Meso-scale Modeling of Polymer Mechanical Properties

 

  The mechanical properties of polymers are diverse in respect to chemical identity and physical properties of the polymer, such as molecular weight and composition. The modelling of polymer systems is important to guide research for polymer materials and in developing new novel sytems such and synthetic spider-fibers. In systems such as spider-fibers, microstructure elements play an important role, which raises the need for coarse-grained models to address the time and length scales of interest.

 

     Coarse-grained approximations have been used in modelling polymers for many years. Polymer segments can be treated as an ideal chain, wherein several repeat units of the polymer are treated as a single segment which has no coupling in orientation to the neighboring segments. Further coarse-graining can be accomplished by treating many repeat units as a concentrated mass with a stretching potential between its neighbors. These models are shown in figure 1. 

 

     A different way to view a polymer segment is as a probability distribution of where the sub-segment units will lie; a density cloud. When considering how to represent a segment of polymer with known end points, this distribution of sub-segment units can be calculated via Monte-Carlo simulation. This representation has promise to reproduce actual mechanical behavior of polymer systems of a wide variety of chemical composition and physical properties. A representation of this concept is illustrated in figure 2.

 

To model real systems a lattice network consisting of coarse-grained polymer segments is constructed (figure 3). A description of the energy associated with a specific network configuration is then needed to model the dynamic response of the network. By straining the network, the mechanical response from the coarse-grained approximation is recovered. Showing agreement of the models mechanical response to experimently known systems is the first step to establishing this coarse-grained model as a guide to experimental research to develop new polymer materials.