Relaxation spectrum of a polymer network with included particles: A regular cubic network model with mutual friction

Dynamic moduli of magneto-sensitive elastomers: a coarse-grained network model

“…36 , was widely used to describe the longscale dynamics of usual non-magnetic rubbers. 48,52 As in the previous works for networks of different structure, [35][36][37][38][46][47][48][49]52 we start from the coarse-grained cubic network model in order to study the low-scale dynamics of magneto-sensitive elastomers. In refs.…”

“…On the other hand, the cubic network model is widely used to describe the mechanical properties of three-dimensional isotropic polymer networks. [35][36][37][38][39][46][47][48][49] In ref. 48 it was shown that the mechanical properties under external stress, provided by the cubic network model, coincide with the results for Gaussian networks with random orientations of the network strands in the linear response regime.…”

“…37, 38 and 47 it was shown that the coarse-grained network model describes correctly the low-frequency dynamics of multi-segmental network models. Recently, the coarse-grained network model was modified to study the low-frequency dynamics of polymer networks with included particles 46,49 as well as the dynamics of anisotropic networks with LC-order 35 or under external forces. 48,52 As in the previous studies for networks of different structures, [35][36][37][38][46][47][48][49]52 we start from the coarse-grained cubic network model in order to study the low-scale dynamics of magneto-sensitive elastomers.…”

“…Recently, the coarse-grained network model was modified to study the low-frequency dynamics of polymer networks with included particles 46,49 as well as the dynamics of anisotropic networks with LC-order 35 or under external forces. 48,52 As in the previous studies for networks of different structures, [35][36][37][38][46][47][48][49]52 we start from the coarse-grained cubic network model in order to study the low-scale dynamics of magneto-sensitive elastomers. Using this model, we take explicitly into account both the elastic interactions between the magnetic particles included into a united network structure and the magnetic interactions between them.…”

“…Besides, to derive eqn (14), relation (10) between M* and the structural parameters f, n and E 0 was taken into account. To solve eqn (14) we use the new coordinates, which, for the cubic network, are related to the Fourier transform: [35][36][37][38]46,47,49,52 QðhÞ ¼ X…”