Vincent Ballenegger
Associate professor

List of publications

Ice and clathrates

  1. Cage occupancies in nitrogen clathrate hydrates from Monte Carlo simulations
    V. Ballenegger 
    J. Phys. Chem. C  (to appear)    (2019) HAL   →AbstractComparisons of Gibbs ensemble Monte Carlo simulations with experimental data for the cage occupancies in N2 clathrate hydrates are performed to assess the accuracy of such simulations, to refine the effective potentials employed, and to help interpret recently measured large cage over small cage occupancy ratios. Different sets of interaction potentials for N2-N2, N2-H2O and H2O-H2O interactions are considered. Some of them fail to reproduce the known experimental fact that some large cages are doubly occupied at 273 K and high pressures. The best agreement between simulations and experiments is obtained when using a new N-O interaction potential derived in this work by averaging an ab-initio potential energy surface for the N2-H2O dimer. 
  2. Sensitivity of predicted gas hydrate occupancies on treatment of intermolecular interactions
    C. Thomas, S. Picaud, V. Ballenegger, and O. Mousis 
    J. Chem. Phys.  132  104510  (2010) →AbstractThe sensitivity of gas hydrate occupancies predicted on the basis of van der Waals-Platteeuw theory is investigated, as a function of the intermolecular guest-water interaction potential model, and of the number of water molecules taken into account. Simple analytical correction terms that account for the interactions with the water molecules beyond the cutoff distance are introduced, and shown to improve significantly the convergence rate, and hence the efficiency of the computation of the Langmuir constants. The predicted cage occupancies in pure methane and pure carbon dioxide clathrates, calculated using different recent guest-water pair potentials models derived from ab initio calculations, can vary significantly depending on the model. That sensitivity becomes especially strong in the case of multiple guest clathrates. It is shown that the abundances of coenclathrated molecules in multiple guest clathrate hydrates potentially formed on the surface of Mars can vary by more than two orders of magnitude depending on the model. These results underline the strong need for experimental data on pure and multiple guest clathrate hydrates, in particular in the temperature and pressure range that are relevant in extreme environment conditions, to discriminate among the theoretical models. 
  3. Variability of the methane trapping in martian subsurface clathrate hydrates
    C. Thomas, O. Mousis, S. Picaud, and V. Ballenegger 
    Planet. Space Sci.  57  42--47  (2009) →AbstractRecent observations have evidenced traces of methane (CH(4)) heterogeneously distributed in the martian atmosphere. However, because the lifetime of CH(4) in the atmosphere of Mars is estimated to be around 300-600 years on the basis of photochemistry, its release from a subsurface reservoir or an active primary source of methane have been invoked in the recent literature. Among the existing scenarios, it has been proposed that clathrate hydrates located in the near subsurface of Mars could be at the origin of the small quantities of the detected CH(4). Here, we accurately determine the composition of these clathrate hydrates, as a function of temperature and gas phase composition, by using a hybrid statistical thermodynamic model based on experimental data. Compared to the other recent works, our model allows us to calculate the composition of clathrate hydrates formed from a more plausible composition of the martian atmosphere by considering its main compounds, i.e. carbon dioxide, nitrogen and argon, together with methane. Besides, because there is no low temperature restriction in our model, we are able to determine the composition of clathrate hydrates formed at temperatures corresponding to the extreme ones measured in the polar caps. Our results show that methane enriched clathrate hydrates could be stable in the subsurface of Mars only if a primitive CH(4)-rich atmosphere has existed or if a subsurface source of CH(4) has been (or is still) present. 
  4. Clathration of volatiles in the solar nebula and implications for the origin of titan's atmosphere
    O. Mousis, J. I. Lunine, C. Thomas, M. Pasek, U. Marbaeuf, Y. Alibert, V. Ballenegger, D. Cordier, Y. Ellinger, F. Pauzat, and S. Picaud 
    Astrophys. J.  691  1780--1786  (2009) →AbstractWe 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 similar to 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 to or after the completion of Titan. Thus, krypton and xenon may have been sequestrated in the form of XH(3)(+) 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. We finally discuss the subsequent observations that would allow us to determine which of these processes is the most likely. 
  5. A theoretical investigation into the trapping of noble gases by clathrates on Titan
    C. Thomas, S. Picaud, O. Mousis, and V. Ballenegger 
    Planet. Space Sci.  56  1607--1617  (2008) →AbstractIn this paper, we use a statistical thermodynamic approach to quantify the efficiency with which clathrates on the surface of Titan trap noble gases. We consider different values of the Ar, Kr, Xe, CH(4), C(2)H(6) and N(2) abundances in the gas phase that may be representative of Titan's early atmosphere. We discuss the effect of the various parameters that are chosen to represent the interactions between the guest species and the ice cage in our calculations. We also discuss the results of varying the size of the clathrate cages. We show that the trapping efficiency of clathrates is high enough to significantly decrease the atmospheric concentrations of Xe and, to a lesser extent, of Kr, irrespective of the initial gas phase composition, provided that these clathrates are abundant enough on the surface of Titan. In contrast, we find that Ar is poorly trapped in clathrates and, as a consequence, that the atmospheric abundance of argon should remain almost constant. We conclude that the mechanism of trapping noble gases via clathration can explain the deficiency in primordial Xe and Kr observed in Titan's atmosphere by Huygens, but that this mechanism is not sufficient to explain the deficiency in Ar.  
  6. Clathrate hydrates as a sink of noble gases in Titan's atmosphere
    C. Thomas, O. Mousis, V. Ballenegger, and S. Picaud 
    Astron. Astrophys.  474  L17--L20  (2007) →AbstractWe 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 Huygens probe during its descent on January 14, 2005. However, in order to interpret the subsolar abundance of primordial Ar also revealed by Huygens, other processes that occurred either during the formation of Titan or during its evolution must be also invoked. 
  7. Molecular dynamics study of diffusion of formaldehyde in ice
    V. Ballenegger, S. Picaud, and C. Toubin 
    Chem. Phys. Lett.  432  78--83  (2006)   →AbstractWe report a Molecular Dynamics simulation study of the diffusion process of formaldehyde (CH2O) in proton-disordered ice Ih at atmospheric pressure, in the temperature range 200-273 K. CH2O molecules diffuse in ice predominantly by jumping between B sites (bond-breaking mechanism), but substitutional diffusion can also be observed. At 260 K, the diffusion constant is predicted to be 4 x 10(-7) cm(2)/S with the TIP4P-Ew water model, and 3 x 10(-7) cm(2)/S with the TIP4P/Ice water model. 

Long-range force, Particle-Mesh Ewald and P3M methods

  1. Communication: On the origin of the surface term in the Ewald formula
    V. Ballenegger 
    J. Chem. Phys.  140    (2014) →Abstract{A transparent derivation of the Ewald formula for the electrostatic energy of a periodic three-dimensional system of point charges is presented. The problem of the conditional convergence of the lattice sum is dealt with by separating off, in a physically natural and mathematically simple way, long-range non-absolutely integrable contributions in the series. The general expression, for any summation order, of the surface (or dipole) term emerges very directly from those long-range contributions. (C) 2014 AIP Publishing LLC.} 
  2. How to Convert SPME to P3M: Influence Functions and Error Estimates
    V. Ballenegger, J. J. Cerda, and C. Holm 
    J. Chem. Theory Comput.  8  936--947  (2012) →AbstractWe demonstrate explicitly how the two seemingly different particle mesh Ewald methods, the smooth particle mesh Ewald (SPME) and the particle particle particle mesh (P3M), can be mathematically transformed into each other. This allows us in particular to convert the error estimate of the P3M method in the energy-conserving scheme (also known as "P3M with analytic differentiation") into an error estimate for the SPME method, via a simple change of the lattice Green function. Our error estimate is valid for any values of the SPME parameters (mesh size, spline interpolation order, Ewald splitting parameter, real-space cutoff distance), including odd orders of splines. The problem with the self-forces is avoided thanks to an analytical formula that allows to subtract them directly within the particle mesh calculation. Plots of the accuracy of the SPME forces are provided for a wide range of parameter values. The main use of the error estimate is to allow simulation program to scan quickly the multidimensional parameter space to find the best set of parameters to achieve a target accuracy at the smallest computational cost. As a byproduct, we show how a SPME code can be transformed into a P3M version by changing a few lines of code. We demonstrate also that the P3M lattice Green function can be approximated by a closed farm expression, computable on-the-fly, that provides essentially the same accuracy as the full function. 
  3. Removal of spurious self-interactions in particle-mesh methods
    V. Ballenegger, J. J. Cerda, and C. Holm 
    Comput. Phys. Commun.  182  1919--1923  (2011)   →AbstractWe derive an analytic formula for subtracting the spurious self-forces in particle-mesh methods that use the analytical differentiation scheme, such as the Smooth Particle Mesh Ewald (SPME) method and the Particle-Particle Particle-Mesh (P3M) method with analytical differentiation. The impact of the self-forces on the accuracy of the particle-mesh methods is investigated, and it is shown that subtracting them can improve the accuracy of the calculation for some choices of the method's parameters. It is also suggested to subtract exactly the approximate, mesh-computed, self-energy of each particle, replacing them by the exact value. Subtracting in this way the self-energy and self-force of each particle not only improves the accuracy, but also reduces the violation of momentum and energy conservation in particle-mesh methods with analytical differentiation. 
  4. Particle-particle particle-mesh method for dipolar interactions: On error estimates and efficiency of schemes with analytical differentiation and mesh interlacing
    J. J. Cerda, V. Ballenegger, and C. Holm 
    J. Chem. Phys.  135  184110  (2011)   →AbstractThe interlaced and non-interlaced versions of the dipolar particle-particle particle-mesh (P(3)M) method implemented using the analytic differentiation scheme (AD-P(3)M) are presented together with their respective error estimates for the calculation of the forces, torques, and energies. Expressions for the optimized lattice Green functions, and for the Madelung self-forces, self-torques and self-energies are given. The applicability of the theoretical error estimates are thoroughly tested and confirmed in several numerical examples. Our results show that the accuracy of the calculations can be improved substantially when the approximate (mesh computed) Madelung self-interactions are subtracted. Furthermore, we show that the interlaced dipolar AD-P(3)M method delivers a significantly higher accuracy (which corresponds approximately to using a twice finer mesh) than the conventional method, allowing thereby to reduce the mesh size with respect to the non-interlaced version for a given accuracy. In addition, we present similar expressions for the dipolar ik-differentiation interlaced scheme, and we perform a comparison with the AD interlaced scheme. Rough tests for the relative speed of the dipolar P(3)M method using ik-differentiation and the interlaced/non-interlaced AD schemes show that when FFT computing time is the bottleneck, usually when working at high precisions, the interlaced AD-scheme can be several times faster than the other two schemes. For calculations with a low accuracy requirement, the interlaced version can perform worse than the ik and the non-interlaced AD schemes. 
  5. Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions
    V. Ballenegger, A. Arnold, and J. J. Cerda 
    J. Chem. Phys.  131  094107  (2009)   →AbstractWe introduce a regularization procedure to define electrostatic energies and forces in a slab system of thickness h that is periodic in two dimensions and carries a net charge. The regularization corresponds to a neutralization of the system by two charged walls and can be viewed as the extension to the two-dimensional (2D)+h geometry of the neutralization by a homogeneous background in the standard three-dimensional Ewald method. The energies and forces can be computed efficiently by using advanced methods for systems with 2D periodicity, such as MMM2D or P3M/ELC, or by introducing a simple background-charge correction to the Yeh-Berkowitz approach of slab systems. The results are checked against direct lattice sum calculations on simple systems. We show, in particular, that the Madelung energy of a 2D square charge lattice in a uniform compensating background is correctly reproduced to high accuracy. A molecular dynamics simulation of a sodium ion close to an air/water interface is performed to demonstrate that the method does indeed provide consistent long-range electrostatics. The mean force on the ion reduces at large distances to the image-charge interaction predicted by macroscopic electrostatics. This result is used to determine precisely the position of the macroscopic dielectric interface with respect to the true molecular surface. 
  6. The optimal P3M algorithm for computing electrostatic energies in periodic systems
    V. Ballenegger, J. J. Cerda, O. Lenz, and C. Holm 
    J. Chem. Phys.  128  034109  (2008)   →AbstractWe optimize Hockney and Eastwood's particle-particle particle-mesh algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in three-dimensional periodic charged systems. To this end we construct an optimal influence function that minimizes the root-mean-square (rms) errors of the energies. As a by-product we derive a new real-space cutoff 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). 
  7. P3M algorithm for dipolar interactions
    J. J. Cerda, V. Ballenegger, O. Lenz, and C. Holm 
    J. Chem. Phys.  129  234104  (2008)   →AbstractAn extension to the (PM)-M-3 algorithm for electrostatic interactions is presented that allows to efficiently compute dipolar interactions in periodic boundary conditions. Theoretical estimates for the root-mean-square error of the forces, torques, and the energy are derived. The applicability of the estimates is tested and confirmed in several numerical examples. A comparison of the computational performance of the new algorithm to a standard dipolar-Ewald summation methods shows a performance crossover from the Ewald method to the dipolar (PM)-M-3 method for as few as 300 dipolar particles. In larger systems, the new algorithm represents a substantial improvement in performance with respect to the dipolar standard Ewald method. Finally, a test comparing point-dipole-based and charged-pair based models shows that point-dipole-based models exhibit a better performance than charged-pair based models. 

Thermodynamics of (weakly quantum) partially ionized gases

  1. The screened cluster equation of state for hydrogen-helium mixtures: Atomic, molecular, and ionic contributions from first principles
    Alastuey A. Ballenegger V. and Wendland D. 
    Contrib. Plasm. Phys.  58  114-121  (2018) →Abstract{We present a method that provides reliable equations of state for partially ionized gases at moderate densities. The gas is described within the physical picture in terms of a quantum plasma made with nuclei and electrons interacting via the Coulomb potential. The method relies on the screened cluster representation derived elsewhere and is obtained by resummations of Mayer-like diagrammatics for the equivalent classical gas of loops. The contributions to the thermodynamics of atoms, molecules, or ions are described by cluster functions built with simple diagrams involving a few elementary particles and screened interactions. All quantum and collective mechanisms at work are embedded in these cluster functions, which can be computed numerically by sampling the corresponding path integrals. The usefulness and accuracy of this formalism is illustrated by considering a hydrogen-helium mixture under solar interior conditions. As a by-product of our calculations, we also exhibit the density dependence of the two-body cluster function analogous to the second virial coefficient in a hydrogen gas.} 
  2. Quantum screened interactions in moderately dense plasmas and atomic contributions to thermodynamics
    V. Ballenegger, D. Wendland, and A. Alastuey 
    Contrib. Plasm. Phys.  57  106-125  (2017)
  3. Comment on ``Direct linear term in the equation of state of plasmas''
    A. Alastuey, V. Ballenegger, and W. Ebeling 
    Physical Review E  92    (2015) HAL  
  4. Quantum partition functions of composite particles in a hydrogen-helium plasma via path integral Monte Carlo
    D. Wendland, V. Ballenegger, and A. Alastuey 
    J. Chem. Phys.  141    (2014) →Abstract{We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H-, H-2(+), and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities. (C) 2014 AIP Publishing LLC.} 
  5. Atomic Ionization and Molecular Dissociation in a Hydrogen Gas within the Physical Picture
    A. Alastuey and V. Ballenegger 
    Contrib. Plasm. Phys.  52  95--99  (2012)   →AbstractWe study a hydrogen gas at low densities within the physical picture. Recombination processes leading to the formation of atoms and molecules are properly taken into account via the well-known Ebeling function and a new four-body partition function. Our method provides a reliable equation of state which covers the plasma, atomic and molecular phases 
  6. The divergent atomic partition function or how to assign correct statistical weights to bound states
    V. Ballenegger 
    Ann. Phys.  524  103--105  (2012)  
  7. Thermodynamics of atomic and ionized hydrogen: Analytical results versus equation-of-state tables and Monte Carlo data
    A. Alastuey and V. Ballenegger 
    Phys. Rev. E  86  066402  (2012) HAL     →AbstractWe 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. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E-H|/kT) included (E-H similar or equal to -13.6 eV). Those truncated expansions describe the first five nonideal 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 the 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, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (rho similar to 10(-2) g/cm(3)), some discrepancies among the SLT, OPAL, and PIMC results are observed. 
  8. Pressure of a Partially Ionized Hydrogen Gas: Numerical Results from Exact Low Temperature Expansions
    A. Alastuey and V. Ballenegger 
    Contrib. Plasm. Phys.  50  46--53  (2010) HAL     →AbstractWe consider a partially ionized hydrogen gas at low densities, where it reduces almost to an ideal mixture made with hydrogen atoms in their ground-state, ionized protons and ionized electrons. By performing systematic low-temperature expansions within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential, exact formulae for the first five leading corrections to the ideal Saha equation of state have been derived [A. Alastuey, V. Ballenegger et al., J. Stat. Phys. 130, 1119 (2008)]. Those corrections account for all effects of interactions and thermal excitations up to order exp(E(H)/kT) included, where E(H) similar or equal to -13.6 eV is the ground state energy of the hydrogen atom. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve suitably truncated internal partition functions of H(2) molecules and H(-) and H(2)(+) ions, for which no analytical formulae are available in closed form. We estimate those partitions functions at finite temperature via a simple phenomenology based on known values of rotational and vibrational energies. This allows us to compute numerically the leading deviations to the Saha pressure along several isotherms and isochores. Our values are compared with those of the OPAL tables (for pure hydrogen) calculated within the ACTEX method. 
  9. Exact asymptotic expansions for the thermodynamics of hydrogen gas in the Saha regime
    A. Alastuey and V. Ballenegger 
    J. Phys. A - Math. Theor.  42  214031  (2009) HAL     →AbstractWe 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. 
  10. Exact results for thermodynamics of the hydrogen plasma: Low-temperature expansions beyond Saha theory
    A. Alastuey, V. Ballenegger, F. Cornu, and P. A. Martin 
    J. Stat. Phys.  130  1119--1176  (2008)   →AbstractWe study hydrogen in the Saha regime, within the physical picture in terms of a quantum proton-electron plasma. Long ago, Saha showed that, at sufficiently low densities and low temperatures, the system behaves almost as an ideal mixture made with hydrogen atoms in their groundstate, ionized protons and ionized electrons. More recently, that result has been rigorously proved in some scaling limit where both temperature and density vanish. In that Saha regime, we derive exact low-temperature expansions for the pressure and internal energy, where density rho is rescaled in units of a temperature-dependent density rho* which controls the cross-over between full ionization (rho << rho*) and full atomic recombination (rho >>rho*). Each term reduces to a function of rho/rho* times temperature-dependent functions which decay exponentially fast when temperature T vanishes. Scaled expansions are ordered with respect to the corresponding decay rates. Leading terms do reduce to ideal contributions obtained within Saha theory. We consistently compute all corrections which are exponentially smaller by a factor exp(beta E (H) ) at most, where E (H) is the negative groundstate energy of a hydrogen atom and beta=1/(k (B) T). They include all effects arising from both the Coulomb potential and the quantum nature of the particles: excitations of atoms H, formation of molecules H-2, ions H-2(+) and H-, thermal and pressure ionization, plasma polarization, screening, interactions between atoms and ionized charges, etc. Scaled low-temperature expansions can be viewed as partial resummations of usual virial expansions up to arbitrary high orders in the density. 
  11. Dielectric versus conductive behaviour in quantum gases: exact results for the hydrogen plasma
    V. Ballenegger and P. A. Martin 
    Physica A  328  97--144  (2003)   →AbstractWe study the electrical susceptibility of a hydrogen gas at equilibrium, partially ionized by thermal excitations. The gas is described as a quantum plasma of point protons and electrons, interacting via the Coulomb potential. Using the newly developed diagrammatical technique of screened cluster expansions, we calculate exactly the wavenumber-dependent susceptibility in the atomic limit, where most charges are bound into hydrogen atoms. A transition from conductive to dielectric behaviour occurs when the wavelength is decreased well below the Debye screening length. The standard formula for the dielectric function of an ideal gas of hydrogen atoms is recovered in an appropriate scaling limit. The derivation treats all effects arising from the Coulomb interaction (screening, binding, polarization) in a fully coherent way, without intermediate approximation nor modelization. 
  12. Screened cluster expansions for partially ionized gases
    A. Alastuey, V. Ballenegger, F. Cornu, and P. A. Martin 
    J. Stat. Phys.  113  455--503  (2003)   →AbstractWe consider a partially ionized gas at thermal equilibrium, in the Saha regime. The system is described in terms of a quantum plasma of nuclei and electrons. In this framework, the Coulomb interaction is the source of a large variety of phenomena occurring at different scales: recombination, screening, diffraction, etc. In this paper, we derive a cluster expansion adequate for a coherent treatment of those phenomena. The expansion is obtained by combining the path integral representation of the quantum gas with familiar Mayer diagrammatics. In this formalism, graphs have a clear physical interpretation: vertices are associated with recombined chemical species, while bonds describe their mutual interactions. The diagrammatical rules account exactly for all effects in the medium. Applications to thermodynamics, van der Waals forces and dielectric versus conductive behaviour will be presented in forthcoming papers. 
  13. Quantum Coulomb systems: some exact results in the atomic limit
    V. Ballenegger and P. A. Martin 
    Physica A  306  59--67  (2002)   →AbstractWe review a number of exact results concerning the recombined electron-proton gas. The recombination problem can be formulated in precise terms in the atomic limit. In this limit one lets the density and the temperature tend to zero in a coupled way so that the resulting energy-entropy balance favors the formation of certain chemical species. This enables to develop a clear understanding of the dielectric versus conducting behavior in the system. In particular, we give a first principle derivation of the dielectric constant of the dilute atomic gas without presupposing the existence of atoms. The analysis relies on the path integral representation of the Coulomb gas together with Mayer diagrammatic techniques. 
  14. Quantum Mayer graphs for Coulomb systems and the analog of the Debye potential
    V. Ballenegger, P. A. Martin, and A. Alastuey 
    J. Stat. Phys.  108  169--211  (2002)   →AbstractWithin the Feynman-Kac path integral representation, the equilibrium quantities of a quantum plasma can be represented by Mayer graphs. The well known Coulomb divergencies that appear in these series are eliminated by partial resummations. In this paper, we propose a resummation scheme based on the introduction of a single effective potential phi that is the quantum analog of the Debye potential. A low density analysis of phi shows that it reduces, at short distances, to the bare Coulomb interaction between the charges (which is able to lead to bound states). At scale of the order of the Debye screening length kappa(D)(-1), phi approaches the classical Debye potential and, at large distances, it decays as a dipolar potential (this large distance behaviour is due to the quantum nature of the particles). The prototype graphs that result from the resummation obey the same diagrammatical rules as the classical graphs of the Abe-Meeron series. We give several applications that show the usefulness of phi to account for Coulombic effects at all distances in a coherent way. 

Dielectric fluids, ferrofluids

  1. Semiflexible magnetic filaments near attractive flat surfaces: a Langevin dynamics study
    P. A. Sanchez, J. J. Cerda, V. Ballenegger, T. Sintes, O. Piro, and C. Holm 
    Soft Matter  7  1809--1818  (2011)   →AbstractThe adsorption of stiff magnetic filaments close to an attractive surface is studied thoroughly via extensive Langevin dynamics simulations (LD). Magnetic filaments are represented by a coarse-grained bead-spring model where each bead bears a point dipole located at its center and the excluded volume interaction is introduced via a soft-core repulsive potential. We find strong evidence for the existence of two transitions as the temperature is lowered. First, the system undergoes a continuum phase transition from the desorbed to the adsorbed state. This transition is followed by a second structural transition that takes place when the filaments are already adsorbed. The adsorption transition is found to be very similar to the one observed for stiff non-magnetic polymer chains [Sintes et al., Macromolecules 2001, 34, 1352-1357] where the chain bending interaction plays a similar role as the magnetic component of the present case. However, the tendency of the magnetic chains to stretch is reversed by a further reduction in temperature and the chains tend to form closed adsorbed loops leading to a second structural transition. A representation of the phase diagram for the adsorption of magnetic filaments is determined here for the first time. We also present a novel way to determine the temperature at which the chain is adsorbed that is based on the analysis of the change in the number of trains, tails and loops developed by the polymer chain during the adsorption process. 
  2. Study of the structure factor anisotropy and long range correlations of ferrofluids in the dilute low-coupling regime
    J. J. Cerda, E. Elfimova, V. Ballenegger, E. Krutikova, A. Ivanov, and C. Holm 
    J. Magn. Magn. Mater.  323  1246--1253  (2011)   →AbstractDipolar soft-sphere (DSS) fluids in the dilute low-coupling regime are studied via Molecular Dynamic simulations and the extension of a theoretical formalism previously used for dipolar hard spheres in which new terms for the virial expansion of the radial distribution function corresponding to the three-particle contribution are presented and tested for the zero and non-zero magnetic field case. A thorough comparison with simulations shows that the extended formalism is able to account for the structure factors of DSS with and without externally applied magnetic fields in the dilute low-coupling regime: quantitative agreement between theory and simulations is found for dipolar coupling parameters lambda less than or similar to 2, and volume fraction phi less than or similar to 0.25. When lambda>1 the new added term to the virial expansion is observed to play a crucial role in order to match quantitatively theory and simulations at zero field. In the presence of an external magnetic field our tests show that further improvements are needed and only new terms with Langevin function dependences can significatively contribute to improve the predictions for the dilute low-coupling regime. Numerical simulations show that despite that the ferrofluids considered here are in the dilute low-coupling regime, when an external field is applied, important correlations along the parallel direction to the field and depletion phenomena along the perpendicular direction are observed in the averaged density surrounding a particle.  
  3. Behavior of bulky ferrofluids in the diluted low-coupling regime: Theory and simulation
    J. J. Cerda, E. Elfimova, V. Ballenegger, E. Krutikova, A. Ivanov, and C. Holm 
    Phys. Rev. E  81  011501  (2010)   →AbstractA theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is lambda less than or similar to 2, and the volume fraction is phi less than or similar to 0.25. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5. 
  4. Dipolar fluctuations in the bulk and at interfaces
    V. Ballenegger, R. Blaak, and J. P. Hansen 
    Lect. Notes Phys.  704  45--63  (2006)   →AbstractThe dielectric response of classical polar fluids is by now well understood for bulk systems, where the permittivity can be calculated by a variety of methods within the linear response regime. Near interfaces or inhomogeneities, one may attempt to describe the dielectric response of the fluid using a local dielectric tensor epsilon(r), for which an explicit expression can be derived from linear response theory. This chapter describes the limitations of this approach, exemplified by Molecular Dynamics simulations of polar fluids confined to a slit or a spherical cavity. 
  5. Dielectric permittivity profiles of confined polar fluids
    V. Ballenegger and J. P. Hansen 
    J. Chem. Phys.  122  114711  (2005)   →AbstractThe dielectric response of a simple model of,a polar fluid near neutral interfaces is examined by a combination of linear response theory and extensive molecular dynamics simulations. Fluctuation expressions for a local permittivity tensor is an element of(r) are derived for planar and spherical geometries, based on the assumption of a purely local relationship between polarization and electric field. While the longitudinal component of e exhibits strong oscillations on the molecular scale near interfaces, the transverse component becomes ill defined and unphysical, indicating nonlocality in the dielectric response. Both components go over to the correct bulk permittivity beyond a few molecular diameters. Upon approaching interfaces from the bulk, the permittivity tends to increase, rather than decrease as commonly assumed, and this behavior is confirmed for a simple model of water near a hydrophobic surface. An unexpected finding of the present analysis is the formation of "electrostatic double layers" signaled by a dramatic overscreening of an externally applied field inside the polar fluid close to an interface. The local electric field is of opposite sign to the external field and of significantly larger amplitude within the first layer of polar molecules. 
  6. Structure and dielectric properties of polar fluids with extended dipoles: results from numerical simulations
    V. Ballenegger and J. P. Hansen 
    Mol. Phys.  102  599--609  (2004)   →AbstractThe strengths and shortcomings of the point dipole model for polar fluids of spherical molecules are illustrated by considering the physically more relevant case of extended dipoles formed by two opposite charges +/-q separated by a distance d (dipole moment mu = qd). Extensive molecular dynamics simulations on a high-density dipolar fluid are used to analyse the dependence of the pair structure, dielectric constant epsilon and dynamics as a function of the ratio d/sigma (sigma is the molecular diameter), for a fixed dipole moment mu. The point dipole model is found to agree well with the extended dipole model up to d/sigma similar or equal to 0.3. Beyond that ratio, epsilon shows a non-trivial variation with d/sigma. When d/sigma > 0.6, a transition is observed towards a hexagonal columnar phase; the corresponding value of the dipole moment is found to be substantially lower than the value of the point dipole required to drive a similar transition. 
  7. Local dielectric permittivity near an interface
    V. Ballenegger and J. P. Hansen 
    Europhys. Lett.  63  381--387  (2003) →AbstractA statistical mechanics expression is derived for the space-dependent dielectric permittivity of a polar solvent near an interface. The asymptotic behaviour of this local permittivity is calculated in the low-density limit, near a planar interface. The potential of mean force between two ions is shown to agree with the prediction of macroscopic electrostatics for large separations parallel to the interface. 
  8. Onsager model for a variable dielectric permittivity near an interface
    R. Finken, V. Ballenegger, and J. P. Hansen 
    Mol. Phys.  101  2559--2568  (2003) →AbstractUsing a generalization 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. 
  9. Statistical mechanics of dipolar fluids: dielectric constant and sample shape
    A. Alastuey and V. Ballenegger 
    Physica A  279  268--286  (2000)   →AbstractWe give a new proof that the constitutive relation of macroscopic electrostatics holds in a dipolar fluid with a sample shape independent dielectric constant. Our approach is based on a BGY-like hierarchy equation which allows us to calculate the canonical one-body density function up to linear order in the electric field, in the thermodynamic limit. The dielectric constant comes out as an integral over a 3-point correlation function of the infinite unperturbed (unpolarized) system, from which one can recover the well-known formula for epsilon in terms of the 2-point direct correlation function. 
  10. The Ewald-Oseen extinction theorem and extinction lengths
    V. C. Ballenegger and T. A. Weber 
    Am. J. Phys.  67  599--605  (1999)   →AbstractWe give an elementary demonstration of the extinction theorem for electromagnetic waves at normal incidence on a plane surface of a medium. We stress that the extinction of the incident wave nd its replacement with a wave of index of refraction n takes place throughout the medium rather than in the surface layers. Although the extinction theorem is usually thought to apply only to dielectrics, we extend the theorem to include conductors. We use the macroscopic fields in which the contributions of the oscillating dipoles in a dielectric or the induced currents in a conductor are already summed. Our elementary derivation of the extinction theorem should be readily accessible to advanced undergraduates since it depends only on the superposition principle and the solution of the wave equation. An analogy is made between this extinction and the cancellation of the electric field inside a conductor placed in a static electric field. We also study the more advanced case of propagation of radiation in a dilute random medium in which the wavelength is small relative to the interparticle distance and find that an analogous extinction of the incident wave takes place. Furthermore, for the dilute random medium, we estimate the length into the medium for which a large fraction, (1-1/e), of the incident radiation has interacted with the particles making up the medium. This length is much larger than any lengths associated with the extinction theorem itself.