F Rother et al 1997 J. Phys. A: Math. Gen. 30 2669 doi:10.1088/0305-4470/30/8/014
Crossover from the dilute to the dense phase for self-repelling polymer chains: finite size effects and relation to zero-component Landau - Ginzburg - Wilson theory
F Rother
, L Schäfer and P Grassberger
Using a recently established perturbative approach we analyse a single polymer chain or a few chains floating in a good solvent contained in a finite box with periodic boundary conditions. We calculate to one-loop order the partition function and the equation of state relating segment concentration to segment chemical potential 
, and we discuss in detail the chain length distribution for a `field theoretic' ensemble of chains characterized by fixed . Our results obey finite size scaling and cover the whole crossover from the dilute 
to the dense 
limit, where 
is the critical chemical potential. The different limits evolve smoothly from one another. The theoretical results for the chain length distribution are compared with Monte Carlo simulations of self-avoiding walks on a cubic lattice. We find a good agreement between our results and the simulation data.
- PACS
-
61.25.H- Macromolecular and polymers solutions; polymer melts
05.70.Jk Critical point phenomena
- MSC
-
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
-
Soft matter, liquids and polymers
- Dates
-
Issue 8 (21 April 1997)
Received 28 November 1996
-
Crossover from the dilute to the dense phase for self-repelling polymer chains: finite size effects and relation to zero-component Landau - Ginzburg - Wilson theory
F Rother et al 1997 J. Phys. A: Math. Gen. 30 2669
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