arXiv subjects

C. Peterson

Publications and source records attributed to C. Peterson.

21 records · Page 2Linked to original sources

arXiv1995

A Blocking Technique for Emulating Very Large Polyelectrolytes

A new Monte Carlo method for computing thermodynamical properties of very large polyelectrolytes is presented. It is based on a renormalization group relating the original polymer to a smaller system, where in addition to the naively rescaled forces, a corrective nearest-neighbor interaction originating from the short distance Coulomb cutoff is introduced. The method is derived for low T but is in the unscreened case valid for all T. Large polymers with N monomers are emulated by Monte Carlo calculations on smaller systems, K=N/Q. The computational gain of the method is Q^3. It is explored with emphasis on room temperature. Results for N=10000 are presented.

chem-ph↗

arXiv1995

Titrating Polyelectrolytes - Variational Calculations and Monte Carlo Simulations

Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being used as variational parameters to minimize the free energy. For the titrating charges, a mean field approach is used. The accuracy is tested against Monte Carlo data for up to 1000 monomers. For an unscreened chain, excellent agreement is obtained for the end-to-end distance and the apparent dissociation constant. With screening, the thermodynamical properties are invariably well described, although the structural agreement deteriorates. A very simple rigid-rod approximation is also considered, giving surprisingly good results for certain properties.

chem-ph↗

arXiv1993

A Variational Approach to the Structure and Thermodynamics of Linear Polyelectrolytes with Coulomb and Screened Coulomb Interactions

A variational approach is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing monomer-monomer force constants as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N^3. The method has the additional advantage that the entropy is easily computed. An analysis of the high and low temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities. The accuracy of the approximations introduced are tested against Monte Carlo simulations for problem sizes ranging from N=20 to 1024. Very good performance is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the isotropic Gaussian Ansatz becomes less efficient with shorter range interactions. As a by-product a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes - 2048 monomers.

hep-lat↗