Luc Belloni

Electrolytes at interfaces: accessing the first nanometers using X-ray standing waves

Ion-surface interactions are of high practical importance in a wide range of technological, environmental and biological problems. In particular, they ultimately control the electric double layer structure, hence the interaction between particles in aqueous solutions. Despite numerous achievements, progress in their understanding is still limited by the lack of experimental determination of the surface composition with appropriate resolution. Tackling this challenge, we have developed a method based on X-ray standing waves coupled to nano-confinement which allows the determination of ion concentrations at a solid-solution interface with a sub-nm resolution. We have investigated mixtures of KCl/CsCl and KCl/KI in 0.1 mM to 10 mM concentrations on silica surfaces and obtained quantitative information on the partition of ions between bulk and Stern layer as well as their distribution in the Stern layer. Regarding partition of potassium ions, our results are in agreement with a recent AFM study. We show that in a mixture of KCl and KI, chloride ions exhibit a higher surface propensity than iodide ions, having a higher concentration within the Stern layer and being on average closer to the surface by ≈1-2 Å, in contrast to the solution water interface. Confronting such data with molecular simulations will lead to a precise understanding of ionic distributions at aqueous interfaces.

Finite-size corrections in simulation of dipolar fluids

Monte Carlo simulations of dipolar fluids are performed at different numbers of particles N = 100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,Ω) is accumulated in terms of projections gmnl(r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominates in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals, and bridge functions can be derived from box sizes as small as N ≈ 100, even with existing long-range tails. In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the 1/N dependence of the gmnl(r) is shown to disagree with the, yet well-accepted, prediction of the literature.

Exact molecular direct, cavity, and bridge functions in water system

The exact molecular bridge function of the extended simple point charge model of liquid water at room temperature is extracted from Monte Carlo (MC) simulation data. The projections gμνmnl(r) onto rotational invariants of the highly directional pair distribution function g(r,Ω) are accumulated during simulation performed with N = 512 molecules (cubic box size L ≈ 25 Å). Making intensive use of anisotropic integral equation techniques, the molecular Ornstein-Zernike equation fed with the MC data available at short distances and completed beyond L/2 with the hypernetted chain closure valid at long distances is then inverted in order to derive on the whole r range the direct correlation function cμνmnl(r), the cavity function yμνmnl(r), the negative excess potential of mean force lnyμνmnl(r), and, finally, the holy grail in such liquid state theory, the bridge function bμνmnl(r) projections. For completeness, the short distance domain inside the soft core can be reached, thanks to the use of a specially designed anisotropic finite potential which replaces the true one between a single pair of molecules in the simulation. The final bridge function b(r,Ω) of bulk water presents strong, non-universal directional features and can now serve as a reference for approximated bridge functions or functionals in liquid physics of aqueous solvents and solutions.

What Does Second Harmonic Scattering Measure in Diluted Electrolytes

We derive a theoretical expression of the second harmonic scattering signal in diluted electrolytes compared with bulk water. We show that the enhancement of the signal with respect to pure water observed recently for electrolytes at very low dilution in the micromolar range is a mere manifestation of the Debye screening that makes the infinite-range dipole-dipole solvent correlations in 1/ r3 disappear as soon as the ionic concentration becomes finite. In q space, this translates into a correlation function having a well known singular behavior around q = 0, which drives the observed ionic effects. We find that the signal is independent of the ion-induced long-range behavior of the function ⟨cos ϕ( r)⟩ that has been recently discussed. We find also that the enhancement depends on the experimental geometry and occurs only for in-plane polarization detection, as observed experimentally. On the contrary, the measured isotope effect between light and heavy water cannot be fully explained.

Screened Coulombic Orientational Correlations in Dilute Aqueous Electrolytes

The ion-induced long-range orientational order between water molecules recently observed in second harmonic scattering experiments and illustrated with large scale molecular dynamics simulations is quantitatively explained using the Ornstein-Zernike integral equation approach of liquid physics. This general effect, not specific to hydrogen-bonding solvents, is controlled by electroneutrality conditions, dipolar interactions, and dielectric+ionic screening. As expected, all numerical theories recover the well-known analytical expressions established 40 years ago.

Finite-size corrections in numerical simulation of liquid water

Monte Carlo (MC) simulations of the SPC/E liquid water model are performed at two numbers of molecules N = 100 and 512 and in canonical NVT, isobaric NPT, and grand canonical μVT ensembles. The molecular non-spherically symmetric pair distribution function g(r, Ω) (pdf) is accumulated in terms of projections gμνmnl(r) onto rotational invariants. The precisely measured differences between N values and between ensembles are in very good agreement with the theoretical predictions for the expected finite-size corrections of different origins: (1) the canonical simulation is affected by explicit corrections due to the absence of density fluctuations. Beyond the well-known shift in the long-range asymptote, all projections exhibit rich short-range contributions. These corrections vanish exactly in the isobaric ensemble provided that the pdf is constructed using the rigorous definition. (2) In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the disagreement with the prediction of the literature, already noticed recently for dipolar fluids, is confirmed in the present site-site model. (3) The implicit corrections originate from the coupling between the environment around a given particle and that around its periodic images in the neighboring cells. The recent, powerful MC/HNC mixed integral equation, which offers a complete and exact description of the molecular correlations in the whole real and Fourier spaces, enables us to quantify the observed N-dependence in the pdf projections down to the sub 10-3 levels.