| dc.contributor.author | Livadaru, Lucian. | en_US |
| dc.date.accessioned | 2014-10-21T12:37:39Z | |
| dc.date.available | 2002 | |
| dc.date.issued | 2002 | en_US |
| dc.identifier.other | AAINQ75703 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55855 | |
| dc.description | In this work, we demonstrate, implement and critically assess the capabilities and the limitations of the Transfer Matrix (TM) method to the statistical mechanics of single polymer molecules within their classical models. We first show how the TM can be employed with the help of computers, to provide highly accurate results for the configurational statistics of polymers in theta-conditions. We proceed gradually from simple to complex polymer models, analyzing their statistical properties as we vary the model parameters. | en_US |
| dc.description | In the order of their complexity, the polymer models approached in this work are: (i) the freely jointed chain (FJC); (ii) the freely rotating chain (FRC); (iii) the rotational isomeric state (RIS) model with and without energy parameters; (iv) the continuous rotational potential model (for n-alkanes); (v) an interacting chain model (ICM) with virtual bonds for poly(ethylene glycol)(PEG). | en_US |
| dc.description | The Statistical Mechanics of polymer chains is carried out in both the Helmholtz and Gibbs ensembles, depending on the quantities of interest. In the Helmholtz ensemble the polymer's Green function is generally a function of both the spatial coordinates and orientations of chain bonds. In the Gibbs ensemble its arguments are the bond orientations with respect to an applied external force. This renders the latter ensemble more feasible for an accurate study of the mechanical properties of the mentioned models. | en_US |
| dc.description | We adapt the TM method to study statistical and thermodynamical properties of various models, including: chain end distribution functions, characteristic ratios, mean square radius of gyration, Kuhn length, static structure factor, pair correlation function, force-extension curves, Helmholtz and Gibbs free energies. | en_US |
| dc.description | For all cases, the TM calculations yielded accurate results for all these quantities. Wherever possible, we compared our findings to other results, theoretical or experimental in literature. A great deal of effort was focused on precise determination of the stretching response for each model for a wide range of applied external forces. A remarkable finding on the functional form of the stretching curve is the similar behavior that the FRC and the continuous rotational potential model present to the FJC model in the large-force regime, in contrast to the RIS and the ICM for PEG, which display drastic differences. We found that the latter two models, while reliable for the study of unperturbed chains, do not realistically represent polymers under the action of a strong external force. In that situation, a larger set of rotational states must be included for an accurate description. | en_US |
| dc.description | The influence of the chain length and model parameters, where applicable, on the spatial configuration of polymer chains is investigated in great detail. In the complex stages of the modeling we analyze the effects of the energy parameters incorporated in the models. We use this information to extract the Kuhn and persistence lengths and make a comparison to the Gaussian chain distribution. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 2002. | en_US |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | | en_US |
| dc.subject | Physics, Condensed Matter. | en_US |
| dc.title | Transfer matrix approach to the statistical mechanics of single polymer molecules. | en_US |
| dc.type | text | en_US |
| dc.contributor.degree | Ph.D. | en_US |
