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Particles inside Electrolytes with Ion-specific Interactions, Their Effective Charge Distributions and Effective Interactions

In this work, we explore the statistical physics of colloidal particles that interact with electrolytes via ion-specific interactions. Firstly we study particles interact weakly with electrolyte using linear response theory. We find that the mean potential around a particle is linearly determined by the {\em effective charge distribution} of the particle, which depends both on the bare charge distribution and on ion-specific interactions. We also discuss the effective interaction between two such particles and show that, in far field regime, it is bilinear in the effective charge distributions of two particles. We subsequently generalize the above results to the more complicated case where particles interact strongly with the electrolyte. Our results indicate that in order to understand the statistical physics of non-dilute electrolytes, both ion-specific interactions and ionic correlations have to be addressed in a single unified and consistent framework.