Fluids in contact with a hard surface: Universality of the bridge functions for the density profile

The modified hypernetted chain theory (MHNC) for density profiles of fluids in contact with a hard, smooth surface is found to possess a remarkably simple and interesting property: The accuracy of the MHNC and the universality of the bridge functions for the density profiles can be tested without resort to any detailed solution of the integral equations. It is given by the degree of universality of the bulk bridge parameter (e.g., η for the Percus–Yevick hard‐sphere bridge function) when expressed in terms of the second partial derivative of the free energy with respect to the density F. The function η (F) as obtained from MHNC calculations for bulk simple fluids is found to be remarkably independent of the pair potential. As an example for the accuracy of the resulting method, the one‐component plasma near a hard wall is discussed.