P. Müller

Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf-Kaishew theorem)

Abstract A generalised Wulf–Kaishew theorem is given describing the equilibrium shape (ES) of an isolated 3D crystal A deposited coherently onto a lattice mismatched planar substrate. For this purpose a free polyhedral crystal is formed then homogeneously strained to be accommodated onto the lattice mismatched substrate. During its elastic inhomogeneous relaxation the epitaxial contact remains coherent so that the 3D crystal drags the atoms of the contact area and produces a strain field in the substrate. The ES of the deposit is obtained by minimising at constant volume the total energy (bulk and surface energies) taking into account the bulk elastic relaxation. Our main results are as follows. (1) Epitaxial strain acts against wetting (adhesion) so that globally it leads to a thickening of the ES. (2) Owing to strain the ES changes with size. More precisely the various facets extension changes, some facets decreasing, some others increasing. (3) Each dislocation entrance, necessary for relaxing plastically too large crystals abruptly modifies the ES and thus the different facets extension in a jerky way. (4) In all cases the usual self-similarity with size is lost when misfit is considered. We illustrate these points for box-shaped and truncated pyramidal crystals. Some experimental evidence is discussed.A generalised Wulf-Kaishew theorem is given describing the equilibrium shape (ES) of an isolated 3D crystal A deposited coherently onto a lattice mismatched planar substrate. For this purpose a free polyhedral crystal is formed then homogeneously strained to be accommodated onto the lattice mismatched substrate. During its elastic inhomogeneous relaxation the epitaxial contact remains coherent so that the 3D crystal drags the atoms of the contact area and produces a strain field in the substrate. The ES of the deposit is obtained by minimising at constant volume the total energy (bulk and surface energies) taking into account the bulk elastic relaxation. Our main results are: (1) Epitaxial strain acts against wetting (adhesion) so that globally it leads to a thickening of the ES. (2) Owing to strain the ES changes with size. More precisely the various facets extension changes, some facets decreasing, some others increasing. (3) Each dislocation entrance, necessary for relaxing plastically too large crystals abruptly modifies the ES and thus the different facets extension in a jerky way. (4) In all cases the usual self-similarity with size is lost when misfit is considered. We illustrate these points in case of box shaped and truncated pyramidal crystals. Some experimental evidences are discussed.

Adsorption Kinetics of Amphiphilic Diblock Copolymers: From Kinetically Frozen Colloids to Macrosurfactants

We investigated the spontaneous adsorption properties of charged amphiphilic diblock copolymers on hydrophobic surfaces and explained the transition of behavior from depleting frozen colloids (that do not adsorb at all) to fast adsorbing macrosurfactants when the hydrophobicity of the nonsoluble block is reduced. Three copolymer families have been used with the same hydrophilic block poly(acrylic acid), a weak acid whose ionization alpha can be varied by changing the pH. The hydrophobic blocks polystyrene, PS, poly(n-butyl acrylate), PBA, and poly(diethylene glycol ethyl ether acrylate), PDEGA, have interfacial tensions with water gammacore/solvent, respectively, of 32, 20, and 3 mN/m. We were mainly interested in the regime of high ionization alpha > 0.3, where PAA chains have no affinity for hydrophobic surfaces, and we verified experimentally that micelles do not adsorb directly. With the three copolymer families we show that the adsorption kinetics at an early stage is driven by the self-assembly properties in bulk solution: adsorption is hampered for PS-b-PAA (physically/kinetically frozen micelles in solution), controlled by unimer extraction for PBA-b-PAA (nonequilibrium micelles in solution with very low CMC < 10-4 wt %), and controlled by unimer diffusion and electrostatic repulsion for PDEGA-b-PAA (micelles at equilibrium in solution with high CMC is approximately 1-5 wt %). This explains the power law dependences of adsorption with concentration as C-1 for PBA-b-PAA and C-2 for PDEGA-b-PAA. It is finally the interfacial tension with water of the nonsoluble block and not its glass transition that is the main control of bulk solution self-assembly and consequently of the adsorption kinetics properties of amphiphilic diblocks. We also proved by preparative GPC that the fraction of non-self-assembling diblock chains, which exists in all highly hydrophobic amphiphilic diblock systems, plays a negligible role in the adsorption properties. Finally, we investigated the intrinsic thermodynamic affinity between amphiphilic diblocks and hydrophobic surfaces. We show quantitatively that this affinity depends dominantly on the interfacial energies between the hydrophobic block, the surface, and water: diblocks with strongly hydrophobic nonsoluble blocks (PS, PBA) have a low affinity for weakly hydrophobic surfaces, and oppositely, diblocks with weakly hydrophobic nonsoluble block (PDEGA) have a universal affinity for hydrophobic surfaces (like small-molecule surfactants but for different physical reasons). Finally, we showed via surface rheology that when adsorption occurs anchoring is strong and irreversible for very hydrophobic diblocks (PBA-b-PAA) and weaker and (partially) reversible for less hydrophobic diblocks (PDEGA-b-PAA).

About the measurement of absolute isotropic surface stress of crystals

Abstract Some recent publications report measurements of the curvature of thin asymmetric sheets and deduce the difference of surface stress ( s 1 − s 2 ) of both its faces 1 and 2 using a simple formula due to Stoney. An exact formulation gives a relation where ( s 1 + s 2 ) enters also. It is shown here how, for thin sheets, ( s 1 − s 2 ) and ( s 1 + s 2 ) can be measured and therefore the absolute surface stresses s 1 and s 2 . For thicker sheets, only ( s 1 − s 2 ) can be measured. Two experimental methods for measuring the absolute surface stresses are proposed.

Self-assembly of charged amphiphilic diblock copolymers with insoluble blocks of decreasing hydrophobicity: from kinetically frozen colloids to macrosurfactants.

We have investigated the self-assembly properties in aqueous solution of amphiphilic diblock copolymers with insoluble blocks of different hydrophobicity and demonstrated that the condition to obtain dynamic micelles is to design samples with insoluble blocks of low enough hydrophobicity. We focus here on results with new water-soluble amphiphilic diblock copolymers poly(diethyleneglycol ethylether acrylate)-b-poly(acrylic acid), or PDEGA-b-PAA. The physical characteristics of PDEGA-b-PAA micelles at high ionization have been determined by small angle neutron scattering (SANS). We show that PDEGA-b-PAA samples form micelles at thermodynamic equilibrium. The critical micelle concentrations (CMCs) decrease strongly with ionic strength and temperature due to a solvent quality decrease for, respectively, the corona and the core. This behavior of reversible aggregation is remarkable as compared to the behavior of kinetically frozen aggregation that has been widely observed with samples of similar architecture and different hydrophobic blocks, for example, poly(styrene)-b-poly(acrylic acid), PS-b-PAA, and poly(butyl acrylate)-b-poly(acrylic acid), PBA-b-PAA. We have measured the interfacial tension between water and the homopolymers PDEGA and PBA at, respectively, 3 and 20 mN/m at room temperature, which permits one to estimate the energy cost to extract a unimer from a micelle. The results are consistent with a micelle association that is fast for PDEGA-b-PAA and kinetically frozen PBA-b-PAA. Hence, PDEGA-b-PAA samples form a new system of synthetic charged macrosurfactant with unique properties of fast dynamic association, tunable charge, and water solubility even at temperatures and NaCl concentrations as high as 65 °C and 1 M.

Conformational analysis and estimation of the persistence length of DNA using atomic force microscopy in solution

The worm-like chain model describes the mechanical properties of semi-flexible polymers by introducing a certain correlation length along the contour. This correlation length is called the persistence length. Using atomic force microscopy in solution, we performed measurements of the persistence length of DNA molecules. We found good agreement between the theoretical model and experimental data. However, the measured persistence length values in solution differ from those found by several authors using the same technique but in dry air. In order to determine the contribution of the electrostatic persistence length to the total persistence length, we varied the salt concentration. We found a large discrepancy between the Odijk, Skolnick and Fixman theory and our measurements. The effect of divalent ions and the omission in the theory of the dependence of non-electrostatic persistence length on salt concentration are qualitatively invoked.

Asymptotic behaviour of stress establishment in thin films

The purpose of this letter is to investigate the asymptotic behaviour of stress establishment in two-dimensional supported films. For this purpose, surface excess quantities are corrected for finite size effects arising from long-range interactions. The predicted results are compared with the available experimental data for Ge/Si(001) and Au/Ni(111) systems.

Interfacial Activity of Phosphonated-PEG Functionalized Cerium Oxide Nanoparticles

In a recent publication, we have highlighted the potential of phosphonic acid terminated PEG oligomers to functionalize strong UV absorption cerium oxide nanoparticles, which yield suspensions that are stable in aqueous or organic solvents and are redispersible in different solvents after freeze-drying. In the present work, we highlight the interfacial activity of the functional ceria nanoparticles and their potential to modify hydrophobic surfaces. We first investigated the phosphonated-PEG amphiphilic oligomers behavior as strong surface active species forming irreversibly adsorbed layers. We then show that the oligomers interfacial properties translate to the functional nanoparticles. In particular, the addition of a small fraction of phosphonated-PEG oligomers with an extra C16 aliphatic chain (stickers) into the formulation enabled the tuning of (i) the nanoparticles adsorption at the air/water, polystyrene/water, oil/water interfaces and (ii) the particle/particle interaction in aqueous solutions. We also found that dense and closely packed two-dimensional monolayers of nanoceria can be formed by spontaneous adsorption or surface compression using a Langmuir trough. A hexagonal organization controlled by reversible and repulsive interaction has been characterized by GISAXS. Mono- or multilayers can also be stably formed or transferred on solid surfaces. Our results are key features in the field of polymer surface modification, solid-stabilized emulsions (Pickering), or supracolloidal assemblies.

Deformation of an elastic thin solid induced by a liquid droplet

The aim of this study is to formulate and solve the equilibrium shape of a liquid droplet of contact radius r0 in the middle of an elastic isotropic thin solid sheet of radius l, by using the different surface concepts such as surface free energy and surface stress. This is achieved by determining the form of the interfaces as a result of minimization of the total free energy of the system. The profiles are obtained from integration of Eulers differential equations. An interpretation of these equations is given in terms of mechanical forces. In the domain 0 10 when considering usual solids of Young-modulus E = 1012 erg cm−3. Earth gravity does not influence markedly the results for drops with r0 < 0.1 cm. The effect of surface stress s depends on the characteristic length |s|/D. It becomes numerically important only for very thin sheets. The total surface stress in 0 < r < r0 may enhance or decrease the sag according its sign. Instabilities (buckling) may occur above some limiting value |s|/D. For negative surface stress, the profile outside the droplet (r0 < r < l) shows oscillations which represent a stable situation. A sheet without droplet with negative surface stress shows buckling if its size l exceeds some critical value. The presence of a droplet is able to stabilize this situation. The final equilibrium problem is only solved by optimizing also the size r0 of the droplet so that the total free energy is minimal. From this, the wetting angle α and the deformation angle β at the triple line are given analytically. The elastic properties of the sheet determine not only β but also influences slightly α. Finally, according to a tradition going back to Young-Maxwell and for the purpose in hands, we consider average thermodynamic forces acting along the triple line. We show that Young-Maxwells construction based on Neumanns triangle is possible. Our equations show that Youngs famous equation of wetting is true up to the second order of the deformation angle β. Calculating this order an extended Youngs equation is given. Our general result is easily brought to the special cases where the droplet lies either on a membrane or on another liquid surface.

Elastic relaxation during 2D epitaxial growth : a study of in-plane lattice spacing oscillations

The purpose of this paper is to report some new experimental and theoretical results about the analysis of in-plane lattice spacing oscillations during two-dimensional (2D) homo and hetero epitaxial growth. The physical origin of these oscillations comes from the finite size of the strained islands. The 2D islands may thus relax by their edges, leading to in-plane lattice spacing oscillations during the birth and spread of these islands. On the one hand, we formulate the problem of elastic relaxation of a coherent 2D epitaxial deposits by using the concept of point forces and demonstrate that the mean deformation in the islands exhibits an oscillatory behaviour. On the other hand, we calculate the intensity diffracted by such coherently deposited 2D islands by using a mean model of a pile-up of weakly deformed layers. The amplitude of in-plane lattice spacing oscillations is found to depend linearly on the misfit and roughly linearly on the nucleation density. We show that the nucleation density may be approximated from the full-width at half maximum of the diffracted rods at half coverages. The predicted dependence of the in-plane lattice spacing oscillations amplitude with the nucleation density is thus experimentally verified on V/Fe(001), Mn/Fe(001), Ni/Fe(001), Co/Cu(001) and V/V(001).

Step-driven molecular adsorption of Sb on Si(111)

Abstract Adsorption of Sb on a misoriented Si(111) surface is investigated by thermodesorption Auger spectroscopy. The spectra reveal that, in the submonolayer range, new adsorption states appear for the vicinal surface which do not exist for the nominal one. Quenched molecular-dynamics simulations, in which Si and Sb are modeled by many-body tight-binding potentials, allow us to interpret these new states as due to a molecular adsorption at the steps instead of a dissociative one on the terraces.