Onsager model for a variable dielectric permittivity near an interface

Using a generalisation of an Onsager type approach, we are able to predict a dielectric permittivity profile of an inhomogeneous dipolar fluid in the presence of a dielectric interface. The reaction and cavity fields are calculated semi-analytically using bispherical coordinates. An asymptotic expression for the local permittivity is derived as a function of distance from the interface.Comment: 20 pages, 4 figures, submitted to Molecular Physic

Dipolar depletion effect on the differential capacitance of carbon based materials

The remarkably low experimental values of the capacitance data of carbon based materials in contact with water solvent needs to be explained from a microscopic theory in order to optimize the efficiency of these materials. We show that this experimental result can be explained by the dielectric screening deficiency of the electrostatic potential, which in turn results from the interfacial solvent depletion effect driven by image dipole interactions. We show this by deriving from the microscopic system Hamiltonian a non-mean-field dipolar Poisson-Boltzmann equation. This can account for the interaction of solvent molecules with their electrostatic image resulting from the dielectric discontinuity between the solvent medium and the substrate. The predictions of the extended dipolar Poisson-Boltzmann equation for the differential capacitance are compared with experimental data and good agreement is found without any fitting parameters

Thermodynamics of atomic and ionized hydrogen : analytical results versus OPAL tables and Monte Carlo data

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact Scaled Low-Temperature (SLT) expansion, which provides a rigorous extension of the well known virial expansion -- valid in the fully ionized phase -- into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al, J. Stat. Phys. {\bf 130}, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to to order $\exp(|E_H|/kT)$ included ($E_H \simeq -13.6$ eV). Those truncated expansions describe the first five non-ideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom $H$, ions $H^-$ and $H_2^+$, molecule $H_2$, ...) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for molecule $H_2$ and ions $H^-$ and $H_2^+$, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion with the OPAL EOS and data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulae reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities ($\rho\sim10^{-2}$ g/cm$^3$), some discrepancies between the SLT, OPAL and PIMC results are observed

The optimal P3M algorithm for computing electrostatic energies in periodic systems

We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M) algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in 3D periodic charged systems. To this end we construct an optimal influence function that minimizes the RMS errors in the energies. As a by-product we derive a new real-space cut-off correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the RMS error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies, and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size and charge assignment order).Comment: 31 pages, 3 figure

Etude des phénomènes d'écran et de polarisation dans un plasma quantique par la méthode des graphes de Mayer

This thesis is devoted to the study of screening and polarisation effects in a quantum plasma of electrons and protons, when the system is close to a dilute gas of hydrogen atoms. This atomic phase is obtained by considering a coupled low-density and low-temperature limit, in which the binding of charges into hydrogen atoms is favored. We study the electrical susceptibility of this plasma using a fugacity expansion of this function obtained from a resummed Mayer diagrammatic series. This expansion -- which is non-perturbative with respect to electric charge and Planck's constant -- allows to take into account systematically, at low densities, all phenomena induced by the Coulomb interactions, among which atomic and molecular binding and screening effects. We exhibit in particular a regime where the plasma's susceptibility measures the dielectric screening effect due to the polarisability of the hydrogen atoms. We consider also in this thesis the problem of dealing with the boundary effect that occurs when a finite dielectric sample is polarized under the influence of a static electric field. We describe the dielectric material as a classical dipolar fluid confined to a certain region, and we calculate its mean polarisation using statistical mechanics. We show that in the thermodynamical limit, this polarisation satisfies the local dielectric law of macroscopic electrostatics, with a dielectric constant that is a bulk property, independent of the sample's shape

Clathration of Volatiles in the Solar Nebula and Implications for the Origin of Titan's atmosphere

We describe a scenario of Titan's formation matching the constraints imposed by its current atmospheric composition. Assuming that the abundances of all elements, including oxygen, are solar in the outer nebula, we show that the icy planetesimals were agglomerated in the feeding zone of Saturn from a mixture of clathrates with multiple guest species, so-called stochiometric hydrates such as ammonia hydrate, and pure condensates. We also use a statistical thermodynamic approach to constrain the composition of multiple guest clathrates formed in the solar nebula. We then infer that krypton and xenon, that are expected to condense in the 20-30 K temperature range in the solar nebula, are trapped in clathrates at higher temperatures than 50 K. Once formed, these ices either were accreted by Saturn or remained embedded in its surrounding subnebula until they found their way into the regular satellites growing around Saturn. In order to explain the carbon monoxide and primordial argon deficiencies of Titan's atmosphere, we suggest that the satellite was formed from icy planetesimals initially produced in the solar nebula and that were partially devolatilized at a temperature not exceeding 50 K during their migration within Saturn's subnebula. The observed deficiencies of Titan's atmosphere in krypton and xenon could result from other processes that may have occurred both prior or after the completion of Titan. Thus, krypton and xenon may have been sequestrated in the form of XH3+ complexes in the solar nebula gas phase, causing the formation of noble gas-poor planetesimals ultimately accreted by Titan. Alternatively, krypton and xenon may have also been trapped efficiently in clathrates located on the satellite's surface or in its atmospheric haze.Comment: Accepted for publication in The Astrophysical Journa

Clathrate hydrates as a sink of noble gases in Titan's atmosphere

We use a statistical thermodynamic approach to determine the composition of clathrate hydrates which may form from a multiple compound gas whose composition is similar to that of Titan's atmosphere. Assuming that noble gases are initially present in this gas phase, we calculate the ratios of xenon, krypton and argon to species trapped in clathrate hydrates. We find that these ratios calculated for xenon and krypton are several orders of magnitude higher than in the coexisting gas at temperature and pressure conditions close to those of Titan's present atmosphere at ground level. Furthermore we show that, by contrast, argon is poorly trapped in these ices. This trapping mechanism implies that the gas-phase is progressively depleted in xenon and krypton when the coexisting clathrate hydrates form whereas the initial abundance of argon remains almost constant. Our results are thus compatible with the deficiency of Titan's atmosphere in xenon and krypton measured by the {\it Huygens} probe during its descent on January 14, 2005. However, in order to interpret the subsolar abundance of primordial Ar also revealed by {\it Huygens}, other processes that occurred either during the formation of Titan or during its evolution must be also invoked.Comment: Astronomy & Astrophysics Letters, in pres

Exact aymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime

We consider the hydrogen quantum plasma in the Saha regime, where it almost reduces to a partially ionized atomic gas. We briefly review the construction of systematic expansions of thermodynamical functions beyond Saha theory, which describes an ideal mixture of ionized protons, ionized electrons and hydrogen atoms in their ground-state. Thanks to the existence of rigorous results, we first identify the simultaneous low-temperature and low-density limit in which Saha theory becomes asymptotically exact. Then, we argue that the screened cluster representation is well suited for calculating corrections, since that formalism accounts for all screening and recombination phenomena at work in a more tractable way than other many-body methods. We sketch the corresponding diagrammatical analysis, which leads to an exact asymptotic expansion for the equation of state. That scaled low-temperature expansion improves the analytical knowledge of the phase diagram. It also provides reliable numerical values over a rather wide range of temperatures and densities, as confirmed by comparisons to quantum Monte Carlo data.Comment: 10 page

Self-consistent equation for an interacting Bose gas

We consider interacting Bose gas in thermal equilibrium assuming a positive and bounded pair potential $V(r)$ such that 0<\int d\br V(r) = a<\infty. Expressing the partition function by the Feynman-Kac functional integral yields a classical-like polymer representation of the quantum gas. With Mayer graph summation techniques, we demonstrate the existence of a self-consistent relation $\rho (\mu)=F(\mu-a\rho(\mu))$ between the density $\rho$ and the chemical potential $\mu$, valid in the range of convergence of Mayer series. The function $F$ is equal to the sum of all rooted multiply connected graphs. Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in the mean-field limit $\gamma\to 0$ only tree diagrams contribute and function $F$ reduces to the free gas density. We also investigate how to extend the validity of the self-consistent relation beyond the convergence radius of Mayer series (vicinity of Bose-Einstein condensation) and study dominant corrections to mean field. At lowest order, the form of function $F$ is shown to depend on single polymer partition function for which we derive lower and upper bounds and on the resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.