Communication: Driven Brownian transport in eccentric septate channels

In eccentric septate channels the pores connecting adjacent compartments are shifted off-axis, either periodically or randomly, so that straight trajectories parallel to the axis are not allowed. Driven transport of a Brownian particle in such a channel is characterized by a strong suppression of the current and its dispersion. For large driving forces, both quantities approach an asymptotic value, which can be analytically approximated in terms of the stationary distribution of the particle exit times out of a single channel compartment.     

Columnar discotics in confined geometries

The influence of geometric confinement on the state of order and on the glass relaxation process was investigated for a triphenylene derivative able to display a highly ordered plastic columnar phase in the bulk. The compound was incorporated into porous glasses - characterized by a narrow size distribution - with average pore diameters of 20, 7.5, 5 and 2.5 nm. The X-ray diagrams revealed the presence of a hexagonal order, yet the lattice spacing is significantly reduced with decreasing pore size and the reflections become broad. The X-ray doublet reflection, superimposed on the halo which is characteristic for the bulk plastic columnar phase, is absent in all cases. It is replaced by a single broad intracolumnar reflection which indicates that the confinement destabilizes the plastic phase in favour of the hexagonal ordered phase. A further observation is that the intracolumnar correlation length is reduced with decreasing pore size. The confinement was furthermore found to cause a transition from a strong glass (bulk material) to a fragile glass former, obviously induced by the structural modification.     

Ionic liquids in confined geometries

Over recent years the Surface Force Apparatus (SFA) has been used to carry out model experiments revealing structural and dynamic properties of ionic liquids confined to thin films. Understanding characteristics such as confinement induced ion layering and lubrication is of primary importance to many applications of ionic liquids, from energy devices to nanoparticle dispersion. This Perspective surveys and compares SFA results from several laboratories as well as simulations and other model experiments. A coherent picture is beginning to emerge of ionic liquids as nano-structured in pores and thin films, and possessing complex dynamic properties. The article covers structure, dynamics, and colloidal forces in confined ionic liquids; ionic liquids are revealed as a class of liquids with unique and useful confinement properties and pertinent future directions of research are highlighted.     

Columnar discotics in confined geometries

The influence of geometric confinement on the state of order and on the glass relaxation process was investigated for a triphenylene derivative able to display a highly ordered plastic columnar phase in the bulk. The compound was incorporated into porous glasses - characterized by a narrow size distribution - with average pore diameters of 20, 7.5, 5 and 2.5 nm. The X-ray diagrams revealed the presence of a hexagonal order, yet the lattice spacing is significantly reduced with decreasing pore size and the reflections become broad. The X-ray doublet reflection, superimposed on the halo which is characteristic for the bulk plastic columnar phase, is absent in all cases. It is replaced by a single broad intracolumnar reflection which indicates that the confinement destabilizes the plastic phase in favour of the hexagonal ordered phase. A further observation is that the intracolumnar correlation length is reduced with decreasing pore size. The confinement was furthermore found to cause a transition from a strong glass (bulk material) to a fragile glass former, obviously induced by the structural modification.     

Liquid crystal phases in confined geometries

ABSTRACT

The orientation control of liquid crystal (LC) phases is essential for fundamental studies as well as practical applications. Surface treatment and topographic confinement have emerged as two of the most effective tools to control ordering and orientation of various types of LC phases. This review is intended to give an overview of the LC phases controlled in confined geometries at micro- and nanometre scales, in which the orientation control methods and the effective analytical techniques will be covered. Finally, the review closes with the applications using such confined LC phases.     

Melting of Lennard-Jones clusters in confined geometries

The melting of Lennard-Jones (argon) clusters of various size (N = 500 to 10000 atoms), confined in a rigid matrix, is studied by molecular dynamics simulations. For spherical clusters we show the existence of a cluster size below which the dependence of the melting temperature cannot be described by the classical Gibbs-Thompson equation. We also provide evidence of the formation of a quasi-liquid layer at the surface of mesoscopic clusters. A good agreement is found between the theoretical model due to Celestini et al. and the simulation results obtained in this work. The melting of an ellipsoidal cluster is also investigated. We observe, in agreement with recent experimental and theoretical work, that the thickness of the molten layer is larger in the region of higher local curvature.     

Droplet growth and transition to coalescence in confined geometries

A thermodynamic theory is developed to predict growth, rearrangement to a close-packed ensemble, and transition to a deformed or coalesced state for droplets in a confined space. For the close-packed configuration, analysis of forced interactions between confined droplets yields analytical criteria for predicting whether droplets will deform and if they will coalesce. Relevant nondimensional parameters are identified to generalize results in terms of energy barrier maps, and their use for predicting interacting droplet behavior is described.     

DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

The slow dielectric Debye relaxation of monoalcohols in confined geometries

Broadband dielectric relaxation measurements have been performed on monoalcohols confined in the quasi-two-dimensional space between clay platelets and the quasi-one-dimensional pores of approximately 10 A? diameter in a molecular sieve. Interestingly, the results show that the slow Debye-like process is present even in these severe confinements, proving that structural models that are based on two-dimensional or three-dimensional cluster formations as the structural origin of the Debye-like process can be excluded. Rather, the insensitivity of its time-scale to confinements suggests that it is of local character and in some way related to the lifetime or breaking and reformation of hydrogen bonds.     

Electrolysis in nanochannels for in situ reagent generation in confined geometries

In situ generation of reactive species within confined geometries, such as nanopores or nanochannels is of significant interest in overcoming mass transport limitations in chemical reactivity. Solvent electrolysis is a simple process that can readily be coupled to nanochannels for the electrochemical generation of reactive species, such as H(2). Here the production of hydrogen-rich liquid volumes within nanofluidic structures, without bubble nucleation or nanochannel occlusion, is explored both experimentally and by modeling. Devices comprised of multiple horizontal nanochannels intersecting planar working and quasi-reference electrodes were constructed and used to study the effects of confinement and reduced working volume on the electrochemical reduction of H(2)O to H(2) and OH(-). H(2) production in the nanochannel-embedded electrode reactor output was monitored by fluorescence emission of fluorescein, which exhibits a pH-dependent emission intensity. Initially, the fluorescein solution was buffered to pH 6.0 prior to stepping the potential cathodic of E(0)' for the generation of OH(-) and H(2). Because the electrochemical products are obtained in a 2:1 stoichiometry, local measurements of pH during and after the cathodic potential steps can be converted into H(2) production rates. Independent experimental estimates of the local H(2) concentration were then obtained from the spatiotemporal fluorescence behavior and current measurements, and these were compared with finite element simulations accounting for electrolysis and subsequent convection and diffusion within the confined geometry. Local dissolved H(2) concentrations were correlated to partial pressures through Henry's Law and values as large as 8.3 atm were obtained at the most negative potential steps. The downstream availability of electrolytically produced H(2) in nanochannels is evaluated in terms of its possible use as a downstream reducing reagent. The results obtained here indicate that H(2) can easily reach saturation concentrations at modest overpotentials.     

Monomer density profiles for polymer chains in confined geometries: massive field theory approach

Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.     

Communication: Universal Markovian reduction of Brownian particle dynamics

Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density J(0), we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by J(0) and defines a sequence {J(n)}(n∈N) of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple one-term recurrence relation for this sequence and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of J(0), convergence is fast enough to be useful in practice for an effective Ohmic reduction of the dissipative dynamics.     

Anomalous transport in molecularly confined spaces

We develop a novel theory to predict the density dependence of the diffusivity of simple fluids in a molecularly sized nanopore with diffusely reflecting walls, incorporating nearest neighbor intermolecular interactions within the framework of the recent oscillator model of low density transport arising from this laboratory. It is shown that when the pore width is about two molecular diameters, at sufficiently high densities these interactions lead to a repulsive inner core, as a result of which the diffusing molecules undergo more frequent reflections at the wall. This leads to a reduction in diffusivity with increase in density, which is consistent with molecular dynamics simulation results, and contrasts with the behavior in larger pores where the transport coefficient has previously been shown to increase with increase in density due to viscouslike intermolecular interactions. At low densities the behavior is opposite, with the inner core becoming more attractive with increase in density, which can lead to an increase in diffusivity. The theory consistently explains molecular dynamics simulation results when the inhomogeneous pair distribution function of moving particles in the pore is axially periodic, suggesting concerted motion of neighboring molecules. It is also shown that a potential of mean force concept is inadequate for describing the influence of intermolecular interactions on transport.     

Charge transport in confined concentrated solutions: A minireview

This Minireview summarizes several recent experiments clouding over prevailing theoretical understanding of charge transport behaviors in electrochemical systems; they are nonlinear concentration dependence of ionic conductivity, ultra-long Debye length in ionic liquids, nonmonotonic double layer charging behavior, and anomalous increase in area specific capacitance with decreasing nanopore size. Theoretical activities reveal that nanoconfinement and high concentration exert strong influence on charge distribution and transport via strong ion-ion correlations and ion-wall interactions. By exemplifying where and why classical theories of charge transport fail, we defy the popular point of view that theoretical electrochemistry is well-established and we are left with applications of these theories only.     

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.