Yukawa multipole electrostatics and nontrivial coupling between electrostatic anddispersion interactions in electrolytes

Abstract

An exact treatment of screened electrostatics in electrolyte solutions is presented. Inelectrolytes the anisotropy of the exponentially decaying electrostatic potentialfrom a molecule extends to the far field region. The full directional dependenceof the electrostatic potential from a charged or uncharged molecule remains inthe longest range tail (i.e. from all multipole moments). In particular, the rangeof the potential from an ion and that from an electroneutral polar particle isgenerally exactly the same. This is in contrast to the case in vacuum or pure polarliquids, where the potential from a single charge is longer ranged than that from adipole, which is, itself, longer ranged than the one from a quadrupole etc. Theorientational dependence of the exponentially screened electrostatic interaction betweentwo molecules in electrolytes is therefore rather complex even at long distances.These facts are formalized in Yukawa multipole expansions of the electrostaticpotential and the pair interaction free energy based on the Yukawa function familyexp(−κr)/rm, wherer is the distance,κ is a decayparameter and m is a positive integer. The expansion is formally exact for electrolytes with molecular solventand in the primitive model, provided the non-Coulombic interactions between the particlesare sufficiently short ranged. The results can also be applied in the Poisson–Boltzmannapproximation. Differences and similarities to the ordinary multipole expansion ofelectrostatics are pointed out.On the other hand, when the non-Coulombic interactions between theconstituent particles of the electrolyte solution contain a dispersion1/r6 potential, the electrostatic potential from a molecule decays like a power law for longdistances rather than as a Yukawa function. This is due to nontrivial coupling between theelectrostatic and dispersion interactions. There remains an exponentially decayingcomponent in the electrostatic potential, but it becomes oscillatory in the presence of thedispersion interactions. For weak dispersion forces and low electrolyte concentrations, thewavelength is, however, long compared to the decay length of the exponentialdecay. In other cases the qualitative behaviour may be substantially differentfrom the conventional picture. The Green function for the electrostatic potential(the ‘screened Coulomb potential’) in simple electrolytes ultimately decays likeconst/r6 forlarge r, where the constant prefactor depends on the ratio between the strengthof the dispersion forces and the square of the average ionic charge,(q++|q−|)/2.