Electrical double layers in aqueous solvent

Early in the '80s, using the just constructed surface force apparatus, Pashley and Israelachvili began accumulating accurate data on electrical double layer repulsion between charged mica surfaces in different electrolyte solutions. Many aspects of the data were readily explained with the DLVO theory, other required accurate solutions of the primitive model for the double layer [1]. However, at higher electrolyte concentrations surface force apparatus data showed strong, oscillatory short-range repulsion that was interpreted as an effect of the hydration structure surrounding the ions [2]. It was called the "hydration force" and it did not correspond to any theory. The failure of the theory could easily be traced to the neglect of the molecular nature of solvent.

In order to understand the anomalies in double layer interaction at small surface separations ("the hydration force") we need to explicitly consider the effect of the solvent [3]. An exact theory at the Born-Oppenheimer level was formulated [4] by constructing electrical double layers in two separate steps that later lead to convenient and accurate approximations: (i) a reference system consisting of solvent between the surfaces, and (ii) ions interacting with other ions and with surfaces via the potentials of mean force evaluated in the reference system. The mapping is achieved by extending the McMillan-Mayer transformation to the nonuniform fluid between the surfaces. The results indicate approximate additivity of short- and long-range effects in ion density and pressure, as observed earlier in numerical work. After two approximation steps, we arrive at a practical and accurate method for calculating properties of planar aqueous double layers. Numerical results provide new understanding of the Stern layer and the hydration force.

Initial state: background water or electrolyte   Uncharged surfaces are introduced and nonuniform reference state forms between the surfaces. Pressure in the reference state resulting from short-range interactions is additive to the ionic pressure calculated in step 3. Surfaces are charged forming full double layer. Ionic pressure is approximately calculated using potentials of mean force or effective potentials calculated at finite salt concentration.

To perform practical calculations, the last step requires use of a pairwise potential approximation. Working with aqueous solvent becomes very similar to the calculations in the primitive model. Ion-ion potential and ion-surface potential enter as the respective potentials of mean force calculated in the uncharged reference system, and pressure in the reference system is added to the total pressure.

Examples from Refs. [5] and [6]:

Short-range part of the effective potential between two Na+ ions in the solution	Free energy of interaction of charged mica surfaces. The measurements are compared with the theory described above. Simulation data on ion-surface interaction that are required for more accurate calculation are still not available.

Compared to the Poisson-Boltzmann equation, calculations that include the oscillatory short-range part of the effective potential between the ions indicate higher counterion density near a surface and hence a more effective screening of the surface charge. Counterions near a surface preferably assume separations corresponding to the minima of the mutual potential. This denser layer of favourably packed hydrated counterions (called the Stern layer or the Manning condensed layer in colloid science and polyelectrolyte work respectively) extends some 6-7 Å away from the surface and causes the apparent reduction of the surface charge or surface potential. If surface separations are decreased to about 14 Å, denser surface layers come into contact resulting in stronger repulsion that resembles a distinct new force. The present accuracy in force calculation needs improvement, but it appears that at short separations the pressure returns to the level expected without hydration, rather than showing additional hydration repulsion.

1. R. Kjellander and S. Marcelja, Inhomogenous Coulomb fluids with image interactions between planar surfaces, Journal of Chemical Physics 82 (1985) 2122-2135.
2. R. M. Pashley and J. N. Israelachvili, Molecular layering of water in thin films between mica surfaces and its relation to hydration forces, J. Colloid Interface Sci. 101 (1984) 511-523.
3. S. Marcelja, Hydration in electrical double layers, Nature (London) 385 (1997) 689-690.
4. S. Marcelja, Exact description of electrical double layers, Langmuir, 16 (2000) 6081-6083; 50 free electronic reprints are available from Langmuir at http://pubs.acs.org/reprint-request?la000266j/z7ko
5. R. Kjellander, A. Lyubartsev and S. Marcelja, Calculation of pressure in electrical double layers, Journal of Chemical Physics 114 (2001) 9565-9577.
6. S. Marcelja, Short-range forces in surface and bubble interaction, Current Opinion in Colloid and Interface Science 9 (2004) 165-167
   
   

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8/3/2005