On the Elasticity of Polymer Model Networks Containing Finite Loops

• DOI: 10.1021/acs.macromol.9b00996
• Publication Date: 2019-08-14T17:38:01Z
• Authors: Michael Lang
• Keywords: Elasticity

Based upon the resistor analogy and using ideal loop gas approximation (ILGA), it is shown that only pending loops reduce modulus of an otherwise perfect network made monodisperse strands junctions identical functionality. Thus, cycle rank with structures removed (cyclic branched) sufficient to characterize modulus, if can be employed. It further impossible incorporate finite cycles into a polymer such individual are at equilibrium conformations while maintaining simultaneously force balance junctions. Therefore, provides for phantom networks containing loops. Improved approaches constructed from considering junctions, which requires knowledge distribution cross-link fluctuations in imperfect networks. Assuming all lower bound estimate Gph ≈ (ξ – cfL1)kT/V obtained within ILGA end-linked model limit L1 ≪ ξ. Here, number primary ("pending") loops, ξ network, k Boltzmann constant, V volume sample, T absolute temperature. cf functionality-dependent coefficient, is, ≈2.56 junction functionality f = 3 ≈3.06 4, converges quickly toward ≈4.2 large f. Further corrections beyond addressed briefly.