A Method for Elastic Homogenization of Bimodal Networks

The properties of soft materials with heterogeneous network composition are studied. These materials are distinguished by their particular composition. Bimodal networks are formed by two types of chemically identical polymer chains, for example, polydimethylsiloxane. However, they differ in molecular weight of each of the components. Long and short chains are mixed, after which they are randomly connected at the ends with the help of a common vulcanizing agent. In contrast to cross-linking, the original clear dispersion of the chain lengths is thus preserved and, accordingly, it is possible to control it. To determine the macromechanical properties of these materials, an improved micromechanical model was developed. Two separate statistical spaces are introduced for bimodal materials. Each of them contains the microsphere of unit vectors of initial chainorientations in the corresponding fraction. The averaging on a solid network is performed taking into account the specific shares of each fraction. A relationship that establishes the kinematic relationship between macro- and microdeformations of each individual fraction is derived. The response of the network to an external macroscopic deformation is determined by the equilibrium of internal microstretches and is found by solving a minimization problem with constraints. The performance of the developed model is demonstrated by the example of several previously examined bimodal elastomers. The results display good qualitative and quantitative agreement with experimental data.