Monotonic and oscillatory density profiles at the free liquid surface for simple atomic fluids

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Abstract
The singlet Born-Green-Yvon (BGY) equation is solved iteratively to obtain density profiles ρ(1)(z) at the free liquid surface for Lennard-Jones fluids at a variety of temperatures. Both monotonic and oscillatory profiles are obtained. Three methods of closing the BGY (i.e. specifying the pair distribution g (2)(r 1, r 2) in the interphase region) are used. All methods produce monotonic density profiles at higher temperatures whilst one yields oscillatory profiles of period about one atomic diameter at lower temperatures. The iterative procedure differs from those previously reported. It would appear that the closure approximations either over- or under-constrain the interface profile, in spite of hydrostatic equilibrium across the interface. The constraining effect is evidenced by a shift in Gibbs surface location for each successive iteration of the BGY. (The shift in all cases appears to converge to a small non-zero value.) Our approach takes into account the suppressant effect of these shifts when iterative profiles are superposed during the course of iteration. Previous studies reported only monotonic profiles, or numerical instability for the cases where oscillatory profiles develop in our work. The closure which yields the oscillatory profile is that which most over-constrains the interface.