Debye–Hückel theory of model polyelectrolytes

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Abstract
We use the superposition principle and suitable expansions to derive the exact Coulomb and Debye–Hückel screened potentials of certain discrete, periodic, charge distribution modeling real extended polyions. Using these potentials, we extend the range of validity of the Debye–Hückel condensation theory of Manning to higher mobile ion concentrations where consideration of ionic size and the specific polyion structure leads to explicit corrections of the limiting law results. It is found that, in the limit of infinite dilution and as far as colligative properties are concerned, all extended polyions of interest are satisfactorily modeled by the simple continuously charged straight line picture introduced by Manning. This should not be the case in applications, where the polyion potential enters directly (e.g., NMR spectroscopy). The range of the validity of the Debye–Hückel condensation approach is estimated through comparison with some typical experimental data.