Attraction of like-charged macroions in the strong-coupling limit

Abstract

Abstract. Like-charged macroions attract each other as a result of strong electrostatic correlations in the presence of multivalent counterions or at low temperatures. We investigate the effective electrostatic interaction between i) two like-charged rods and ii) two like-charged spheres using the recently introduced strong-coupling theory, which becomes asymptotically exact in the limit of large coupling parameter (i.e. for large counterion valency, low temperature, or high surface charge density on macroions). In contrast to previous applications of the strong-coupling theory, we deal with curved surfaces and an additional parameter, referred to as Manning parameter, is introduced, which measures the ratio between the radius of curvature of macroions to the Gouy-Chapman length. This parameter, together with the size of the confining box enclosing the two macroions and their neutralizing counterions, controls the counterion-condensation process that directly affects the effective interactions. For sufficiently large Manning parameters (weakly-curved surfaces), we find a strong long-ranged attraction between two macroions that form a closely-packed bound state with small surface-to-surface separation of the order of the counterion diameter in agreement with recent simulations results. For small Manning parameters (highly-curved surfaces), on the other hand, the equilibrium separation increases and the macroions unbind from each other as the confinement volume increases to infinity. This occurs via a continuous universal unbinding transition for two charged rods at a threshold Manning parameter of ξc = 2/3, while the transition is strongly discontinuous for spheres because of a pronounced potential barrier at intermediate distances. Unlike the cylindrical case, the attractive forces between spheres disappear for increasing confinement volume due to the complete de-condensation of counterions. Scaling arguments suggest that for moderate values of coupling parameter, strong-coupling predictions remain valid for sufficiently small surface-to-surface separations.PACS. 87.15.-v Biomolecules: structure and physical properties -82.70.Dd Colloids -87.15.Nn Properties of solutions; aggregation and crystallization of macromolecules

Correlation effects, image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

“…But certainly, for trivalent point-like ions, we expect the Hartree approximation to breakdown, close to the surface of the macro-ion. Near the surface, a strong-coupling regime [3] will hold, as Ξ is so high. Yet, the situation may be a little more subtle for real ions with valences larger than, or equal to, three.…”

“…The unmodified PB equation for a uniformly charged cylinder may be inadequate in describing the interaction for a variety of reasons. Correlation effects [1][2][3][4][5][6][7][8][9][10][11], image charge effects [1,5,8,10,12,13], solvent effects [12,[14][15][16][17][18][19], and structure of charged groups at the macro-ion surface [1,12,[19][20][21][22] may all play an important role. Though, the relative degree of each of these effects is likely to depend on the particular properties of the type of macro-ion under consideration, most importantly its shape, charge density and surface charge distribution of fixed charged groups.…”

“…Correlation effects may lead to two predicted phenomena, that of charge inversion [1,7,23,24] and samecharge attraction [1,3,5,7,9,11,25]. In charge inversion, the amount of positive charge, due to counter-ions, exceeds the surface charge density of the macro-ion effectively making it of opposite charge to its fixed charged groups.…”

“…One way of handling some of these effects, in a systematic way, is to reformulate the statistical-mechanical model that describes the macro-ion electrolyte system into a statistical field theory [3,42,43]. The advantage in such a formulation is that the mean field of the fluctuating field used in such a theory is proportional to the thermally averaged electrostatic field.…”

“…Such self-consistent approximations have enjoyed notable success in other areas of condensed matter physics, and may yet provide a new useful line of attack in understanding polyelectrolyte interactions. These particular field theories, which arise from such models, enjoy another important advantage: one can do a strong-coupling expansion [3,5,10]. Such an expansion is valid when the ions in solution are highly correlated.…”