Cross-Over Between First-Order and Critical Wetting at the Liquid-Vapour Interface of n-Alkane/Methanol Mixtures: Tricritical Wetting and Critical Prewetting

A simple mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn–Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Further, gravitational thinning of the wetting phase is incorporated. The calculation of the spreading coefficient S is extended to the experimentally relevant situation in which the bulk adsorbate is slightly away from two-phase coexistence due to gravity. Analysis of this novel approximation to S for systems with short-range forces leads to the conclusion that the surface specific heat exponents _s =1,1/2, and 0, for first-order wetting, tricritical wetting and critical wetting, respectively, are robust with respect to (weak) gravitational thinning, consistently with experiment. For three different systems the adsorption is calculated as a function of temperature and compared with the experimentally measured ellipticity. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment.     

Some aspects of the wetting transition1

The wetting of an attractive planar wall by liquid at liquid-gas coexistence is investigated from a microscopic point of view. A model for interface detachment due to thermal fluctuations is first worked out. An empirical framework for distinguishing between first-order and continuous wetting transitions is then set up, and quantified by the introduction of the van der Waals mean field model. This is solved for strong, short-range and weak, long-range forces. The role of fluctuations is reconsidered, and the nature of the required corrections examined, both for wall-fluid and fluid-fluid interfaces.This paper was presented at the conference on the Statistical Mechanics of Phase Transitions-Mathematical and Physical Aspects, Tebo, Czechoslovakia, September 1–6, 1986.     

Nonuniform van der Waals theory

The liquid-vapor interface of a confined fluid at the condensation phase transition is studied in a combined hydrostatic/mean-field limit of classical statistical mechanics. Rigorous and numerical results are presented. The limit accounts for strongly repulsive short-range forces in terms of local thermodynamics. Weak attractive longer-range ones, like gravitational or van der Waals forces, contribute a self-consistent mean potential. Although the limit is fluctuationfree, the interface is not a sharp Gibbs interface, but its structure is resolved over the range of the attractive potential. For a fluid of hard balls with –r ^–6 interactions the traditional condensation phase transition with critical point is exhibited in the grand ensemble: A vapor state coexists with a liquid state. Both states are quasiuniform well inside the container, but wall-induced inhomogeneities show up close to the boundary of the container. The condensation phase transition of the grand ensemble bridges a region of negative total compressibility in the canonical ensemble which contains canonically stable proper liquid-vapor interface solutions. Embedded in this region is a new, strictly canonical phase transition between a quasiuniform vapor state and a small droplet with extended vapor atmosphere. This canonical transition, in turn, bridges a region of negative total specific heat in the microanonical ensemble. That region contains subcooled vapor states as well as superheated very small droplets which are microcanonically stable.     

Wetting at a polymer gel–vapor interface; a system not influenced by a long-range van der Waals contribution

The exterior of a cross-linked polymer gel resembles a polymer brush. Such gel including its brush can be swollen by a good solvent. The detachment of the solvent–vapor (L–V) interface from the brush is controlled by the adsorption of polymer segments onto this interface and is to a very good approximation not influenced by long-range van der Waals contributions. A wetting transition in this system coincided with the adsorption–desorption transition for chains onto such L–V interface and has various unusual features. There are several indications that in practice this system should feature a second-order wetting transition.     

Theoretical investigation of van der Waals forces between solid surfaces at nanoscales

A theoretical investigation of van der Waals forces acting between two solid silicon surfaces at separations from zero to approximately 20 nm is presented. We focused our efforts on the analysis of different factors that can cause deviations from the classical pressure–distance dependence p  1/D³. It is demonstrated that a layer (oxide or water) at any of the surfaces influences the pressure up to distances, which are an order of magnitude larger than its own thickness. A jump on the p(D) curve is expected at contact of the adsorbed liquid layers. The retardation of van der Waals forces at 5 < D < 20 nm has the similar effect on the pressure as 1 nm oxide layers. At the far end of this range the pressure decreases by 30% due to the retardation. Nanoscale roughness plays a great role when the surfaces are close-to-contact, the crucial factor is the height distribution of asperities. However, their curvature and surface density are also important, as well as the amount of adsorbed water.     

What controls the thickness of wetting layers near bulk criticality?

We study the thickness of wetting layers in the binary-liquid mixture cyclohexane methanol. Far from the bulk critical point, the wetting layer thickness is independent of temperature, resulting from the competition between van der Waals and gravitational forces. Upon approaching the bulk critical temperature [t=(T(c)-T)/T(c)-->0], we observe that the wetting layer thickness diverges as t(-beta) with effective critical exponent beta=0.23+/-0.06. This is characteristic of a broad, intermediate scaling regime for the crossover from van der Waals wetting to critical scaling. We predict beta=beta/3 approximately 0.11, with beta the usual bulk-order parameter critical exponent, showing a small but significant difference with experiment.     

Effect of long-range forces on surface freezing

We examine the effect of long-range van der Waals interactions on surface freezing (SF) in linear hydrocarbon chain molecules, and the wetting criteria of the bulk liquid by the crystalline surface phase. We find that although the effect of van der Waals interactions is small for SF of normal alkanes, it is important for SF of dry and hydrated alcohols. We also find that the long-range interactions should not be ignored in the interpretation of wetting phenomena in recent experimental results. The results are in good agreement with recent experiments.     

Dewetting of polymer films by ion implantation

We report dewetting of thermodynamically stable, thick (∼ 100 nm) polystyrene films by titanium ion implantation. The dynamic dewetting patterns in time evolution are recorded. The dewetting mechanism is determined to be heterogeneous nucleation, where the defects and Ti nanoparticles formed by ion implantation serve as the nuclei. In addition, we observe abundant rims with regular polygonal shapes in dewetting patterns. This is attributed to fingering instability, which results from the balance between the driving force arisen from thermally induced surface tension gradient and the resistive forces from the combination of friction force, Laplace pressure and long-range van der Waals interactions. Finally, a model based on mass conservation is used to qualitatively describe the transition from circular to polygonal shaped rims at a critical diameter for holes.     

Second‐Order Dispersion Forces. I. Equations of Motion

Equations of motion for polarization on the S–P atomic transition in a weak resonance field have been derived taking into account the Van der Waals interaction between atoms. The case of two atoms is considered within the Wigner–Weisskopf formalism and generalized to the case of identical atoms in a weak resonance field, where the saturation is negligible. It is found that two equations of motion are necessary: one of them for the polarization and another one for an effective polarization relaxation rate.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

Contribution of macroscopic van der Waals interactions to friction forces

Using an approximation linear in velocities, an expression is obtained for friction forces due to nonretarded macroscopic van der Waals interactions. These forces are generated when field drag effects by a moving medium are taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 102–107, November, 1976.The author is grateful to Yu. S. Barash for critical remarks and discussions.     

Force spectroscopy in noncontact mode

We have analyzed the possibility of using noncontact scanning force microscopy (NCAFM) to detect variations in surface composition, i.e., to detect a ‘spectroscopic image' of the sample. This ability stems from the fact that the long-range forces, acting between the AFM tip and sample, depend on the composition of the AFM tip and sample. The long-range force can be magnetic, electrostatic, or van der Waals forces. Detection of the first two forces is presently used in scanning force microscopy technique, but van der Waals forces have not been used. We demonstrate that the recovery of spectroscopic image has a unique solution. Furthermore, the spectroscopic resolution can be as good as lateral one.     

Vibrational predissociation dynamics and internal rotation in aromatic van der Waals complexes

The Vibrational Predissociation (VP) lifetimes and dissociation channels are reported for the van der Waals complexes p-DiFluoroBenzene-Ar (pDFB-Ar), pDFB-N₂ and p-FluoroToluene-Ar (pFT-Ar). The dissociation occurs on theS ₁ potential energy surface after excitation of an S₁ ring breathing level with _vib 800 cm^–1. Trends are observed in the lifetimes and dissociation channels as the experiments move among the complexes. The VP characteristics of pFT-Ar are most distinctive. As opposed to all other aromatic complexes, pFT-Ar has little VP channel selectivity. These complexes are members of a set chosen to explore the VP vibrational dynamics by systematic changes of complex level structure. The change from pDFB-Ar to pDFB-N₂ introduces nearly free internal rotation in the complex partner and an additional van der Waals mode. pFT-Ar introduces a nearly free internal rotation attached directly to the ring. We discuss how these changes may be related to the observed VP dynamics.     

Theory of adsorbed thin films of helium

A model is proposed for the density profile in films of liquid helium adsorbed on solid substrates at temperatures below the -point. According to the model, the inhomogeneous part of the density profile is described by the contribution of van der Waals forces at all distances from the substrate greater than the thickness of the frozen helium layer. The connection between the mass of helium adsorbed on the surface and the average film thickness obtained on the basis of this model agrees with adsorption isotherms measured experimentally and may be used for a reliable determination of the thickness of thin films.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 16–20, September, 1981.     

Moment of van der Waals forces between anisotropic bodies

We find the moment of the van der Waals forces between two anisotropic uniaxial thick plates separated by a thick gap filled with isotropic material. Errors which occurred in [2, 3] in a discussion of this effect are pointed out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 21, No. 11, pp. 1637–1643, November, 1978.In conclusion, we thank V. L. Ginzburg, who brought the existence of the effect discussed in this article to the attention of the author.     

Differentielle Streuquerschnitte bei der Wechselwirkung neutraler Moleküle Messungen der Kleinwinkelstreuung

A molecular beam apparatus of high angular resolution is described, and measurements of the angular intensity distribution of alkali beams scattered at small angles (15 seconds of arc to 1 degree) by crossed beams of various gases and vapours are presented. Formulas, connecting the measured intensity with the differential cross section in the center of mass system, are derived, considering the velocity distribution in the beams and the geometry of the experimental set-up. The measurements show, that the differential cross section can be calculated down to very low angles (order of magnitude 10 minutes of arc) by means of classical mechanics, taking only into account the long-range attractive van der Walls interaction. At smaller angles, deviations, predicted by quantum mechanics, can be observed. If the potential of the van der Waals forces is written in the formV(r)=?C/r ^s, a method is outlined to determine bothC ands from the measured angular intensity distribution.     

Third-order approximation of the temperature expansion for a Bogolyubov “chain”

A solution of the Bogolyubov chain is found for a binary distribution function in the third-order approximation of the temperature expansion. The corresponding equations of state are obtained for a van der Waals crystal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 60–64,'November, 1976.     

Selective reflection spectroscopy on the UV third-resonance line of Cs: Simultaneous probing of a van der Waals atom-surface interaction sensitive to far IR couplings and interatomic collisions

We report on the analysis of FM selective reflection experiments on the 6S _1/2 → 8P _3/2 transition of Cs at 388 nm, and on the measurement of the surface van der Waals interaction exerted by a sapphire interface on Cs(8P _3/2). Various improvements in the systematic fitting of the experiments have permitted us to supersede the major difficulty of a severe overlap of the hyperfine components, originating, on the one hand, in a relatively small natural structure, and, on the other hand, on a large pressure broadening imposed by the high atomic density needed for the observation of selective reflection on a weak transition. The strength of the van der Waals surface interaction is evaluated to be 73 ± 10 kHz μm³. An evaluation of the pressure shift of the transition is also provided as a by-product of the measurement. Finally, we discuss the significance of an apparent disagreement between the experimental measurement of the surface interaction, and the theoretical value calculated for an electromagnetic vacuum at a null temperature. The possible influence of the thermal excitation of the surface is evoked, because the dominant contributions to the van der Waals interaction for Cs(8P _3/2) lie in the far-infrared range. Original Text ? Astro, Ltd., 2007.