Intramolecular relaxation dynamics in semiflexible dendrimers

The intramolecular relaxation dynamics of semiflexible dendrimers in dilute solutions are theoretically investigated in the framework of optimized Rouse-Zimm formalism. Semiflexibility is implemented by modeling topological restrictions on the bond directions and orientations of the respective bond-vectors. Based on our recently developed approach for semiflexible dendrimers [A. Kumar and P. Biswas, Macromolecules 43, 7378 (2010)], the mechanical and dielectric relaxation moduli are studied as functions of local flexibility parameters and branching topology. It is rather interesting to observe that semiflexibility affects the local modes of G'(ω) and Δε'(ω), which have lower relaxation rate with increasing bond restrictions, while the collective modes with small relaxation rate remain almost constant. The relaxation dynamics of the flexible dendrimer is similar to that of the semiflexible dendrimer with unrestricted bond orientations (Φ = 0) and is flanked by the compressed (Φ = 30°) and expanded (Φ = 150°) conformations, respectively. The effect of semiflexibility is typically reflected in the intermediate frequency regime. The expanded conformations of semiflexible dendrimers display a power-law behavior in the intermediate frequency regime for both loss and storage modulus resembling fractal structures, while the compressed and unrestricted bond orientation conformations exhibit an approximately logarithmic dependence. The power-law exponent is found to be similar to the flexible dendrimers with excluded volume interactions. Thus, by tuning Φ, a spectrum of dynamic relaxation pattern is obtained spanning a broad range of conformations from a power-law fractal network to a non-fractal one. In certain limits, this highly generalized model captures the characteristics of flexible dendrimers and also resembles La Ferla's model semiflexible dendrimers. The influence of hydrodynamic interactions reduces the dynamical range and the width of the intermediate domain by decreasing the smaller relaxation rates and increasing the higher relaxation rates correspondingly.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystal and in a model supercooled liquid

Recent optical Kerr effect experiments have revealed a power law decay of the measured signal with a temperature independent exponent at short-to-intermediate times for a number of liquid crystals in the isotropic phase near the isotropic-nematic transition and supercooled molecular liquids above the mode coupling theory critical temperature. In this work, the authors investigate the temperature dependence of short-to-intermediate time orientational relaxation in a model thermotropic liquid crystal across the isotropic-nematic transition and in a binary mixture across the supercooled liquid regime in molecular dynamics simulations. The measure of the experimentally observable optical Kerr effect signal is found to follow a power law decay at short-to-intermediate times for both systems in agreement with recent experiments. In addition, the temperature dependence of the power law exponent is found to be rather weak. As the model liquid crystalline system settles into the nematic phase upon cooling, the decay of the single-particle second-rank orientational time correlation function exhibits a pattern that is similar to what has been observed for supercooled liquids.     

Photoswitchable Phase Separation and Oligonucleotide Trafficking in DNA Coacervate Microdroplets

Coacervate microdroplets produced by liquid–liquid phase separation have been used as synthetic protocells that mimic the dynamical organization of membrane‐free organelles in living systems. Achieving spatiotemporal control over droplet condensation and disassembly remains challenging. Herein, we describe the formation and photoswitchable behavior of light‐responsive coacervate droplets prepared from mixtures of double‐stranded DNA and an azobenzene cation. The droplets disassemble and reassemble under UV and blue light, respectively, due to azobenzene trans/cis photoisomerisation. Sequestration and release of captured oligonucleotides follow the dynamics of phase separation such that light‐activated transfer, mixing, hybridization, and trafficking of the oligonucleotides can be controlled in binary populations of the droplets. Our results open perspectives for the spatiotemporal control of DNA coacervates and provide a step towards the dynamic regulation of synthetic protocells.     

Mesoscopic dynamics of diffusion-influenced enzyme kinetics

A particle-based mesoscopic model for enzyme kinetics is constructed and used to investigate the influence of diffusion on the reactive dynamics. Enzymes and enzyme-substrate complexes are modeled as finite-size soft spherical particles, while substrate, product, and solvent molecules are point particles. The system is evolved using a hybrid molecular dynamics-multiparticle collision dynamics scheme. Both the nonreactive and reactive dynamics are constructed to satisfy mass, momentum, and energy conservation laws, and reversible reaction steps satisfy detailed balance. Hydrodynamic interactions among the enzymes and complexes are automatically accounted for in the dynamics. Diffusion manifests itself in various ways, notably in power-law behavior in the evolution of the species concentrations. In accord with earlier investigations, regimes where the product production rate exhibits either monotonic or nonmonotonic behavior as a function of time are found. In addition, the species concentrations display both t(-1/2) and t(-3/2) power-law behavior, depending on the dynamical regime under investigation. For high enzyme volume fractions, cooperative effects influence the enzyme kinetics. The time dependent rate coefficient determined from the mass action rate law is computed and shown to depend on the enzyme concentration. Lifetime distributions of substrate molecules newly released in complex dissociation events are determined and shown to have either a power-law form for rebinding to the same enzyme from which they were released or an exponential form for rebinding to different enzymes. The model can be used and extended to explore a variety of issues related concentration effects and diffusion on enzyme kinetics.     

Dynamics of Synthetic Membraneless Organelles in Microfluidic Droplets

Cells can form membraneless organelles by liquid–liquid phase separation. As these organelles are highly dynamic, it is crucial to understand the kinetics of these phase transitions. Here, we use droplet‐based microfluidics to mix reagents by chaotic advection and observe nucleation, growth, and coarsening in volumes comparable to cells (pL) and on timescales of seconds. We apply this platform to analyze the dynamics of synthetic organelles formed by the DEAD‐box ATPase Dhh1 and RNA, which are associated with the formation of processing bodies in yeast. We show that the timescale of phase separation decreases linearly as the volume of the compartment increases. Moreover, the synthetic organelles coarsen into one single droplet via gravity‐induced coalescence, which can be arrested by introducing a hydrogel matrix that mimics the cytoskeleton. This approach is an attractive platform to investigate the dynamics of compartmentalization in artificial cells.     

Morphological phase separation in unstable thin films: pattern formation and growth

We present results from a comprehensive numerical study of morphological phase separation (MPS) in unstable thin liquid films on a 2-dimensional substrate. We study the quantitative properties of the evolution morphology via several experimentally relevant markers, e.g., correlation function, structure factor, domain-size and defect-size probability distributions, and growth laws. Our results suggest that the late-stage morphologies exhibit dynamical scaling, and their evolution is self-similar in time. We emphasize the analogies and differences between MPS in films and segregation kinetics in unstable binary mixtures.     

Orientational dynamics and energy landscape features of thermotropic liquid crystals: An analogy with supercooled liquids

Recent optical kerr effect (OKE) studies have revealed that orientational relaxation of rodlike nematogens near the isotropic-nematic (I-N) phase boundary and also in the nematic phase exhibit temporal power law decay at intermediate times. Such behaviour has drawn an intriguing analogy with supercooled liquids. Here, we have investigated the single-particle and collective orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I-N phase boundary, the system behaves like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system.     

Phase separation of a binary two-dimensional core-softened fluid

Using molecular dynamics simulations, we study the phase separation in a binary two-dimensional core-softened fluid with different size ratios and concentrations. The correlation functions for both components are analyzed to show the dependence of the configurational structure of the binary fluid on size ratio and concentration. A phase separation diagram is obtained and the structural features of the phase separation are further investigated using the direct imaging method.     

Computational studies of ionic liquids: Size does matter and time too

Taking the molecular ionic liquid 1-ethyl-3-methylimidazolium triflate as a reference system, the size and time dependence of molecular dynamics simulation studies is analyzed in a systematic way. Based on an all atom force field, trajectories of 70 ns length, covering samples of 8-2000 ion pairs, were generated and analyzed in terms of structure as well as single particle and collective dynamics. Although 50 ion pairs seemed sufficient for structure, at least 500 ion pairs were needed for the correct handling of dynamics. For larger systems a linear regime is found, i.e., the respective dynamical properties are a linear function of the inverse box length. In case of translational diffusion coefficients, this linear relation can be rationalised in hydrodynamic terms. The respective formula is essentially determined by viscosity and the inverse box length. Concerning the time dependence, consistent dynamical properties required a time period of 20-30 ns. Nevertheless, size dependence dominates time dependence and has to be primarily addressed.     

Critical polymer-polymer phase separation in ternary solutions

We study polymer-polymer phase separation in a common good solvent by means of Monte Carlo simulations of the bond-fluctuation model. Below a critical, chain-length-dependent concentration, no phase separation occurs. For higher concentrations, the critical demixing temperature scales nonlinearly with the total monomer concentration, with a power law relatively close to a renormalization-group prediction based on "blob" scaling arguments. We point out that earlier simulations and experiments have tested this power-law dependence at concentrations outside the validity regime of the scaling arguments. The critical amplitudes of the order parameter and the zero-angle scattering intensity also exhibit chain-length dependences that differ from the conventional predictions but are in excellent agreement with the renormalization-group results. In addition, we characterize the variation of the average coil shape upon phase separation.     

Dynamics of phase separation in mesomorphic mixtures

We describe the dynamics of phase separation and transition processes, in binary mesomorphic mixtures with the help of a system of two coupled partial derivative equations. We emphasize, both analytically and numerically, that, depending on the regions of the phase diagram, the dynamical behaviour may result either from a two step process (first the phase transition, then the phase separation) or from a process showing salient features of the Cahn-Hilliard spinodal decomposition (bicontinuous periodic networks in the transient stages). The dynamics of evolution of the domain patterns are illustrated with the help of numerical simulations in which homeotropic and planar anchorages are visualized.     

Communication: On the origin of the non-Arrhenius behavior in water reorientation dynamics

We combine molecular dynamics simulations and analytic modeling to determine the origin of the non-Arrhenius temperature dependence of liquid water's reorientation and hydrogen-bond dynamics between 235 K and 350 K. We present a quantitative model connecting hydrogen-bond exchange dynamics to local structural fluctuations, measured by the asphericity of Voronoi cells associated with each water molecule. For a fixed local structure the regular Arrhenius behavior is recovered, and the global anomalous temperature dependence is demonstrated to essentially result from a continuous shift in the unimodal structure distribution upon cooling. The non-Arrhenius behavior can thus be explained without invoking an equilibrium between distinct structures. In addition, the large width of the homogeneous structural distribution is shown to cause a growing dynamical heterogeneity and a non-exponential relaxation at low temperature.     

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.     

Nanospheres in phase-separating multicomponent fluids: a three-dimensional dissipative particle dynamics simulation

The dynamics of phase separation of three-dimensional fluids containing nanospheres, which interact preferentially with one of the two fluids, is studied by means of large-scale dissipative particle dynamics simulations. We systematically investigated the effect of volume fraction, radius, and mass of the nanoparticles on both kinetics and morphology of the binary mixture. We found that nanospheres lead to a reduction of domain growth which is intensified as their volume fraction is increased for a given radius of nanoparticles, or as the nanoparticles radius is decreased for a given volume fraction. Up to moderate volume fractions of nanoparticles, the growth law, however, is found to be identical to that pure binary fluids, i.e., R(t) approximately t(n), with n=1. For relatively high volume fractions of nanoparticles, a diffusive growth regime was detected. The crossover to the slower growth regime as the nanoparticles volume fraction is increased or their radius is decreased is associated with the crystallization of the nanospheres within the preferred component. These results are qualitatively in good agreement with previous two-dimensional simulations using molecular dynamics [M. Laradji and G. MacNevin, J. Chem. Phys. 119, 2275 (2003)] and a time-dependent Ginzburg-Landau model [M. Laradji, J. Chem. Phys. 120, 9330 (2004)], as well as recent experiments.     

Two-stage phase separation in ternary colloid-polymer mixtures

Whilst binary colloid-polymer mixtures have been studied in detail over the past few decades, here the first results are presented on a ternary mixture involving two particle sizes. Novel and unusual phase separation kinetics are found, with a liquid phase separating from an aggregate phase.     

Colloidal structures from bulk demixing in liquid crystals

This experimental paper deals with phase separations of binary mixtures composed of a continuous liquid crystal phase and an isotropic dispersed phase. In contrast to isotropic binary mixtures, the investigated mixtures do not lead to a full phase separation but to a self-ordering of colloidal particles, as reported earlier (Loudet, J. C. et al. Nature 2000, 407, 611). We present here further aspects of such phase separations which include the kinetics of the phase separation, the origin of the formation of dislocation-like patterns, the influence of surfactants, chiral additives, and temperature on the formed colloidal structures. The present results show that (i) the dislocations in chain arrays can be seen as kinetically frozen defects, (ii) temperature can be used to control the size of the domains formed upon demixing, (iii) a slight change in surface chemistry, via the addition of surfactants, profoundly alters the formed colloidal structures, and (iv) chiral additives allow the formation of unique helical pearl chains which reflect the symmetry of the liquid crystal phase they are embedded in.     

Correlation between Dynamic Heterogeneity and Local Structure in a Room‐Temperature Ionic Liquid: A Molecular Dynamics Study of [bmim][PF6]

The complex dynamics of a room‐temperature ionic liquid, 1‐n‐butyl‐3‐methylimidazolium hexafluorophosphate ([bmim][PF₆]), is studied using equilibrium classical molecular dynamics simulations in the temperature range of 250–450 K. The activation energies for the self‐diffusion of ions are around 30–34 kJ mol^?1, with that of the anion a little higher than that for the cation. The electrical conductivity of the liquid is calculated and good agreement with experiments is obtained. Structural relaxation is studied through the decay of coherent (total density–density correlation) and incoherent (self part of density–density correlation) intermediate scattering functions over a range of temperatures and wave vectors relevant to the system. The relaxation data are used to identify and characterize two processes, α and β. The dependence of the two relaxation times on temperature and wave vector is obtained. The dynamical heterogeneity of the ions determined through the non‐Gaussian parameter indicates the motion of the cation to be more heterogeneous than that of the anion. The faster ones among the cations are coordinated to faster anions, while slower cations are surrounded predominantly by slower anions. Thus, the dynamical heterogeneity in this ionic liquid is shown to have structural signatures.     

Kinetics of the grating formation in holographic polymer-dispersed liquid crystals: NMR measurement of diffusion coefficients

Polymer films with embedded liquid crystal inclusions (polymer-dispersed liquid crystals) are superb composites for addressable windows, flexible displays and optical storage. Their scattering behavior and electro-optic properties depend essentially on the shape and size of the liquid crystal inclusions, which are typically formed by phase separation from a multicomponent homogeneous mixture. Here, pulsed field gradient NMR is used to measure the self-diffusion coefficients of the liquid crystal and a photo-reactive monomer, which compose such a precursor mixture. The kinetics of holographic grating formation in this mixture can be predicted by inserting the NMR diffusion coefficient of the monomer and the polymerization rate in a reaction diffusion model. The ratio of diffusion rate over reaction rate is found to be in the limiting regime in which the kinetics of the grating formation is not sensitive to this parameter.     

Solvent viscosity dependence of the folding rate of a small protein: distributed computing study

By using distributed computing techniques and a supercluster of more than 20,000 processors we simulated folding of a 20-residue Trp Cage miniprotein in atomistic detail with implicit GB/SA solvent at a variety of solvent viscosities (gamma). This allowed us to analyze the dependence of folding rates on viscosity. In particular, we focused on the low-viscosity regime (values below the viscosity of water). In accordance with Kramers' theory, we observe approximately linear dependence of the folding rate on 1/gamma for values from 1-10(-1)x that of water viscosity. However, for the regime between 10(-4)-10(-1)x that of water viscosity we observe power-law dependence of the form k approximately gamma(-1/5). These results suggest that estimating folding rates from molecular simulations run at low viscosity under the assumption of linear dependence of rate on inverse viscosity may lead to erroneous results.