About Computational Models 

In this web site, a large variety of digital models of molecules, nanoparticles and materials is collected. Models are given as sets of coordinates of all atoms present in the nanoparticle, cluster, molecule or supercell. The models have been carefully designed and created by taking into account a large number of factors. All models can be printed using a 3D printer (preferably color 3D printer). 

Models of Nanoparticles

Nanoparticles are defined as particles of materials with their one, two or all three dimensions limited to the length elow 100 nm. There are a number of factors to consider for creating models of nanoparticles. These factors are outlines as follows. 

1.  The crystal structure of the material. For known materials, the crystal structure should be taken from the published sources. For new materials the crystal structure should be carefully elaborated. 
2. The size of the nanoparticles. Nanoparticles often have size in excess of 5 - 10 nm, and the number of atoms in such nanoparticles is beyond the capabilities of modern computational methods. Therefore, it is important to select smaller nanoparticles that adequately represent important properties of larger nanoparticles. 
3. The surfaces of the nanoparticle. During the sythesis, nanoparticles are aften prepared in amorphous state and then subjected to crystallization. Depending on conditions of synthesis and crystalization, different external facets appear in the nanoparticles, and the ratio of the different facets is different. Thus, the shape of the nanoparticles should be carefully crafted. 
4. The surface groups. The external surfaces, edges and vertices of nanoparticles often have to contain extralattice atoms and functional groups. For example, nanoparticles of titanium dioxide of anatase phase always have to have surface groups to keep the valent state of titanium (IV). Additionally, surface hydroxyl groups are always present in oxide nanoparticles prepared in aqueous systems. Some other surface groups can be introduced intentionally for tailoring the properties of the material. 

Therefore, creation of elaborate models of nanoparticles is a multistep task that requires significant time and experience. However the resultant models bring a lot of new exciting insights into the properties of nanosized objects. 

Models of bulk materials

Materials with a large size of particles or that form macroscopic objects can be modelled using cluster models or periodic models. The cluster models generally resemble models of nanoparticles. However, they can be crafted to possess some predominant facets that are of interest for a given investigation. 

Periodic models are fragments of bulk material that contain one or more unit cells of the crystal lattice. Such periodic models are called supercells. During the process of modeling, the supercell is treated with periodic boundary conditions (PBC) that actually mean that opposite sides of the supercell are considered connected. In designing the supercell models, the following factors are important. 

1. The crystal structure of the material. 
2. The size and shape of the supercell. 
3. Surface groups in the pores of the material. 
4. Dopants and their locations. 

As one can see, modeling using PBC is usually an easier task. However, the precision of the planewave approximation involved in the PBC DFT computations is usually significantly smaller than the precision of non-periodic DFT computations. 

The digital computational models on sale in this web site are 3D printable. Color 3D printer is most suitable for printing of models since different atoms should be printed in different color.

Selected Materials

Titanium Dioxide TiO₂

Titanium dioxide in its pristine form is a white powder. There are three major crystallographic modifications (phases) of TiO₂: anatase, brookite and rutile. Besides, there are several less known crystal phases. 

Anatase has a tetragonal lattice  with the following parameters:

a = b = 3.785 Å, c = 9.513 Å, α = β = γ = 90°  

Titanium dioxide in anatase phase can have a variety of facets on its surface. Most thermodynamically stable surfaces are {101}, {001} and {100}. The last surface is equivalent to surface {010} because of the symmetry of the unit cell of crystal lattice. 

Titanium dioxide is produced worldwide in million tons quantity each year. Its major applications include pigment filling in paints, colorant in plastics, pharmaceutical products, toothpaste and other materials, light absorbing material component in dye sensitized solar cells, catalysis in various sensors, photocatalysis for air purification and self-cleaning surfaces. 

The research on titanium dioxide is important because its properties depend strongly on particles phase, size, shape, doping, defects and surface groups.