Elasticiy of polymers with internal topological
constraints
August 2002, University of Cambridge
The thesis addresses a wide range of topics in polymer physics: it comprises an investigation of the mechanical behaviour of single twist-storing polymers, a network theory of helix-forming polymers, a theory of entanglement effects in isotropic and nematic rubbers, and an exploration of soft elastic modes in biaxial nematic liquid crystal elastomers.
Single twist-storing, i.e. torsionally rigid, polymers admit another external variable besides the imposed end-to-end distance: the link number keeps track of how much one end of the polymer has been wound up while the other end has been kept clamped; it is the conjugate variable to the torques felt at the clamped ends of the polymer. We find that a twist-storing polymer has a particular force-extension curve depending on the link number due to the formation of plectonemes, double helical structures commonly known from writhing phone cords.
Polymers can be crosslinked to form networks, gels or rubbers, thereby creating a structure which couples macroscopic deformations to the microscopic chain configurations. There are three chapters addressing aspects of this area.
Biological polymers often form helices, which, on stretching, can be either created or suppressed. We develop a model for a network consisting of helix-forming polymers and investigate how a macroscopic deformation affects the helical content in the network.
The microscopic theory of networks encounters difficulties in describing the molecular entanglement effects which are permanent in a network in contrast to polymer melts. We propose an improvement of the simplest model based on the ideas of polymer reptation confined in effective tubes. Subsequently, we apply it to nematic rubbers, an example of a liquid crystalline elastomer.
The last chapter is devoted to the theory of biaxial nematic elastomers, focusing on the manifold of soft elastic modes, when large deformations can occur without energy cost, an effect unique to liquid crystal elastomers.