Friction through molecular adsorption at the sliding interface of hydrogels: theory and experiments.

We report on the frictional properties of thin (≈µm) poly(dimethylacrylamide) hydrogel films within contacts with spherical silica probes. In order to focus on the contribution to friction of interfacial dissipation, a dedicated rotational setup is designed which allows to suppress poroelastic flows while ensuring a uniform velocity field at the sliding interface. The physical-chemistry of the interface is varied from the grafting of various silanes on the silica probes. Remarkably, we identify a velocity range in which the average frictional stress systematically varies with the logarithm of the sliding velocity. This dependency is found to be sensitive to the physical-chemistry of the silica surfaces. Experimental observations are discussed in the light of a molecular model where friction arises from thermally activated adsorption of polymer chains at the sliding interface, their elastic stretching and subsequent desorption. From this theoretical description, our experimental data provide us with adhesion energies and characteristic times for molecular adsorption that are found consistent with the physico-chemistry of the chemically-modified silica surfaces.

How emulsified droplets induce the bursting of suspended films of liquid mixtures.

Emulsion droplets of silicone oil (PDMS) are widely used as antifoaming agents but, in the case of non-aqueous foams, the mechanisms responsible for the bursting of the films separating the bubbles remain unclear. We consider a ternary non-aqueous liquid mixture in which PDMS-rich microdroplets are formed by spontaneous emulsification. In order to quantitatively assess the effect of the emulsified microdroplets, we measure the lifetime of sub-micrometer-thick suspended films of these emulsions as well as the time variations of their thickness profiles. We observe that a droplet entering the film reduces its lifetime by inducing a local and fast thinning. In most cases, we ascribe it to the spreading of the drop at one of the film interfaces with air, which drags the underlying liquid and eventually causes the film to burst rapidly. We explain why, despite slower spreading, more viscous droplets cause films to burst more efficiently. More rarely, microdroplets may bridge the two interfaces of the film, resulting in an even more efficient bursting of the film, which we explain.

Complexity in Wetting Dynamics.

The spreading dynamics of a droplet of pure liquid deposited on a rigid, nonsoluble substrate has been extensively investigated. In a purely hydrodynamic description, the dynamics of the contact line is determined by a balance between the energy associated with the capillary driving force and the energy dissipated by the viscous shear in the liquid. This balance is expressed by the Cox-Voinov law, which relates the spreading velocity to the contact angle. More recently, complex situations have been examined in which dissipation and/or the driving force may be strongly modified, leading to sometimes spectacular changes in wetting dynamics. We review recent examples of effects at the origin of deviations from the hydrodynamic model, which may involve physical or chemical modifications of the substrate or of the wetting liquid, occurring at scales ranging from the molecular to the mesoscopic.

Swelling induced debonding of thin hydrogel films grafted on silicon substrates.

We report on the delamination of thin (≈µm) hydrogel films grafted to silicon substrates under the action of swelling stresses. Poly(dimetylacrylamide) (PDMA) films are synthesized by simultaneously cross-linking and grafting preformed polymer chains onto the silicon substrate using a thiol-ene reaction. The grafting density at the film/substrate interface is tuned by varying the surface density of reactive thiol-silane groups on the silicon substrate. Delamination of the films from well controlled line defects with low adhesion is monitored under a humid water vapor flow ensuring full saturation of the polymer network. A propagating delamination of the film is observed under the action of differential swelling stresses at the debonding front. A threshold thickness for the onset of this delamination is evidenced which is increasing with grafting density while the debonding velocity is also observed to decrease with an increase in grafting density. These observations are discussed within the framework of a nonlinear fracture mechanics model which assumes that the driving force for crack propagation is the difference between the swelling state of the bonded and delaminated parts of the film. Using this model, the threshold energy for crack initiation was determined from the measured threshold thickness and discussed in relation to the surface density of reactive thiol groups on the substrate.

Uptake kinetics of spontaneously emulsified microdroplets at an air-liquid interface.

Understanding the transfers occurring at the interfaces between emulsions and air is required to predict the properties of foamed emulsions, used for example as antifoaming lubricants or for oil extraction. Whereas bubbling oil-in-water emulsions have been studied in details, oil-in-oil emulsions have received less attention. We consider a phase-separating mixture of three oils being Polydimethylsiloxane (PDMS), decane and cyclopentanol. PDMS is dispersed as submicrometer-sized droplets by spontaneous emulsification. In bulk, we show that the time evolution of the emulsion is driven by undelayed coalescence of the Brownian microdroplets. At the freshly created interface of an air bubble created in the emulsion, we use tensiometry measurements to investigate the uptake kinetics of PDMS-rich microdroplets at the air-liquid interface. Specifically, we evidence two mechanisms of uptake: the advection of droplets at the interface during bubble swelling, followed by their diffusion on a longer time scale. We model the growth of the PDMS-rich layer at the interface and, finally, we establish the surface energy of a thin film of PDMS-rich phase squeezed between air and liquid as a function of its thickness.

Spinodal stratification in micellar films between oil and silica.

We report on the thinning mechanisms of supported films of surfactant (nTAB) solutions above the critical micellar concentration. The films are formed by pressing an oil drop immersed in an aqueous surfactant solution on a silica surface. Depending on the length of the carbon chain of the surfactant and its concentration, two modes of destabilization of the stratified films are observed. The first one proceeds by heterogeneous nucleation, characterized by the lateral expansion of the domain of lower thickness as evidenced long ago in suspended micellar films. In addition, the simultaneous stepwise thinning of several domains, called spinodal stratification, is observed here in supported films. We measure the time evolution of the thickness of the films, and we discuss the selection mechanism of each destabilization mode.

Dramatic Slowing Down of Oil/Water/Silica Contact Line Dynamics Driven by Cationic Surfactant Adsorption on the Solid.

We report on the contact line dynamics of a triple-phase system silica/oil/water. When oil advances onto silica within a water film squeezed between oil and silica, a rim forms in water and recedes at constant velocity. We evidence a sharp (three orders of magnitude) decrease of the contact line velocity upon the addition of cationic surfactants above a threshold concentration, which is slightly smaller than the critical micellar concentration. We show that, with or without surfactant, and within the range of small capillary numbers investigated, the contact line dynamics can be described by a friction term that does not reduce to pure hydrodynamical effects. In addition, we derive a model that successfully accounts for the selected contact line velocity of the rim. We further demonstrate the strong increase of the friction coefficient with surfactant bulk concentration results from the strongly nonlinear adsorption isotherm of surfactants on silica. From the variations of the friction coefficient and spreading parameter with surface concentration, we suggest a picture in which the part of the adsorbed surfactants that are strongly bound to the silica interface is trapped under the oil droplet and is responsible for the large increase in line friction.

Transient sliding of thin hydrogel films: the role of poroelasticity.

We report on the transient frictional response of contacts between a rigid spherical glass probe and a micrometer-thick poly(dimethylacrylamide) hydrogel film grafted onto a glass substrate when a lateral relative motion is applied to the contact initially at rest. From dedicated experiments with in situ contact visualization, both the friction force and the contact size are observed to vary well beyond the occurrence of a full sliding condition at the contact interface. Depending on the imposed velocity and on the static contact time before the motion is initiated, either an overshoot or an undershoot in the friction force is observed. These observations are rationalized by considering that the transient is predominantly driven by the flow of water within the stressed hydrogel networks. From the development of a poroelastic contact model using a thin film approximation, we provide a theoretical description of the main features of the transient. We especially justify the experimental observation that the relaxation of friction force Ft(t) toward steady state is uniquely dictated by the time-dependence of the contact radius a(t), independently on the sliding velocity and on the applied normal load.

Rouse 2D Diffusion of Polymer Chains in Low Density Precursor Films of Polybutadiene Melts.

We took advantage of pseudopartial wetting to promote the spreading of precursor films whose surface density smoothly decays to zero away from a sessile droplet. By following the spreading dynamics of semidilute precursor films of polybutadiene melts on silicon wafers, we measure molecular diffusion coefficients for different molar masses and temperatures. For homopolymers, chains follow a thermally activated 2D Rouse diffusion mechanism, with an activation energy revealing polymer segment interactions with the surface. This Rouse model is generalized to chains with specific terminal groups.

Combining Ellipsometry and AFM To Probe Subnanometric Precursor Film Dynamics of Polystyrene Melts.

We investigate the evolution over time of the space profiles of precursor films spreading away from a droplet of polymer in the poorly explored pseudo-partial wetting case. We use polystyrene melt droplets on oxidized silicon wafers. Interestingly, the film thicknesses measured by ellispometric microscopy are found in the 0.01 to 1 nm range. These thicknesses were validated by atomic force microscopy measurements performed on the textured film obtained after quenching at room temperature. From this, an effective thickness is obtained and compares well to the thicknesses measured by ellipsometry, validating the use of an optical method in this range of thickness. Ellipsometric microscopy provides a height resolution below the ångström with lateral resolution, image size, and framerate well adapted to spreading precursor films. From this, we demonstrate that precursor films of polystyrene consist of polymer chains with a surface density decreasing to zero away from the droplet. We further find that the polymer chains follow a simple diffusive law with the diffusion coefficient independent of density. This demonstrates that polystyrene chains spread independently in precursor films in pseudo-partial wetting condition. This behavior differs significantly from the case of chains spreading in total wetting for which the diffusion coefficient was found in the literature to depend on surface density or thickness.

Swelling Dynamics of Surface-Attached Hydrogel Thin Films in Vapor Flows.

Hydrogel coatings absorb water vapor, or other solvents, and, as such, are good candidates for antifog applications. In the present study, the transfer of vapor from the atmosphere to hydrogel thin films is measured in a situation where water vapor flows alongside the coating which is set to a temperature lower than the ambient temperature. The effect of the physico-chemistry of the hydrogel film on the swelling kinetics is particularly investigated. By using model thin films of surface-grafted polymer networks with controlled thickness, varied cross-links density, and varied affinity for water, we were able to determine the effect of the film hygroscopy on the dynamics of swelling of the film. These experimental results are accounted for by a diffusion-advection model that is supplemented with a boundary condition at the hydrogel surface: we show that the latter can be determined from the equilibrium sorption isotherms of the polymer films. Altogether, this paper offers a predictive tool for the swelling kinetics of any hydrophilic hydrogel thin film.

Friction of Poroelastic Contacts with Thin Hydrogel Films.

We report on the frictional behavior of thin poly(dimethylacrylamide) hydrogel films grafted on glass substrates in sliding contact with a glass spherical probe. Friction experiments are carried out at various velocities and normal loads applied with the contact fully immersed in water. In addition to friction force measurements, a novel optical setup is designed to image the shape of the contact under steady-state sliding. The velocity dependence of both friction force Ft and contact shape is found to be controlled by a Péclet number, Pe, defined as the ratio of the time τ needed to drain the water out of the contact region to a contact time a/ v, where v is the sliding velocity and a is the contact radius. When Pe < 1, the equilibrium circular contact achieved under static normal indentation remains unchanged during sliding. Conversely, for Pe > 1, a decrease in the contact area is observed together with the development of a contact asymmetry when the sliding velocity is increased. A maximum in Ft is also observed at Pe ≈1. These experimental observations are discussed in the light of a poroelastic contact model based on a thin-film approximation. This model indicates that the observed changes in contact geometry are due to the development of a pore pressure imbalance when Pe > 1. An order-of-magnitude estimate of the friction force and its dependence on normal load and velocity are also provided under the assumption that most of the frictional energy is dissipated by poroelastic flow at the leading and trailing edges of the sliding contact.

Water film squeezed between oil and solid: drainage towards stabilization by disjoining pressure.

The spontaneous drainage of aqueous solutions of salt squeezed between an oil drop and a glass surface is studied experimentally. The thickness profile of the film is measured in space and time by reflection interference microscopy. As the film thins down, three regimes are identified: a capillary dominated regime, a mixed capillary and disjoining pressure regime, and a disjoining pressure dominated regime. These regimes are modeled within the lubrication approximation, and the role of the disjoining pressure is precisely investigated in the limit of thicknesses smaller than the range of electrostatic interactions. We derive simple analytical laws describing the drainage dynamics, thus providing tools to uncouple the effect of the film geometry from the effects of the disjoining or capillary pressures.

Understanding the role of molar mass and stirring in polymer dissolution.

When a dry soluble polymer is put in contact with a large quantity of solvent, it swells and forms a transient gel, and eventually, yields a dilute solution of polymers. Everyday lab experience shows that when the molar mass is large, namely tens of times larger than entanglement mass, this dissolution process is slow and difficult and may require stirring. Here, in agreement with previous results, we found that the time needed to turn a dry grain into a dilute solution is not limited by water diffusion in the glassy or semi-crystalline dry polymer, but rather by the life-time of the transient gel made of entangled chains. In addition, we shed new light on the dissolution process by demonstrating that, in contrast to theoretical predictions, the gel life-time is not governed by reptation. We show instead that swelling is simply controlled by the osmotic pressure and the gel permeability until the overlap concentration is reached within the gel. At this stage, the gel turns into a dilute solution in which polymers are dispersed by natural convection. The observed dependence of the dissolution process on the molar mass therefore originates from the molar mass dependent overlap concentration. Under stirring, or forced convection, the polymer gel disappears at a higher critical concentration that depends on the shear rate. We suggest a description of the experimental data which uses the rheological flow curves of the solutions of the considered polymer. Inversely, dissolution times of polymer powders under stirring can be inferred from classical rheological measurements of the polymer solutions at varied concentrations.

Wetting of polymers by their solvents.

We review the studies on the wetting of soluble polymeric substrates by their solvents, both in the literature and conducted in our group in the past decade. When a droplet of solvent spreads on a soluble polymer layer, its wetting angle can strongly vary with the contact line velocity even at capillary numbers smaller than unity, in contrast to non-soluble substrates. The solvent content in the polymer is a key parameter for the spreading dynamics; that content is set by the initial conditions, but also by the transfers occurring from the droplet to the polymer layer during spreading. We focus on hydrophilic amorphous polymers that are glassy at room temperature, and we discuss the consequences on wetting of the very large changes in the polymer physical properties induced by solvent sorption. We finally present new results on polymers of varying molar masses, and show how they open new perspectives for a better understanding of powder dissolution.

Surface fluctuations of liquids confined on flat and patterned solid substrates.

We report experimental measurements of the surface fluctuations of micron-thick oil films spread onto a solid substrate. We use a recently developed optical technique based on the measurement of the deflection of a laser beam triggered by changes in the local surface slope. When the liquid is spread on a flat substrate, fluctuation dynamics slow down as the thickness is decreased, in quantitative agreement with previous predictions. In addition, we investigate the consequences on surface fluctuations of the patterning of the substrate with a rectangular grating. For liquid film thicknesses smaller than the typical wavelength probed, we demonstrate that surface fluctuations are modified by the underlying pattern: The shape of the fluctuation spectra varies periodically with the spatial position over the pattern and, in addition, the fluctuations become locally anisotropic. However, the spatially averaged spectrum is isotropic.

Glass transition accelerates the spreading of polar solvents on a soluble polymer.

We study the wetting of polymer layers by polar solvents. As previously observed, when a droplet of solvent spreads, both its contact angle and velocity decrease with time as a result of solvent transfers from the droplet to the substrate. We show that, when the polymer is initially glassy, the angle decreases steeply for a given value of the velocity, Ug. We demonstrate that those variations result from a plasticization, i.e., a glass transition, undergone by the polymer layer during spreading, owing to the increase of its solvent content. By analyzing previous predictions on the wetting of rigid and soft viscoelastic substrates, we relate Ug to the viscosity of the polymer gel close to the glass transition. Finally, we derive an analytical prediction for Ug based on existing predictions for the water transfer from the droplet to the substrate. Using polar solvents of different natures, we show that the experimental data compare well to the predicted expression for Ug.

Dynamic wetting on a thin film of soluble polymer: effects of nonlinearities in the sorption isotherm.

The wetting dynamics of a solvent on a soluble substrate interestingly results from the rates of the solvent transfers into the substrate. When a supported film of a hydrosoluble polymer with thickness e is wet by a spreading droplet of water with instantaneous velocity U, the contact angle is measured to be inversely proportionate to the product of thickness and velocity, eU, over two decades. As for many hydrosoluble polymers, the polymer we used (a polysaccharide) has a strongly nonlinear sorption isotherm φ(a(w)), where φ is the volume fraction of water in the polymer and aw is the activity of water. For the first time, this nonlinearity is accounted for in the dynamics of water uptake by the substrate. Indeed, by measuring the water content in the polymer around the droplet φ at distances as small as 5 µm, we find that the hydration profile exhibits (i) a strongly distorted shape that results directly from the nonlinearities of the sorption isotherm and (ii) a cutoff length ξ below which the water content in the substrate varies very slowly. The nonlinearities in the sorption isotherm and the hydration at small distances from the line were not accounted for by Tay et al., Soft Matter 2011, 7, 6953. Here, we develop a comprehensive description of the hydration of the substrate ahead of the contact line that encompasses the two water transfers at stake: (i) the evaporation-condensation process by which water transfers into the substrate through the atmosphere by the condensation of the vapor phase, which is fed by the evaporation from the droplet itself, and (ii) the diffusion of liquid water along the polymer film. We find that the eU rescaling of the contact angle arises from the evaporation-condensation process at small distances. We demonstrate why it is not modified by the second process.

Laser-induced force on a microfluidic drop: origin and magnitude.

The localized heating produced by a tightly focused infrared laser leads to surface tension gradients at the interface of microfluidic drops covered with surfactants, resulting in a net force on the drop whose origin and magnitude are the focus of this paper. First, by colocalization of the surfactant micelles with a fluorescent dye, we demonstrate that the heating alters their spatial distribution, driving the interface out of equilibrium. This soluto-capillary effect opposes and overcomes the purely thermal dependence of the surface tension, leading to reversed interfacial flows. As the surface of the drop is set into motion, recirculation rolls are created outside and inside the drop, which we measure using time-resolved micro-Particle Image Velocimetry. Second, the net force produced on the drop is measured using an original microfluidic design. For a drop 300 microm-long and 100 microm-wide, we obtain a force of 180 nN for a laser power of 100 mW. This micro-dynanometer further shows that the magnitude of the heating, which is determined by the laser power and its absorption in the water, sets the magnitude of the net force on the drop. On the other hand, the dynamics of the force generation is limited by the time scale for heating, which has independently been measured to be tau(Theta) = 4 ms. This time scale sets the maximum velocity that the drops can have and still be blocked, by requiring that the interface passes the laser spot in a time longer than tau(Theta). The maximum velocity is measured at U(max) = 0.7 mm/s for our geometric conditions. Finally, a scaling model is derived that describes the blocking force in a confined geometry as the result of the viscous stresses produced by the shear between the drop and the lateral walls.

Time-resolved temperature rise in a thin liquid film due to laser absorption.

The temperature increase of a thin water layer is investigated, both experimentally and numerically, when the layer is heated by an infrared laser. The laser is focused to a waist of 5.3 microm inside a 28 microm gap that contains fluorescent aqueous solutions between two glass slides. Temperature fields are measured using the temperature sensitivity of rhodamine-B, while correcting for thermal diffusion using rhodamine-101, which is insensitive to temperature. In the steady state, the shape of the hot region is well fitted with a Lorentzian function whose width ranges between 15 and 30 microm , increasing with laser power. At the same time, the maximum temperature rise ranges between 10 and 55 degrees C and can display a decrease at high laser powers. The total energy stored in the sample increases linearly with the laser power. The dynamics of the heating occurs with two distinct time scales: (i) a fast time ( tau_{Theta} = 4.2 ms in our case) which is the time taken to reach the maximum temperature at the laser position and the maximum temperature gradient, and (ii) a slow time scale for the spatial profile to reach its final width. The temperature field obtained numerically agrees quantitatively with the experiments for low laser powers but overpredicts the temperature rise while underpredicting the profile width for high powers. The total energy shows good agreement between experiments and simulations for all laser powers, suggesting that the discrepancies are due to a broadening of the laser, possibly due to a thermal lensing effect.