Theory for the three-dimensional Mercedes-Benz model of water

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.

Ion pairing in molecular simulations of aqueous alkali halide solutions

Using classical molecular dynamics simulations, we study ion-ion interactions in water. We study the potentials of mean force (PMF) for the full set of alkali halide ion pairs, and in each case, we test different parameter sets for modeling both the water and the ions. Altogether, we compared 300 different PMFs. We also calculate association equilibrium constants (KA) and compare them to two types of experiments. Of additional interest here was the proposition of Collins called the "law of matching water affinities", where the relative affinity of ions in solution depends on the matching of cation and anion sizes. From observations on the relative depths of the free energies of the contact ion pair (CIP) and the solvent-shared ion pair (SIP), along with related solvent structure analyses, we find a good correlation with this proposition: small-small and large-large should associate in water, and small-large should be more dissociated.

Economic analysis in the process of the preparation of river basin management plans in Slovenia: the Drava River Basin pilot study

According to the EU Directive 2000/60/EC (Water Framework Directive, hereinafter called: WFD), several steps have to be worked out on the way towards the good water status. For this goal, some of the main elements of the river basin management plans are the programme of measures. The programme of measures has to include basic and supplementary measures. In addition, it has to check the implementation of European Directives into the national law and has to estimate the effects of these rules on the quality of the water bodies. If these regulations are not sufficient to reach the good status of water, supplementary measures have to be applied. The paper gives an overview of how basic and supplementary measures for wastewater treatment were considered in the Drava River Basin. The main stress is given to the implementation of the EU Directive 91/271/EEC (the Urban Waste Water Treatment Directive, hereinafter called: UWWTD), as part of the basic measures as defined in Annex VI of WFD and its results in the Drava River Basin.

Theoretical aspects and computer simulations of flexible charged oligomers in salt-free solutions

The structural and thermodynamic properties of a model solution containing flexible charged oligomers and an equivalent number of counterions were studied by means of the canonical Monte Carlo simulation and integral equation theory. The oligomers were represented as freely jointed chains of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions were modeled as charged hard spheres and the solvent as a dielectric continuum. Simulations were performed for a set of model parameters, independently varying the chain length and concentration of the oligomers. Structural properties in the form of pair distribution functions were calculated as functions of model parameters. In addition, thermodynamic properties such as the excess energy of solution and the excess chemical potential of counterions were obtained. These properties were correlated with the conformational averages of oligomers as reflected in the end-to-end distances and radii of gyration obtained from the simulations. The relation with the experimental data for heats of dilution and for the activity coefficient is discussed. Finally, theories based on Wertheim's integral equation approach (product reactant Ornstein-Zernike approach) [J. Stat. Phys. 42, 477 (1986)] in the so-called polymer mean spherical and polymer hypernetted chain approximations were tested against the new and existing computer simulations. For the values of parameters examined in this study, the integral equation theory yields semiquantitative agreement with computer simulations.