Local-functional theory of critical adsorption

Critical energy-density profile near walls

We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is "wet." It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface.

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980)PHYADX0378-437110.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ(r), where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ(r) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h_{1}, where the surface order parameter ψ(a) is determined by h_{1} and is independent of the radius a. If r considerably exceeds a, ψ(r) decays as r^{-(1+η)} for a sphere and r^{-(1+η)/2} for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.

Crossover aspects in Ising strips under the influence of variable surface fields and a grain boundary

I use an exact variational formulation of Mikheev and Fisher to study the critical Ising strip with a grain boundary and confining surfaces characterized by arbitrary and different surface magnetic fields. Energy density profiles that serve as order parameters of the system within the used method show strong nonmonotonous behavior in the vicinity of confining surfaces. I consider short-distance expansion of energy density profiles. New universal amplitudes associated with distant-wall corrections exhibit nontrivial crossover behaviors from positive to negative values as the field's variables are continuously varied. Casimir amplitudes calculated in a self-contained manner are characterized by complex manifolds which may comprise two disconnected positive wings separated by an area of negative values. I define and determine the generalized de Gennes-Fisher amplitude, which strongly suggests that a stress tensor is present within one of the distant-wall corrections. This is an unanticipated result given that a similar discovery for standard extraordinary (E) and ordinary (O) surface universality classes was based on the conformal invariance symmetry, which is broken under the present boundary conditions. A grain boundary essentially influences both energy density profiles and Casimir amplitudes, besides surface fields with a number of accompanying features that are examined in detail. We present closed analytic forms of energy density profiles for standard (N) and (O) BCs: ɛNN(x,g),ɛOO(x,g),ɛNO(x,g) [(N) is the normal surface universality class, g is the grain boundary's strength, x is the relative distance x:=z/L with L as a film width], thus enabling us to deduce their important symmetry properties and to have a detailed insight into their general behaviors.

Critical-point universality in adsorption: the effect of charcoal on a mixture of isobutyric acid and water near the consolute point

The mixture of isobutyric acid and water has a consolute point at a temperature of 25.75 °C and mole fraction 0.1148 isobutyric acid. When charcoal is added to this mixture, the concentration of isobutyric acid is reduced by adsorption. We have measured the action of charcoal on solutions of isobutyric acid and water as a function of isobutyric acid mole fraction at temperatures of 25.85 and 32.50 °C. At the higher temperature, the specific adsorption density (y(2)(α)/m) satisfies the Freundlich equation (y(2)(α)/m)=KX(2)(1/n), where y(2)(α) is the mass of isobutyric acid adsorbed, m is the mass of charcoal, X(2) is the equilibrium mole fraction of isobutyric acid, n is the Freundlich index, and K=K(T) is an amplitude that depends upon the temperature T. At 25.85 °C, a critical endpoint is located at an isobutyric acid mole fraction X(2)(ce)=0.09. When compared with the Freundlich equation at this temperature, a plot of the specific adsorption density as a function of X(2) in the vicinity of the critical-endpoint composition assumes a shape which is reminiscent of the derivative of a Dirac delta function. Using critical-point scaling theory, we show that this divergent pattern is consistent with the principle of critical point universality.

Comparison of critical adsorption scaling functions obtained from neutron reflectometry and ellipsometry

Carpenter et al. [Phys. Rev. E 59, 5655 (1999); 61, 532 (2000)] managed to explain ellipsometric critical adsorption data collected from the liquid-vapor interface of four different critical binary liquid mixtures near their demixing critical temperature using a single model. This was the first time a single universal function had been found which could quantitatively describe the surface critical behavior of many different mixtures. There have also been various attempts to investigate this surface critical behavior using neutron and x-ray reflectometries. Results have been mixed and have often been at variance with Carpenter et al. In this paper, the authors show that neutron reflectometry data collected from a crystalline quartz-critical mixture interface, specifically deuterated water plus 3-methylpyridine, can be quantitatively explained using the model of Carpenter et al. derived from ellipsometric data.

Critical adsorption at silicon surfaces in binary liquid mixtures

In critical binary liquid mixtures the preferential adsorption that occurs at liquid-vapor or liquid-solid surfaces is expected to be described by a universal surface scaling function. In this paper, we show that aniline strongly adsorbs at an oxide-coated Si wafer surface from a critical mixture of aniline + cyclohexane where this solid-liquid adsorption can be described by the same universal function found at liquid-vapor surfaces. For a tetrabromoethane + n-dodecane critical mixture the n-dodecane adsorption on an alkylsilane coated Si wafer cannot be described by previously determined adsorption functions. We speculate that this discrepancy is caused by chemical heterogeneities at the alkylsilane surface due to differing surface distributions of -CH3 and -CH2- groups within the silane layer.

Scaling for interfacial tensions near critical endpoints

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the full neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function both of temperature and of density/order parameter or chemical potential/ordering field. Accurate nonclassical critical exponents and reliable estimates for the universal amplitude ratios are included naturally on the basis of the "extended de Gennes-Fisher" local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out "manually." Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio -3.25+/-0.05 is predicted.

Ellipsometric study of undersaturated critical adsorption

At the liquid-vapor surface of a critical AB binary liquid mixture, if the surface energies sigma(A)<<sigma(B), then component A completely saturates the surface and one is in the regime of strong critical adsorption where the local volume fraction at the surface is solely a function of z/xi where xi is the bulk correlation length and z is the depth into the liquid. If, however, sigma(A) approximately sigma(B) then the surface composition is a sensitive function of the surface energy difference Deltasigma=sigma(A)-sigma(B) and the surface is "undersaturated." We study this undersaturated critical adsorption regime using a homologous series of critical binary liquid mixtures. Component B (methyl formate) is fixed, while component A is varied from n-undecane to n-tetradecane. With increasing carbon chain length Deltasigma changes systematically from a negative to a positive value. We find that the experimental results, in both the one- and two-phase regions, are well described by a universal surface scaling function G(z/xi,h(1)t(-Delta(1))), where h(1) approximately Deltasigma, t=[T(c)-T]/T(c) is the reduced temperature relative to the critical temperature (T(c)), and Delta(1) is a universal surface critical exponent. These results are in conformity with theoretical predictions.