Nanoparticle Taylor Dispersion Near Charged Surfaces with an Open Boundary.

The dispersive spreading of microscopic particles in shear flows is influenced both by advection and thermal motion. At the nanoscale, interactions between such particles and their confining boundaries become unavoidable. We address the roles of electrostatic repulsion and absorption on the spatial distribution and dispersion of charged nanoparticles in near-surface shear flows, observed under evanescent illumination. The electrostatic repulsion between particles and the lower charged surface is tuned by varying electrolyte concentrations. Particles leaving the field of vision can be neglected from further analysis, such that the experimental ensemble is equivalent to that of Taylor dispersion with absorption. These two ingredients modify the particle distribution, deviating strongly from the Gibbs-Boltzmann form at the nanoscale studied here. The overall effect is to restrain the accessible space available to particles, which leads to a striking, tenfold reduction in the spreading dynamics as compared to the noninteracting case.

Elastohydrodynamic Relaxation of Soft and Deformable Microchannels.

Hydrodynamic flows in compliant channels are of great interest in physiology and microfluidics. In these situations, elastohydrodynamic coupling leads to (i) a nonlinear pressure-vs-flow-rate relation, strongly affecting the hydraulic resistance; and (ii), because of the compliance-enabled volume storage, a finite relaxation time under a stepwise change in pressure. This latter effect remains relatively unexplored, even while the timescale can vary over a decade in typical situations. In this study we provide time-resolved measurements of the relaxation dynamics for thin and soft, rectangular microfluidic channels. We describe our data using a perturbative lubrication approximation of the Stokes equation coupled to linear elasticity, while taking into account the effect of compliance and resistance of the entrance. The modeling allows us to completely describe all of the experimental results. Our Letter is relevant for any microfluidic scenario wherein a time-dependent driving is applied and provides a first step in the dynamical description of compliant channel networks.

Near-surface rheology and hydrodynamic boundary condition of semi-dilute polymer solutions.

Understanding confined flows of complex fluids requires simultaneous access to the mechanical behaviour of the liquid and the boundary condition at the interfaces. Here, we use evanescent wave microscopy to investigate near-surface flows of semi-dilute, unentangled polyacrylamide solutions. By using both neutral and anionic polymers, we show that monomer charge plays a key role in confined polymer dynamics. For solutions in contact with glass, the neutral polymers display chain-sized adsorbed layers, while a shear-rate-dependent apparent slip length is observed for anionic polymer solutions. The slip lengths measured at all concentrations collapse onto a master curve when scaled using a simple two-layer depletion model with non-Newtonian viscosity. A transition from an apparent slip boundary condition to a chain-sized adsorption layer is moreover highlighted by screening the charge with additional salt in the anionic polymer solutions. We anticipate that our study will be a starting point for more complex studies relating the polymer dynamics at interfaces to their chemical and physical composition.

Self-Similar Relaxation of Confined Microfluidic Droplets.

We report an experimental study concerning the capillary relaxation of a confined liquid droplet in a microscopic channel with a rectangular cross section. The confinement leads to a droplet that is extended along the direction normal to the cross section. These droplets, found in numerous microfluidic applications, are pinched into a peanutlike shape thanks to a localized, reversible deformation of the channel. Once the channel deformation is released, the droplet relaxes back to a pluglike shape. During this relaxation, the liquid contained in the central pocket drains towards the extremities of the droplet. Modeling such viscocapillary droplet relaxation requires considering the problem as 3D due to confinement. This 3D consideration yields a scaling model incorporating dominant dissipation within the droplet menisci. As such, the self-similar droplet dynamics is fully captured.

Interface-Sensitive Raman Microspectroscopy of Water via Confinement with a Multimodal Miniature Surface Forces Apparatus.

Modern interfacial science is increasingly multidisciplinary. Unique insight into interfacial interactions requires new multimodal techniques for interrogating surfaces with simultaneous complementary physical and chemical measurements. Here, we describe the design and testing of a microscope that incorporates a miniature surface forces apparatus (µSFA) in sphere vs flat geometry for force-distance measurements, while simultaneously acquiring Raman spectra of the confined zone. The simple optical setup isolates independent optical paths for (i) the illumination and imaging of Newton's rings and (ii) Raman scattering excitation and efficient signal collection. We benchmark the methodology by examining Teflon thin films in asymmetric (Teflon-water-glass) and symmetric (Teflon-water-Teflon) configurations. Water is observed near the Teflon-glass interface with nanometer-scale sensitivity in both the distance and Raman signals. We perform chemically resolved, label-free imaging of confined contact regions between Teflon and glass surfaces immersed in water. Remarkably, we estimate that the combined approach enables vibrational spectroscopy with single water monolayer sensitivity within minutes. Altogether, the Raman-µSFA allows exploration of molecular confinement between surfaces with chemical selectivity and correlation with interaction forces.

Multimodal Miniature Surface Forces Apparatus (µSFA) for Interfacial Science Measurements.

Advances in the research of intermolecular and surface interactions result from the development of new and improved measurement techniques and combinations of existing techniques. Here, we present a new miniature version of the surface forces apparatus-the µSFA-that has been designed for ease of use and multimodal capabilities with the retention of the capabilities of other SFA models including accurate measurements of the surface separation distance and physical characterization of dynamic and static physical forces (i.e., normal, shear, and friction) and interactions (e.g., van der Waals, electrostatic, hydrophobic, steric, and biospecific). The small physical size of the µSFA, compared to previous SFA models, makes it portable and suitable for integration into commercially available optical and fluorescence light microscopes, as demonstrated here. The large optical path entry and exit ports make it ideal for concurrent force measurements and spectroscopy studies. Examples of the use of the µSFA in combination with surface plasmon resonance (SPR) and Raman spectroscopy measurements are presented. Because of the short working distance constraints associated with Raman spectroscopy, an interferometric technique was developed and applied to calculate the intersurface separation distance based on Newton's rings. The introduction of the µSFA will mark a transition in SFA usage from primarily physical characterization to concurrent physical characterization with in situ chemical and biological characterization to study interfacial phenomena, including (but not limited to) molecular adsorption, fluid flow dynamics, the determination of surface species and morphology, and (bio)molecular binding kinetics.

Slip-mediated dewetting of polymer microdroplets.

Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap-shaped polystyrene microdroplets, with nonequilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy. We find that slip has a strong influence on the droplet evolutions, both on the transient nonspherical shapes and contact line dynamics. The observations are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition.

Contact Dependence and Velocity Crossover in Friction between Microscopic Solid/Solid Contacts.

Friction at the nanoscale differs markedly from that between surfaces of macroscopic extent. Characteristically, the velocity dependence of friction between apparent solid/solid contacts can strongly deviate from the classically assumed velocity independence. Here, we show that a nondestructive friction between solid tips with radius on the scale of hundreds of nanometers and solid hydrophobic self-assembled monolayers has a strong velocity dependence. Specifically, using laterally oscillating quartz tuning forks, we observe a linear scaling in the velocity at the lowest accessed velocities, typically hundreds of micrometers per second, crossing over into a logarithmic velocity dependence. This crossover is consistent with a general multicontact friction model that includes thermally activated breaking of the contacts at subnanometric elongation. We find as well a strong dependence of the friction on the dimensions of the frictional probe.

Nucleated dewetting in supported ultra-thin liquid films with hydrodynamic slip.

This study reveals the influence of the surface energy and solid/liquid boundary condition on the breakup mechanism of dewetting ultra-thin polymer films. Using silane self-assembled monolayers, SiO2 substrates are rendered hydrophobic and provide a strong slip rather than a no-slip solid/liquid boundary condition. On undergoing these changes, the thin-film breakup morphology changes dramatically - from a spinodal mechanism to a breakup which is governed by nucleation and growth. The experiments reveal a dependence of the hole density on film thickness and temperature. The combination of lowered surface energy and hydrodynamic slip brings the studied system closer to the conditions encountered in bursting unsupported films. As for unsupported polymer films, a critical nucleus size is inferred from a free energy model. This critical nucleus size is supported by the film breakup observed in the experiments using high speed in situ atomic force microscopy.

Influence of bidisperse self-assembled monolayer structure on the slip boundary condition of thin polymer films.

Alkylsilane self-assembled monolayers (SAMs) are often used as model substrates for their ease of preparation and hydrophobic properties. We have observed that these atomically smooth monolayers also provide a slip boundary condition for dewetting films composed of unentangled polymers. This slip length, an indirect measure of the friction between a given liquid and different solids, is switchable and can be increased [R. Fetzer et al., Phys. Rev. Lett. 95, 127801 (2005); O. Bäumchen et al., J. Phys.: Condens. Matter 24, 325102 (2012)] if the alkyl chain length is changed from 18 to 12 backbone carbons, for example. Typically, this change in boundary condition is affected in a quantized way, using one or the other alkyl chain length, thus obtaining one or the other slip length. Here, we present results in which this SAM structure is changed in a continuous way. We prepare bidisperse mixed SAMs of alkyl silanes, with the composition as a control parameter. We find that all the mixed SAMs investigated show an enhanced slip boundary condition as compared to the single-component SAMs. The slip boundary condition is accessed using optical and atomic force microscopy, and we describe these observations in the context of X-ray reflectivity measurements. The slip length, varying over nearly two orders of magnitude, of identical polymer melts on chemically similar SAMs is found to correlate with the density of exposed alkyl chains. Our results demonstrate the importance of a well characterized solid/liquid pair, down to the angstrom level, when discussing the friction between a liquid and a solid.

Controlling Marangoni-induced instabilities in spin-cast polymer films: How to prepare uniform films.

In both research and industrial settings spincoating is extensively used to prepare highly uniform thin polymer films. However, under certain conditions, spincoating results in films with non-uniform surface morphologies. Although the spincoating process has been extensively studied, the origin of these morphologies is not fully understood and the formation of non-uniform spin-cast films remains a practical problem. Here we report on experiments demonstrating that the formation of surface instabilities during spincoating is dependent on temperature. Our results suggest that non-uniform spin-cast films form as a result of the Marangoni effect, which describes flow due to surface tension gradients. We find that both the wavelength and amplitude of the pattern increase with temperature. Finally, and most important from a practical viewpoint, the non-uniformities in the film thickness can be entirely avoided simply by lowering the spin coating temperature.

Relaxation of non-equilibrium entanglement networks in thin polymer films.

It is known that polymer films, prepared by spin coating, inherit non-equilibrium configurations which can affect macroscopic film properties. Here we present the results of crazing experiments that support this claim; our measurements indicate that the as-cast chain configurations are strongly stretched as compared to equilibrium Gaussian configurations. The results of our experiments also demonstrate that the entanglement network equilibrates on a time scale comparable to one reptation time. Having established that films can be prepared with an equilibrium entanglement network, we proceed by confining polymers to films in which the thickness is comparable to the molecular size. By stacking two such films, a bilayer is created with a buried entropic interface. Such an interface has no enthalpic cost, only an entropic penalty associated with the restricted configurations of molecules that cannot cross the mid-plane of the bilayer. In the melt, the entropic interface heals as chains from the two layers mix and entangle with one another; crazing measurements allow us to probe the dynamics of two films becoming one. Healing of the entropic interface is found to take less than one bulk reptation time.

Beyond Tanner's law: crossover between spreading regimes of a viscous droplet on an identical film.

We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin film (Tanner's law regime) to that of a droplet leveling on a film thicker than the droplet itself. In both regimes, the droplet's excess surface area decreases towards the equilibrium configuration of a flat liquid film, but with a different power law in time. Additionally, the characteristic leveling time depends on molecular properties, the size of the droplet, and the thickness of the underlying film. Flow within the film makes this system fundamentally different from a droplet spreading on a solid surface. We thus develop a theoretical model based on thin film hydrodynamics that quantitatively describes the observed crossover between the two leveling regimes.

Self-similarity and energy dissipation in stepped polymer films.

The surface of a thin liquid film with a nonconstant curvature is unstable, as the Laplace pressure drives a flow mediated by viscosity. We present the results of experiments on one of the simplest variable curvature surfaces: a thin polymer film with a step. Height profiles are measured as a function of time for a variety of molecular weights. The evolution of the profiles is shown to be self-similar. This self-similarity offers a precise measurement of the capillary velocity by comparison with numerical solutions of the thin film equation. We also derive a master expression for the time dependence of the excess free energy as a function of the material properties and film geometry. The experiment and theory are in excellent agreement and indicate the effectiveness of stepped polymer films to elucidate nanoscale rheological properties.

Numerical solutions of thin-film equations for polymer flows.

We report on the numerical implementation of thin-film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus on two particular cases inspired by experiments: the leveling of a step at the free surface of a polymer film, and the leveling of a polymer droplet over an identical film. In each case, we first discuss the long-term self-similar regime reached by the numerical solution before comparing it to the experimental profile. The agreement between theory and experiment is excellent, thus providing a versatile probe for nanorheology of viscous liquids in thin-film geometries.

Adsorption-induced slip inhibition for polymer melts on ideal substrates.

Hydrodynamic slip, the motion of a liquid along a solid surface, represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with polymer reptation implies extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de Gennes model was confirmed using dewetting experiments on ultra-smooth, low-energy substrates. Here, we use capillary leveling-surface tension driven flow of films with initially non-uniform thickness-of polymeric films on these same substrates. Measurement of the slip length from a robust one parameter fit to a lubrication model is achieved. We show that at the low shear rates involved in leveling experiments as compared to dewetting ones, the employed substrates can no longer be considered ideal. The data is instead consistent with a model that includes physical adsorption of polymer chains at the solid/liquid interface.

Influence of slip on the Plateau-Rayleigh instability on a fibre.

The Plateau-Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid-liquid interface. Here we revisit the Plateau-Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre-liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid-liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.

Nanofluidics of thin polymer films: linking the slip boundary condition at solid-liquid interfaces to macroscopic pattern formation and microscopic interfacial properties.

If a thin liquid film is not stable, different rupture mechanisms can be observed causing characteristic film morphologies: spinodal dewetting and dewetting by nucleation of holes. This rupturing entails liquid flow and opens new possibilities to study microscopic phenomena. Here we use this process of dewetting to gain insight on the slip boundary condition at the solid-liquid interface. Having established hydrodynamic models that allow for the determination of the slip length in a dewetting experiment based on nucleation, we move on to the quantification and molecular description of slip effects in various systems. For the late stage of the dewetting process involving the Rayleigh-Plateau instability, several distinct droplet patterns can be observed. We describe the importance of slip in determining what pattern may be found. In order to control the slip length, we use polymeric liquids on different hydrophobic coatings of silicon wafers. We find that subtle changes in the coating can lead to large changes in the slip length. Thus, we gain insight into the question of how the structure of the substrate affects the slip length.

Relaxation and intermediate asymptotics of a rectangular trench in a viscous film.

The surface of a thin liquid film with nonconstant curvature flattens as a result of capillary forces. While this leveling is driven by local curvature gradients, the global boundary conditions greatly influence the dynamics. Here, we study the evolution of rectangular trenches in a polystyrene nanofilm. Initially, when the two sides of a trench are well separated, the asymmetric boundary condition given by the step height controls the dynamics. In this case, the evolution results from the leveling of two noninteracting steps. As the steps broaden further and start to interact, the global symmetric boundary condition alters the leveling dynamics. We report on full agreement between theory and experiments for the capillary-driven flow and resulting time dependent height profiles, a crossover in the power-law dependence of the viscous energy dissipation as a function of time as the trench evolution transitions from two noninteracting to interacting steps, and the convergence of the profiles to a universal self-similar attractor that is given by the Green's function of the linear operator describing the dimensionless linearized thin film equation.

Swelling molecular entanglement networks in polymer glasses.

Entanglements in a polymer network are like knots between the polymer chains, and they are at the root of many phenomena observed in polymer systems. When a polymer glass is strained, cracklike deformations called crazes may be formed and the study of these regions can reveal much about the nature of entanglements. We have studied crazes in systems that are blends of long polymer chains diluted with chains of various small molecular weights. The range of diluting chain lengths is such that a fraction of them have conformations leading to entanglements. It has been found that a system with more short chains added acts like one in which the entanglement density is smaller than that in an undiluted system. We propose a model that quantitatively predicts the density of effective entanglements of a polydisperse system of polymer chains which is consistent with our experimental data.