Comment on "Simple theory for the critical adsorption of a fluid"

Abstract

Henderson [Phys. Rev. A 32, 2336 (1985)] has proposed that the critical exponent for adsorption should be either \ensuremath{\gamma} or \ensuremath{\gamma}/2, where \ensuremath{\gamma} is the (bulk) compressibility exponent. It is shown that both results are artifacts of the mean spherical approximation (MSA) employed by Henderson. The MSA, and closely related closures of the wall-particle Ornstein-Zernike equation, are essentially linear-response approximations which neglect nonlinearities that are crucial in critical adsorption, even at the mean-field level. Our argument is made explicit by re-deriving the correct (Fisher--de Gennes) exponent \ensuremath{\nu}-\ensuremath{\beta} and illustrating the failings of linearized treatments. Since the latter also fail to describe complete wetting, their validity is restricted to states well removed from bulk two-phase coexistence.