arXiv subjects

Olivier Pierre-Louis

Publications and source records attributed to Olivier Pierre-Louis.

28 records · Page 2Linked to original sources

arXiv2018

Crystal growth in nano-confinement: Subcritical cavity formation and viscosity effects

We report on the modeling of the formation of a cavity at the surface of crystals confined by a flat wall during growth in solution. Using a continuum thin film model, we discuss two phenomena that could be observed when decreasing the thickness of the liquid film between the crystal and the wall down to the nanoscale. First, in the presence of an attractive van der Waals contribution to the disjoining pressure, the formation of the cavity becomes sub-critical, i.e., discontinuous. In addition, there is a minimum supersaturation required to form a cavity. Second, when the thickness of the liquid film between the crystal and the substrate reaches the nanoscale, viscosity becomes relevant and hinders the formation of the cavity. We demonstrate that there is a critical value of the viscosity above which no cavity will form. The critical viscosity increases as the square of the thickness of the liquid film. A quantitative discussion of model materials such as Calcite, Sodium Chlorate, Glucose and Sucrose is provided.

cond-mat.soft↗

arXiv2018

Cavity formation in confined growing crystals

Growing crystals form a cavity when placed against a wall. The birth of the cavity is observed both by optical microscopy of sodium chlorate crystals (NaClO$_3$) growing in the vicinity of a glass surface, and in simulations with a thin film model. The cavity appears when growth cannot be maintained in the center of the contact region due to an insufficient supply of growth units through the liquid film between the crystal and the wall. We obtain a non-equilibrium morphology diagram characterizing the conditions under which a cavity appears. Cavity formation is a generic phenomenon at the origin of the formation of growth rims observed in many experiments, and is a source of complexity for the morphology of growing crystals in natural environments. Our results also provide restrictions for the conditions under which compact crystals can grow in confinement.

cond-mat.other↗

arXiv2018

Thin film modeling of crystal dissolution and growth in confinement

We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the non-equilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution. We find that in steady-state, diverging (power-law) crystal-surface repulsions lead to flat contacts with a monotonic increase of the dissolution rate as a function of the load. Forces induced by viscous dissipation then surpass those due to disjoining pressure at large enough loads. In contrast, finite repulsions (exponential) lead to sharp pointy contacts with a dissolution rate independent on the load and on the liquid viscosity. Ultimately, in steady-state the crystal never touches the substrate when pressed against it, independently from the nature of the crystal-surface interaction due to the combined effects of viscosity and surface tension.

cond-mat.soft↗

arXiv2015

Transition to coarsening for confined one-dimensional interfaces with bending rigidity

We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimension hydrodynamic model, where membranes are effectively one-dimensional objects. In a previous work [T. Le Goff et al, Phys. Rev. E 90, 032114 (2014)], we have shown that this model predicts frozen states caused by bending rigidity-induced oscillatory interactions between kinks (or domain walls). We here demonstrate that in the presence of tension, potential asymmetry, or thermal noise, there is a finite threshold above which frozen states disappear, and perpetual coarsening is restored. Depending on the driving force, the transition to coarsening exhibits different scenarios. First, for membranes under tension, small tensions can only lead to transient coarsening or partial disordering, while above a finite threshold, membrane oscillations disappear and perpetual coarsening is found. Second, potential asymmetry is relevant in the non-conserved case only, i.e. for permeable walls, where it induces a drift force on the kinks, leading to a fast coarsening process via kink-antikink annihilation. However, below some threshold, the drift force can be balanced by the oscillatory interactions between kinks, and frozen adhesion patches can still be observed. Finally, at long times, noise restores coarsening with standard exponents depending on the permeability of the walls. However, the typical time for the appearance of coarsening exhibits an Arrhenius form. As a consequence, a finite noise amplitude is needed in order to observe coarsening in observable time.

cond-mat.soft↗

arXiv2015

Kink dynamics with oscillating forces

It is well known that the dynamics of a one-dimensional dissipative system driven by the Ginzburg-Landau free energy may be described in terms of interacting kinks: two neighbouring kinks at distance $\ell$ feel an attractive force $F(\ell)\approx\exp(-\ell)$. This result is typical of a bistable system whose inhomogeneities have an energy cost due to surface tension, but for some physical systems bending rigidity rather than surface tension plays a leading role. We show that a kink dynamics is still applicable, but the force $F(\ell)$ is now oscillating, therefore producing configurations which are locally stable. We also propose a new derivation of kink dynamics, which applies to a generalized Ginzburg-Landau free energy with an arbitrary combination of surface tension, bending energy, and higher-order terms. Our derivation is not based on a specific multikink approximation and the resulting kink dynamics reproduces correctly the full dynamics of the original model. This allows to use our derivation with confidence in place of the continuum dynamics, reducing simulation time by orders of magnitude.

cond-mat.stat-mech↗

arXiv2014

Frozen states and order-disorder transition in the dynamics of confined membranes

The adhesion dynamics of a membrane confined between two permeable walls is studied using a two-dimensional hydrodynamic model. The membrane morphology decomposes into adhesion patches on the upper and the lower walls and obeys a nonlinear evolution equation that resembles that of phase separation dynamics, which is known to lead to coarsening, i.e. to the endless growth of the adhesion patches. However, due to the membrane bending rigidity the system evolves towards a frozen state without coarsening. This frozen state exhibits an order-disorder transition when increasing the permeability of the walls.

cond-mat.soft↗

arXiv2014

Giant Slip at Liquid-Liquid Interfaces Using Hydrophobic Ball Bearings

Liquid-gas-liquid interfaces stabilized by hydrophobic beads behave as ball bearings under shear and exhibit a giant slip. Using a scaling analysis and molecular dynamics simulations we predict that, when the contact angle theta between the beads and the liquid is large, the slip length diverges as R rho(-1) (pi -theta)(-3) where R is the bead radius, and theta is the bead density. DOI: 10.1103/PhysRevLett.110.104504

cond-mat.soft↗

arXiv2012

Princess and the Pea at the nanoscale: Wrinkling and delamination of graphene on nanoparticles

Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, resulting from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum elastic model and have important implications for strain-engineering the electronic properties of graphene.

cond-mat.mes-hall↗

arXiv2012

Nonlinear wavelength selection in surface faceting under electromigration

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as $t^{1/2}$. For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady-states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening {\it before} reaching a continuous family of stable non-equilibrium steady-states.

cond-mat.mtrl-sci↗

arXiv2007

Dewetting of a solid monolayer

We report on the dewetting of a monolayer on a solid substrate, where mass transport occurs via surface diffusion. For a wide range of parameters, a labyrinthine pattern of bilayer islands is formed. An irreversible regime and a thermodynamic regime are identified. In both regimes, the velocity of a dewetting front, the wavelength of the bilayer island pattern, and the rate of nucleation of dewetted zones are obtained. We also point out the existence of a scaling behavior, which is analyzed by means of a geometrical model.

cond-mat.soft↗