Effects of counterion size on the attraction between similarly charged surfaces |
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Authors: | Zelko Jasna Iglic Ales Kralj-Iglic Veronika Kumar P B Sunil |
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Institution: | Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana, Ljubljana, Slovenia. |
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Abstract: | Interaction between similarly charged surfaces can be attractive at high electrostatic coupling constants Ξ = l(B)Z(2)/μ(GC), where l(B) is the Bjerrum length, μ(GC) the Gouy-Chapman length, and Z the valency of counterions. While this effect has been studied previously in detail, as a function of surface charge density and valency of the pointlike counterions, much less is known about the effect of counterion size. We apply the Wang-Landau sampling Monte Carlo (MC) simulation method to compute the free energy F as a function of the scaled distance between the plates D?=D/μ(GC) for a range of Ξ and scaled counterion radii R?=R/μ(GC). We find that for large Ξ and small ion radius, there is a global equilibrium distance D?=D?(eq)=2(1+R?), correctly giving the expected value at the point counterion limit. With increasing R? the global minimum in F(D?) changes to a metastable state and finally this minimum vanishes when R? reaches a critical value, which depends on Ξ. We present a state diagram indicating approximate boundaries between these three regimes. The Wang-Landau MC method, as it is applied here, offers a possibility to study a wide spectrum of extended problems, which cannot be treated by the use of contact value theorem. |
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