An exactly solvable model for a colloid–polymer mixture in one-dimension

We consider the equilibrium properties of a simple one-dimensional model for a colloid–polymer mixture in which the colloids are modelled by hard rods and the polymers are treated as ideal particles excluded from the colloids by a certain distance. By mapping the binary mixture to an effective one-component Hamiltonian the model can be solved exactly for size ratios σp/σc≡q<1, where σc and σp are the lengths of colloid and polymer rods, respectively. We compare exact results for the osmotic pressure and free-volume fraction with those of the free-volume approximation, developed in the study of model colloid–polymer mixtures in three dimensions, in order to establish where that approximation is accurate and where it breaks down.