Measuring structure and interactions in colloidal fluids using test-particle insertion

We use the Potential Distribution Theorem to evaluate distribution functions from equilibrium configurations using test-particle insertion. We use this methodology to determine the contact value of the pair distribution function in hard-disk systems: in contrast with the conventional distance-histogram method, the insertion measurement is exact and does not require an approximate extrapolation. The resulting equations of state in both simulations and a hard-disk colloidal model system agree well with the predictions of Scaled Particle Theory. We also provide the first experimental measurement of the cavity distribution function y(2)(r) inside the hard core. We next develop a model-free technique for measuring the pair potential u(2)(r) in pairwise-additive fluids, by matching the insertion and distance-histogram measurements of g(2)(r) using an iterative predictor-corrector scheme. We test the method extensively in simulation, before applying it successfully in a fluid of superparamagnetic colloidal particles, obtaining the anticipated form of u(2)(r) and the correct dependence on the applied magnetic field. We then extend the scheme to measure the full set of pair potentials in multicomponent fluids, demonstrating its efficacy in a three-component simulation. We show that a given n-body distribution function g(n) (n>2) can be measured using n different insertion routes, which correspond to simultaneous insertion of between 1 and n test particles. We use these methods to measure g(3) in simulation: while the noise depends strongly on the number of simultaneous insertions, the resolution is superior to that of the distance-histogram method. Finally, we consider systems with three-body interactions. We show that matching g(2)(r) alone gives an effective pair potential which is unable to reproduce g(3) in pairwise-additive simulations. We therefore extend the predictor-corrector scheme to measure the three-body interaction u(3) by matching g(3), and test it in simulation. The scheme broadly recovers the correct u(3), but requires further development to reduce the noise.