force as well as the bond-bending models. In the latter (bond-bending model), the elastic energy (H) of the network is contributed both by the central force (spring constant) part and the... 

It was noted in Ref. 12b that such important physical characteristic exists as elasticity of the spatial H-bond network, which is usually employed [15, 16, 19] for calculations of water spectra. As is intuitively clear, this elasticity should be somehow related to the R-band spectrum, since the stretching vibration, determined by the H-bond elasticity, is believed [16, 35, 51] to present the origin of this band in water. As a basic mechanism, one could regard an additional power loss due to interaction with the a.c. field of the H-bond vibrations. However in Ref. 7, as well as in Ref. 12b, a physical picture relating the CS well to bending vibrations was not established. 

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