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X-ray structural analysis

Analysis of suspended layer of alkali ions on a surface of silica sol by synchrotron X-ray reflectivity and scattering


  • Yuriy VOLKOV

Primary authors



Solutions of SiO$_2$ nanoparticles (with typical diameter of 5--25 nm) in water stabilized by a small amount of alkali ions --- known as silica sols --- exhibit strong gradient of the surface potential at the sol/air interface. It has been shown previously that under such boundary conditions charged silica nanoparticles ($Qsim 1000$ $bar e$) form a macroscopically flat layer near the surface, its depth proportional to the Debye screening length within the bulk solution, while alkali cations are accumulated in a thin suspended film directly at the surface [1].

We present new systematic data on the structural properties of suspended cation layers for silica sols enriched with Na$^+$, K$^+$, Cs$^+$ and Rb$^+$ ions, based on the measurements of X-ray reflectivity (XRR), grazing-incidence diffuse scattering (XDS) and small-angle X-ray scattering (SAXS). Measurements were performed at beamline ID31 (ESRF, Grenoble) with photon wavelength $lambda = 0.1747pm 0.0003$ Å ($E approx 71$ keV), beam size $10times 250$ $mu$m, peak intensity $I_{max} sim 10^{19}$ photons/s. SAXS data were analyzed by fitting the particles' structure factors in frames of rigid spheres approximation using ATSAS software suite [2]. XRR and XDS data were analyzed in frames of a self-consistent model-independent approach [3], which allowed us to simultaneously extract depth-graded distribution of volumetric electron density $rho(z)$ as well as power spectral density functions of in-plane surface roughness $bar C(nu)$, including "hidden" M$^+$-layer/substrate interface, without any a priori assumptions on either sample internal structure or statistical properties of surface roughness.

Fitting of SAXS results indicates that characteristic diameter distributions of SiO$_2$ nanoparticles increase with dopation by Cs$^+$ and Rb$^+$ for $0.6pm 0.1$ nm compared to Na$^+$, which indicates additional adsorption of alkali ions at the nanoparticles. $rho(z)$ distributions extracted from XRR data show characteristic density peaks near external interface corresponding to the suspended ions layer with thickness $d approx 7ldots 12$ Å; estimation of two-dimensional surface concentration of ions yields $Theta = (5pm 1)cdot 10^{18}$ m$^{-2}$, which corresponds to known theoretical predictions for two-dimensional Wigner crystal [1,4]. Effective rms heights of surface roughness obtained from XDS data give $sigma = (3.0pm 0.2)$ Å within spatial frequency range $nu = 10^{-5}ldots 10^{-1}$ nm$^{-1}$, which corresponds to theoretical values in frames of capillary waves theory [5]. However, extracted power spectral density functions $bar C(nu)$ are found to diverge substantially from the capillary waves-based prediction in frequency range $nu < 10^{-4}$ nm$^{-1}$. This can be interpreted according to the "roughness scaling" model [6] as a superposition of two different roughness distribution, which indicates possible presence of at least two different structural phases across the surface.

Additionally, preliminary experiments for reproduction of a whispering gallery (WG) phenomenon on liquid silica sol has been conducted; the data obtained in the present work are planned to be applied to further quantitative assessment and modeling of X-ray wave propagation in WG case.

The present work has been supported by the Federal Agency of Scientific Organizations (Agreement No 007-ГЗ/Ч3363/26).

[1] A.M. Tikhonov // J. Chem. Phys. 130, 024512 (2009).

[2] P.V. Konarev, M.V. Petoukhov et al. // J. Appl. Cryst. 39, 277 (2006).

[3] I.V. Kozhevnikov, L. Peverini, E. Ziegler // Phys. Rev. B 85, 125439 (2012).

[4] Y. Burak, D. Andelman, H. Orland // Phys. Rev. E 70, 016102 (2004).

[5] F. Buff, R. Lovett, F. Stillinger // Phys. Rev. Lett. 15, 621 (1965).

[6] S. Majaniemi, T. Ala-Nissila, J. Krug // Phys. Rev. B 53, 8071 (1996).