Dressed ion theory for bulk symmetric electrolytes in the restricted primitive model

Abstract

The correlation functions of bulk symmetric electrolytes in the restricted primitive model are analyzed using the formalism of the dressed ion theory of Kjellander and Mitchell [Chem. Phys. Lett. 200, 76 (1992), J. Chem. Phys. 101, 603 (1994)]. An important result of this analysis is that the exact theory for the pair correlation functions can be cast in a form that is virtually identical to that of the Debye–Hückel theory provided one uses the renormalized charges of the ions—‘‘dressed ions’’—instead of bare ion charges. In the current work the (state dependent) charges of these dressed ions are investigated using the HNC approximation. The asymptotic decay of the pair correlation functions are analyzed in terms of the effective point charges of the ions and the effective permittivity of the electrolyte solution, concepts which are given rigorous and physically transparent definitions in the dressed ion theory. Several transitions between regimes with different qualitative behavior of the pair correlation functions are demonstrated, in addition to the well-known transition between monotonic and oscillatory damped decay. By means of an analysis of the singularities of the correlation functions in complex Fourier space, dressed ion theory provides a general method to determine these transitions from numerical pair correlation data and in this paper results are given for symmetric electrolytes with monovalent and divalent ions.

Screening and asymptotic decay of pair distributions in asymmetric electrolytes

“…This situation has been found for 2:2 electrolytes at moderately high concentrations. 26 If the electrolyte is charge symmetric but has slightly different short-range interactions between the different ionic species, d Q is nearly zero at the poles that correspond to those where d Q is identically zero in the totally symmetric case. When such a pole is leading, h NN (r) dominates in h i j (r) for large r. This is the case of dominance of number correlations discussed by Carvalho and Evans.…”

“…Such a relationship had previously been found in approximate theories. 6,24 Detailed studies of the decay behavior in symmetric binary electrolytes in the bulk have been carried out by Ennis and co-workers, 25,26 Carvalho and Evans, 27 and Attard. 28 Carvalho et al also studied the charge-symmetric but sizeasymmetric electrolyte.…”

The decay of pair correlation functions in ionic fluids: A dressed ion theory analysis of Monte Carlo simulations

“…At sufficiently high concentrations a second pole of ĥ QQ (k) at kϭiЈ will become important for the long-range correlations. If we include the term associated with this second pole the asymptotic expression for the charge-charge fluctuations h QQ (r) for dilute RPM electrolytes is 9,13 …”

“…͑22͒ somewhat by using simple tricks like the following tail correction. 13 Provided h QQ 0 (r) ϳC exp(Ϫ␥r)/r for large r, where C and ␥ are constants, the tail contribution of the integral can be approximated as the analytic integral I tail ϭC ͵ r cut ϱ dr exp͑Ϫ␥r ͒sinh͑ r͒, ͑A4͒…”

“…1,2,6-13 The numerical results of these studies have, however, been restricted to various approximations. [6][7][8][9][10][11][12][13] In this work we extract decay parameters of various ionion correlation functions from radial distributions calculated via Monte Carlo simulations of size-symmetric 1:1, 1:2, and 2:2 electrolytes in the primitive model. The motivation for this is partly to investigate how decay parameters can be extracted from simulations, partly to compare the results from the simulations with theoretical predictions and numerical results from calculations using the hypernetted chain ͑HNC͒ approximation.…”