Polymer networks between two parallel planar surfaces
The formation and mechanical properties of a polymer network on and between two flat parallel surfaces are investigated. Most treatments of surface-attached polymers have been limited to scaling theory. In the present investigation we probe the physics of the system by means of a mathematical description of the random crosslinking of ideal (or phantom) chains. We modify an existing bulk model of network formation by Deam and Edwards, with polymer-polymer crosslinks, to include surfaces and polymer-surface crosslinks. We investigate two variations of this model: in the first place, the polymer-surface links are formed anywhere along the contours of the long, ideal polymer chains. In the second brush network model, the surface links are restricted to one endpoint of each macromolecule. Within the framework of replica theory, we compute statistical averages and the elastic properties of the systems such as the stress-strain relationship. In both cases the elastic modulus of the bulk network is altered, and has a characteristic form due to the confinement. Furthermore, we find that the stress-strain relationship depends on the manner of crosslinking.