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Register a new userFree-energy functional of the Debye-Huckel model of two-component plasmas
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We present a generalization of the Debye-Huckel free-energy-density functional of simple fluids to the case of two-component systems with arbitrary interaction potentials. It allows one to obtain the two-component Debye-Huckel integral equations through its minimization with respect to the pair correlation functions, leads to the correct form of the internal energy density, and fulfills the virial theorem. It is based on our previous idea, proposed for the one-component Debye-Huckel approach, and which was published recently cite{Piron16}. We use the Debye-Kirkwood charging method in the same way as in cite{Piron16}, in order to build an expression of the free-energy density functional. Main properties of the two-component Debye-Huckel free energy are presented and discussed, including the virial theorem in the case of long-range interaction potentials.
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The Debye-Huckel approximation to the free-energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Huckel equivalent to the functional derived in the hyper-netted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Huckel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.
In previous publications [arXiv:1608.08430, arXiv:1704.06502], the authors have proposed Debye-Huckel-approximate free-energy functionals of the pair distribution functions for one-component fluid and two-component plasmas. These functionals yield the corresponding Debye-Huckel integral equations when they are minimized with respect to the pair distribution functions, lead to correct thermodynamic relations and fulfill the virial theorem. In the present addendum, we update our results by providing simpler functionals that have the same properties. We relate these functionals to the approaches of Lado [Phys. Rev. A 8:2548, 1973] and of Olivares and McQuarrie [J. Chem. Phys. 65:3604, 1976]. We also discuss briefly the non-uniqueness issue that is raised by these results.
Classical MD data on the charge-charge dynamic structure factor of two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are analyzed using the sum rules and other exact relations. The convergent power moments of the imaginary part of the model system dielectric function are expressed in terms of its partial static structure factors, which are computed by the method of hypernetted chains using the Deutsch effective potential. High-frequency asymptotic behavior of the dielectric function is specified to include the effects of inverse bremsstrahlung. The agreement with the MD data is improved, and important statistical characteristics of the model TCP, such as the probability to find both electron and ion at one point, are determined.
Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble their bulk counterparts. For instance, the electrostatic potential of a point charge at an air-water interface falls off as $r^{-3}$, where $r$ is the distance from the charge, exhibiting a dipolar behaviour. This behaviour is often assumed to be generic, and is widely referred to when interpreting experimental results. Here we explicitly calculate the in-plane potential of a point charge at an interface between two electrolyte solutions with different dielectric permittivities and Debye screening lengths. We show that the asymptotic behaviour of this potential is neither a dipole, which characterises the potential at air-water interfaces, nor a screened monopole, which describes the bulk behaviour in a single electrolyte solution. By considering the same problem in arbitrary dimensions, we find that the physics behind this difference can be traced to the asymmetric propagation of the interaction in the two media. Our results are relevant, for instance, to understand the physics of charged colloidal particles trapped at oil-water interfaces.
In a previous paper we showed that dynamical density shocks occur in the non-relativistic expansion of dense single component plasmas relevant to ultrafast electron microscopy; and we showed that fluid models capture these effects accurately. We show that the non-relativistic decoupling of the relative and center of mass motions ceases to apply and this coupling leads to novel behavior in the relativistic dynamics under planar, cylindrical, and spherical symmetries. In cases where the relative motion of the bunch is relativistic, we show that a dynamical shock emerges even in the case of a uniform bunch with cold initial conditions; and that density shocks are in general enhanced when the relative motion becomes relativistic. Furthermore, we examine the effect of an extraction field on the relativistic dynamics of a planar symmetric bunch.
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