The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav–Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned microporous polymer surfaces obtained by the breath figure method and levitating ordered water microdroplet clusters.

We report the negative effective mass metamaterials based on the electro-mechanical coupling exploiting plasma oscillations of free electron gas. The negative mass appears as a result of the vibration of a metallic particle with a frequency ω which is close to the frequency of the plasma oscillations of the electron gas $m_2$, relative to the ionic lattice $m_1$. The plasma oscillations are represented with the elastic spring constant $k_2={\omega }_p^2{m}_2$, where ${\omega }_p$ is the plasma frequency. Thus, the metallic particle vibrating with the external frequency ω is described by the effective mass $m_{eff}=m_1+\frac{m_2{\omega }_p^2}{{\omega }_p^2-{\omega }^2}$, which is negative when the frequency $\omega$ approaches ${\omega }_p$ from above. The idea is exemplified with two conducting metals, namely Au and Li embedded in various matrices. We treated a one-dimensional lattice built from the metallic micro-elements $m_{eff}$ connected by ideal springs with the elastic constant $k_1$ representing various media such as polydimethylsiloxane and soda-lime glass. The optical and acoustical branches of longitudinal modes propagating through the lattice are elucidated for various ratios $\frac{{\omega }_1}{{\omega }_p}$, where ${\omega }_1^2=\frac{k_1}{m_1}$ and $k_1$ represents the elastic properties of the medium. The 1D lattice, built from the thin metallic wires giving rise to low frequency plasmons, is treated. The possibility of the anti-resonant propagation, strengthening the effect of the negative mass occurring under ω = ω_p = ω₁, is addressed.

Hierarchical honeycomb patterns were manufactured with breath-figures self-assembly by drop-casting on the silicone oil-lubricated glass substrates. Silicone oil promoted spreading of the polymer solution. The process was carried out with industrial grade polystyrene and polystyrene with molecular mass $M_w=35,000\frac{g}{mol}$ . Both polymers gave rise to patterns, built of micro and nano-scaled pores. The typical diameter of the nanopores was established as 125 nm. The mechanism of the formation of hierarchical patterns was suggested. Ordering of the pores was quantified with the Voronoi tessellations and calculation of the Voronoi entropy. The Voronoi entropy for the large scale pattern was $S_{vor}=0.6-0.9$ , evidencing the ordering of pores. Measurement of the apparent contact angles evidenced the Cassie-Baxter wetting regime of the porous films.

The Voronoi entropy for random patterns and patterns demonstrating various elements of symmetry was calculated. The symmetric patterns were characterized by the values of the Voronoi entropy being very close to those inherent to random ones. This contradicts the idea that the Voronoi entropy quantifies the ordering of the seed points constituting the pattern. Extension of the Shannon-like formula embracing symmetric patterns is suggested. Analysis of Voronoi diagrams enables the elements of symmetry of the patterns to be revealed.

The authors analyzed the motion of diamagnetic bodies that float on diamagnetic liquids. The motion was inspired by the deformation of the diamagnetic liquid surface by a magnetic field, called the ‘Moses effect’. The influence of the surface tension on the shape of the well pushed out by the steady magnetic field (B ≅ 0·35T) acting on the surface of the liquid was studied both experimentally and theoretically for water, silicone oil and aqueous surfactant solution. The suggested mathematical approach accurately predicted the shape of the well, depending on the surface tension of the liquid. Qualitative analysis is reported regarding the motion of floating diamagnetic polymers and metallic objects driven by the Moses effect. The impact of the bulk magnetic force on the motion is minor for all of the studied diamagnetic rafts. The influences of gravity and interfacial forces on the displacement of rafts may be of a comparable order of magnitude.

The impact of the Corona, dielectric barrier discharge, and low pressure radiofrequency air plasmas on the chemical composition and wettability of medical grade polyvinylchloride was investigated. Corona plasma treatment exerted the most pronounced increase in the hydrophilization of polyvinylchloride. The specific energy of adhesion of the pristine and plasma-treated Polyvinylchloride (PVC) tubing is reported. Plasma treatment increased markedly the specific free surface energy of PVC. The kinetics of hydrophobic recovery following plasma treatment was explored. The time evolution of the apparent contact angle under the hydrophobic recovery is satisfactorily described by the exponential fitting. Energy-dispersive X-ray spectroscopy of the chemical composition of the near-surface layers of the plasma-treated catheters revealed their oxidation. The effect of the hydrophobic recovery hardly correlated with oxidation of the polymer surface, which is irreversible and it is reasonably attributed to the bulk mobility of polymer chains.