Wetting and domain-growth kinetics in confined geometries

Impact of complex topology of porous media on phase separation of binary mixtures

Porous materials, which are characterized by the large surface area and percolated nature crucial for transport, play an important role in many technological applications including battery, ion exchange, catalysis, microelectronics, medical diagnosis, and oil recovery. Phase separation of a mixture in such a porous structure should be strongly influenced by both surface wetting and strong geometrical confinement effects. Despite its fundamental and technological importance, however, this problem has remained elusive for a long time because of the difficulty associated with the complex geometry of pore structures. We overcome this by developing a novel phase-field model of two coupled order parameters, the composition field of a binary mixture and the density field of a porous structure. We find that demixing behavior in complex pore structures is severely affected by the topological characteristics of porous materials, contrary to the conventional belief that it can be inferred from the behavior in a simple cylindrical pore. Our finding not only reveals the physical mechanism of demixing in random porous structures but also has an impact on technological applications.

Phase separation of triethylamine and water in native and organically modified silica nanopores

A mixture of triethylamine and water is a lower critical solution temperature system that demixes (separates into individual phases) on heating. Differential scanning calorimetry has been applied to study the process of demixing in native and organically modified silica nanopores whose size varied from 4 to 30 nm. It has been found that in both types of nanopores, the temperature and enthalpy of demixing decrease significantly with decreasing the pore size. Isoconversional kinetic analysis has been utilized to determine the activation energy and pre-exponential factor of the process. It has been demonstrated that the depression of the transition temperature upon nanoconfinement is associated with acceleration of the process due to lowering of the activation energy. Nanoconfinement has also been found to lower the pre-exponential factor of the process that has been linked to a decrease in the molecular mobility.

Three-dimensional reconstruction of liquid phases in disordered mesopores usingin situsmall-angle scattering

Small-angle scattering of X-rays (SAXS) or neutrons is one of the few experimental methods currently available for thein situanalysis of phenomena in mesoporous materials at the mesoscopic scale. In the case of disordered mesoporous materials, however, the main difficulty of the method lies in the data analysis. A stochastic model is presented, which enables one to reconstruct the three-dimensional nanostructure of liquids confined in disordered mesopores starting from small-angle scattering data. This so-called plurigaussian model is a multi-phase generalization of clipped Gaussian random field models. Its potential is illustrated through the synchrotron SAXS analysis of a gel permeated with a critical nitrobenzene/hexane solution that is progressively cooled below its consolute temperature. The reconstruction brings to light a wetting transition whereby the nanostructure of the pore-filling liquids passes from wetting layers that uniformly cover the solid phase of the gel to plugs that locally occlude the pores. Using the plurigaussian model, the dewetting phenomenon is analyzed quantitatively at the nanometre scale in terms of changing specific interface areas, contact angle and specific length of the triple line.

Phase separation of a binary liquid in anodic aluminium oxide templates: a structural study by small angle neutron scattering

The radial nanostructure of the binary liquid triethylamine/water confined in 60 nm diameter independent cylindrical pores of anodic aluminium oxide membranes is studied by small angle neutron scattering. It is shown that composition inhomogeneities are present in the confined mixtures well below the bulk critical point. An analysis of the neutron scattering form factor reveals the existence of an adsorbed water layer of a few nanometers at the liquid/alumina interface, coexisting with a TEA-rich phase in the core.

Phase Separation of a Binary Liquid System in Controlled-Pore Glass

The phase separation behaviour and the dynamics of concentration fluctuations of binary liquid mixtures are strongly influenced by confinement effects. We have investigated this confinement effect for the binary system isobutyric acid iBA + D2O imbibed into a mesoporous silica glass (CPG-10). The dynamics of the mixture are studied in the one-phase region as well as in the phase-separated state by means of neutron spin echo spectroscopy (NSE). Moreover, the averaged structures of the liquid are explored by means of small angle neutron scattering (SANS) leading to a length scale 4 < ξ < 9 nm for the fluctuations. The associated effective diffusion coefficient Deff as obtained for NSE is found to decrease with temperature ny nearly one order of magnitude in the temperature range from 75°C to 25°C.

Transient interfacial patterns and instabilities associated with liquid film adhesion and spreading

A surface force apparatus was used to study surface shape changes during the adhesion and spreading of a polymer melt on a bare mica surface. Transient fingers were observed during the initial, rapid spreading process, pointing radially out from the initial adhesive contact point. The fingers had microscopic widths and lengths but submicroscopic thicknesses. They eventually disappeared, leaving a more slowly growing circular neck with a smooth, featureless polymer-air surface. The mean radius of the spreading meniscus (neck) was found to follow a scaling relationship with time of the form (ri + ro)/2 proportional, variant tn, with n = 0.128, while the ends of the fingers grew according to ro proportional, variant tn, with n = 0.10. These rates agree with the values of n = 0.100-0.125 predicted by classical wetting theories for circular macroscopic droplets (i.e., radially symmetric, without fingers) spreading on a solid surface. The lifetime of the transient fingering patterns increases with the polymer viscosity as tau proportional, variant etan, with n = 2.1 +/- 0.2. A circular trough or depression in the film was observed just beyond where the fingers ended, which appears to be a source of the material for the advancing fingers. In addition, beyond the trough, circular ripples/waves were observed on the polymer melt film surface. Such patterns may arise quite generally whenever a perturbation occurs that changes the local forces, thereby inducing a bulge or depression in a liquid film or surface. Thus, we observe similar fingers and ripples/waves during the spreading of liquid polybutadiene on (the immiscible and more viscous) liquid poly(dimethylsiloxane), suggesting that the phenomenon may exist in various liquid adhesion and spreading situations. For low viscosity liquids such as water and low molecular weight oils, our scaling relations suggest that the transient patterns will exist for only a few microseconds; this is likely the reason for why they have not yet been observed.

Kinetics of phase separation in thin films: simulations for the diffusive case

We study the diffusion-driven kinetics of phase separation of a symmetric binary mixture (AB), confined in a thin-film geometry between two parallel walls. We consider cases where (i) both walls preferentially attract the same component (A), and (ii) one wall attracts and the other wall attracts (with the same strength). We focus on the interplay of phase separation and wetting at the walls, which is referred to as surface-directed spinodal decomposition (SDSD). The formation of SDSD waves at the two surfaces, with wave vectors oriented perpendicular to them, often results in a metastable layered state (also referred to as "stratified morphology"). This state is reminiscent of the situation where the thin film is still in the one-phase region but the surfaces are completely wet, and hence coated with thick wetting layers. This metastable state decays by spinodal fluctuations and crosses over to an asymptotic growth regime characterized by the lateral coarsening of pancakelike domains. These pancakes may or may not be coated by precursors of wetting layers. We use Langevin simulations to study this crossover and the growth kinetics in the asymptotic coarsening regime.

Condensation phenomena in nanopores: A Monte Carlo study

The nonequilibrium dynamics of condensation phenomena in nanopores is studied via Monte Carlo simulations of a lattice-gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore geometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density. Phase-separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in the presence of a random wall-particle potential and gives rise to a temperature-dependent growth exponent. A geometric roughness of the pore wall only delays the onset of a pure domain growth.

Local structure of a phase-separating binary mixture in a mesoporous glass matrix studied by small-angle neutron scattering

The mesoscopic structure of the binary system isobutyric acid + heavy water (D(2)O) confined in a porous glass (controlled-pore silica glass, mean pore width ca. 10 nm) was studied by small-angle neutron scattering at off-critical compositions in a temperature range above and below the upper critical solution point. The scattering data were analyzed in terms of a structure factor model similar to that proposed by Formisano and Teixeira [Eur. Phys. J. E 1, 1 (2000)], but allowing for both Ornstein-Zernike-type composition fluctuations and domainlike structures in the microphase-separated state of the pore liquid. The results indicate that the phase separation in the pores is shifted by ca. 10 K and spread out in temperature. Microphase separation is pictured as a transition from partial segregation at high temperature, due to the strong preferential adsorption of water at the pore wall, to a tube or capsule configuration of the two phases at low temperatures, depending on the overall composition of the pore liquid. Results for samples in which the composition of the pore liquid can vary with temperature due to equilibration with extra-pore liquid are consistent with this picture.

Phase behavior and local structure of a binary mixture in pores: Mean-field lattice model calculations for analyzing neutron scattering data

We investigate the phase behavior of an asymmetric binary liquid A-W mixture confined between two planar homogenous substrates (slit pore). Molecules of species W interact preferentially with the solid walls via a long-range potential. Assuming nearest-neighbor attractions between the liquid molecules, we employ a lattice-gas model and a mean-field approximation for the grand potential. Minimization of this potential yields the density profiles of thermodynamically stable phases for fixed temperature, chemical potentials of both species, pore width and strengths of attraction. This model is used to analyze experimental small-angle neutron-scattering (SANS) data on the microscopic structure of the binary system isobutyric acid (iBA)+heavy water (D2O) inside a mesoscopic porous matrix (controlled-pore glass of about 10 nm mean pore width). Confinement-independent model parameters are adjusted so that the theoretical liquid-liquid coexistence curve in the bulk matches its experimental counterpart. By choosing appropriate values of the pore width and the attraction strength between substrates and water we analyze the effect of confinement on the phase diagram. In addition to a depression of the liquid-liquid critical point we observe surface induced phase transitions as well as water-film adsorption near the walls. The temperature dependence of the structure of water-rich and iBA-rich phases of constant composition are discussed in detail. The theoretical predictions are consistent with results of the SANS study and assist their interpretation.

Water dynamics and dewetting transitions in the small mechanosensitive channel MscS

The dynamics of confined water in capillaries and nanotubes suggests that gating of ion channels may involve not only changes of the pore geometry, but also transitions between water-filled and empty states in certain locations. The recently solved heptameric structure of the small mechanosensitive channel of Escherichia coli, MscS, has revealed a relatively wide (7-15 A) yet highly hydrophobic transmembrane pore. Continuum estimations based on the properties of pore surface suggest low conductance and a thermodynamic possibility of dewetting. To test the predictions we performed molecular dynamics simulations of MscS filled with flexible TIP3P water. Irrespective to the initial conditions, several independent 6-ns simulations converged to the same stable state with the pore water-filled in the wider part, but predominantly empty in the narrow hydrophobic part, displaying intermittent vapor-liquid transitions. The polar gain-of-function substitution L109S in the constriction resulted in a stable hydration of the entire pore. Steered passages of Cl(-) ions through the narrow part of the pore consistently produced partial ion dehydration and required a force of 200-400 pN to overcome an estimated barrier of 10-20 kcal/mole, implying negligibly low conductance. We conclude that the crystal structure of MscS does not represent an open state. We infer that MscS gate, which is similar to that of the nicotinic ACh receptor, involves a vapor-lock mechanism where limited changes of geometry or surface polarity can locally switch the regime between water-filled (conducting) and empty (nonconducting) states.

Density fluctuations near the liquid-gas critical point of a confined fluid

We report the results of an experimental study of the effect of a dilute silica network on liquid-gas critical phenomena in carbon dioxide (CO2). Using small-angle neutron scattering, we measured the correlation length of the density fluctuations in bulk (xi(bulk)) and confined CO2 (xi(conf)) as a function of temperature and average fluid density. We find that quenched disorder induced by an aerogel suppresses density fluctuations: xi(conf) loses the Ising model divergence characteristic of xi(bulk) and does not exceed the size of pores in the homogeneous region.

Phase behavior and dynamics of fluids in mesoporous glasses

Equilibrium and dynamical relaxation behavior of fluids confined in disordered mesoporous glasses such as Vycor are studied based on a lattice model using mean field theory and Monte Carlo simulations. Preferential attractive interactions between the solid surfaces and the fluid suppresses macroscopic phase separation, while making the relaxation rate increasingly slow. The free energy landscape characterized by the presence of the many metastable minima separated by finite barriers dominates both the static and dynamic behavior of fluids at low temperature. Our results provide additional insight into the nature of hysteresis in adsorption measurements of gases in porous glasses.

Tunneling and optical spectroscopy of semiconductor nanocrystals

The use of a combination of tunneling and optical spectroscopy to investigate the size and shape-dependent level structure and single-electron charging phenomena in semiconductor nanocrystals is reviewed. The artificial atom character of semiconductor nanocrystal quantum dots is manifested in both the discrete level structure and in the charging multiplicity of the single-electron tunneling data, revealing s and p atomic-like states. Such states can be directly imaged using scanning tunneling microscopy, providing the extent and symmetry of the envelope wavefunctions. A detailed description of the effect of the tunneling geometry on the single-electron tunneling spectra is presented. Correlation of the optical and tunneling data allows for the assignment of the level spectrum. The generality of this powerful combination is further demonstrated in the study of quantum rods that manifest the transition from zero-dimensional quantum dots to one-dimensional quantum wires.

Phase transitions and quantum effects in pore condensates: a path integral Monte Carlo study

Lennard-Jones condensates in cylindrical pores are studied by path integral Monte Carlo simulations with particular emphasis on phase transitions and quantum effects. The pore diameter effect and the influence of the interaction strength between the cylinder wall and the adsorbate particles on the structures and the location of the phase boundaries is studied and the quantum effect on the phase diagram is quantified by path integral Monte Carlo simulations. In case of strong wall-particle interactions good qualitative agreement with recent experimental results for the freezing of Ar-pore condensates is found. Meniscus structures in the solid phase are obtained as well as unexpected condensate structures for the system with the lighter Ne-particles due to quantum delocalization effects. The quantum effect on the freezing temperature can be as large as 10% in these systems.

Low-temperature phase separation of a binary liquid mixture in porous materials studied by cryoporometry and pulsed-field-gradient NMR

The low-temperature liquid-liquid phase separation of the partially miscible hexane-nitrobenzene mixture imbibed in porous glasses of different pore sizes from 7 to 130 nm has been studied using 1H NMR (nuclear magnetic resonance) cryoporometry and pulse field gradient NMR methods. The mixture was quenched below both its upper critical solution temperature (T(cr)) and the freezing point of nitrobenzene. The size distribution of frozen nitrobenzene domains was derived through their melting point suppression according to the Gibbs-Thompson relation. The obtained data reveal small initial droplets of nitrobenzene surrounded by hexane, which are created as the temperature is decreased below T(cr) and which thereafter coalesce by a droplet-diffusion mechanism. The inter-relation between the pore size and the found size distribution and shapes of nitrobenzene domains is discussed, as well as several aspects of molecular self-diffusion.

Capillary condensation as a morphological transition

The process of capillary condensation/evaporation in cylindrical pores is considered within the idea of symmetry breaking. Capillary condensation/evaporation is treated as a morphological transition between the wetting film configurations of different symmetry. We considered two models: (i) the classical Laplace theory of capillarity and (ii) the Derjaguin model which takes into account the surface forces expressed in terms of the disjoining pressure. Following the idea of Everett and Haynes, the problem of condensation/evaporation is considered as a transition from bumps/undulations to lenses. Using the method of phase portraits, we discuss the mathematical mechanisms of this transition hidden in the Laplace and Derjaguin equations. Analyzing the energetic barriers of the bump and lens formation, it is shown that the bump formation is a prerogative of capillary condensation: for the vapor-liquid transition in a pore, the bump plays the same role as the spherical nucleus in a bulk fluid. We show also that the Derjaguin model admits a variety of interfacial configurations responsible for film patterning at specific conditions.

Phase-morphology map of polymer-blend thin films confined to narrow strips

Upon lateral confinement, a critical polymer-blend film at 200 degrees C has been directed to form tube, capsule, confined domain, and multiple domain configurations. A phase-morphology map is produced by varying the confinement width ( W) and film thickness ( h(0)), and interpreted using a single pore model. Using the known correlation length, capsule length, and W, the boundary, in terms of W/h(0), between configurations is predicted and found to be in good agreement with experiment. This morphology map has potential applications for microencapsulating drugs and self-assembled conducting wires.

Computer simulations of phase equilibrium for a fluid confined in a disordered porous structure

We present calculations of the phase diagrams of a Lennard-Jones 12-6 fluid confined in a disordered porous structure made up of a dispersion of spherical particles, following up on an earlier work on the same system. In particular we present additional calculations using more realizations of the matrix and we investigate the applicability of the Gibbs-Duhem integration method to the calculation of phase equilibrium in these systems. The essential picture of disordered and inhomogeneous coexisting vapor and liquid phases, which emerged in the earlier work, is confirmed by the new calculations. However, a second phase transition associated with the wetting of the porous material by the fluid is found to be more sensitive to variations of the matrix realization. While for the present model this transition appears for particular realizations of the matrix, it does not seem to survive averaging over realizations.

Simple views on critical binary liquid mixtures in porous glass

A simple scenario, different from previous attempts, is proposed to resolve the problem of the slow phase separation dynamics of binary liquid mixtures confined in porous Vycor glass. We demonstrate that simply mutual diffusion, renormalized by critical composition fluctuations and geometrical hindrance of the porous glass, accounts for the slow phase separation kinetics. Capillary invasion studies of porous Vycor glass by the critical isobutyric acid-water mixture, close to the consolute solution temperature, corroborate our analysis.

Monte Carlo approach to the gas-liquid transition in porous materials

The gas-liquid transition of a "quenched-annealed"(QA) system is studied by grand-canonical Monte Carlo simulation. The "quenched" particles are hard spheres within configurations chosen randomly from those of an equilibrium hard-sphere system at given density. The fluid particles interact with the matrix particles by a hard-core potential and with each other by a hard-core potential and an additional potential of a Lennard-Jones type. Our results are in good qualitative agreement with various theoretical approaches. With increasing matrix density the critical temperature is lowered compared to that of the bulk system and the gap between the gas and liquid densities narrowed. Our simulations confirm, for this QA system, the possibility of two fluid-fluid transitions substituting for the unique gas-liquid transition of the bulk system. They demonstrate the necessity to average over a significant number of matrix realizations in order to obtain a quantitative location of the phase coexistence lines.

Effects of quenched disorder on the orientational order of the octylcyanobiphenyl liquid crystal

Deuteron NMR (DNMR) measurements were performed with high-temperature and spectral resolution on the octylcyanobiphenyl (8CB) liquid crystal confined to the randomly interconnected pores of silica aerogel as a function of temperature and silica density. The aerogel density was varied by one order of magnitude and the temperature spanned the isotropic (I), nematic (N), and smectic-A (SmA) phases of 8CB. For all samples, the liquid crystal was confined to pores smaller than the micron-sized magnetic coherence length. Thus the observed line shapes reflect the director pattern, n(r-->), and the orientational order, Q, as dictated by the porous host. The DNMR spectral patterns are consistent with powder line shapes representative of a randomized n(r-->) characterized by a single Q. The nematic domains formed are of finite dimension that likely exceeds the confining size. The weakly first-order nematic-to-isotropic phase transition becomes less discontinuous with decreasing pore size, eventually becoming continuous at an aerogel density between 0.36 and 0.5 g/cm(3). In the most severe confinement, no phase transitions are observed with only a continuous evolution of Q present. The orientational order is suppressed from the bulk's with no enhancement upon the onset of the SmA phase. This indicates a decoupling of nematic and smectic order parameters and a severe suppression of the SmA phase by this porous media.