Rounding of phase transitions in cylindrical pores

Polymer solution structure and dynamics within pores of hexagonally close-packed nanoparticles

Using coarse-grained molecular dynamics simulations, we examine structure and dynamics of polymer solutions under confinement within the pores of a hexagonally close-packed (HCP) nanoparticle system with nanoparticle diameter fifty times that of the polymer Kuhn segment size. We model a condition where the polymer chain is in a good solvent (i.e., polymer-polymer interaction is purely repulsive and polymer-solvent and solvent-solvent interactions are attractive) and the polymer-nanoparticle and solvent-nanoparticle interactions are purely repulsive. We probe three polymer lengths (N = 10, 114, and 228 Kuhn segments) and three solution concentrations (1, 10, and 25%v) to understand how the polymer chain conformations and chain center-of-mass diffusion change under confinement within the pores of the HCP nanoparticle structure from those seen in bulk. The known trend of bulk polymer R_g² decreasing with increasing concentration no longer holds when confined in the pores of HCP nanoparticle structure; for example, for the 114-mer, the HCP 〈R_g²〉 at 1%v concentration is lower than HCP 〈R_g²〉 at 10%v concentration. The 〈R_g²〉 of the 114-mer and 228-mer exhibit the largest percent decline going from bulk to HCP at the 1%v concentration and the smallest percent decline at the 25%v concentration. We also provide insight into how the confinement ratio (CR) of polymer chain size to pore size within tetrahedral and octahedral pores in the HCP arrangement of nanoparticles affects the chain conformation and diffusion at various concentrations. At the same concentration, the N = 114 has significantly more movement between pores than the N = 228 chains. For the N = 114 polymer, the diffusion between pores (i.e., inter-pore diffusion) accelerates the overall diffusion rate for the confined HCP system while for the N = 228 polymer, the polymer diffusion in the entire HCP is dominated by the diffusion within the tetrahedral or octahedral pores with minor contributions from inter-pore diffusion. These findings augment the fundamental understanding of macromolecular diffusion through large, densely packed nanoparticle assemblies and are relevant to research focused on fabrication of polymer composite materials for chemical separations, storage, optics, and photonics. We perform coarse-grained molecular dynamics simulations to understand structure and dynamics of polymer solutions under confinement within hexagonal close packed nanoparticles with radii much larger than the polymer chain's bulk radius of gyration.

Hysteresis curves reveal the microscopic origin of cooperative CO2 adsorption in diamine-appended metal-organic frameworks

Diamine-appended metal-organic frameworks (MOFs) of the form Mg₂(dobpdc)(diamine)₂ adsorb CO₂ in a cooperative fashion, exhibiting an abrupt change in CO₂ occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a first-order phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO₂ chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, providing a physical understanding of cooperative adsorption in this industrially important class of materials.

Phase behavior of colloid-polymer mixtures in planar, spherical, and cylindrical confinement: A density functional theory study

The Asakura-Oosawa (AO) model of colloid-polymer mixtures has been extensively studied over the past several decades both via computer simulations and Density Functional Theory (DFT). At this point, its structural and thermodynamic properties both in the bulk and in contact with flat structureless walls are well understood. At the same time, the phase behavior of AO mixtures in spherical cavities and cylindrical pores, while thoroughly investigated by simulations, has not received a comparably detailed DFT treatment. In this paper, we use the DFT results for the AO model in the bulk and under planar confinement as a point of reference for studying its thermodynamic and structural properties in cavities and pores. The accuracy of the DFT approach is assessed by comparing its predictions with the available extensive simulation data; good overall agreement is generally found with some notable exceptions in the vicinity of wetting and drying transitions. The deviations of the phase behavior in confinement from the bulk phase diagram are analyzed using the Kelvin equation, which is seen to work reasonably well under moderate confinement, i.e., for sufficiently large radii of confining cavities and pores.

Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials

Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.

Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

Dependences of Formation and Transition of the Surface Condensation Mode on Wettability and Temperature Difference

In this work, we use molecular dynamics (MD) simulations to investigate the dependences of formation and transition of surface condensation mode on wettability (β) and vapor-to-surface temperature difference (ΔT). We build a map of different surface condensation modes against β and ΔT based on plenty of MD simulation results and reveal five formation mechanisms and two transition mechanisms. At low β and ΔT, the high free energy barrier (ΔG*) prevents any surface clusters from surviving, therefore no-condensation (NC) is observed. The formation of dropwise condensation (DWC) could evolve from either nucleation or film rupture. Similarly, the formation of filmwise condensation (FWC) could evolve from either nucleation or the adsorption-induced film. The transition between NC and DWC is determined by ΔG* according to classical nucleation theory. The transition between DWC and FWC depends on the stability of condensate film; there emerges the competition between the trend that the uneven condensate film contracts and ruptures to droplets favored by lower β and the trend that the uneven condensate film continues growing promoted by higher ΔT. We finally present a schematic overview of all of the mechanisms revealed for a better understanding of the physical phenomenon of the surface condensation mode.

Eutectic liquid crystal mixture E7 in nanoporous alumina. Effects of confinement on the thermal and concentration fluctuations

The eutectic mixture of liquid crystals E7 is studied in confinement by means of thermal and dielectric measurements. The uniform 1-D confinement provided by self-ordered nanoporous alumina leads to a decrease in the nematic to isotropic transition temperature due to interaction with the pore surface, e.g. surface anchoring. The prevalence of certain dynamic modes of relaxation is found to depend on the surface properties of the confining pores. The dynamics (i.e., relaxation times) were found to accelerate with increasing confinement, resulting in a decreasing glass temperature, independent of surface treatment. From the pre- and meta-transitional dependence of the dielectric permittivity on temperature we are able to deduce a weakening effect of confinement on the nematic to isotropic (N/I) transition which allows the determination of a critical pore diameter (in the range from 11 nm to 23 nm) below which the transition becomes continuous. Comparison of the N/I transition of E7 to those of its constituent liquid crystals reveals a significantly weaker transition occurring over a widened temperature range. This suggest the importance of concentration fluctuations in rounding first order phase transitions that are triggered by the different length scales and ranges of nematic stability in E7. The results have an impact beyond the present case and for several soft materials (e.g. oligomers used as OLEDs, polymers, colloids) as it demonstrates the importance of concentration fluctuations in addition to thermal fluctuation on the strength of phase transitions.

Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an L×L×D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D>6 lattice spacings.

Hysteresis in the temperature dependence of the IR bending vibration of deeply cooled confined water

Using Fourier Transform Infrared (FTIR) spectroscopy, we investigate the temperature dependence of the bending vibrations of water confined in the pores of a silica hydrogel in the temperature interval of 270-180 K. We also investigate the presence of thermal hysteresis by cooling and reheating temperature scans. The results clearly show the presence, at about 230 K, of a crossover in the temperature dependence of the IR spectra; moreover, the presence of hysteresis is clearly demonstrated. By comparing FTIR data with neutron diffraction data and previous calorimetric data on the same samples, we conclude that the crossover and the hysteretical behavior do not involve a water glass transition or crystallization but are related to a first-order-like liquid-liquid transition.

Phase transitions in disordered mesoporous solids

Fluids confined in mesoporous solids exhibit a wide range of physical behavior including rich phase equilibria. While a notable progress in their understanding has been achieved for fluids in materials with geometrically ordered pore systems, mesoporous solids with complex pore geometries still remain a topic of active research. In this work we study phase transitions occurring in statistically disordered linear chains of pores with different pore sizes. By considering, quite generally, two phase change mechanisms, nucleation and phase growth, occurring simultaneously we obtain the boundary transitions and the scanning curves resulting upon reversing the sign of the evolution of the chemical potential at different points along the main transition branches. The results obtained are found to reproduces the key experimental observations, including the emergence of hysteresis and the scanning behavior. By deriving the serial pore model isotherm we suggest a robust framework for reliable structural analysis of disordered mesoporous solids.

Molecular dynamics simulation of heterogeneous nucleation on nanotubes

Condensation rate inside and outside the tube depends on the pore diameter and length.

Logarithmic finite-size effects on interfacial free energies: phenomenological theory and Monte Carlo studies

The computation of interfacial free energies between coexisting phases (e.g., saturated vapor and liquid) by computer simulation methods is still a challenging problem due to the difficulty of an atomistic identification of an interface and interfacial fluctuations on all length scales. The approach to estimate the interfacial tension from the free-energy excess of a system with interfaces relative to corresponding single-phase systems does not suffer from the first problem but still suffers from the latter. Considering d-dimensional systems with interfacial area L(d-1) and linear dimension L(z) in the direction perpendicular to the interface, it is argued that the interfacial fluctuations cause logarithmic finite-size effects of order ln(L)/L(d-1) and order ln(L(z))/L(d-1), in addition to regular corrections (with leading-order const/L(d-1)). A phenomenological theory predicts that the prefactors of the logarithmic terms are universal (but depend on the applied boundary conditions and the considered statistical ensemble). The physical origin of these corrections are the translational entropy of the interface as a whole, "domain breathing" (coupling of interfacial fluctuations to the bulk order parameter fluctuations of the coexisting domains), and capillary waves. Using a new variant of the ensemble switch method, interfacial tensions are found from Monte Carlo simulations of d = 2 and d = 3 Ising models and a Lennard-Jones fluid. The simulation results are fully consistent with the theoretical predictions.

Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: role of interfacial fluctuations and domain breathing

The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions L parallel and Lz perpendicular to the interface with various boundary conditions in the canonical or grand canonical ensemble can be studied. Using two- and three-dimensional Ising models, the nature of the occurring logarithmic finite-size corrections is studied. It is found crucial to include interfacial fluctuations due to "domain breathing."

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.

Critical behaviour of the Ising ferromagnet confined in quasi-cylindrical pores: a Monte Carlo study

The critical behaviour of the Ising ferromagnet confined in pores of radius R and length L is studied by means of Monte Carlo computer simulations. Quasi-cylindrical pores are obtained by replicating n-times a triangular lattice disc of radius R, where L = na and a is the spacing between consecutive replications. So, spins placed at the surface of the pores have less nearest-neighbours (NN) as compared to 8 NN for spins in the bulk. These "missing neighbour" effects undergone by surface spins cause a strong suppression of surface ordering, leading to an ordinary surface transition. Also, the effect propagates into the bulk for small tubes (R ≤ 12) and the effective critical temperature of the pores is shifted towards lower values than in the bulk case. By applying the standard finite-size scaling theory, subsequently supported by numerical data, we concluded that data collapse of relevant observables, e.g., magnetization (m), susceptibility, specific heat, etc., can only be observed by comparing simulation results obtained by keeping the aspect ratio C ≡ R∕L constant. Also, by extrapolating "effective" R-dependent critical temperatures to the thermodynamic limit (R → ∞, C fixed), we obtained T(C)(∞) = 6.208(4). As suggested by finite-size scaling arguments, the magnetization is measured at the critical point scales according to [|m|]Tc R(β/ν) is proportional to [R/L](1/2), where β and ν are the standard exponents for the order parameter and the correlation length, respectively. Furthermore, it is shown that close to criticality the axial correlation length decreases exponentially with the distance. That result is the signature of the formation of (randomly distributed) alternating domains of different magnetization, which can be directly observed by means of snapshot configurations, whose typical length (ξ) is given by the characteristic length of the exponential decay of correlations. Moreover, we show that at criticality ξ = 0.43(2)R.

Controlling the wetting properties of the Asakura-Oosawa model and applications to spherical confinement

We demonstrate for the Asakura-Oosawa model and an extension of this model that uses continuous rather than hard potentials, how wetting properties at walls can be easily controlled. By increasing the interaction range of the repulsive wall potential acting on the colloids (while keeping the polymer-wall interactions constant) polymers begin to substitute colloids at walls and the system can be driven from complete wetting of colloids via partial wetting to complete wetting of polymers. As an application, we discuss the morphology and wetting behavior of colloid-polymer mixtures in spherical confinement. We apply the recently developed 'ensemble switch method' where the Hamiltonian is extended to a combination of a system with walls and of a system without walls to calculate the surface excess free energies of colloid-rich and polymer-rich phases. The contact angle then is inferred from Young's equation.

Formation of metastable structures by phase separation triggered by initial composition gradients in thin films

Phase separation kinetics of a binary (A,B) mixture contained in a thin film of thickness D induced by a quench from the one-phase region into the miscibility gap is studied by simulations using a Cahn-Hilliard-Cook model. The initial randomly mixed state (50% A, 50% B) contains a concentration gradient perpendicular to the film, while the surfaces of the film are "neutral" (no preference for either A or B). In thermal equilibrium, a pattern of large A-rich and B-rich domains must result, separated by domain walls oriented perpendicularly to the external surfaces of the thin film. However, it is shown that for many choices of D and the strength of the initial gradient Ψ(g), instead a very long-lived metastable layered structure forms, with two domains separated by a single interface parallel to the external walls. The transient time evolution that leads to this structure is interpreted in terms of a competition between domain growth in the bulk and surface-directed spinodal decomposition caused by the gradient during the initial stages. A surprising and potentially useful finding is that a moderate concentration gradient perpendicular to the film does not favor the layered structure but facilitates the approach toward the true equilibrium with just two domain walls perpendicular to the film. This mechanism may have useful applications in producing layered materials.

Phase separation in fluids exposed to spatially periodic external fields

When a fluid is confined within a spatially periodic external field, the liquid-vapor transition is replaced by a different transition called laser-induced condensation (LIC) [Götze et al., Mol. Phys. 101, 1651 (2003)]. In d=3 dimensions, the periodic field induces an additional phase, characterized by large density modulations along the field direction. At the triple point, all three phases (modulated, vapor, and liquid) coexist. At temperatures slightly above the triple point and for low (high) values of the chemical potential, two-phase coexistence between the modulated phase and the vapor (liquid) is observed; by increasing the temperature further, both coexistence regions terminate in critical points. In this paper, we reconsider LIC using the Ising model to resolve a number of open issues. To be specific, we (1) determine the universality class of the LIC critical points and elucidate the nature of the correlations along the field direction, (2) present a mean-field analysis to show how the LIC phase diagram changes as a function of the field wavelength and amplitude, (3) develop a simulation method by which the extremely low tension of the interface between modulated and vapor or liquid phase can be measured, (4) present a finite-size scaling analysis to accurately extract the LIC triple point from finite-size simulation data, and (5) consider the fate of LIC in d=2 dimensions.

Suppression of phase transitions in a confined rodlike liquid crystal

The nematic-to-isotropic, crystal-to-nematic, and supercooled liquid-to-glass temperatures are studied in the liquid crystal 4-pentyl-4'-cyanobiphenyl (5CB) confined in self-ordered nanoporous alumina. The nematic-to-isotropic and the crystal-to-nematic transition temperatures are reduced linearly with the inverse pore diameter. The finding that the crystalline phase is completely suppressed in pores having diameters of 35 nm and below yields an estimate of the critical nucleus size. The liquid-to-glass temperature is reduced in confinement as anticipated by the model of rotational diffusion within a cavity. These results provide the pertinent phase diagram for a confined liquid crystal and are of technological relevance for the design of liquid crystal-based devices with tunable optical, thermal, and dielectric properties.

Single-file water in nanopores

Water molecules confined to pores with sub-nanometre diameters form single-file hydrogen-bonded chains. In such nanoscale confinement, water has unusual physical properties that are exploited in biology and hold promise for a wide range of biomimetic and nanotechnological applications. The latter can be realized by carbon and boron nitride nanotubes which confine water in a relatively non-specific way and lend themselves to the study of intrinsic properties of single-file water. As a consequence of strong water-water hydrogen bonds, many characteristics of single-file water are conserved in biological and synthetic pores despite differences in their atomistic structures. Charge transport and orientational order in water chains depend sensitively on and are mainly determined by electrostatic effects. Thus, mimicking functions of biological pores with apolar pores and corresponding external fields gives insight into the structure-function relation of biological pores and allows the development of technical applications beyond the molecular devices found in living systems. In this Perspective, we revisit results for single-file water in apolar pores, and examine the similarities and the differences between these simple systems and water in more complex pores.

Density hysteresis of heavy water confined in a nanoporous silica matrix

A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We interpret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid-liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved.

Simulation evidence for nonlocal interface models: two correlation lengths describe complete wetting

Monte Carlo simulations of (fluctuating) interfaces in Ising models confined between competing walls at temperatures above the wetting transition are presented and various correlation functions probing the interfacial fluctuation are computed. Evidence for the nonlocal interface Hamiltonian approach of A. O. Parry et al. [Phys. Rev. Lett. 93, 086104 (2004)] is given. In particular, we show that two correlation lengths exist with different dependence on the distance D between the walls.