Bo Jönsson, Magnus Ullner, Carsten Peterson, Ola Sommelius and Bo Söderberg Titrating Polyelectrolytes -- Variational
Calculations and Monte Carlo Simulations
Journal of Physical Chemistry 100, 409-417
(1996)Abstract:Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. In the variational treatment, the Coulomb potentials are emulated by harmonic repulsive forces between all monomers; the force constants are used as
variational parameters. The accuracy of the variational
approach is tested against Monte Carlo data. Excellent
agreement is obtained for the end-to-end separation and the
apparent dissociation constant for the unscreened Coulomb
chain. The short-range screened Coulomb potential is more
difficult to handle variationally and its structural features
are less well described, although the thermodynamic
properties are predicted with the same accuracy as for the
unscreened chain. The number of variational parameters is of
the order of N^{2}, where N is of the
number of monomers, and the computational effort scales like
N^{3}. In addition, a simplified variational
procedure with only two parameters is pursued, based on a
rigid-rod approximation of the polymer. It gives surprisingly
good accuracy for certain physical properties.LU TP 95-01 |