Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the ‘ant in the labyrinth’) on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Rufigallol-based self-assembled supramolecular architectures

Discotic liquid crystals have been attracting growing interest not only because of the fundamental importance as model systems for the study of charge and energy transport but also due to their potential application in organic electronic devices. The 1,2,3,5,6,7-hexahydroxy-9,10-anthraquinone, commonly known as rufigallol, is one of the earliest systems reported to form columnar mesophases. Over the past 25 years, more than 100 discotic liquid crystals based on this core have been realized and studied for various physical properties. This review summarizes synthesis and thermal behaviour of all these materials. A brief summary of various physical studies on these materials has also been given.     

Hydrophobic and Ionic-Interactions in Bulk and Confined Water with Implications for Collapse and Folding of Proteins

Water and water-mediated interactions determine the thermodynamics and kinetics of protein folding, protein aggregation and self-assembly in confined spaces. To obtain insights into the role of water in the context of folding problems, we describe computer simulations of a few related model systems. The dynamics of collapse of eicosane shows that upon expulsion of water the linear hydrocarbon chain adopts an ordered helical hairpin structure with 1.5 turns. The structure of dimer of eicosane molecules has two well ordered helical hairpins that are stacked perpendicular to each other. As a prelude to studying folding in confined spaces we used simulations to understand changes in hydrophobic and ionic interactions in nano-sized water droplets. Solvation of hydrophobic and charged species change drastically in nano-scale water droplets. Hydrophobic species are localized at the boundary. The tendency of ions to be at the boundary where water density is low increases as the charge density decreases. The interactions between hydrophobic, polar, and charged residue are also profoundly altered in confined spaces. Using the results of computer simulations and accounting for loss of chain entropy upon confinement we argue and then demonstrate, using simulations in explicit water, that ordered states of generic amphiphilic peptide sequences should be stabilized in cylindrical nanopores.     

A Short History of Phase Transitions in Ionic Fluids

The paper reviews the development of theory and experiments concerning the nature of the critical point in ionic fluids. Because of the long‐range nature of the Coulomb interactions the possibility of mean‐field critical behaviour was discussed as a possibility. Although some experiments supported mean‐field criticality, simulations on the model fluid of charged hard spheres and later experiments on ionic solutions have shown that phase transition of ionic systems belong to the Ising universality class like phase transitions in non‐ionic fluids. Experiments concerning the crossover from Ising to mean field‐behaviour are discussed as well as systematic differences between the phase behaviour predicted for the model fluid of charged hard spheres and that observed in ionic solutions (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of argon cluster with proton seeding

ABSTRACT

We employ force-field molecular dynamics simulations to investigate the kinetics of nucleation to new liquid or solid phases in a dense gas of particles, seeded with ions. We use precise atomic pair interactions, with physically correct long-range behaviour, between argon atoms and protons. Time dependence of molecular cluster formation is analysed at different proton concentration, temperature and argon gas density. The modified phase transitions with proton seeding of the argon gas are identified and analysed. The seeding of the gas enhances the formation of nano-size atomic clusters and their aggregation. The strong attraction between protons and bath gas atoms stabilises large nano-clusters and the critical temperature for evaporation. An analytical model is proposed to describe the stability of argon-proton droplets and is compared with the molecular dynamics simulations.     

Theory of intramolecular spin relaxation by translational diffusion in locally ordered fluids

In locally ordered fluids, such as macromolecular solutions, clays and lyotropic liquid crystals, nuclear spin relaxation can be induced by modulation, through translational diffusion of the fluid molecules, of the magnitude and orientation of the residual intramolecular spin-lattice coupling tensor, which is only partially averaged by local molecular motions near an interface. A theory of spin relaxation in locally ordered fluids bounded by planar interfaces is developed, with special emphasis on effects of translational diffusion. The theory is based on a continuous diffusion model (CDM) which, in contrast to the commonly adopted discrete exchange model (DEM), treats equilibrium and time-dependent distribution functions in a self-consistent way. A striking feature of translational diffusion in heterogeneous systems is the abundance of reencounters with previously visited interfacial regions. It is demonstrated that these diffusional reencounters, which are inherent in the CDM theory, may lead to a relaxation behaviour which is qualitatively different from that predicted by the DEM theory. Furthermore, it is seen that the widespread concept of intrinsic relaxation rate (associated with a spatial region) and the fast/slow exchange classification are not generally valid. The formal framework of the CDM theory allows molecular interactions of any complexity to be introduced. In this paper a mean-field model based on the nonlinear Poisson-Boltzmann equation is used to obtain analytic expressions for the spectral density functions that determine the relaxation behaviour in the presence and in the absence of spectral line splittings.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Vortex-glass phases in type-II superconductors

A review is given on the theory of vortex-glass phases in impure type-II superconductors in an external field. We begin with a brief discussion of the effects of thermal fluctuations on the spontaneously broken U(1) and translation symmetries, on the global phase diagram and on the critical behaviour. Introducing disorder we restrict ourselves to the experimentally most relevant case of weak uncorrelated randomness which is known to destroy the long-ranged translational order of the Abrikosov lattice in three dimensions. Elucidating possible residual glassy ordered phases, we distinguish between positional and phase-coherent vortex glasses. The study of the behaviour of isolated vortex lines and their generalization directed elastic manifolds in a random potential introduces further important concepts for the characterization of glasses. The discussion of elastic vortex glasses, i.e. topologically ordered dislocation-free positional glasses in two and three dimensions occupy the main part of our review. In particular, in three dimensions there exists an elastic vortex-glass phase which still shows quasi-long-range translational order: the 'Bragg glass'. It is shown that this phase is stable with respect to the formation of dislocations for intermediate fields. Preliminary results suggest that the Bragg-glass phase may not show phasecoherent vortex-glass order. The latter is expected to occur in systems with weak disorder only in higher dimensions (or for strong disorder, as the example of unscreened gauge glasses shows). We further demonstrate that the linear resistivity vanishes in the vortex-glass phase. The vortex-glass transition is studied in detail for a superconducting film in a parallel field. Finally, we review some recent developments concerning driven vortex-line lattices moving in a random environment.     

Search for optical biaxiality in discotic liquid crystals

Using a high-finesses Fabry-Perot structure, we examine the behaviour of discotic liquid crystals for possible biaxiality. This is done by confining the discotic liquid crystals in the Fabry-Perot cavity and examining the mode structure in presence and absence of an applied electric field. It is concluded that at least in the discotic liquid crystal that we have examined, there is no evidence of biaxiality.     

Phase separation and structure in a concentrated colloidal dispersion of uniform plates

The structure and phase behaviour of a colloidal dispersion of plate-like particles are described. The plates are nickel (II) hydroxide and have short-range, repulsive interactions and a low polydispersity. As the concentration of the plates is increased, an equilibrium phase separation between a columnar phase and a less ordered phase is observed. Complementary measurements using small-angle neutron and small-angle X-ray scattering have been used to distinguish the columnar phase from other possible ordered structures. Previously isotropic-nematic phase transitions have been observed [#!ref1!#], however this dispersion forms the more highly ordered columnar phase, due to the aspect ratio and the low polydispersity of the plate-like particles. The concentration at which phase separation occurs, increases as the range of the particle interactions is reduced. This system provides an interesting model for comparison with theory and calculations of structures in liquid crystal and mesophase in which the particle interactions can be altered. Received 24 February 1999     

液晶胆甾相中的分子短程关联

向列相液晶的二粒子集团理论被推广应用于研究胆甾相二维模型.手征性分子固定在三维简单立方晶格的格点上,而分子取向限制在二维.理论结果表明,平衡态螺旋波矢依赖于温度的变化,且存在胆甾相到向列相相变.通过考虑分子间短程关联,二粒子集团理论的数值结果较平均场理论更接近Monte Carlo模拟结果.     

Phase diagram of a ternary mixture of cholesterol and saturated and unsaturated lipids calculated from a microscopic model

We employ a molecular model to study a ternary mixture of saturated lipid, with tails of 16 carbons, a monounsaturated lipid with tails of 18 carbons, and cholesterol. The model, solved within mean-field theory, produces several forms of phase diagrams depending upon the relative strengths of interactions, but only one that shows the coexistence of two liquid phases observed in experiment. The lipids in the phase rich in cholesterol are more ordered than those in the other. The binary cholesterol, saturated lipid system also exhibits liquid, liquid coexistence.     

Anomalous scattering in supercooled ST2 water

ABSTRACT

Large-scale molecular dynamics (MD) simulations of systems containing up to 256,000 molecules were performed to investigate the scattering behaviour of the ST2 water model at deeply supercooled conditions. The simulations reveal that ST2 exhibits anomalous scattering, reminiscent of that observed in experiment, which is characterised by an increase in the static structure factor at low wavenumbers. This unusual behaviour in ST2 is linked with coupled fluctuations in density and local tetrahedral order in the liquid. The Ornstein–Zernike correlation length estimated from the anomalous scattering component exhibits power-law growth upon cooling, consistent with the existence of a liquid–liquid critical point (LLCP) in the ST2 model at ca. 245 K. Further, spontaneous liquid–liquid phase separation is observed upon thermally quenching a large system with 256,000 water molecules below the predicted critical temperature into the two-phase region. The large-scale MD simulations therefore confirm the existence of a metastable liquid–liquid phase transition in ST2 and support findings from previous computational studies performed using smaller systems containing only a few hundred molecules. We anticipate that our analysis may prove useful in interpreting recent scattering experiments that have been performed to search for an LLCP in deeply supercooled water.     

Room temperature supramolecular columnar liquid crystals formed by hydrogen bonding of isoquinoline derivatives

We report new self-assembled discotic liquid crystals exhibiting columnar mesophases at room temperature, which are constructed by intermolecular hydrogen bonding between the core of 1,3,5-trihydroxybenzene or 1,3,5-cyclohexanetricarboxylic acid and the peripheral molecules of isoquinoline derivatives. The mesomorphic properties of supramolecular liquid crystals were investigated by differential scanning calorimetry, polarized optical microscopy, and X-ray diffraction studies. The self-assembled liquid crystals exhibited rectangular columnar phases (Col_ro) with an ordered stacking structure of the mesogens in a column at room temperature, regardless of the type of the core molecule, due probably to the close-packed aromatic rings around a core molecule and the angular structure in three arms of the discotic mesogen. These room temperature columnar phases are rare examples for the discotic liquid crystals, and our findings in the present study provide a new way to prepare low melting columnar liquid crystalline materials for molecular electronics.     

Universal power law in the orientational relaxation in thermotropic liquid crystals

We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of model systems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.     

Annihilation on a percolation cluster

The diffusion-controlled reaction A+A = 0 on a percolation cluster (fractal system) is investigated analytically and by means of Monte Carlo simulations. The conclusion about reaction kinetics and particle distribution behaviour obtained by a generalized of the Smoluchovsky theory to fractal systems are confirmed by simulations.     

Order-disorder transition in the solid phase of a charged hard sphere model

We investigate the solid phases of the restricted primitive model (RPM). Monte Carlo simulations show the existence of an order-disorder transition from a substitutionally disordered face centered cubic lattice (fcc) to a new ordered fcc structure which is proposed as the ground state of the RPM at the close packing density. Our results suggest that the new phase might turn out in a new triple point in the RPM phase diagram involving three solid phases: CsCl, fcc ordered and fcc disordered structures. The order-disorder transition is also studied using the cell theory. The theory shows good agreement with the simulation results and suggests that the transition is weakly first order.     

Molecular dynamics study of the primary ferrofluid aggregate formation

Investigations of the phase transitions and self-organization in the magnetic aggregates are of the fundamental and applied interest. The long-range ordering structures described in the Tománek's systematization (M. Yoon, and D. Tománek, 2010 [1]) are not yet obtained in the direct molecular dynamics simulations. The resulted structures usually are the linear chains or circles, or, else, amorphous (liquid) formations. In the present work, it was shown, that the thermodynamically equilibrium primary ferrofluid aggregate has either the long-range ordered or liquid phase. Due to the unknown steric layer force and other model idealizations, the clear experimental verification of the real equilibrium phase is still required. The predicted long-range ordered (crystallized) phase produces the faceting shape of the primary ferrofluid aggregate, which can be recognized experimentally. The medical (antiviral) application of the crystallized aggregates has been suggested. Dynamic formation of all observed ferrofluid nanostructures conforms to the Tománek's systematization.     

Multiscale coarse graining of diblock copolymer self-assembly: from monomers to ordered micelles

Starting from a microscopic lattice model, we investigate clustering, micellization, and micelle ordering in semidilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse-graining strategy, whereby the AB copolymers are mapped onto ultrasoft dumbells with monomer-averaged effective interactions between the centers of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n approximately 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.