The structure and material properties of polymer networks can depend sensitively on changes in the environment. There is a great deal of progress in the development of stimuli-responsive hydrogels for applications like sensors, self-repairing materials or actuators. Biocompatible, smart hydrogels can be used for applications, such as controlled drug delivery and release, or for artificial muscles. Numerical studies have been performed on different length scales and levels of details. Macroscopic theories that describe the network systems with the help of continuous fields are suited to study effects like the stimuli-induced deformation of hydrogels on large scales. In this article, we discuss various macroscopic approaches and describe, in more detail, our phase field model, which allows the calculation of the hydrogel dynamics with the help of a free energy that considers physical and chemical impacts. On a mesoscopic level, polymer systems can be modeled with the help of the self-consistent field theory, which includes the interactions, connectivity, and the entropy of the polymer chains, and does not depend on constitutive equations. We present our recent extension of the method that allows the study of the formation of nano domains in reversibly crosslinked block copolymer networks. Molecular simulations of polymer networks allow the investigation of the behavior of specific systems on a microscopic scale. As an example for microscopic modeling of stimuli sensitive polymer networks, we present our Monte Carlo simulations of a filament network system with crosslinkers.
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