Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of different morphologies such as droplets, channels or thin films is studied theoretically using the general framework of surface or interface thermodynamics. The first variation of the interfacial free energy leads to the well-known Laplace equation and a generalized Young equation which involves spatially dependent interfacial tensions. Furthermore, we perform the second variation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability criterion. The latter criterion is then applied to cylindrical segments or channels on homogeneous and structured surfaces. Received 4 August 1999     

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the lamellar and L₃ sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface. Received 4 November 1998     

Transfer of smectic films to a solid substrate by the method of Maclennan

We investigate monolayers of 2-alcohols (2-C9 to 2-C16) obtained by placing a drop of pure alcohol at the water surface. These alcohols are chiral molecules and we study the racemic mixtures. By ellipsometry and surface tension measurements we are able to characterize the 2D crystallization-melting transition with temperature. We find a first order transition. Using X-ray under grazing incidence we show that the racemic mixture crystallizes at 2D on a hexagonal cell. We find a parity effect on the lateral pressure at the transition and on the stability of the Bragg peak. We compare all results with those observed for 1-alcohols. Received: 11 April 1997 / Revised: 18 August 1997 / Accepted: 9 October 1997     

A method for calculating the surface tension of a droplet in a lattice-gas model with long-range interaction

Since the droplet of the lattice-gas model with long-range interaction is not circular and is determined by the Wulff construction due to surface tension anisotropy, a calculation method of the surface tension of the droplet is proposed in this paper. The calculated surface tension is in good agreement with the surface tension measured by using the Laplace's formula in consideration of the surface thickness. Received 15 March 2000 and Received in final form 31 May 2000     

Phase transitions in diglyceride monolayers studied by computer simulations,pressure-area isotherms and X-ray diffraction

Summary 1,2-sn-diglyceride monolayers exhibit unique and complex phase transitions as a function of surface pressure. The dynamical response of the layer on expanding the film has been investigated by computer simulations, (π-A) isotherms and grazing-incidence X-ray diffraction. Good agreement is found between the simulations and experiments. The Langmuir film undergoes two phase transitions occurring at 38.3 and 39.8 ?²/molecule. The transition at low surface density is associated with a tilt of ≈14° in the direction close to nearest neighbour. The first transition is unique for the diglyceride molecules and has not been observed for other amphiphilic molecules. It is driven by a competition of hydrophobic/hydrophilic and intra/intermolecular forces and can be pictured as a ?seesaw? mechanism. Due to the close packing of the chains at high surface pressure, thesn-1 ester group aligns with the alkyl chain, and only thesn-2 ester group is favoured to lay at the aqueous interface. Hydrophilic forces attract thesn-1 ester group, but its motion towards the aqueous subphase is hindered by intra- and intermolecular chain interactions. On expansion, the intermolecular interaction decreases, and at the first transition, the intramolecular interaction between the two chains is strong enough to cause a ?swelling? of the molecules. The diffraction pattern determined in the different mesophases reveals that the layer maintains its hexagonal structure up to the second phase. Concomitant with the tilt, the structure relaxed from a hexagonal to a distorted hexagonal lattice. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

The confinement of smectics with a strong anchoring

We examine several geometric features of the confinement of lamellar materials in complex geometries. When the anchoring of a sample at its boundaries (smectic-fluid interfaces or smectic-solid substrates interfaces) is strong enough, the geometric approximation of parallel layers can be extended to the bounding surface of the sample. Depending on the concavity of the interface, a strong planar anchoring is then compatible (or not) with a smectic organization in the bulk. We give the simplest smectic organization which satisfies a planar anchoring everywhere on the interface of axisymmetric inverse SmA droplets and compute its curvature energy. Eventually, the reason is given why the textures of direct and inverse SmA droplets are so much different (as it was first noticed in the pioneering work on SmA of Friedel and Grandjean). Received 11 May 2000     

Fluctuations at the domain edges of nematic liquid crystals in two dimensions

Capillary waves and director fluctuations reduce the surface tension of a non-anchoring unbound nematic surface by comparable amounts. These are relatively small effects in three dimensions, but in two dimensions they become more significant. We examine the conditions in two dimensions under which they dominate explicitly within the framework of a model of the Maier-Saupe type. We find that for reasonable physical parameters of the model the onset of the fluctuation dominated regime generally preempts the nematic-isotropic transition. We conclude that processes which are sensitive to line tension, such as Ostwald ripening during two-dimensional liquid-gas phase separation, are much more strongly coupled to anisotropic molecular interactions and associated nematic ordering than in three dimensions. Received 10 February 1999 and Received in final form 29 March 1999     

The lamellar-disorder interface: one-dimensional modulated profiles

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points. Received: 28 March 1997 / Revised: 6 February 1998 / Accepted: 16 February 1998     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

Stability of thin polymer films on a corrugated substrate

We study the wetting behaviour of thin polystyrene (PS) films on regularly corrugated silicon substrates. Below a critical film thickness the PS films are unstable and dewet the substrates. The dewetting process leads to the formation of nanoscopic PS channels filling the grooves of the corrugated substrates. Films thicker than the critical thickness appear stable and follow the underlying corrugation pattern. The critical thickness is found to scale with the radius of gyration of the unperturbed polymer chains. Received 6 April 2000 and Received in final form 24 August 2000     

Variable focal lens controlled by an external voltage: An application of electrowetting

We use electrocapillarity in order to change the contact angle of a transparent drop, thus realizing a lens of variable focal length (B. Berge, J. Peseux, Patent deposited in Grenoble France, October 8th 1997, numéro d'enregistrement national 97 12781). The key point is the application of gradients of wettability, which control the shape of the drop edge, in our case a centered circle of variable radius. The quality and reversibility of the lens are surprisingly good. The optical power variation can be 5 to 10 times the one of the human eye, for a comparable diameter, with a typical response time of 0.03 s and a dissipated power of a few mW. Received 1 December 1999     

Wetting of phospholipid membranes on hydrophilic surfaces - Concepts towards self-healing membranes

We report on the wetting behavior of phospholipid membranes on solid surfaces immersed in aqueous solution. Using fluorescence microscopy, the spreading velocity of fluid bilayers advancing from a lipid source is investigated. The kinetic spreading coefficient was measured as a function of temperature for pure DMPC membranes and as a function of charge density and cholesterol content for binary membranes. A theoretical model for the membrane flow is presented, which takes into account the liquid crystalline bilayer architecture of the lipid membrane. The spreading power results from the membrane-solid VdW interaction and is dissipated in hydrodynamic shear flow as well as by inter-monolayer friction within the bilayer. The frictional drag causes a dynamic tension gradient in the spreading membrane, which is manifested by a single exponential decay of the fluorescence intensity profile along the spreading direction. Obstacles are shown to act as pinning centers deforming the advancing line interface. However, no depinning was observed, since the centers are circumflown without abrupt relaxation. Received 6 November 1998     

Spinodal dewetting of thin liquid films at soft interfaces

We study theoretically the behavior of nanoscopic liquid films L (thickness e) intercalated between a solid S and a rubber R (elastic modulus μ). Thickness modulations involve a healing length , which results from a competition between elastic and disjoining pressure. With van der Waals interactions, , where a is a molecular size and h₀ the rubber capillary length ( , interfacial tension). If the Hamaker constant of the intercalated liquid is negative, the film dewets by amplification of peristaltic fluctuations (“spinodal dewetting”). The typical size of the contacts is predicted to scale like for films of thicknesses . The rise time of the fastest mode, predicted to scale like , should be very sensitive to the film thickness. Received 11 February 2000 and Received in final form 22 May 2000     

Polyelectrolytes tethered to a free surface

Several attempts have been already carried out in order to tether charged chains by an end at a free fluctuating surface. We review here most of these attempts and focus on how close the physics of charged brushes can be investigated by such an approach. We first describe results about films of charged-neutral diblock copolymers spread at the surface of water. Results can be mostly rationalized in terms of charged brushes although additional structurations and fluctuations of the interface can be observed. The latter deformations are also observed when adsorbed layers of charged-neutral diblock copolymers are considered. At last, we examine how free suspended films of charged-neutral diblock copolymers can be viewed as two opposing charged brushes, both in terms of thickness and pressure. Received 9 May 2000     

Adsorption and spreading of polymers at plane interfaces; theory and molecular dynamics simulations

Nonequilibrium processes play a key role in the adsorption kinetics of macromolecules. It is expected that the competition between transport of polymer towards an interface and its subsequent spreading has a significant influence on the adsorbed amount. An increase of the transport rate can lead to an increase of the adsorbed amount, especially when the polymer has too little time to spread at the interface. In this study we present both molecular dynamics simulations and analytical calculations to describe some aspects of the adsorption kinetics. From MD simulations on a poly(ethylene oxide) chain in vacuum near a graphite surface, we conclude that the spreading process can, in first approximation, be described by either a simple exponential function or by first-order reaction kinetics. Combining these spreading models with the transport equations for two different geometries (stagnation-point flow and overflowing cylinder) we are able to derive analytical equations for the adsorption kinetics of polymers at solid-liquid and at liquid-fluid interfaces. Received: 18 July 1997 / Received in final form: 27 October 1997 / Accepted: 6 November 1997     

Humidity effects on the stability of a sandpile

Humidity is well-known to significantly affect the mechanical properties, static as well as dynamic, of granular materials. We present the method of humidification of granular media from an under-saturated vapor that we designed in order to experimentally quantify such moisture-induced effects under accurately-controlled humidity conditions. We report the quantitative measurements of the maximum angle of stability of a pile made of small glass beads, as a function of the relative vapor pressure, up to close to saturation. The results obtained with liquids differing in their wetting properties on glass, namely water and heptane, are presented. It is shown that the wetting properties of the liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. Received 26 October 1998 and Received in final form 30 March 1999     

Coalescence in 2 dimensions: experiments on thin copolymer films and numerical simulations

This paper presents on one hand the experimental study of the coalescence kinetics of two closed bidimensional fluid domains at the surface of a multilayered dibloc copolymer film, and on the other hand a numerical simulation of the same evolution. The latter is based on ”diffusive” phenomenological equations which are surface conservative and which neglect the 2-dimensional viscosity of the layers. The successive shapes observed in the experiments and obtained from the simulation are very close. It would not be the case if the 2D viscosity was significant. Received : 17 march 1997 / Revised : 11 september 1997 / Accepted : 2 december 1997     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999