Fickian crossover and length scales from two point functions in supercooled liquids

Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self-scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The length scale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characteristic time scale is several times larger than the alpha relaxation time. A second crossover length scale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back to the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to Gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.     

Localized and Collective Motions in HET‐s(218‐289) Fibrils from Combined NMR Relaxation and MD Simulation

Nuclear magnetic resonance (NMR) relaxation data and molecular dynamics (MD) simulations are combined to characterize the dynamics of the fungal prion HET‐s(218‐289) in its amyloid form. NMR data is analyzed with the dynamics detector method, which yields timescale‐specific information. An analogous analysis is performed on MD trajectories. Because specific MD predictions can be verified as agreeing with the NMR data, MD was used for further interpretation of NMR results: for the different timescales, cross‐correlation coefficients were derived to quantify the correlation of the motion between different residues. Short timescales are the result of very local motions, while longer timescales are found for longer‐range correlated motion. Similar trends on ns‐ and μs‐timescales suggest that μs motion in fibrils is the result of motion correlated over many fibril layers.     

Structure and dynamics of surfactant interfaces in organically modified clays

Organic modification of clays with surfactants is required for the preparation of polymer-clay nanocomposites for a variety of applications. We have studied the structure and dynamics of interfaces in synthetic clays modified with phosphonium surfactants. The chemical shifts, line widths, and relaxation times measured by 31P, 13C, and 1H NMR and the relaxation times measured by impedance spectroscopy allow us to monitor the dynamics over a wide range of time scales. The results show that the phosphonium headgroup is most restricted and that the mobility increases with increasing separation from the clay surface. The carbon chemical shifts show that the 16-carbon and 12-carbon surfactant tails of hexadecyltributyl phosphonium and dodecytriphenyl phosphonium are disordered at the interface and experience mobility over a range of time scales. The dynamics depend most strongly on the structure of the surfactant headgroup, and tributylphosphoniums are more mobile than the triphenylphosphoniums. Two dimensional chemical shift anisotropy spin exchange experiments show that the phosphorus atoms in the triphenylphosphonium surfactant are immobile on the clay surface on a 1 s time scale. The dynamics measured by impedance spectroscopy show a similar dependence on headgroup structure, even though the processes occur on very different time scales and length scales. The relationship between the structure and dynamics of the interface and the properties of composites are considered.     

Hierarchical dynamics in allostery following ATP hydrolysis monitored by single molecule FRET measurements and MD simulations

We report on a study that combines advanced fluorescence methods with molecular dynamics (MD) simulations to cover timescales from nanoseconds to milliseconds for a large protein. This allows us to delineate how ATP hydrolysis in a protein causes allosteric changes at a distant protein binding site, using the chaperone Hsp90 as test system. The allosteric process occurs via hierarchical dynamics involving timescales from nano- to milliseconds and length scales from Ångstroms to several nanometers. We find that hydrolysis of one ATP is coupled to a conformational change of Arg380, which in turn passes structural information via the large M-domain α-helix to the whole protein. The resulting structural asymmetry in Hsp90 leads to the collapse of a central folding substrate binding site, causing the formation of a novel collapsed state (closed state B) that we characterise structurally. We presume that similar hierarchical mechanisms are fundamental for information transfer induced by ATP hydrolysis through many other proteins.

We report on a study that combines advanced fluorescence methods with molecular dynamics simulations to cover timescales from nanoseconds to milliseconds for a large protein, the chaperone Hsp90.     

Chiral studies in amorphous solids: the effect of the polymeric glassy state on the racemization kinetics of bridged paddled binaphthyls

Optical activity, used here for the first time to gain information about the amorphous solid state, allows previously unavailable insight into the dynamic properties of polymer glasses and their effect on a chemical process. This is accomplished by dispersing in polymer glasses atropisomeric bridged binaphthyls with appended oligophenyl paddles of varying sizes and studying the racemization kinetics as a function of temperature. The racemization occurs by a simple one-dimensional twisting motion and, without effect on the intrinsic mechanism, sweeps out a variable volume of the matrix as the paddle length is increased. The racemization is limited by the polymer matrix only for probes with a minimum paddle size and only when the time scale for racemization is comparable to the time scale for segmental motion of the polymer matrix. The high barrier for this racemization is unique in probe studies of glasses and causes these overlapping time scales to occur significantly below the glass transition temperature. These measurements yield a clear quantitative view of the role of segmental dynamics on the racemization kinetics of the binaphthyls and allow the important demonstration, via the transition from first-order to stretched exponential kinetics, that heterogeneous dynamics persist deep within the glassy state.     

Characterization of ultrafast processes at metal/solution interfaces: Towards femtoelectrochemistry

The essential part of electrochemistry is charge transfer. To understand this process in great detail, one needs to probe the relevant kinetics and dynamics on time scales spanning from femtoseconds to seconds or even longer. Although a conventional electrochemical detection scheme is sufficient for nanosecond or slower processes, it does not offer high enough time resolution for probing ultrafast processes, such as solvent reorganization, electron tunneling, and surface isomerization, that occur on faster, for example picosecond or femtosecond, timescales. These are indispensable parameters in the advanced charge transfer theories. In this review, some recent studies using ultrashort lasers to explore the ultrafast dynamics at the metal/solution interface are reviewed. The focus is on optical pump-probe and optical pump-push with electrochemical probe schemes. The connection of these studies with conventional electrochemistry and the limitations of these detection schemes are discussed.     

Introducing a cellular automaton as an empirical model to study static and dynamic properties of molecules adsorbed in zeolites

A new lattice gas cellular automaton (LGCA) simulation approach to study static and dynamic properties of molecules adsorbed in zeolites is proposed. The motivation for the present work arises from the ongoing effort to develop efficient numerical tools where conventional approaches like molecular dynamics and Monte Carlo have been revealed as inefficient for a real extension of length and time scales in such inhomogeneous systems. Our LGCA is constituted by a constant number of interacting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature. The main input for our model comes from data such as (i) local density dependent mean-field potentials and transition probabilities obtained from atomistic simulations that will be used as the starting point to derive adsorption and diffusion properties and (ii) thermodynamic and kinetic data obtained from experiments and/or other simulation methods. Our numerically less demanding LGCA has been tested over three different systems. The obtained results are in excellent agreement with the experimental and theoretical reported data.     

Light-driven unidirectional rotation in a molecule: ROKS simulation.

We present a first-principles molecular dynamics study of the excited-state motion in a molecule that has recently been proven to exhibit light-driven unidirectional rotation. The simulations show that the directed motion is due to the complex excited-state dynamics on ultrashort timescales in the chiral system.     

Dynamics and Structure of Biopolyelectrolytes Characterized by Dielectric Spectroscopy

Structural properties of Na-DNA and Na-HA aqueous solutions can be quantified using dielectric spectroscopy in the frequency range 100 Hz–100 MHz. Two relaxation modes are typically detected that can be attributed to diffusive motion of polyion counterions. The overall study as a function of polyion length, concentration and added salt concentration demonstrates that the motion of polyion counterions detected at MHz frequencies probes collective properties, whereas the motion at kHz range probes single-chain properties of polyelectrolytes. Fundamental length scales found to characterize the polyelectrolyte structure differ for the dilute and semidilute regime and also depend on the strength of electrostatic interactions and the flexibility. Characteristic length scales detected in the dielectric spectroscopy measurements compare well with the fundamental length scales predicted by theory and comply with those extracted from small-angle X-ray scattering.     

Molecular dynamics at low time resolution

The internal dynamics of macromolecular systems is characterized by widely separated time scales, ranging from fraction of picoseconds to nanoseconds. In ordinary molecular dynamics simulations, the elementary time step Δt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale in order not to cut-off physical effects. We show that in systems obeying the overdamped Langevin equation, it is possible to systematically correct for such discretization errors. This is done by analytically averaging out the fast molecular dynamics which occurs at time scales smaller than Δt, using a renormalization group based technique. Such a procedure gives raise to a time-dependent calculable correction to the diffusion coefficient. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps Δt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy model and the denaturation of a protein.     

Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

End-monomer Dynamics in Semiflexible Polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) ?r(2)(t)? ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling ?r(2)(t)? ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log?r(2)(t)?/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.     

Scalable fine-grained parallelization of plane-wave-based ab initio molecular dynamics for large supercomputers

Many systems of great importance in material science, chemistry, solid-state physics, and biophysics require forces generated from an electronic structure calculation, as opposed to an empirically derived force law to describe their properties adequately. The use of such forces as input to Newton's equations of motion forms the basis of the ab initio molecular dynamics method, which is able to treat the dynamics of chemical bond-breaking and -forming events. However, a very large number of electronic structure calculations must be performed to compute an ab initio molecular dynamics trajectory, making the efficiency as well as the accuracy of the electronic structure representation critical issues. One efficient and accurate electronic structure method is the generalized gradient approximation to the Kohn-Sham density functional theory implemented using a plane-wave basis set and atomic pseudopotentials. The marriage of the gradient-corrected density functional approach with molecular dynamics, as pioneered by Car and Parrinello (R. Car and M. Parrinello, Phys Rev Lett 1985, 55, 2471), has been demonstrated to be capable of elucidating the atomic scale structure and dynamics underlying many complex systems at finite temperature. However, despite the relative efficiency of this approach, it has not been possible to obtain parallel scaling of the technique beyond several hundred processors on moderately sized systems using standard approaches. Consequently, the time scales that can be accessed and the degree of phase space sampling are severely limited. To take advantage of next generation computer platforms with thousands of processors such as IBM's BlueGene, a novel scalable parallelization strategy for Car-Parrinello molecular dynamics is developed using the concept of processor virtualization as embodied by the Charm++ parallel programming system. Charm++ allows the diverse elements of a Car-Parrinello molecular dynamics calculation to be interleaved with low latency such that unprecedented scaling is achieved. As a benchmark, a system of 32 water molecules, a common system size employed in the study of the aqueous solvation and chemistry of small molecules, is shown to scale on more than 1500 processors, which is impossible to achieve using standard approaches. This degree of parallel scaling is expected to open new opportunities for scientific inquiry.     

Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall

We used the platelet adhesive dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet's ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = . (1.56H + 0.66) for H > 0.3 microm. Our results demonstrate that at timescales relevant to shear flow in blood Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates >100 s-1 is large enough (>200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbalpha-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that, for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency, and dissociative binding phenomena under flow at physiological shear rates (>50 s(-1)).     

Static and dynamic light scattering in turbid suspensions

The application of static and dynamic light scattering to many colloidal systems of practical interest has often been considered too complicated due to strong multiple scattering. There are two new approaches to overcome this problem. One of them aims at suppressing contributions from multiple scattering using novel cross‐correlation schemes. While this relies on the suppression of multiple scattering, the so‐called diffusing wave spectroscopy (DWS) works in the limit of very strong multiple scattering. DWS can be used for the characterization of dynamic and static properties of colloidal systems on a large range of time and length scales ranging from a few Ångstroms to hundreds of nanometers. We demonstrate that a wealth of information can be obtained from these methods on the structure, dynamics, interaction effects, stability, aggregation, and sol‐gel transition in colloidal dispersions.     

Structural dynamics of supercooled water from quasielastic neutron scattering and molecular simulations

One of the outstanding challenges presented by liquid water is to understand how molecules can move on a picosecond time scale despite being incorporated in a three-dimensional network of relatively strong H-bonds. This challenge is exacerbated in the supercooled state, where the dramatic slowing down of structural dynamics is reminiscent of the, equally poorly understood, generic behavior of liquids near the glass transition temperature. By probing single-molecule dynamics on a wide range of time and length scales, quasielastic neutron scattering (QENS) can potentially reveal the mechanistic details of water's structural dynamics, but because of interpretational ambiguities this potential has not been fully realized. To resolve these issues, we present here an extensive set of high-quality QENS data from water in the range 253-293 K and a corresponding set of molecular dynamics (MD) simulations to facilitate and validate the interpretation. Using a model-free approach, we analyze the QENS data in terms of two motional components. Based on the dynamical clustering observed in MD trajectories, we identify these components with two distinct types of structural dynamics: picosecond local (L) structural fluctuations within dynamical basins and slower interbasin jumps (J). The Q-dependence of the dominant QENS component, associated with J dynamics, can be quantitatively rationalized with a continuous-time random walk (CTRW) model with an apparent jump length that depends on low-order moments of the jump length and waiting time distributions. Using a simple coarse-graining algorithm to quantitatively identify dynamical basins, we map the newtonian MD trajectory on a CTRW trajectory, from which the jump length and waiting time distributions are computed. The jump length distribution is gaussian and the rms jump length increases from 1.5 to 1.9 A? as the temperature increases from 253 to 293 K. The rms basin radius increases from 0.71 to 0.75 A? over the same range. The waiting time distribution is exponential at all investigated temperatures, ruling out significant dynamical heterogeneity. However, a simulation at 238 K reveals a small but significant dynamical heterogeneity. The macroscopic diffusion coefficient deduced from the QENS data agrees quantitatively with NMR and tracer results. We compare our QENS analysis with existing approaches, arguing that the apparent dynamical heterogeneity implied by stretched exponential fitting functions results from the failure to distinguish intrabasin (L) from interbasin (J) structural dynamics. We propose that the apparent dynamical singularity at ～220 K corresponds to freezing out of J dynamics, while the calorimetric glass transition corresponds to freezing out of L dynamics.     

ChemNetworks: A complex network analysis tool for chemical systems

Many intermolecular chemical interactions persist across length and timescales and can be considered to form a “network” or “graph.” Obvious examples include the hydrogen bond networks formed by polar solvents such as water or alcohols. In fact, there are many similarities between intermolecular chemical networks like those formed by hydrogen bonding and the complex and distributed networks found in computer science. Contemporary network analyses are able to dissect the complex local and global changes that occur within the network over multiple time and length scales. This work discusses the ChemNetworks software, whose purpose is to process Cartesian coordinates of chemical systems into a network/graph formalism and apply topological network analyses that include network neighborhood, the determination of geodesic paths, the degree census, direct structural searches, and the distribution of defect states of network. These properties can help to understand the network patterns and organization that may influence physical properties and chemical reactivity. The focus of ChemNetworks is to quantitatively describe intermolecular chemical networks of entire systems at both the local and global levels and as a function of time. The code is highly general, capable of converting a wide variety of systems into a chemical network formalism, including complex solutions, liquid interfaces, or even self‐assemblies. © 2013 Wiley Periodicals, Inc.