Binding between water and models of poly(ethylene oxide), (CH 2 -CH 2 -O) n , n ) 2-40, has been studied using the topographic features of the electrostatic potential, V(r), and standard density functional theory methods. It was found that, in general, the contour around the minima of the oxygen atoms overlap forming a negativevalued spiral coiled around a positive-valued helix. The positive zone defines a helical groove in the O-C-C-O units where minima lone pairs critical points are located. Topological analysis of the water molecule has also suggested that the attractive electrostatic effect between the positive water O-H zone and the negative PEO lone pairs plays an important role in the hydrogen bonding of the PEO-water system. Thus, the V(r) topology predicts a coil of water molecules around the PEO chain forming hydrogen bonding with two sites of ether oxygens. This coil is formed in such a way that more water molecules accumulate on the cavities surrounding the poly(ethylene oxide)'s oxygen atoms where the minima of the negative zone are located.

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The solubility parameters, δ, of several asphaltene models were calculated by mean of an atomistic NPT ensemble. Continental and archipelago models were explored. A relationship between the solubility parameter and the molecule structure was determined. In general, increase of the fused-rings number forming the aromatic core and the numbers of heteroatoms such as oxygen, nitrogen, and sulfur produces an increase of the solubility parameter, while increases of the numbers and length of the aliphatic chains yield a systematic decrease of this parameter. Molecules with large total carbon atom number at the tails, n(c), and small aromatic ring number, n(r), exhibit the biggest values of δ, while molecules with small n(c) and large n(r) show the smallest δ values. A good polynomial correlation δ = 5.967(n(r)/n(c)) - 3.062(n(r)/n(c))(2) + 0.507(n(r)/n(c))(3) + 16.593 with R(2) = 0.965 was found. The solubilities of the asphaltene models in toluene, heptane, and amphiphiles were studied using the Scatchard-Hildebrand and the Hansen sphere methodologies. Generally, there is a large affinity between the archipelago model and amphiphiles containing large aliphatic tails and no aromatic rings, while continental models show high affinity for amphiphiles containing an aromatic ring and small aliphatic chains.

Density functional theory (DFT) calculations combined with surface thermodynamic arguments and the Gibbs-Curie-Wulff equilibrium morphology formalism have been employed to explore the effect of the reaction conditions, temperature (T), and gas-phase partial pressures (p H 2 and p H 2 S ) on the stability of low Miller index ruthenium sulfide (RuS 2 ) surfaces. The calculated thermodynamic surface stabilities and the resulting equilibrium morphology models suggest that unsupported RuS 2 nanoparticles in HDS conditions are like to a polyhedron with six, eight, and twelve (100), (111), and (102) faces, respectively. The area of these faces covers about 40%, 37%, and 23% of the total particle, respectively. The atomic basins of the outermost individual atoms of the exposed surfaces were determined using the quantum theory of atoms in molecules methodology. Direct visualization of these basins has shown that a hole just at the middle of the outermost sulfur basins provides access to uncovered metal sites. Analysis of the electrostatic potential mapped onto a selected electron density isocontour (0.001 au) on the exposed surface reveals a very high potential reactivity of these holes toward electrodonating reagents. Consequently, the high attraction between these uncovered sites and S atoms coming from reagent polluting molecules makes these kinds of particles quite active for HDS catalysis.

Let H m be the space of planar homogeneous polynomial vector fields of degree m endowed with the coefficient topology. We characterize the set 0 m of the vector fields of H m that are structurally stable with respect to perturbations in H m and we determine the exact number of the topological equivalence classes in 0 m . The study of structurally stable homogeneous polynomial vector fields is very useful for understanding some interesting features of inhomogeneous vector fields. Thus, by using this characterization we can do first an extension of the Hartman Grobman Theorem which allows us to study the critical points of planar analytical vector fields whose k-jets are zero for all k