This thesis provides a picture on the thermo-elastic behavior of polymer molecules with biological relevance. In particular, this essay deals with the thermo-elasticity of single polymer molecules subjected to uniform stretching (generated by an applied force) or non-uniform stretching (generated by an external field). Analytical expressions and molecular dynamics simulations are elaborated considering some generalizations of the freely-jointed chain (FJC) and the worm-like chain (WLC) models. The analytical theory, based on classical statistical mechanics, allows a rigorous mathematical treatment, while the study of complex systems is covered by means of Monte Carlo simulations. On the one hand, the uniform stretching of a single polymer, imposed by an external pulling force, is pursued for studying the statistical mechanics of small molecules. When the thermodynamic limit is not satisfied, different boundary conditions (either Helmholtz or Gibbs ensemble) yield different elastic behavior, showing the fascinating intrication native to the thermodynamics of small systems. This complexity is shown to be even more suggestive when investigating bistable molecules of which domains exhibit transitions between two stable states. This scenario leads from cooperative to non-cooperative response of each domain to the external force, depending on the specific statistical ensemble considered. Universal scaling laws are provided, governing the overall elasticity of the polymer systems. On the other hand, the non-uniform stretching of a single molecule, imposed by an external field, is studied to analyze the average configurational properties of polymers and leads to another very intricating scenario concerning the behavior of the variances describing the fluctuations of the system. Furthermore, for the WLC model our attention fall in the investigation of the forceextension curve, for which we derive new approximated expressions for a chain immersed into an external field.
The elastic behavior of polymer chains: theory and simulations
MANCA, FABIO
2013-06-05
Abstract
This thesis provides a picture on the thermo-elastic behavior of polymer molecules with biological relevance. In particular, this essay deals with the thermo-elasticity of single polymer molecules subjected to uniform stretching (generated by an applied force) or non-uniform stretching (generated by an external field). Analytical expressions and molecular dynamics simulations are elaborated considering some generalizations of the freely-jointed chain (FJC) and the worm-like chain (WLC) models. The analytical theory, based on classical statistical mechanics, allows a rigorous mathematical treatment, while the study of complex systems is covered by means of Monte Carlo simulations. On the one hand, the uniform stretching of a single polymer, imposed by an external pulling force, is pursued for studying the statistical mechanics of small molecules. When the thermodynamic limit is not satisfied, different boundary conditions (either Helmholtz or Gibbs ensemble) yield different elastic behavior, showing the fascinating intrication native to the thermodynamics of small systems. This complexity is shown to be even more suggestive when investigating bistable molecules of which domains exhibit transitions between two stable states. This scenario leads from cooperative to non-cooperative response of each domain to the external force, depending on the specific statistical ensemble considered. Universal scaling laws are provided, governing the overall elasticity of the polymer systems. On the other hand, the non-uniform stretching of a single molecule, imposed by an external field, is studied to analyze the average configurational properties of polymers and leads to another very intricating scenario concerning the behavior of the variances describing the fluctuations of the system. Furthermore, for the WLC model our attention fall in the investigation of the forceextension curve, for which we derive new approximated expressions for a chain immersed into an external field.
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