Contact values of pair distribution functions in colloidal hard disks by test-particle insertion

We apply Henderson’s method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method’s flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry