Carsten Peterson, Ola Sommelius and Bo Söderberg Scaling and Scale-Breaking in
Polyelectrolytes Journal of Chemical
Physics 105, 5233-5241 (1996)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-neighbour interaction the scaling is restored, making possible an efficient blocking method for emulating very large polyelectrolytes using small systems. The high temperature behaviour 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 the end-to-end distance. This window
corresponds to situations where the range of the potential
interpolates between the bond length and the size of the
chain. This scaling behaviour, which is verified by Monte
Carlo results, is 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.LU TP 95-25 |