Rosa Ramirez

Coefficient of restitution of colliding viscoelastic spheres.

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution epsilon depends on the impact velocity g as epsilon=1-gamma(1)g(1/5)+gamma(2)g(2/5)-/+..., in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients gamma(1) and gamma(2). Using these and few next expansion coefficients for epsilon(g) we construct a Padé approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence epsilon(g) for ice particles.

Thermal convection in fluidized granular systems

Thermal convection is observed in molecular dynamic simulations of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a square box. Boundaries introduce no shearing or time dependence, but the energy injection comes from a slip (shear-free) thermalizing base. The top wall is perfectly elastic and lateral boundaries are either elastic or periodic. The spontaneous temperature gradient appearing in the system due to the inelastic collisions, combined with gravity, produces a buoyancy force that, when dissipation is large enough, triggers convection.

Molecular density functional theory of solvation: From polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.

Molecular density functional theory: application to solvation and electron-transfer thermodynamics in polar solvents.

A molecular density functional theory of solvation is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position- and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, the unknown excess term of the functional can be approximated by the angular-dependent direct correlation function of the pure solvent. This function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation. The corresponding functional can then be minimized on a three-dimensional cubic grid for positions and a Gauss-Legendre angular grid for orientations to provide the solvation free energy of embedded molecules at the same time as the solvent three-dimensional microscopic structure. This functional minimization procedure is much more efficient than direct molecular dynamics simulations combined with thermodynamic integration schemes. The approach is shown to be also pertinent to the molecular-level determination of electron-transfer properties such as reaction free energy and reorganization energy. It is illustrated for molecular solvation and photochemical electron-transfer reactions in acetonitrile, a prototypical polar aprotic solvent.

Temperature inversion in granular fluids under gravity

We study, via hydrodynamic equations, the granular temperature profile of a granular fluid under gravity and subjected to energy injection from a base. It is found that there exists a turn-up in the granular temperature and that, far from the base, it increases linearly with height. We show that this phenomenon, observed previously in experiments and computer simulations, is a direct consequence of the heat flux law, different form Fouriers, in granular fluids. The positive granular temperature gradient is proportional to gravity and a transport coefficient μ0, relating the heat flux to the density gradients, that is characteristic of granular systems. Our results provide a method to compute the value μ0 for different restitution coefficients. The theoretical predictions are verified by means of molecular dynamics simulations, and the value of μ0 is computed for the two-dimensional inelastic hard sphere model. We provide, also, a boundary condition for the temperature field that is consistent with the modified Fouriers law.

Dressed molecule theory for liquids and solutions: An exact charge renormalization formalism for molecules with arbitrary charge distributions

An exact statistical mechanical theory for fluid mixtures of rigid molecules with arbitrary charge distributions, sizes, and shapes is presented. It deals with many-body effects in electrostatic interactions between molecules in fluids and can, for example, be applied to mixtures of polar molecules and to solutions of electrolytes or colloidal dispersions in polar molecular solvents. All solute and solvent molecules are treated on the same fundamental level in statistical mechanics. The exact screened Coulomb potential φ0(r) for the solution is given a general definition. A renormalized charge distribution ρi0 for each molecule of any species i is uniquely defined such that the total electrostatic potential from each i molecule is exactly given by φ0 with ρi0 as the source. By using ρi0 when calculating the interaction between the molecule and the total electrostatic potential from any source, one includes the indirect effects from the surrounding polarizable molecular medium on the electrostatic part of ...

Hydrodynamic theory for granular gases

A granular gas subjected to a permanent injection of energy is described by means of hydrodynamic equations derived from a moment expansion method. The method uses as reference function not a Maxwellian distribution f(M) but a distribution f(0)=Phif(M), such that Phi adds a fourth cumulant kappa to the velocity distribution. The formalism is applied to a stationary conductive case showing that the theory fits extraordinarily well the results coming from our Newtonian molecular dynamic simulations once we determine kappa as a function of the inelasticity of the particle-particle collisions. The shape of kappa is independent of the size N of the system.

Conductivity and viscosity behavior of asymmetric phosphonium iodides.

In this work, we report the physicochemical properties of a variety of aliphatic phosphonium iodide (API) salts, including thermal degradation. Also, we compared the conductivity, viscosity, and fragility behavior of APIs to similar molten systems and related these properties to their structure. Our investigation has found that APIs have an intermediate fragility behavior. We plotted the conductivity and viscosity data of APIs according to Waldens rule and found that they can be classified as an associated ionic liquid (AIL), an intermediate between a true ionic liquid and a molecular species. Lastly, we correlated the structure and behavior of APIs and similar polarizable anions, such as the diacetamide anion.

Accurate evaluation of the angular-dependent direct correlation function of water

The direct correlation function (DCF) plays a pivotal role in addressing the thermodynamic properties with non-mean-field statistical theories of liquid state. This work provides an accurate yet efficient calculation procedure for evaluating the angular-dependent DCF of bulk SPC∕E water. The DCF here represented in a discrete angles basis is computed with two typical steps: the first step involves solving the molecular Ornstein-Zernike equation with the input of total correlation function extracted from simulation; the resultant DCF is then polished in second step at small wavelength for all orientations in order to match correct thermodynamic properties. This function is also discussed in terms of its rotational invariant components. In particular, we show that the component c112(r) that accounts for dipolar symmetry reaches already its long-range asymptotic behavior at a short distance of 4 Å. With the knowledge of DCF, the angular-dependent bridge function of bulk water is thereafter computed and discussed in comparison with referenced hard-sphere bridge functions. We conclude that, even though such hard-sphere bridge functions may be relevant to improve the calculation of Helmholtz free energies in integral equations or density functional theory, they are doomed to fail at a structural level.

Screened Coulomb potential and the renormalized charges of ions and molecules in electrolyte solutions

We consider solutions that consist of solute and solvent molecules of arbitrary sizes, shapes and internal charge distributions. The free energy of interaction (the potential of mean force) between the molecules is analysed in terms of a screened Coulomb potential and renormalized charge distributions of the molecules. The emphasis in this work is to bring out a simple physical interpretation of the theory, but the treatment is based on exact statistical mechanical theory without any approximations. The results thereby are the true properties of the system for given pair interaction potentials between the constituent particles. In general, the electric potential from any molecule in the solution can be exactly obtained for all distances by using a (generalized) screened Coulomb potential, provided the source charges constitute a renormalized charge distribution of the molecule. When charge renormalization is done consistently, macroions, small ions and solvent molecules are treated in fundamentally the same manner and all particles acquire renormalized charge distributions that generally are different from their actual (bare) distributions. The electrostatic free energy of interaction is given by the interaction between the renormalized charge distributions of the molecules as mediated by the screened Coulomb potential. The exact formalism is also used for the primitive model of electrolytes. The concepts in the general theory are illustrated by expressing the Poisson–Boltzmann and hypernetted chain (HNC) approximations in this alternative framework. Conditions are given under which the exact theory predicts the existence of attractive electrostatic interaction between two identical particles at large distances from each other.