Аннотация
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 on the order of N-2,
where N is 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.
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