Asymptotic density profiles for liquid-vapor interfaces

Includes bibliographical references (pages 49-50)The nature of the density profile in the vicinity of the liquid-\ud vapor interface is determined by a statistical mechanical approach\ud based on the Born-Green equation which involves two unknowns in the\ud interfacial region: the density function and the pair correlation\ud function.\ud Elimination of the correlation function by means of the\ud Pressing-Mayer distribution function of homogeneous fluid yields the\ud nonlinear integral equation determining density as a function of\ud position through the interface.\ud By considering the outer asymptotic regions of the interface\ud bordering on the bulk phases, the equation can be linearized in the\ud deviation of the local density from the bulk value.\ud For molecules interacting with a square-well potential, analytical\ud solutions are obtained at a series of temperatures spanning\ud the entire range of coexistence of liquid and vapor. These asymptotic\ud solution for the density function exhibit exponential behavior on\ud the vapor side of the interface but the behavior on the liquid side\ud depends on temperature, being exponential at the higher temperatures\ud but changing over to a damped oscillation below a certain temperature\ud - and eventually becoming a pure oscillation at a still lower temperature.\ud In this way, the liquid becomes compatible with the vapor\ud phase as the temperature rises toward the critical point where the\ud phases must merge into one while in the other direction as the temperature\ud becomes lower it prepares the way for the appearance of the\ud crystallized solid