Glenn H. Fredrickson
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567295
- eISBN:
- 9780191717956
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567295.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses methods for converting the many body problem in interacting polymer fluids to a statistical field theory. Auxiliary field transforms are introduced, that decouple interactions ...
More
This chapter discusses methods for converting the many body problem in interacting polymer fluids to a statistical field theory. Auxiliary field transforms are introduced, that decouple interactions among polymer species and reduce the problem to that of individual polymers interacting with one or more fluctuating fields — the subject of Chapter 3. Examples of models for a variety of systems are enumerated, including polymer solutions, blends, block and graft copolymers, polyelectrolytes, liquid crystalline polymers, and polymer brushes.Less
This chapter discusses methods for converting the many body problem in interacting polymer fluids to a statistical field theory. Auxiliary field transforms are introduced, that decouple interactions among polymer species and reduce the problem to that of individual polymers interacting with one or more fluctuating fields — the subject of Chapter 3. Examples of models for a variety of systems are enumerated, including polymer solutions, blends, block and graft copolymers, polyelectrolytes, liquid crystalline polymers, and polymer brushes.
Glenn H. Fredrickson
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198567295
- eISBN:
- 9780191717956
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567295.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and ...
More
This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and operators for polymer segment density and stress are introduced. Analytical approximation schemes for solving the Fokker-Planck equations and evaluating operators are presented. Effective numerical methods are also described, with an emphasis on spectral collocation techniques.Less
This chapter examines the subject of polymers experiencing external potential fields that vary in space. The statistical mechanical problem is reduced to the solution of Fokker-Planck equations, and operators for polymer segment density and stress are introduced. Analytical approximation schemes for solving the Fokker-Planck equations and evaluating operators are presented. Effective numerical methods are also described, with an emphasis on spectral collocation techniques.
