Article

Optical Models for the Characterization of Silica Nanosphere Monolayers Prepared by the Langmuir-Blodgett Method Using Ellipsometry in the Quasistatic Regime

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Abstract

We investigated different optical models (one-layer, multilayer, parametric multilayer, and statistical parametric) for the ellipsometric characterization of thin films made of silica spheres in the diameter (D) range of 90-450 nm prepared by the Langmuir-Blodgett (LB) technique. As a continuation of a previous work (Nagy, N., et al. Langmuir 2006, 22, 8416) in terms of threshold wavelength determination and optical models, we investigated the wavelength range of the quasistatic limit (requirement for the effective medium approximation) depending onD.We compared the above models in the aspect of fit quality, stability, uncertainty of parameters, and the amount of information that can be obtained from the evaluation. Besides fundamental properties like diameter, coverage, or packing density, using sophisticated models we can also determine the size distribution of the particles. The ellipsometric results were compared with the results of dynamic light scattering and of scanning electron microscopy.

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The validity of various effective medium approximations (EMAs) (Bruggeman, Maxwell-Garnett) was studied for nanostructured systems, where the scale of inhomogeneities is comparable to the wavelength. Langmuir-Blodgett (LB) layers of Stöber silica nanospheres of diameters between 40 and 129 nm are excellent model structures for the experimental verification of the validity of the EMA methods in spectroscopic ellipsometry (SE) evaluation. Nanostructured mono- and multilayered silica films were investigated by SE and reflectance spectroscopy. The effective refractive index and film thickness were determined from the results of multiparameter fitting of SE spectra in the 300-759 nm wavelength region. The distribution of the effective refractive index in the particulate films was calculated assuming an ideal close-packed arrangement of particles. The average deviation from such a structure was deduced from the corrected model by introducing a "fill factor". In the EMA approximation, the spherical shape of the silica particle determines the optical behavior, rather than the "depth distribution" of silica or porosity. Therefore, the shape of particles has a dominant effect on the optical properties of nanoparticulate LB films.
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Stöber silica nanoparticles of diameter about 45, 60 and 100 nm and different hydrophobicity are used to produce monolayers at a water-air interface. Both the surface pressure-area isotherms and the reflectivity angle of incidence curves of the layers have been measured in a Wilhelmy film balance. The contact angle of the as-prepared particles have been determined from the isotherms by two different evaluation methods, and compared to those obtained from in situ scanning angle reflectometry (SAR) measurements. SAR is proved to be an effective tool for the estimation of contact angles on nanoparticles of different wettability, using a modified version of the previously published gradient layer model (E. Hild, T. Seszták, D. Völgyes and Z. Hórvölgyi, Prog. Colloid Polym. Sci., 2004, 125, 61, ref. 1) for evaluation. The results are in fairly good agreement with those determined from the non-dissipative part of the isotherms of the as prepared particles, assuming a weakly cohesive film model (S. Bordács, A. Agod and Z. Hórvölgyi, Langmuir, 2006, 22, 6944, ref. 2). It seems that the traditional way to calculate the contact angle from the film balance experiments (J.H. Clint and N. Quirke, Colloids Surf., A, 1993, 78, 277, ref. 3) results in unreasonably high contact angles for the investigated systems and the homogeneous layer optical model gives unrealistic film thickness values in the case of hydrophobic particles.
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