No abstract

The paper is concerned with the investigation of dental caries treatment by the modern method based on the application of special composite material that can diffuse into the damaged zone, harden by light and prevent tooth decay. Carious disease was modeled as a diffusion process of acid penetration from the oral cavity into the tooth enamel with further dissolution of dental hard tissues in the subsurface layer of enamel. The model of dental caries was mathematically formulated. The solution was obtained by a numerical method using MATLAB. It is shown that the proposed model adequately describes the properties of the examined dental system.

Using atomic force microscopy in the semicontact AFM mode, we examined the surface of the filled elastomer obtained by the rupture method. A feature of the material is that it consists of a soft binder and hard nanofiller particles. Filler particles are usually hidden by a binder layer. In our work, we have shown that the information on the phase shift obtained during scanning makes it possible to look into the subsurface layer and obtain more information about the geometry of the filler particles and their location in the nanocomposite. It is possible to make visible the fragments of particles immersed in the binder, which are almost invisible on the surface relief. This does not require the use of special modes of the atomic force microscope for analysis. It is enough to use the reliable and fast scanning method in semicontact mode.

The authors call for attention to the specifics of conducting experiments on nanoindentation of soft materials (elastomers, polymers), the features of the experimental setup, the material itself, the interaction of the material under study with the scanning elements of the setup, and environmental conditions. The paper shows which of them require to be taken into account in mathematical models, and which can be neglected, or can be almost completely compensated for by others. The following topics are considered: influence of cantilever bending and its inclination, humidity, plasticity, and viscosity, probe jump to the surface, determining the radius of the probe tip curvature, plastics, destruction of the sample during double indentation, size (scale) effect, sample drift, preservation of the probe shape before and after the experiment, time-varying surface properties, and surface energy during contact formation. This work is intended both to simplify further research and to focus efforts on solving acute problems.

A new method of processing of data obtained using atomic force microscopy (AFM) in the oscil-lating nanoindentation mode is proposed. The model of the AFM probe on elastic beam (canti-lever) interaction with a sample is developed. In addition to the static load, applied on a base of the cantilever, a force modulation, according to a harmonic law, is set. This approach makes possible to take into account not only the force of the probe-material interaction but also the phase shift of the cantilever oscillations with respect to a given harmonic signal on the cantilever base as well as the amplitudes ratio of these oscillations. This information allows the presence of the viscosity in the material evaluating. The advantage of the oscillatory regime over quasistatic indentation was shown. It consists in the possibility to exclude the influence of irreversible pro-cesses (plastic, brittle fracture in the material) on the result of the experiment and to reveal the presence of the time dependent behavior. It is shown that the model contains a small amount of constants; methods for their determination are proposed. The calculations, performed using the developed model, made it possible to make a number of recommendations on choosing the can-tilever stiffness to obtain the most informative experimental results. This approach seems per-spective in studying materials with a high degree of stiffness inhomogeneity, including the deter-mination of the local properties of filled nanocomposites near filler particles.