Langevin dynamics simulations of macromolecules on parallel computers

A parallel algorithm is developed that allows efficient Langevin-dynamics simulations of macromolecular coils, which is the usual structure of synthetic polymers in solution and in bulk. Contrary to usual so-called spatial decomposition algorithms, we map the one-dimensional topology of the chain molecule on the parallel computer. The speedup of the algorithm is measured on different multi-processor systems. The reliability of the parallel calculations is shown by comparison with sequential simulations.     

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)].     

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.     

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.     

Quantum charge transport and conformational dynamics of macromolecules

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a quantum charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder. We argue that collapsing conducting polymers may represent a physical realization of quantum small-world networks with dynamical rewiring probability.     

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.     

Crystallization of tethered polyethylene in confined geometries

Ordered poly(ethylene)‐poly(vinylcyclohexane) (PE‐PVCH) block copolymers are employed to study the crystallization of tethered PE in confined geometries. The high T_g of the PVCH component of these materials forces PE chains to crystallize in well‐defined geometries dictated by the mesophase structure of the block copolymer. Effects of chain tethering on crystallization are examined through comparison of singly‐tethered PE chains in PE‐PVCH (EV) diblocks and doubly‐tethered PE in PVCH‐PE‐PVCH (VEV) triblocks. Crystallinity is independent of the block copolymer mesophase structure in both the EV and VEV systems, although crystallinity in VEV depends on the molecular weight of the PE block of the copolymer. Melting temperature data indicate that spatial confinement reduces crystallite size in EV and VEV, and that the double tethering of PE chains in VEV reduces crystallite size further through topological constraints. Crystal nucleation and growth depend strongly on the type of microstructure in both EV and VEV block copolymers. Differences in the overall rate of crystallization are correlated with the dimensional continuity of the PE microdomains. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37:2053–2068, 1999     

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.     

Design of quasisymplectic propagators for Langevin dynamics

A vector field splitting approach is discussed for the systematic derivation of numerical propagators for deterministic dynamics. Based on the formalism, a class of numerical integrators for Langevin dynamics are presented for single and multiple time step algorithms.     

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.     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

Langevin dynamics for rigid bodies of arbitrary shape

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.     

Normal mode partitioning of Langevin dynamics for biomolecules

We propose a novel normal mode multiple time stepping Langevin dynamics integrator called NML. The aim is to approximate the kinetics or thermodynamics of a biomolecule by a reduced model based on a normal mode decomposition of the dynamical space. Our basis set uses the eigenvectors of a mass reweighted Hessian matrix calculated with a biomolecular force field. This particular choice has the advantage of an ordering according to the eigenvalues, which have a physical meaning of being the square of the mode frequency. Low frequency eigenvalues correspond to more collective motions, whereas the highest frequency eigenvalues are the limiting factor for the stability of the integrator. In NML, the higher frequency modes are overdamped and relaxed near their energy minimum while respecting the subspace of low frequency dynamical modes. Our numerical results confirm that both sampling and rates are conserved for an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated, when compared to the full model. For implicitly solvated systems, NML gives a twofold improvement in efficiency over plain Langevin dynamics for sampling a small 22 atom (alanine dipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovine pancreatic trypsin inhibitor) model, with good scaling with system size subject to the number of modes propagated. NML has been implemented in the open source software PROTOMOL.     

Hollow latex particles as submicrometer reactors for polymerization in confined geometries

A method was developed for free‐radical polymerization in the confines of a hollow latex particle. Hollow particles were prepared via the dynamic swelling method from polystyrene seed and divinylbenzene and had hollows of 500–1000 nm. So that these hollow poly(divinylbenzene) particles could function as submicrometer reactors, the particles were filled with a monomer (N‐isopropylacrylamide) via the dispersion of the dried particles in the molten monomer. The monomer that was not contained in the hollows was removed by washing and gentle abrasion. Free‐radical polymerization was then initiated by γ radiolysis in the solid state. Transmission electron microscopy showed that poly(N‐isopropylacrylamide) formed in the hollow interior of the particles, which functioned as submicrometer reactors. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5706–5713, 2004     

Least constraint approach to the extraction of internal motions from molecular dynamics trajectories of flexible macromolecules

We propose a rigorous method for removing rigid-body motions from a given molecular dynamics trajectory of a flexible macromolecule. The method becomes exact in the limit of an infinitesimally small sampling step for the input trajectory. In a recent paper [G. Kneller, J. Chem. Phys. 128, 194101 (2008)], one of us showed that virtual internal atomic displacements for small time increments can be derived from Gauss' principle of least constraint, which leads to a rotational superposition problem for the atomic coordinates in two consecutive time frames of the input trajectory. Here, we demonstrate that the accumulation of these displacements in a molecular-fixed frame, which evolves in time according to the virtual rigid-body motions, leads to the desired trajectory for internal motions. The atomic coordinates in the input and output trajectory are related by a roto-translation, which guarantees that the internal energy of the molecule is left invariant. We present a convenient implementation of our method, in which the accumulation of the internal displacements is performed implicitly. Two numerical examples illustrate the difference to the classical approach for removing macromolecular rigid-body motions, which consists of aligning its configurations in the input trajectory with a fixed reference structure.     

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.