Department of Physics, Faculty of Science, Australian National University, Canberra, Australian Capital Territory 0200, Australia
Phys. Rev. E 48, 3604-3621 (1993)
Abstract
The multicomponent primitive model electrolyte
is analyzed using the Ornstein-Zernike equation and the asymptotic
behavior of the direct correlation function. An approximation for the
screening length is derived from the second-moment condition kappa =
K_D/ sqrt 1-( K_D d)2/2+( K_D d)3/6 , where 1/K_D is the
Debye length and d is the ion diameter. This is accurate up to 1M
concentration for monovalent aqueous electrolytes and considerably
extends the range of validity of the classical Debye-Hükel theory. The
asymptotic behavior of the ionic pair correlation functions is formally
analyzed, and exact expressions are given for the decay length and the
effective charge on the ions in terms of the direct correlation
function. Three different regimes are identified: monotonic exponential,
for K_D d <~ sqrt 2, and two types of damped oscillatory,
electrostatic dominated at intermediate concentrations and core
dominated at high concentrations distinguished by whether or not the
oscillations are in charge or in number density. The electrical double
layer is also analyzed and it is shown that the asymptotic behavior of
the density profiles and the interaction pressure is the same as for the
bulk correlation functions. The hypernetted chain closure (with and
without bridge functions) is used to obtain numerical results for binary
symmetric aqueous electrolytes (monovalent with d=4 and 5 Å, and
divalent with d=4 Å), and the three asymptotic regimes are explored.
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