Sedimentation Equilibrium of Mixtures of Charged Colloids

Contents1 Introduction 11.1 Sedimentation Equilibrium of Mixtures of Charged Colloids . . 11.2 Sedimentation equilibrium of mixtures of charged colloids . . . 22 Overview of required statistical mechanics 52.1 Thermodynamics and Legendre transforms . . . . . . . . . . . 52.2 Phase space distributions and averages . . . . . . . . . . . . . 62.3 Density Functional Theory . . . . . . . . . . . . . . . . . . . . 72.3.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Mean Field Approximation and Local Density Approximation. . . . . . . . . . . . . . . . . . . . . . . . . . 83 Sedimentation of a monodisperse system 113.1 The system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Donnan-method . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Poisson-Boltzmann-method . . . . . . . . . . . . . . . . . . . 134 Sedimentation of a polydisperse mixture 154.1 The system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 The functional and minimum conditions . . . . . . . . . . . . 164.3 Binary systems . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4 Ternary systems . . . . . . . . . . . . . . . . . . . . . . . . . . 234.5 Polydisperse systems . . . . . . . . . . . . . . . . . . . . . . . 254.6 Explanation of phenomena . . . . . . . . . . . . . . . . . . . . 274.6.1 The influence of the diameter . . . . . . . . . . . . . . 304.6.2 The influence of the salt . . . . . . . . . . . . . . . . . 314.6.3 The layer width . . . . . . . . . . . . . . . . . . . . . . 314.6.4 The slope model . . . . . . . . . . . . . . . . . . . . . 324.6.5 Donnan-method for polydisperse cases . . . . . . . . . 384.6.6 The colloidal Brazil nut effect . . . . . . . . . . . . . . 40iii