The fluid of two-dimensional hard disks is investigated over a range of densities by Monte Carlo simulations in order to detect and characterize structural changes which take place when the condition of freezing and melting is approached. A novel method is proposed based on the use of the Voronoi tessellation and a certain shape factor which turns out to be a clear indicator of the presence of different underlying substructures (domains). Close to the freezing condition the probability distribution of the shape factor develops a second distinct maximum corresponding to a predominant presence of near-regular hexagons, whereas the original peak, having its origin primarily in pentagons and distorted hexagons, diminishes and disappears at melting density.

We report results of a systematic and extensive study on the orientational structure of water molecules in the vicinity of apolar solutes of varying size in infinitely diluted aqueous solutions at ambient conditions. A wide range of sizes of the solute, modelled as a Lennard–Jones particle, has been considered including also the limiting case of a smooth planar wall (i.e. a solute of an infinite diameter). Both the bivariate and monovariate angle distributions are used to describe the orientation of water molecules. It is demonstrated that the commonly used latter method may lead to misleading or even erroneous conclusions. It is found that all three considered models of water, SPC/E, TIP4P and TIP5P, exhibit, unlike some simplified models, qualitatively the same behaviour, i.e. with increasing size of the solute only the water molecules in closest proximity of the solute adopt orientations which sacrifice a possible hydrogen bond, whereas the preferred orientation of water molecules farther from the surface, but yet belonging to the first solvation shell, is independent of the solute size.

We examine different spanning probability functions (wrapping and crossing) near the percolation threshold of a supercritical square-well fluid and determine the threshold values of these probabilities, which may be universal for all fluids. It is shown that for a continuous system, over a wide range of system size, the wrapping probabilities can be described by universal scaling functions, whereas the crossing probabilities do not show such universal behavior over the same range of system size. The obtained universal functions for the wrapping probabilities can be used for an estimation of the percolation threshold in fluids in general. The results for the crossing probabilities allow us then to characterize large clusters in real fluids.

We demonstrate improved computational efficiencies of Monte Carlo (MC) simulations for polarisable force fields by implementing the multi-particle-move MC (MPM-MC) method [Moučka F, Rouha M, Nezbeda I. Efficient multiparticle sampling in Monte Carlo simulations on fluids: application to polarizable models. J Phys Chem. 2007;126:224106]. Force bias and smart alternatives along with the Ewald summation and generalised reaction field have been considered and tested for both pure polarisable water models and polarisable aqueous electrolytes. For water, we consider the recently developed Baranyai–Kiss force field [A transferable classical potential for the water molecule. J Chem Phys. 2010;133:144109] and the SWM4-DP force field of Lamoureux et al. [A simple polarizable model of water based on classical Drude oscillators. J Chem Phys. 2003;119:5185], and for electrolytes the polarisable AH/SWM4-DP force field associated with the SWM4-DP solvent. These force fields incorporate polarisability as a charge-on-spring model, and the Baranyai–Kiss model incorporates charges in the form of a Gaussian distribution instead of point charges. For neat water, in addition to calculating the standard thermodynamic properties and water structure and comparing our results with those obtained from standard molecular dynamics simulations, we also investigate its vapour–liquid equilibrium properties. For aqueous electrolyte solutions, we study NaCl at ambient conditions and calculate its density and chemical potential as a function of concentration, representing apparently the first such simulation results using these polarisable models at finite concentrations. Our results demonstrate that MC simulations can be efficiently performed on polarisable models if the MPM method is incorporated.