Particle dynamics and the development of string-like motion in a simulated monoatomic supercooled liquid

The microscopic details of local particle dynamics is studied in a glass-forming one component supercooled liquid modeled by a Dzugutov potential developed for simple metallic glass formers. Our main goal is to investigate particle motion in the supercooled liquid state, and to ascertain the extent to which this motion is cooperative and occurring in quasi-one-dimesional, string-like paths. To this end we investigate in detail the mechanism by which particles move along these paths. In particular, we show that the degree of coherence--that is, simultaneous motion by consecutive particles along a string--depends on the length of the string. For short strings, the motion is highly coherent. For longer strings, the motion is highly coherent only within shorter segments of the string, which we call "microstrings." Very large strings may contain several microstrings within which particles move simultaneously, but individual microstrings within a given string are temporally uncorrelated with each other. We discuss possible underlying mechanism for this complex dynamical behavior, and examine our results in the context of recent work by Garrahan and Chandler [Phys. Rev. Lett. 89, 035704 (2002)] in which dynamic facilitation plays a central role in the glass transition.     

Role of local structure on motions on the potential energy landscape for a model supercooled polymer

We have conducted detailed Monte Carlo and molecular dynamics simulations of a model glass forming polymeric system near its apparent glass transition temperature. We have characterized the local structure of the glass using a Voronoi-Delaunay analysis of local particle arrangements. After a perturbative face elimination, we find that a significant fraction of Voronoi polyhedra consist of 12 pentagonal faces, a sign of icosahedral ordering. Further, we have identified metabasins of particle vibrations on the potential energy landscape on the basis of persistence of particle positions and neighbors over a simulated trajectory. We find that the residence times for vibrations are correlated with a particular Voronoi volume and number of neighbors of a particle; the largest metabasins correspond to particles whose average Voronoi volume is close to the value expected on the basis of the density, and whose approximate number of neighbors is close to 12. The local distortion around a particle, measured in terms of the tetrahedricity of the Delaunay simplices, reveals that the particles with a higher degree of local distortion are likely to transition faster to a neighboring metabasin. In addition to the transition between metabasins, we have also examined the influence of vibrations at inherent structures (IS) on the local structure, and find that the the low frequency modes at the IS exhibit the greatest curvature with respect to the local structure. We believe that these results establish an important connection between the local structure of glass formers and the activated dynamics, thereby providing insights into the origins of dynamic heterogeneities.     

Spatially heterogeneous dynamics and the Adam-Gibbs relation in the Dzugutov liquid

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.     

Inherent structure analysis of protein folding

An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi>0 exceeds that of the native state p0.     

Reveal heterogeneous motion states in single nanoparticle trajectory using its own history

Single particle tracking(SPT)has long been utilized for investigation of complex system dynamics such as nanoparticle-cell interaction,however,the analysis of individual particle motions is always a difficult issue.Existing methods treat each data point or fragment on the recorded trajectory as an isolated"atom"and determine their relationship based on externally predefined models or physical states,which inevitably lead to oversimplification of the associated spatiotemporal complexity.Herein,inspired by the historical analysis in social science,we propose a modeless preprocessing framework for SPT analysis based on the"history"of the particle.This new strategy consists of 3 steps:(1)assign a"history"to each data point and construct successive overlapped historical vectors;(2)perform unsupervised clustering in the vector space to find their relative differences;(3)project differences back to the trajectory by coloring each point accordingly for visualization.As a result,the inner heterogeneity of the particle motion self-emerges as a colored trajectory,exhibiting a global picture of the local state transitions and providing valuable information for further model-based analysis.Since the complexity issues at various spatiotemporal scales have attracted increasing attention,and individual objects such as single molecules,cells,vehicles and even stars in the universe could all be treated as"single particles",this presuppositionless data preprocessing approach could help the investigations of many complex systems in fundamental research.     

A doubly nudged elastic band method for finding transition states

A modification of the nudged elastic band (NEB) method is presented that enables stable optimizations to be run using both the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton and slow-response quenched velocity Verlet minimizers. The performance of this new "doubly nudged" DNEB method is analyzed in conjunction with both minimizers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to 2 orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.     

Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes

In this paper we show that processes such as Brownian motion, convection, sedimentation, and bacterial contamination can cause small particles to move through liquids in a fashion which may be mistaken as nanopropulsion. It is shown that particle tracking and subsequent statistical analysis is essential to ascertain if small particles actually propel themselves, or if they are propelled by another process. Specifically we find that it is necessary to calculate the mean-squared displacement of particles at both short and long time intervals, to show that the direction of propulsion changes coincident with rotation of the particle by Brownian motion, as this allows nanopropulsion to be differentiated from Brownian motion, convection and sedimentation. We also find that bacteria can attach themselves to particles and cause them to be propelled. This leads to motion which appears very similar to nanopropulsion and cannot be differentiated using particle tracking and therefore find that carefully designed control experiments must be performed. Finally, we suggest an experimental protocol which can be used to investigate the motion of small objects and prove if they move due to nanopropulsion.     

Atomistic nature of transient and steady-state responses

We find experimentally that a system comprised of nanosized features no longer shows fixed steady characteristics as in solid-state devices, and instead, because of the chemistry of the nanostructure, the thermal motion of the atoms, and the external fields, the nanosized system shows intermittent behavior, that is, transient behavior. This transient response for nanosized systems might misguide conclusions regarding observed negative differential resistance (NDR) which is due to the collective nuclei rearrangements to more stable conformations under the presence of an applied field yielding, in many cases, resonances between conformations that can sustain during the steady-state period. This NDR yields peculiar behavior that needs to be considered to design molecular and nanoelectronic devices. In addition, the commonly sharp contrast between transient and steady responses blurs at the nanoscale. In nanosize systems, the time constants or transient response times depend on the velocity of the rearrangements of the atoms in the system or molecule.     

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.     

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self?" component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.     

Statistical temperature molecular dynamics: application to coarse-grained beta-barrel-forming protein models

Recently the authors proposed a novel sampling algorithm, "statistical temperature molecular dynamics" (STMD) [J. Kim et al., Phys. Rev. Lett. 97, 050601 (2006)], which combines ingredients of multicanonical molecular dynamics and Wang-Landau sampling. Exploiting the relation between the statistical temperature and the density of states, STMD generates a flat energy distribution and efficient sampling with a dynamic update of the statistical temperature, transforming an initial constant estimate to the true statistical temperature T(U), with U being the potential energy. Here, the performance of STMD is examined in the Lennard-Jones fluid with diverse simulation conditions, and in the coarse-grained, off-lattice BLN 46-mer and 69-mer protein models, exhibiting rugged potential energy landscapes with a high degree of frustration. STMD simulations combined with inherent structure (IS) analysis allow an accurate determination of protein thermodynamics down to very low temperatures, overcoming quasiergodicity, and illuminate the transitions occurring in folding in terms of the energy landscape. It is found that a thermodynamic signature of folding is significantly suppressed by accurate sampling, due to an incoherent contribution from low-lying non-native IS in multifunneled landscapes. It is also shown that preferred accessibility to such IS during the collapse transition is intimately related to misfolding or poor foldability.     

Artificial Accelerators of the Molecular Chaperone Hsp90 Facilitate Rate‐Limiting Conformational Transitions

The molecular chaperone Hsp90 undergoes an ATP‐driven cycle of conformational changes in which large structural rearrangements precede ATP hydrolysis. Well‐established small‐molecule inhibitors of Hsp90 compete with ATP‐binding. We wondered whether compounds exist that can accelerate the conformational cycle. In a FRET‐based screen reporting on conformational rearrangements in Hsp90 we identified compounds. We elucidated their mode of action and showed that they can overcome the intrinsic inhibition in Hsp90 which prevents these rearrangements. The mode of action is similar to that of the co‐chaperone Aha1 which accelerates the Hsp90 ATPase. However, while the two identified compounds influence conformational changes, they target different aspects of the structural transitions. Also, the binding site determined by NMR spectroscopy is distinct. This study demonstrates that small molecules are capable of triggering specific rate‐limiting transitions in Hsp90 by mechanisms similar to those in protein cofactors.     

Electrokinetic particle entry into microchannels

The fundamental understanding of particle electrokinetics in microchannels is relevant to many applications. To date, however, the majority of previous studies have been limited to particle motion within the area of microchannels. This work presents the first experimental and numerical investigation of electrokinetic particle entry into a microchannel. We find that the particle entry motion can be significantly deviated from the fluid streamline by particle dielectrophoresis at the reservoir-microchannel junction. This negative dielectrophoretic motion is induced by the inherent non-uniform electric field at the junction and is insensitive to the microchannel length. It slows down the entering particles and pushes them toward the center of the microchannel. The consequence is the demonstrated particle deflection, focusing, and trapping phenomena at the reservoir-microchannel junction. Such rich phenomena are studied by tuning the AC component of a DC-biased AC electric field. They are also utilized to implement a selective concentration and continuous separation of particles by size inside the entry reservoir.     

Free-standing smectic films at high temperature

Optical reflectivity studies on free-standing liquid crystal films above the bulk smectic temperature range have revealed different melting phenomena. Our measurements are performed on tilted smectic phases (smectic C*, smectic C) using optical microscopy in polarized light in order to visualize the changes of the film structure. We observe the formation of twodimensional defect structures from string-like lines in very thick (about 1000 layers) as well as in thin (about 20 layers) films. In thick films these structures nucleate around the temperature of the bulk smectic-cholesteric phase transition, while in thin films the formation of the defects occurs well above this temperature and just before the thinning transitions. In thick and intermediate thickness films, cholesteric or nematic droplets and a 'quasi-smectic' structure are observed. The films exhibiting the 'quasi-smectic' structure definitely exist at higher temperatures than the smectic films with the same thickness.     

A new cell model for equation of state of polyethylene melt and n-alkane

The connectivity of successive carbon atoms in polymer decreases the degrees of freedom, and hence, the external degrees of freedom should correspond only to translational motion. We therefore, introduce a coarse-grained particle of a few successive monomers. A cell model (or the hard core model with attractive potential) for the particles can accordingly be used for the derivation of the equation of state of polymers. Modifying the classical cell model by Lennard-Jones and Devonshire, we construct a new equation of state for polyethylene melt and for liquid n-alkane; the free volume term is modified by using the Sutherland potential instead of the Lennard-Jones potential. The characteristic quantities P*, V*0, and T* in the equation of state are almost independent of temperature; the principle of corresponding state holds well. Since our equation of state contains the external degrees of freedom explicitly, we can evaluate the external degrees of freedom, c, for CH2. The value of c for the coarse-grained particle is equal to 1, and hence the particle is composed of 1/c repeating units. The linear length of the particle evaluated, 4.09 A at 0 K, is consistent with that obtained by neutron and x-ray scatterings.     

How many amorphous ices are there?

Many acronyms are used in the literature for describing different kinds of amorphous ice, mainly because many different preparation routes and many different sample histories need to be distinguished. We here introduce these amorphous ices and discuss the question of how many of these forms are of relevance in the context of polyamorphism. We employ the criterion of reversible transitions between amorphous "states" in finite intervals of pressure and temperature to discriminate between independent metastable amorphous "states" and between "substates" of the same amorphous "state". We argue that the experimental evidence suggests we should consider there to be three polyamorphic "states" of ice, namely low-(LDA), high-(HDA) and very high-density amorphous ice (VHDA). In addition to the realization of reversible transitions between them, they differ in terms of their properties, e.g., compressibility, or number of "interstitial" water molecules. Thus they cannot be regarded as structurally relaxed variants of each other and so we suggest considering them as three distinct megabasins in an energy landscape visualization.     

Spin-coupled description of aromaticity in the retro Diels-Alder reaction of norbornene

The electronic rearrangements along the lowest-energy path for the gas-phase retro Diels-Alder reaction of norbornene are monitored using spin-coupled theory. We find that the most dramatic changes to the electronic structure occur in a relatively narrow interval in which the system passes through a geometry at which it can be considered to be significantly aromatic. We provide an estimate of the vertical resonance energy. Our results are consistent with the anticipated synchronous "aromatic" nature of this reaction, but we find that the key changes occur a little before the actual transition state is reached.     

Dynamics of a trapped two level atom in a bichromatic laser field: heating,cooling and multistability

We study the influence of the light-force exerted by two optical fields on the motion of a harmonically bound particle, modelled by a two-state system. The radiation force is calculated semiclassically in the limit of weak driving fields and strong damping by spontaneous emission. Depending on the frequency of the two laser fields and the frequency of the free oscillation in the trapping potential we calculate the energy transferred to the particle per cycle. Among various cooling/heating situations we find multistable orbits of finite size in the case of counterpropagating waves.     

Microscopic Motion of Atoms in Simple Liquids at Equilibrium and with Shear Flow

Abstract

We investigate the microscopic mechanism of atomic motion and local stress relaxation in Lennard-Jones, LJ liquids using a new class of correlation functions that emphasise the interplay between an abitrary atom in the fluid and its surrounding shells of atoms. We use the linear momenta and stress tensor to characterise the time dependence of this interaction. We consider a series of correlation functions that give complementary information and build a picture of the single particle and small cluster motion. The central particle and first shell undergo a reversal in momentum at different times after the ‘collision’ of the central particle and its first shell of neighbours. This ‘phase difference’ becomes manifest in the subsequent dynamics probed by the new correlation functions. We also consider the effect of a non-newtonian shear flow on this local dynamical relaxation, using profile biased laminar flow equations of motion. In non-newtonian shear flow we find the momentum transfer between particle and cage to be less pronounced and occur over a wider time range.     

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.