6533b870fe1ef96bd12d0454

RESEARCH PRODUCT

Qualitative characterisation of effective interactions of charged spheres on different levels of organisation using Alexander’s renormalised charge as reference

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Abstract Effective interactions are conveniently determined from experimental or numerical data by fitting a Debye–Huckel potential with an effective charge Z ∗ and an effective electrolyte concentration c ∗ as free parameters. In this contribution we numerically solved the Poisson–Boltzmann equation to obtain the so-called renormalised charge Z PBC ∗ . For sufficiently large bare charge Z one finds a saturation of Z ∗ which scales as Z ∗ = A a / λ B , where a is the particle radius, λ B the Bjerrum length and A a proportionality factor of order (8–10). The saturation value increases with increased total micro-ion concentration and shows a shallow minimum as a function of packing fraction. In addition, the bulk shear modulus G was measured along the melting line of a colloidal crystal to obtain Z G ∗ and molecular dynamics simulations were performed within the primitive model for a pair of particles at different added salt concentration to obtain Z MD ∗ . Z PBC ∗ was then used as reference for an extensive comparison to other effective charges as obtained in the present paper and taken from literature. We observe Z G ∗ to be somewhat smaller than Z PBC ∗ and other bulk experimental effective charges, while the simulation yields Z MD ∗ ≈ Z ≫ Z PBC ∗ . These differences are discussed in the light of charge renormalisation concepts and three and many body interactions.