The surface directed spinodal decomposition of a binary liquid confined inside cylindrical pore is investigated using molecular dynamics simulation. One component of the liquid wets the pore surface while the other remains neutral. A variety of wetting conditions are studied. For the partial wetting case, after an initial period of phase separation, the domains organize themselves into plug-like structure and the system enters into a metastable state. Therefore, a complete phase separation is never achieved. Analysis of domain growth and the structure factor suggests an one-dimensional growth dynamics for partial wetting case. As the wetting interaction is increased beyond a critical value, a transition from the plug-like to tube-like domain formation is observed which corresponds to the full wetting morphology. Thus, a complete phase separation is achieved as the wetting species moves towards the pore surface and forms layers enclosing the non wetting species residing around the axis of the cylinder. The coarsening dynamics of both the species are studied separately. The wetting species is found to follow a two-dimensional domain growth dynamics with a growth exponent 1/2 in the viscous hydrodynamic regime. This was substantiated by the Porod tail of the structure factor. On the other hand, the domain grows linearly with time for the non wetting species. This suggests that the non wetting species behaves akin to a three-dimensional bulk system. An appropriate reasoning is presented to justify the given observations.
We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.
A cylindrical nanopore immersed in a non-additive hard sphere binary fluid is studied by means of integral equation theories and Monte Carlo simulations. It is found that at low and intermediate values of the bulk total number density the more concentrated bulk species is preferentially absorbed by the pore, as expected. However, further increments of the bulk number density lead to an abrupt population inversion in the confined fluid and an entropy driven prewetting transition at the outside wall of the pore. These phenomena are a function of the pore size, the non-additivity parameter, the b…
The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D<W<2 D$), the structure is homogeneous and the system behaves as a one-dimensional Tonks gas. For wider pores, inhomogeneous fluid struc…
We present results of molecular dynamics simulations of water confined in a silica pore. A cylindrical cavity is created inside a vitreous silica cell with geometry and size similar to the pores of real Vycor glass. The simulations are performed at different hydration levels. At all hydration levels water adsorbs strongly on the Vycor surface; a double layer structure is evident at higher hydrations. At almost full hydration the modifications of the confinement-induced site-site pair distribution functions are in qualitative agreement with neutron diffraction experiment. A decrease in the numb…
The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density σ, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with σ, is developed and tested by Molecular Dynamics simulations of a bead-spring model.
The collision dynamics of hard spheres and cylindrical pores is solved exactly, which is the minimal model for a regularly porous membrane. Nonequilibrium event-driven molecular dynamics simulations are used to show that the permeability $P$ of hard spheres of size $σ$ through cylinderical pores of size $d$ follow the hindered diffusion mechanism due to size exclusion as $P \propto (1-σ/d)^2$. Under this law, the separation of binary mixtures of large and small particles exhibits a linear relationship between $α^{-1/2}$ and $P^{-1/2}$, where $α$ and $P$ are the selectivity and permeability of …
We present a neutron scattering analysis of the density and the static structure factor of confined methanol at various temperatures. Confinement is performed in the cylindrical pores of MCM-41 silicates with pore diameters D=24 angstrom and D=35 angstrom. A change of the thermal expansivity of confined methanol at low temperature is the signature of a glass transition, which occurs at higher temperature for the smallest pore. This is an evidence of a surface induced slowing down of the dynamics of the fluid. The structure factor presents a systematic evolution with the pore diameter, which ha…
Understanding how electrolyte-filled porous electrodes respond to an applied potential is important to many electrochemical technologies. Here, we consider a model supercapacitor of two blocking cylindrical pores on either side of a cylindrical electrolyte reservoir. A stepwise potential difference $2Φ$ between the pores drives ionic fluxes in the setup, which we study through the modified Poisson-Nernst-Planck equations, solved with finite elements. We focus our discussion on the dominant timescales with which the pores charge and how these timescales depend on three dimensionless numbers. Ne…
Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $σ$ are varied over a wide range and the crossover from ``mushroom'' to ``brush'' behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $σ$ for large enough pore diameter where the brush…
The study of protein mass transport via atomistic simulation requires time and length scales beyond the computational capabilities of modern computer systems. The raspberry model for colloidal particles in combination with the mesoscopic hydrodynamic method of lattice Boltzmann facilitates coarse-grained simulations that are on the order of microseconds and hundreds of nanometers for the study of diffusive transport of protein-like colloid particles. The raspberry model reproduces linearity in resistance to motion versus particle size and correct enhanced drag within cylindrical pores at off-c…
As a generic model system of an asymmetric binary fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonable well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, pha…
We use Metropolis Monte Carlo and umbrella sampling to calculate the free energies of interaction of two methane molecules and their charged derivatives in cylindrical water-filled pores. Confinement strongly alters the interactions between the nonpolar solutes, and completely eliminates the solvent separated minimum (SSM) that is seen in bulk water. The free energy profiles show that the methane molecules are either in contact or at separations corresponding to the diameter and the length of the cylindrical pore. Analytic calculations that estimate the entropy of the solutes, which are solvat…
We investigate the effect of cylindrical nano-confinement on the phase behaviour of a rigid model of carbon dioxide using both molecular dynamics and well tempered metadynamics. To this aim we study a simplified pore model across a parameter space comprising pore diameter, CO2-pore wall potential and CO2 density. In order to systematically identify ordering events within the pore model we devise a generally applicable approach based on the analysis of the distribution of intermolecular orientations. Our simulations suggest that, while confinement in nano-pores inhibits the formation of known c…
A field theoretic variational approach is introduced to study ion penetration into water-filled cylindrical nanopores in equilibrium with a bulk reservoir. It is shown that (i) an ion located in a neutral pore undergoes two opposing mechanisms: the deformation of its surrounding ionic cloud of opposite charge, with respect to the reservoir, which increases the surface tension and tends to exclude ions form the pore, and (ii) the attractive contribution to the ion self-energy of the repulsive image forces associated with the dielectric jump between the solvent and the pore wall, which becomes m…
Using an algorithm for simulating equilibrium configurations, we study a fluctuating helical polymer either (i) contained in a cylindrical pore or (ii) wound around a cylindrical rod. We work in the regime where both the contour length and the persistence length of the helical polymer are much larger than the diameter of the cylinder. In case (i) we calculate the free energy of confinement and interpret it in terms of a worm-like chain in a pore with an effective diameter that depends on the parameters of the helix. In case (ii) we consider the possibility that one end of the helical polymer e…
We calculate the mean end-to-end distance ($R$) of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius $D$. A self-consistent perturbation theory is used to calculate $R$ as a function of $D$ for impenetrable hard walls and soft walls. In both cases, $R$ obeys the predicted scaling behavior in the limit of large and small $D$. The crossover from the three dimensional behavior ($D\to\infty$) to the fully stretched one dimensional case ($D\to 0$) is non-monotonic. The minimum value of $R$ is found at $D\sim 0.46 R_F$, where $R_F$ is the Flory radius of $R$ at $D \to \…
We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, t, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to t ~ N^2D^(1/3). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different t-results for N up to 2000. We argue that the previous scaling prediction is only as…
Ion transport in porous media is present in a wealth of technologies, e.g., energy storage devices such as batteries and supercapacitors, and environmental technologies such as electrochemical carbon capture and capacitive deionization. Recent studies on flat-plate electrodes have demonstrated that asymmetries in ion properties, such as valences and diffusivities, lead to intriguing and counter-intuitive physical phenomena. Yet, the consequences of such asymmetries to ion transport have seldom been explored in porous geometries. To bridge this knowledge gap, we conduct a perturbation expansion…
We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders …
Using grand canonical Monte Carlo simulations, we have explored the phenomenon of capillary condensation (CC) of Ar at the triple temperature inside infinitely long, cylindrical pores. Pores of radius R= 1 nm, 1.7 nm and 2.5 nm have been investigated, using a gas-surface interaction potential parameterized by the well-depth D of the gas on a planar surface made of the same material as that comprising the porous host. For strongly attractive situations, i.e., large D, one or more (depending on R) Ar layers adsorb successively before liquid fills the pore. For very small values of D, in contrast…
We report on the results of a molecular dynamics simulation study of binodal glassy systems, formed in the process of isochoric rapid quenching from a high-temperature fluid phase. The transition to vitreous state occurs due to concurrent spinodal decomposition and solidification of the matter. The study is focused on topographies of the porous solid structures and their dependence on temperature and average density. To quantify the pore-size distributions, we put forth a scaling relation that provides a robust data collapse in systems with high porosity. We also find that the local density of…
Fluids confined in nanopores exhibit properties different from the properties of the same fluids in bulk, among these properties are the isothermal compressibility or elastic modulus. The modulus of a fluid in nanopores can be extracted from ultrasonic experiments or calculated from molecular simulations. Using Monte Carlo simulations in the grand canonical ensemble, we calculated the modulus for liquid argon at its normal boiling point (87.3~K) adsorbed in model silica pores of two different morphologies and various sizes. For spherical pores, for all the pore sizes (diameters) exceeding 2~nm…
We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhi…
The phase behaviour and structural properties of a monolayer of hard particles is examined in such a confinement, where the adsorbed particles are constrained to the surface of a narrow hard cylindrical pore. The diameter of the pore is chosen such that only first and second neighbour interactions occur between the hard particles. The transfer operator method of Percus and Zhang [Mol. Phys., 69, 347 (1990)] is reformulated to obtain information about the structure of the monolayer. We have found that a true phase transition is not possible in the examined range of pore diameters. The monolayer…
The optical polarimetry technique is used to explore molecular ordering of nematic liquid crystals 5FPFFPP3 embedded in parallel cylindrical channels of alumina membranes with pore walls covered by a SE-1211 polymer film enhancing normal anchoring. A chemical film deposition from organic solution apparently results in inhomogeneous coverage with local islands on the channels walls. Accordingly, a coexistence of differently ordered LC regions (nanodomains), characterized by positive and negative anisotropy, results in a weak effective (average) optical birefringence. Repeated polymer deposition…
We introduce an implicit solvent Molecular Dynamics approach for calculating ionic fluxes through narrow nano-pores and transmembrane channels. The method relies on a dual-control- volume grand-canonical molecular dynamics (DCV-GCMD) simulation and the analytical solution for the electrostatic potential inside a cylindrical nano-pore recently obtained by Levin [Europhys. Lett., 76, 163 (2006)]. The theory is used to calculate the ionic fluxes through an artificial trans-membrane c hannel which mimics the antibacterial gramicidin A channel. Both current-voltage and current-concentration relatio…
Understanding how colloidal suspensions behave in confined environments has a striking relevance in practical applications. Despite the fact that the behaviour of colloids in the bulk is key to identify the main elements affecting their equilibrium and dynamics, it is only by studying their response under confinement that one can ponder the use of colloids in formulation technology. In particular, confining fluids of anisotropic particles in nanopores provides the opportunity to control their phase behaviour and stabilise a spectrum of morphologies that cannot form in the bulk. By properly sel…
The orientational and translational order of a thermotropic ferroelectric liquid crystal (2MBOCBC) imbibed in self-organized, parallel, cylindrical pores with radii of 10, 15, or 20 nm in anodic aluminium oxide monoliths (AAO) are explored by high-resolution linear and circular optical birefringence as well as neutron diffraction texture analysis. The results are compared to experiments on the bulk system. The native oxidic pore walls do not provide a stable smectogen wall anchoring. By contrast, a polymeric wall grafting enforcing planar molecular anchoring results in a thermal-history indepe…
Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover,…
The confinement of liquid crystals inside curved geometries leads to exotic structures, with applications ranging from bio-sensors to optical switches and privacy windows. Here we study how curvature affects the alignment of a cholesteric liquid crystal. We model the system on the mesoscale using the Landau-de Gennes model. Our study was performed in three stages, analysing different curved geometries from cylindrical walls and pores, to toroidal domains, in order to isolate the curvature effects. Our results show that the stresses introduced by the curvature influence the orientation of the l…
The structure of water confined in MCM41 silica cylindrical pores is studied to determine if confined water really is simply a version of the bulk liquid which can be substantially supercooled without crystallisation. A combination of total neutron scattering from the porous silica, both wet and dry,and computer simulation using a realistic model of the scattering substrate isused. The water in the pore is divided into three regions: core, interfacial and overlap. The average local densities of water in these simulations are found to be about 20% lower than bulk water density, while the densit…
Small angle neutron scattering (SANS) is used to measure the density of heavy water contained in 1-D cylindrical pores of mesoporous silica material MCM-41-S-15, with pores of diameter of 15+-1 A. In these pores the homogenous nucleation process of bulk water at 235 K does not occur and the liquid can be supercooled down to at least 160 K. The analysis of SANS data allows us to determine the absolute value of the density of D2O as a function of temperature. We observe a density minimum at 210+-5 K with a value of 1.041+-0.003 g/cm3. We show that the results are consistent with the predictions …
Capillary filling dynamics of liquid n-tetracosane (n-C24H50) in a network of cylindrical pores with 7 and 10 nm mean diameter in monolithic silica glass (Vycor) exhibit an abrupt temperature-slope change at Ts=54 deg C, ~4 deg C above bulk and ~16 deg C, 8 deg C, respectively, above pore freezing. It can be traced to a sudden inversion of the surface tension's T slope, and thus to a decrease in surface entropy at the advancing pore menisci, characteristic of the formation of a single solid monolayer of rectified molecules, known as surface freezing from macroscopic, quiescent tetracosane melt…
We use the Parsons Lee modification of Onsagers second virial theory within the restricted orientation approximation to analyse the phase behaviour of hard cylindrical rods confined in narrow pores Depending on the wall to wall separation we predict a number of distinctly different surface generated nematic phases including a biaxial planar nematic with variable number of layers a monolayer homeotropic and a hybrid T type structure For narrow pores we find evidence of two types of second order uniaxial biaxial transitions depending on the aspect ratio of the particles More specifically we obse…
We analyse a binary mixture of colloidal parallel hard cylindrical particles with identical diameters but dissimilar lengths $L_1$ and $L_2$, with $s=L_2/L_1=3$, confined by two parallel hard walls in a planar slit-pore geometry, using a fundamental--measure density functional theory. This model presents nematic (N) and two types of smectic (S) phases, with first- and second-order N-S bulk transitions and S-S demixing, and surface behaviour at a single hard wall which includes complete wetting by the S phase mediated (or not) by an infinite number of surface-induced layering (SIL) transitions.…
Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N=21-61. The rate of translocation is controlled by a tunable friction coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length N as <tau_1>~ (N-N_p)^alpha, where N_p is the average number of monomers in the nanopore. The exponent approaches the value alpha=2 when the pore friction is…
A theoretical study on the phase behaviors of a polymer solution confined between two coaxial cylindrical walls is presented. For the case of a neutral inner cylinder, the spinodal point derived through the Gaussian fluctuation theory is confinement-independent because of the existence of a free dimension in the system. The kinetic analysis indicates that the fluctuation modes always have a component of a plane wave along the axial direction, which can lead to the formation of a periodic-like concentration pattern. On the other hand, the equilibrium structure of the system is obtained by using…
Based on the capillary pore model (space-charge theory) for combined fluid and ion flow through cylindrical nanopores or nanotubes, we derive the continuum equations modified to include wall slip. We focus on the ionic conductance and streaming conductance, cross-coefficients of relevance for electrokinetic energy conversion and electro-osmotic pumping. We combine the theory with a Langmuir-Stern 1-pK charge regulation boundary condition resulting in a non-monotonic dependence of the cross-coefficients on salt concentration.
We explore the optical birefringence of the nematic binary mixtures 6CB$_{1-x}$7CB$_x$ ($0~\le~x~\le~1$) imbibed into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of $3.4~\le~R~\le 21.0$ nm. The results are compared with the bulk behavior and analyzed with a Landau-de-Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field $σ<1/2$) or continuously (overcritical regime, $σ>1/2$), but in both cases with a characteristic paranematic pr…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence that knowledge of how confinement modifies static behavior can aid in forecasting dynamics. Specifically, molecular simulation studies have shown that the relationship between excess entropy and self diffusivity of a bulk equilibrium fluid changes only modestly when the fluid is isothermally confined, indicating that knowledge of the former might allow semi…
We experimentally study the dynamics of active particles (APs) in a viscoelastic fluid under various geometrical constraints such as flat walls, spherical obstacles and cylindrical cavities. We observe that the main effect of the confined viscoelastic fluid is to induce an effective repulsion on the APs when moving close to a rigid surface, which depends on the incident angle, the surface curvature and the particle activity. Additionally, the geometrical confinement imposes an asymmetry to their movement, which leads to strong hydrodynamic torques, thus resulting in detention times on the wall…
Many biological materials exhibit a multiscale porosity with small, mostly nanoscale pores as well as large, macroscopic capillaries to simultaneously achieve optimized mass transport capabilities and lightweight structures with large inner surfaces. Realizing such a hierarchical porosity in artificial materials necessitates often sophisticated and expensive top-down processing that limits scalability. Here we present an approach that combines self-organized porosity based on metal-assisted chemical etching (MACE) with photolithographically induced macroporosity for the synthesis of single-cry…
We present incoherent quasi-elastic neutron scattering measurements in a wavevector transfer range from 0.4 AA^{-1} to 1.6AA^{-1} on liquid n-hexane confined in cylindrical, parallel-aligned nanochannels of 6 nm mean diameter and 260 micrometer length in monolithic, mesoporous silicon. They are complemented with, and compared to, measurements on the bulk system in a temperature range from 50K to 250K. The time-of-flight spectra of the bulk liquid can be modeled by microscopic translational as well as fast localized rotational, thermally-excited, stochastic motions of the molecules. In the nano…
