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Stuart Whittington

Stuart Whittington

Academic Title: Emeritus Professor

Phone: 416-978-5287

Office: LM 421D

Email:

Research Homepage: http://www.chem.utoronto.ca/~swhittin/

Research

Linear and branched polymer molecules in solution are highly flexible and the prediction of their average conformations using statistical mechanical models is a challenging task. The large-scale properties can be captured in lattice models, and these have two advantages. They can be treated, to some extent, by rigorous combinatorial methods, and also investigated numerically using both Monte Carlo methods and exact enumeration and series analysis approaches. Our group is active in each of these areas.

If the solvent quality is varied the polymer can undergo a collapse transition to a ball or globule, and this has been observed experimentally for the linear case. The theoretical treatment of this transition has attracted a lot of attention, and we are very involved in this area of research. Our other main focus is on topological problems in polymers. Linear polymers are highly self-entangled and these entanglements can be captured as a knot when the polymer undergoes a ring closure reaction. The investigation of the extent of self-entanglement, and how it affects polymer properties, is a central feature of our research.

We are also examining models of random and periodic copolymers. In the periodic case interest focusses on how the copolymer behaves (for instance when it adsorbs or collapses) compared to the corresponding homopolymers. If the copolymer is random, then there are interesting questions about how the properties depend on the particular random sequence of monomers in a copolymer molecule, and how the properties for a particular (randomly chosen) sequence differ from the averages over all sequences. One can show that certain models self-average, ie almost all sequences have certain properties very close to the average value, when the polymer is very long.

Selected Publications

E. Orlandini and S.G. Whittington, Statistical topology of closed curves: Some applications to polymers, Reviews of Modern Physics 79, 611-642 (2007)

R. Martin, E. Orlandini, A.L. Owczarek, A. Rechnitzer and S.G. Whittington, Exact enumeration and Monte Carlo results for self-avoiding walks in a slab, J. Phys. A: Math. Theor. 40, 7509-7521 (2007)

S.G. Whittington, Randomly coloured self-avoiding walks: Adsorption and Localization, Markov Processes Relat. Fields 13, 761-776 (2007)

E.J. Janse van Rensburg, E. Orlandini, M.C. Tesi and S.G. Whittington, Knotting in stretched polygons, J. Phys. A: Math. Theor. 41, 015003 24pp (2008)

E.J. Janse van Rensburg, E. Orlandini, M.C. Tesi and S.G. Whittington, Knot probability of polygons subjected to a force: a Monte Carlo study, J. Phys. A: Math. Theor. 41, 025003 13pp (2008)

J. Alvarez, E.J. Janse van Rensburg, C.E. Soteros and S.G. Whittington, Self-avoiding polygons and walks in slits, J. Phys. A: Math. Theor. 41, 185004 21pp (2008)

R. Brak, P. Dyke, J. Lee, A.L. Owczarek, T. Prellberg, A. Rechnitzer and S.G. Whittington, A self-interacting partially directed walk subject to a force, J. Phys. A: Math. Theor. 42, 085001 30pp (2009)

J. Alvarez and S.G. Whittington, Force-extension relations for adsorbing polymers subject to a force, J. Stat. Mech. P04016 26pp (2009)

S.G. Whittington, Almost unknotted embeddings of graphs and surfaces, Bussei Kenkyu 92, 11-15 (2009)