A method devised by Edwards and Gupta for nematic polymers is implemented here for semiflexible filaments which enforces mean inextensibility. This linearises the path integral so that analytic results can be obtained. I argue that the expressions for the probability density obtained using this approach have merit – successfully reproducing the limiting cases of flexible and rigid chains – and have the advantage of being algebraically simple. I develop an algorithm based on the Metropolis method that can calculate the statistical properties of single chains subject to arbitrary interactions. I use this algorithm to check the analytical results obtained using the mean inextensibility approximation and find they are in close agreement. I highlight the applicability of the algorithm to arbitrary interactions by considering the statistical properties of a single chain which is stearically confined to a tube. I develop a model for the elasticity of semiflexible polymer networks based on the assumption of affine strain that uses the simple analytical expressions for probability densities obtained using mean inextensibility. Under such assumptions, I find that mechanical stretching of filaments must be considered in the network energy. This in turn implies that there are three distinct scaling regimes of the modulus which are relevant to stiff filament networks. I check the validity of the homogenous strain assumption by developing an algorithm capable of calculating the elasticity of a network of filaments subject to arbitrary strains and interaction energies. The effect thermal fluctuations, non-homogeneous deformations and variations in filament length have on elasticity is then explored. I find that all are in fact crucial in determining elasticity correctly, particularly at small strains.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:596735 |
| Date | January 2011 |
| Creators | Blundell, J. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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