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Scaling and scale breaking in polyelectrolytes

Peterson, Carsten LU ; Sommelius, Ola LU and Söderberg, Bo LU (1996) In Journal of Chemical Physics 105(12). p.5233-5241
Abstract

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest-neighbor interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behavior is well reproduced by the analytical high-T expansions even for fairly low temperatures and system sizes. In... (More)

We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest-neighbor interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behavior is well reproduced by the analytical high-T expansions even for fairly low temperatures and system sizes. In addition, results from low-T expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for conformational as well as thermodynamical properties. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behavior, which is verified by Monte Carlo results, is, for the end-to-end distance, consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-T expansion is inaccurate at realistic temperatures. © 1996 American Institute of Physics.

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published
in
Journal of Chemical Physics
volume
105
issue
12
pages
9 pages
publisher
American Institute of Physics
external identifiers
  • scopus:0030244701
ISSN
0021-9606
language
English
LU publication?
yes
id
3235d2fe-96c3-4a75-b996-cd6555f29f56
date added to LUP
2016-10-03 19:18:07
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2017-01-18 14:15:31
@article{3235d2fe-96c3-4a75-b996-cd6555f29f56,
  abstract     = {<p>We consider the thermodynamics of a uniformly charged polyelectrolyte with harmonic bonds. For such a system there is at high temperatures an approximate scaling of global properties like the end-to-end distance and the interaction energy with the chain length divided by the temperature. This scaling is broken at low temperatures by the ultraviolet divergence of the Coulomb potential. By introducing a renormalization of the strength of the nearest-neighbor interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behavior is well reproduced by the analytical high-T expansions even for fairly low temperatures and system sizes. In addition, results from low-T expansions, where the coefficients have been computed numerically, are presented. These results approximate well the corresponding Monte Carlo results at realistic temperatures. A corresponding analysis of screened chains is performed. The situation here is complicated by the appearance of an additional parameter, the screening length. A window is found in parameter space, where scaling holds for conformational as well as thermodynamical properties. This window corresponds to situations where the range of the potential interpolates between the bond length and the size of the chain. This scaling behavior, which is verified by Monte Carlo results, is, for the end-to-end distance, consistent with Flory scaling. Also for the screened chain a blocking approach can be devised, that performs well for low temperatures, whereas the low-T expansion is inaccurate at realistic temperatures. © 1996 American Institute of Physics.</p>},
  author       = {Peterson, Carsten and Sommelius, Ola and Söderberg, Bo},
  issn         = {0021-9606},
  language     = {eng},
  number       = {12},
  pages        = {5233--5241},
  publisher    = {American Institute of Physics},
  series       = {Journal of Chemical Physics},
  title        = {Scaling and scale breaking in polyelectrolytes},
  volume       = {105},
  year         = {1996},
}