Capillary filling in nanostructured porous silicon

Polymeric liquids in mesoporous photonic structures: From precursor film spreading to imbibition dynamics at the nanoscale

Polymers are known to wet nanopores with high surface energy through an atomically thin precursor film followed by slower capillary filling. We present here light interference spectroscopy using a mesoporous membrane-based chip that allows us to observe the dynamics of these phenomena in situ down to the sub-nanometer scale at milli- to microsecond temporal resolution. The device consists of a mesoporous silicon film (average pore size 6 nm) with an integrated photonic crystal, which permits to simultaneously measure the phase shift of thin film interference and the resonance of the photonic crystal upon imbibition. For a styrene dimer, we find a flat fluid front without a precursor film, while the pentamer forms an expanding molecular thin film moving in front of the menisci of the capillary filling. These different behaviors are attributed to a significantly faster pore-surface diffusion compared to the imbibition dynamics for the pentamer and vice versa for the dimer. In addition, both oligomers exhibit anomalously slow imbibition dynamics, which could be explained by apparent viscosities of six and eleven times the bulk value, respectively. However, a more consistent description of the dynamics is achieved by a constriction model that emphasizes the increasing importance of local undulations in the pore radius with the molecular size and includes a sub-nanometer hydrodynamic dead, immobile zone at the pore wall but otherwise uses bulk fluid parameters. Overall, our study illustrates that interferometric, opto-fluidic experiments with mesoporous media allow for a remarkably detailed exploration of the nano-rheology of polymeric liquids.

Digital holographic microscopy implementation for capillary filling measurements in nanoporous materials

We report the implementation of lensless off-axis digital holographic microscopy as a non-destructive optical analyzer for nano-scale structures. The measurement capacity of the system was validated by analyzing the topography of a metallic grid with ≈150nm thick opaque features. In addition, an experimental configuration of self-reference was included to study the dynamics of the capillary filling phenomena in nanostructured porous silicon. The fluid front position as a function of time was extracted from the holograms, and the typical square root of time kinematics was recovered. The results shown are in agreement with previous works on capillary imbibition in similar structures and confirm a first step towards unifying holographic methods with fluid dynamics theory to develop a spatially resolved capillary tomography system for nanoporous materials characterization.

Wettability-defined droplet imbibition in ceramic mesopores

Wettability-defined liquid infiltration into porous materials in nature and several industrial applications is of fundamental interest. Direct observation of wetting-controlled imbibition in mesopores is anticipated to deliver important insights into the interplay between nanoconfined liquid movement and nanoscale wettability. We present a systematic study of water imbibition into mesoporous silica thin films with wetting properties precisely adjusted through chemical functionalization. We observe the liquid infiltration, resulting in an imbibition ring around the water droplet, by top-view imaging using a camera with collimated coaxial illumination. With decreasing hydrophilicity, the maximum imbibition area around the droplet decreases, accompanied by a simultaneous change in the imbibition kinetics and imbibition mechanism. Initially, the imbibition kinetics follow a modified Lucas-Washburn law that considers a strong influence of evaporation. However, with increasing imbibition time after reaching constant imbibition ring dimensions, the imbibition area starts to increase again, causing a deviation from the applied model. This observation is ascribed to water-mediated surface activation at the imbibition front, leading to a slightly increased wettability, which is also confirmed by water adsorption measurements. Furthermore, recently described spontaneous condensation-evaporation imbalances that cause oscillations of the imbibition front could be verified and were studied with regard to changing wetting properties. By increasing the contact angle of the material and therefore the partial pressure needed for capillary condensation, the amplitude of the imbibition front oscillations decreases. These results provide insights into the wettability-defined complex movement of water in mesoporous structures, which has practical implications, e.g., for nano/microfluidic devices and water purification or harvesting.

Precursor Film Spreading during Liquid Imbibition in Nanoporous Photonic Crystals

When a macroscopic droplet spreads, a thin precursor film of liquid moves ahead of the advancing liquid-solid-vapor contact line. Whereas this phenomenon has been explored extensively for planar solid substrates, its presence in nanostructured geometries has barely been studied so far, despite its importance for many natural and technological fluid transport processes. Here we use porous photonic crystals in silicon to resolve by light interferometry capillarity-driven spreading of liquid fronts in pores of few nanometers in radius. Upon spatiotemporal rescaling the fluid profiles collapse on master curves indicating that all imbibition fronts follow a square-root-of-time broadening dynamics. For the simple liquid (glycerol) a sharp front with a widening typical of Lucas-Washburn capillary-rise dynamics in a medium with pore-size distribution occurs. By contrast, for a polymer (PDMS) a precursor film moving ahead of the main menisci entirely alters the nature of the nanoscale transport, in agreement with predictions of computer simulations.

Nanoporous Anodic Alumina Surface Modification by Electrostatic, Covalent, and Immune Complexation Binding Investigated by Capillary Filling

The fluid imbibition-coupled laser interferometry (FICLI) technique has been applied to detect and quantify surface changes and pore dimension variations in nanoporous anodic alumina (NAA) structures. FICLI is a noninvasive optical technique that permits the determination of the NAA average pore radius with high accuracy. In this work, the technique is applied after each step of different surface modification paths of the NAA pores: (i) electrostatic immobilization of bovine serum albumin (BSA), (ii) covalent attachment of streptavidin via (3-aminipropyl)-triethoxysilane and glutaraldehyde grafting, and (iii) immune complexation. Results show that BSA attachment can be detected as a reduction in estimated radius from FICLI with high accuracy and reproducibility. In the case of the covalent attachment of streptavidin, FICLI is able to recognize a multilayer formation of the silane and the protein. For immune complexation, the technique is able to detect different antibody-antigen bindings and distinguish different dynamics among different immune species.

Quantized Self-Assembly of Discotic Rings in a Liquid Crystal Confined in Nanopores

Disklike molecules with aromatic cores spontaneously stack up in linear columns with high, one-dimensional charge carrier mobilities along the columnar axes, making them prominent model systems for functional, self-organized matter. We show by high-resolution optical birefringence and synchrotron-based x-ray diffraction that confining a thermotropic discotic liquid crystal in cylindrical nanopores induces a quantized formation of annular layers consisting of concentric circular bent columns, unknown in the bulk state. Starting from the walls this ring self-assembly propagates layer by layer towards the pore center in the supercooled domain of the bulk isotropic-columnar transition and thus allows one to switch on and off reversibly single, nanosized rings through small temperature variations. By establishing a Gibbs free energy phase diagram we trace the phase transition quantization to the discreteness of the layers' excess bend deformation energies in comparison to the thermal energy, even for this near room-temperature system. Monte Carlo simulations yielding spatially resolved nematic order parameters, density maps, and bond-orientational order parameters corroborate the universality and robustness of the confinement-induced columnar ring formation as well as its quantized nature.

Design of Nanofibrous and Microfibrous Channels for Fast Capillary Flow

The speed of capillary flow is a key bottleneck in improving the performance of nanofluidic and microfluidic devices for various applications including microfluidic diagnostics, thermal management heat pipes, micromolding devices, functional fabrics, and oil-water separators. Here, we present a novel nanofibrous or microfibrous hollow-wedged channel (named as W-Channel), which can significantly speed up the capillary flow. The capillary flow in the initial 100 s in the nanofibrous W-Channel was shown to be 8 times faster than that in the single-layer strip of the same material when placed vertically and over 20 times faster when placed horizontally. The enhanced flow under gravity is attributed to the adaptive interplay of capillary pressure and flow resistance within the triangular hollow wedge between the fibrous layers. The W-Channel can be fabricated following a simple procedure using inexpensive materials such as electrospun nanofibers or microfibrous filter papers.

Real-Time and In-Flow Sensing Using a High Sensitivity Porous Silicon Microcavity-Based Sensor

Porous silicon seems to be an appropriate material platform for the development of high-sensitivity and low-cost optical sensors, as their porous nature increases the interaction with the target substances, and their fabrication process is very simple and inexpensive. In this paper, we present the experimental development of a porous silicon microcavity sensor and its use for real-time in-flow sensing application. A high-sensitivity configuration was designed and then fabricated, by electrochemically etching a silicon wafer. Refractive index sensing experiments were realized by flowing several dilutions with decreasing refractive indices, and measuring the spectral shift in real-time. The porous silicon microcavity sensor showed a very linear response over a wide refractive index range, with a sensitivity around 1000 nm/refractive index unit (RIU), which allowed us to directly detect refractive index variations in the 10⁻⁷ RIU range.

Imbibition Triggered by Capillary Condensation in Nanopores

We study the spatiotemporal dynamics of water uptake by capillary condensation from unsaturated vapor in mesoporous silicon layers (pore radius r_p ≃ 2 nm), taking advantage of the local changes in optical reflectance as a function of water saturation. Our experiments elucidate two qualitatively different regimes as a function of the imposed external vapor pressure: at low vapor pressures, equilibration occurs via a diffusion-like process; at high vapor pressures, an imbibition-like wetting front results in fast equilibration toward a fully saturated sample. We show that the imbibition dynamics can be described by a modified Lucas-Washburn equation that takes into account the liquid stresses implied by Kelvin equation.

Complex Filling Dynamics in Mesoporous Thin Films

The fluid-front dynamics resulting from the coexisting infiltration and evaporation phenomena in nanofluidic systems has been investigated. More precisely, water infiltration in both titania and silica mesoporous films was studied through a simple experiment: a sessile drop was deposited over the film and the advancement of the fluid front into the porous structure was optically followed and recorded in time. In the case of titania mesoporous films, capillary infiltration was arrested at a given distance, and a steady annular region of the wetted material was formed. A simple model that combines Lucas-Washburn infiltration and surface evaporation was derived, which appropriately describes the observed filling dynamics and the annulus width in dissimilar mesoporous morphologies. In the case of wormlike mesoporous morphologies, a remarkable phenomenon was found: instead of reaching a steady infiltration-evaporation balance, the fluid front exhibits an oscillating behavior. This complex filling dynamics opens interesting possibilities to study the unusual nanofluidic phenomena and to discover novel applications.

Modeling the abnormally slow infiltration rate in mesoporous films

The rate of infiltration of fluids into bimodal porous systems was modeled to decrease as the ratio of the pore size to pore neck size was increased.

Optical Monitoring of the Capillary Filling Dynamics Variation in Nanoporous Anodic Alumina toward Sensing Applications

Fluid imbibition-coupled laser interferometry (FICLI) is a technique in which the kinetics of a fluid infiltrating a nanoporous anodic alumina (NAA) membrane is monitored by the interference of a laser beam at the membrane top and bottom surfaces. Further processing of the measured data results in an estimate of the pore radius. In this work, we study the accuracy of FICLI in the detection of small changes in pore radius, and we evaluate the possibility of using such detection as a sensing paradigm. The accuracy is estimated by measuring samples with increasing pore radius, obtained by successive wet etching steps, and repeatability is evaluated by using different liquids. For decreasing pore radius, samples obtained by the successive deposition of polyelectrolyte double layers are used. With the aim of evaluating the possibility of the FICLI method to sense biological binding events, BSA attachment detection is demonstrated by applying FICLI to samples before and after immobilization of the protein. Results show that the technique permits an accurate estimation of the pore radius, the pore-etching rate (with a radius variation of r_etch,DI = 1.05 nm/min ± 0.11 nm/min), and the polyelectrolyte double layer thickness (with a radius variation of r_PAH/PSS = 3.2 nm ± 0.2 nm per polyelectrolyte double layer). Furthermore, the pore radius reduction measured after BSA immobilization (d_BSA = 4.9 nm ± 1.1 nm) is in good agreement with the protein size, as reported in the literature. With these results, we provide a sound basis for the applicability of FICLI as a sensitive technique for the characterization of NAA pore radius modifications.

Capillarity-driven flows at the continuum limit

We experimentally investigate the dynamics of capillary-driven flows at the nanoscale, using an original platform that combines nanoscale pores (⋍3 nm in diameter) and microfluidic features. In particular, we show that drying involves a fine coupling between thermodynamics and fluid mechanics that can be used to generate precisely controlled nanoflows driven by extreme stresses - up to 100 MPa of tension. We exploit these tunable flows to provide quantitative tests of continuum theories (e.g. Kelvin-Laplace equation and Poiseuille flow) across an unprecedented range and we isolate the breakdown of continuum as a negative slip length of molecular dimension. Our results show a coherent picture across multiple experiments including drying-induced permeation flows, imbibition and poroelastic transients.

Nanoscale Capillary Flows in Alumina: Testing the Limits of Classical Theory

Anodic aluminum oxide (AAO) membranes have well-formed cylindrical channels, as small as 10 nm in diameter, in a close packed hexagonal array. The channels in AAO membranes simulate very small leaks that may be present for example in an aluminum oxide device encapsulation. The 10 nm alumina channel is the smallest that has been studied to date for its moisture flow properties and provides a stringent test of classical capillary theory. We measure the rate at which moisture penetrates channels with diameters in the range of 10 to 120 nm with moist air present at 1 atm on one side and dry air at the same total pressure on the other. We extend classical theory for water leak rates at high humidities by allowing for variable meniscus curvature at the entrance and show that the extended theory explains why the flow increases greatly when capillary filling occurs and enables the contact angle to be determined. At low humidities our measurements for air-filled channels agree well with theory for the interdiffusive flow of water vapor in air. The flow rate of water-filled channels is one order of magnitude less than expected from classical capillary filling theory and is coincidentally equal to the helium flow rate, validating the use of helium leak testing for evaluating moisture flows in aluminum oxide leaks.

Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media

Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.

Buried centimeter-long micro- and nanochannel arrays in porous silicon and glass

We developed a simple process to fabricate deeply buried micro- and nanoscale channels in glass and porous silicon from bulk silicon using a combination of ion beam irradiation, electrochemical anodization and high temperature oxidation. The depth, width and length of these structures can be controllably varied and we successfully fabricated an array of centimeter-long buried micro- and nanochannels. This process allows densely packed, arbitrary-shaped channel geometries with micro- to nanoscale dimensions to be produced in a three-dimensional multilevel architecture, providing a route to fabricate complex devices for use in nanofluidics and lab-on-a-chip systems. We demonstrate the integration of these channels with large reservoirs for DNA linearization in high aspect ratio nanochannels.

Inverse problem of capillary filling

The inverse problem of capillary filling, as defined in this work, consists in determining the capillary radius profile from experimental data of the meniscus position l as a function of time t. This problem is central in diverse applications, such as the characterization of nanopore arrays or the design of passive transport in microfluidics; it is mathematically ill posed and has multiple solutions; i.e., capillaries with different geometries may produce the same imbibition kinematics. Here a suitable approach is proposed to solve this problem, which is based on measuring the imbibition kinematics in both tube directions. Capillary filling experiments to validate the calculation were made in a wide range of length scales: glass capillaries with a radius of around 150  μm and anodized alumina membranes with a pores radius of around 30  nm were used. The proposed method was successful in identifying the radius profile in both systems. Fundamental aspects also emerge in this study, notably the fact that the l(t)∝t1/2 kinematics (Lucas-Washburn relation) is not exclusive of uniform cross-sectional capillaries.

Filling dynamics of closed end nanocapillaries

We have studied the filling dynamics of model capillaries using dynamic mean field theory for a confined lattice gas and Kawasaki dynamics simulations. We have found two different scenarios for filling of capped nanocapillaries from the vapor phase. As compared to channels with macroscopic width, in which the filling process occurs by the detachment of the meniscus from the cap, in mesoscopic channels there is an alternative mechanism associated with the spontaneous condensation of the liquid close to the pore opening and its subsequent growth toward the closed pore end. We show that these two scenarios have totally different filling dynamics, providing an additional mechanism for slow capillary condensation kinetics in nanoscopic objects.

Towards implantable porous silicon biosensors

Porous silicon (pSi) is a nanomaterial with salient properties for optical biosensor applications.

Real-time study of protein adsorption kinetics in porous silicon

This paper presents an optical method for real-time monitoring of protein adsorption using porous silicon self-supported microcavities as a label-free detection platform. The study combines an experimental approach with a physical model for the adsorption process. The proposed model agrees well with experimental observations, and provides information about the kinetics of diffusion and adsorption of proteins within the pores, which will be useful for future experimental designs.

Optofluidic characterization of nanoporous membranes

An optofluidic method that accurately identifies the internal geometry of nanochannel arrays is presented. It is based on the dynamics of capillary-driven fluid imbibition, which is followed by laser interferometry. Conical nanochannel arrays in anodized alumina are investigated, which present an asymmetry of the filling times measured from different sides of the membrane. It is demonstrated by theory and experiments that the capillary filling asymmetry only depends on the ratio H of the inlet to outlet pore radii and that the ratio of filling times vary closely as H(7/3). Besides, the capillary filling of conical channels exhibits striking results in comparison to the corresponding cylindrical channels. Apart from these novel results in nanoscale fluid dynamics, the whole method discussed here serves as a characterization technique for nanoporous membranes.

Interplay between shape and roughness in early-stage microcapillary imbibition

Flows in microcapillaries and associated imbibition phenomena play a major role across a wide spectrum of practical applications, from oil recovery to inkjet printing and from absorption in porous materials and water transport in trees to biofluidic phenomena in biomedical devices. Early investigations of spontaneous imbibition in capillaries led to the observation of a universal scaling behavior, known as the Lucas-Washburn (LW) law. The LW allows abstraction of many real-life effects, such as the inertia of the fluid, irregularities in the wall geometry, and the finite density of the vacuum phase (gas or vapor) within the channel. Such simplifying assumptions set a constraint on the design of modern microfluidic devices, operating at ever-decreasing space and time scales, where the aforementioned simplifications go under serious question. Here, through a combined use of leading-edge experimental and simulation techniques, we unravel a novel interplay between global shape and nanoscopic roughness. This interplay significantly affects the early-stage energy budget, controlling front propagation in corrugated microchannels. We find that such a budget is governed by a two-scale phenomenon: The global geometry sets the conditions for small-scale structures to develop and propagate ahead of the main front. These small-scale structures probe the fine-scale details of the wall geometry (nanocorrugations), and the additional friction they experience slows the entire front. We speculate that such a two-scale mechanism may provide a fairly general scenario to account for extra dissipative phenomena occurring in capillary flows with nanocorrugated walls.