Weak Critical Adsorption

We study critical adsorption in the limit of a small surface field (h₁) using a homologous series of critical liquid mixtures where A=n-alkane (C11 to C14) and B=methyl formate. The experimental data, in the one phase regime, is accurately described by a universal surface scaling function G_±(z/x_±, z/l_h) at distance z from the interface with correlation length x_± and surface field length l_h~|h₁|^{- n/D1} where h₁~Ds, the surface energy difference between the two components.

Further readings:  J. -H. J. Cho, B. M. Law, Phys. Rev. Lett. 86, 2070 (2001).
                           J. –H. J. Cho and B. M. Law, Phys. Rev. E 65, 11601 (2001).
 

Comparison of the ellipticity r for the C11 mixture with various theoretical models. Experiment: one- (squares) and two-phase (circles) data. Theory: P± (dashed lines) and G± (solid lines) models. The residuals R=(ri-rGi)/smin are also shown for the G± model (triangles) in the one-phase region.

Comparison of the ellipticity r for the C12, C13, and C14 mixtures. Experiment: one- (squares) and two-phase (circles) data where the open (solid) symbols represent stable (metastable) data. Theory: G±  model (solid lines).

Plot of (lh/ xo+)-D1/n versus |sA-sB|/kBTc for the G± model (circles). The solid line represents a linear fit through this data set with the constraint that the line passes through the origin to ensure that h1=0  (lh --> infinity) when sA=sB.