Is there a higher-order mode coupling transition in polymer blends?

We present simulations on a binary blend of bead-spring polymer chains. The introduction of monomer size disparity yields very different relaxation times for each component of the blend. Competition between two different arrest mechanisms, namely, bulklike dynamics and confinement, leads to an anomalous relaxation scenario for the fast component, characterized by sublinear time dependence for mean squared displacements, or logarithmic decay and convex-to-concave crossover for density-density correlators. These anomalous dynamic features, which are observed over time intervals extending up to 4 decades, strongly resemble predictions of mode coupling theory for nearby higher-order transitions. Chain connectivity extends anomalous relaxation over a wide range of blend compositions.     

Mode coupling and dynamical heterogeneity in colloidal gelation: a simulation study

We present simulation results addressing the dynamics of a colloidal system with attractive interactions close to gelation. Our interaction also has a soft, long-range repulsive barrier that suppresses liquid-gas type phase separation at long wavelengths. The new results presented here lend further weight to an intriguing picture emerging from our previous simulation work on the same system. Whereas mode coupling theory (MCT) offers quantitatively good results for the decay of correlators, closer inspection of the dynamics reveals a bimodal population of fast and slow particles with a very long exchange time scale. This population split represents a particular form of dynamic heterogeneity (DH). Although DH is usually associated with activated hopping and/or facilitated dynamics in glasses, the form of DH observed here may be more collective in character and associated with static (i.e., structural) heterogeneity.     

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.     

Preparation and Ultrafast Optical Characterization of Metal and Semiconductor Colloidal Nano-Particles

The ultrafast dynamics of photoinduced electrons in several metal and semiconductor colloidal nanoparticle systems are characterized using femtosecond laser spectroscopy. Various preparation methods are used and, in several cases, modified for making particles with long-term stability and narrow and controllable size distributions. The particle size and size distribution are determined using transmission electron microscopy and electronic absorption spectroscopy. For aqueous gold and silver colloids, spatial size confinement is found to cause substantially slower electronic relaxation due to reduction of non-equilibrium electron transport and weaker electron-phonon coupling. In gold colloids, photoejection of electrons into the liquid is observed, which is attributed to a two-photon enhanced ionization process. The effect of surfactant on the electron dynamics in CdS colloids is examined and found to be significant, substantiating the notion that electrons are dominantly trapped at the liquid-solid interface. In Ru³⁺-doped TiO₂ colloids, the electronic decay is found to be as fast as or even faster than in undoped TiO₂ and other semiconductor colloids such as CdS, suggesting that ion doping of large bandgap semiconductor colloids is not necessarily effective in lengthening the electron lifetime. In almost all cases studied, the majority of the photoinduced electrons are found to decay within a few tens of picoseconds due to non-radiative relaxation. The results are discussed in the context of the potential applications of metal and semiconductor nano-particles in areas including photocatalysis and photoelectrochemistry.     

Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.     

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.     

Logarithmic relaxation in a kinetically constrained model

We present Monte Carlo simulations on a coarse-grained model for relaxation in binary mixtures. The liquid structure is substituted by a three-dimensional array of cells. A spin variable is assigned to each cell, with values 0 or 1 denoting, respectively, unexcited and excited local states in a mobility field. Change in local mobility (spin flip) is permitted according to kinetic constraints determined by the mobilities of neighboring cells. We introduce two types of cells ("fast" and "slow") with very different rates for spin flip. Fast cells display anomalous relaxation, characterized by a concave-to-convex crossover in dynamic correlators by changing temperature or composition. At intermediate state points logarithmic relaxation is observed over three time decades. These results display striking analogies with dynamic correlators reported in recent simulations on polymer blends.     

Inhomogeneous phase separation kinetics in liquid binary mixtures: Sensitivity to initial local composition 2

The kinetics of phase separation subsequent to a finite temperature quench is assumed to be driven by diffusion on the altered free energy surface and is generally assumed to be slow. The situation can be different in phase separating liquid binary mixtures, especially for systems characterized by the large difference in mutual interactions between solute and solvent molecules. In such cases, the phase separation kinetics could be fast and may get completed within a short time (ns) scale. As a result, in these systems, one may observe diverse dynamical features arising out of local heterogeneity leading to the onset of phase separation through pattern formation, spinodal decomposition, nucleation, and growth. By using a coarse-grained analysis, we examine phase separation kinetics in each spatial grid and indeed observe important effects of initial heterogeneity on the subsequent evolution. Interestingly, we observe slower separation kinetics for those regions that correspond to the composition at the minimum of the high-temperature surface. The heterogeneous dynamics has been captured here through the non-linear susceptibility function, which shows a pattern similar to what is observed in the supercooled liquid. Each grid shows somewhat different dynamics in the three-stage (exponential, power-law, and logarithmic regime) phase separation dynamics. The late stage of phase separation kinetics is usually attributed to the coarsening of the phase-separated domains. However, in a liquid binary mixture, the late-stage power-law decay undergoes a further change. A new dynamical regime arises characterized by a logarithmic time dependence, which is due to the “smoothening” of the rough interface of already well-separated phases. This can also be described as opposite to the roughening transition described by Chui and Weeks [Phys. Rev. Lett. 40, 733 (1978)]. This reverse roughening transition can explain the logarithmic time dependence observed in the simulation.     

Transient absorption spectra and dynamics of InSe nanoparticles

Time-resolved fluorescence and transient absorption results have been obtained for small (approximately 3 nm) and large (approximately 5-8 nm) InSe nanoparticles in room-temperature solutions. The large particles are nonfluorescent, indicating that the conduction band is at M and the optical transition is forbidden. For some fraction of the small particles, the bottom of the conduction band is at Gamma and the optical transition is allowed. The small particle fluorescence measurements indicate that hole trapping occurs on the 200-300 ps time scale. The transient absorption spectra are featureless throughout the visible with a broad maximum at 600-650 nm. The transient absorption kinetics of both small and large particles show a 200-300 ps decay component that is assigned to hole trapping. These kinetics also show a 15 ps decay that has a larger amplitude in the case of the large particles and is assigned to an electron Gamma to M relaxation. The amplitude of this decay indicates that the initial electron and hole intraband transitions result in roughly comparable intensities of the initial transient absorption.     

Dynamic arrest in a liquid of symmetric dumbbells: reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.     

In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.     

Microphase separation induced by interfacial segregation of isotropic, spherical nanoparticles

In a recent experiment by Chung et al. [Nano Lett. 5, 1878 (2005)] and simulation by Stratford et al. [Science 309, 2198 (2005)] on immiscible blends containing nanoscale particles, it was shown that the phase separation of the two polymers can be prevented as a result of the aggregation of the nanoparticles at the interfaces between the two polymers. Motivated by these studies, we performed large scale systematic simulations, based on the dissipative particle dynamics approach, on immiscible binary (A-B) fluids containing moderate volume fractions of isotropic nanoscale spherical particles N. The nanoparticles preferentially segregate at the interfaces between the two fluids if the pairwise interactions between the three components are such that chi(AB)>/chi(AN)-chi(BN)/. We find that at later times, the average domain size saturates to a value, L approximately R(N)/phi(N), where R(N) and phi(N) are the radius and volume fraction of the nanoparticles, respectively. For small nanoparticles, however, full phase separation is observed.     

Equilibrium dynamics of the toy model of dense fluid: the infinite damping limit

We investigate the equilibrium dynamics of our recently proposed toy model of dense fluid in the infinite damping limit. Contrary to naive expectation, the correlators involving the velocity-like variables do not quickly relax away. Instead, after a very fast transient relaxation, they exhibit rather slow relaxations due to the coupling to the density-like variable. Hence, the so-called "hopping" processes are not suppressed even in the large damping limit. These hopping processes can only be controlled by tuning the parameter delta, which is the ratio of the numbers of the components of the velocity-like and the density-like variables in the model. We analytically prove that there must exist an ergodic-to-nonergodic phase transition for delta such that 0 < delta < 1. The slow dynamics and the dynamic transition in the model are distinct from those in the idealized mode coupling theory.     

Computer simulation study of the phase behavior and structural relaxation in a gel-former modeled by three-body interactions

We report a computer simulation study of a model gel-former obtained by modifying the three-body interactions of the Stillinger-Weber potential for silicon. This modification reduces the average coordination number and consequently shifts the liquid-gas phase coexistence curve to low densities, thus facilitating the formation of gels without phase separation. At low temperatures and densities, the structure of the system is characterized by the presence of long linear chains interconnected by a small number of three coordinated junctions at random locations. At small wave vectors the static structure factor shows a nonmonotonic dependence on temperature, a behavior which is due to the competition between the percolation transition of the particles and the stiffening of the formed chains. We compare in detail the relaxation dynamics of the system as obtained from molecular dynamics with the one obtained from Monte Carlo dynamics. We find that the bond correlation function displays stretched exponential behavior at moderately low temperatures and densities, but exponential relaxation at low temperatures. The bond lifetime shows an Arrhenius behavior, independent of the microscopic dynamics. For the molecular dynamics at low temperatures, the mean squared displacement and the (coherent and incoherent) intermediate scattering function display at intermediate times a dynamics with ballistic character and we show that this leads to compressed exponential relaxation. For the Monte Carlo dynamics we always find an exponential or stretched exponential relaxation. Thus we conclude that the compressed exponential relaxation observed in experiments is due to the out-of-equilibrium dynamics.     

Relationship between scattered intensity and separation for particles in an evanescent field

We describe measurements of the scattering of visible light from an evanescent field by both spherical particles (R = 1-10 mum) that are glued to atomic force microscopy (AFM) cantilevers, and by sharp tips (R < 60 nm) that were incorporated onto the cantilevers during manufacture. The evanescent wave was generated at the interface between a flat plate and an aqueous solution, and an atomic force microscope was used to accurately control the separation, h, between the particle and the flat plate. We find that, for sharp tips, the intensity of scattered light decays exponentially with separation between the tip and the plate all the way down to h approximately 0. The measured decay length of scattered intensity, delta, is the same as the theoretical decay length of the evanescent intensity in the absence of the sharp tip. For borosilicate particles, (R = 1-10 mum), the scattering also decays exponentially with separation at large separations. However, when the separation is less than roughly 3delta, the measured scattering intensity is smaller in magnitude than that which would be predicted by extrapolating the exponential decay observed at large separations. For these particles, the scattering approximately fits the sum of two exponentials. The magnitude of the deviation from exponential at contact was roughly 10-15% for R = 1 mum particles and about 30% for larger particles and is larger for s-polarized light. Preliminary experiments on polystyrene particles shows that the scattering is also smaller than exponential at small separations but that the deviation from exponential is larger for p-polarized light. In evanescent wave AFM (EW-AFM) the scattering-separation can be calibrated for situations where the scattering is not exponential. We discuss possible errors that could be introduced by assuming that exponential decay of scattering continues down to h = 0.     

Theory of correlated two-particle activated glassy dynamics: general formulation and heterogeneous structural relaxation in hard sphere fluids

We generalize the nonlinear Langevin equation theory of activated single particle dynamics to describe the correlated motion of two tagged spherical particles in a glass- or gel-forming fluid as a function of their initial separation. The theory is built on the concept of a two-dimensional dynamic free energy surface which quantifies the forces on two particles moving in a cooperative manner. For the hard sphere fluid, above a threshold volume fraction we generically find two relaxation channels corresponding largely, but not exclusively, to a center-of-mass-like displacement and a radial separation of the two tagged particles. The entropic barriers and mean first passage times are computed and found to systematically vary with volume fraction and initial particle separation; both oscillate as a function of the latter in a manner related to the equilibrium pair correlation function. A dynamic correlation length is estimated as the length scale beyond which the two-particle activated dynamics becomes uncorrelated in space and time, and is found to modestly grow with increasing mean relaxation time. The theory is also applied to a simplified model of cage escape, the elementary step of structural relaxation. Predictions for characteristic relaxation times, translation-relaxation decoupling, and stretched-exponential decay of time correlation functions are obtained. A novel mechanism for understanding why strong decoupling emerges in the activated regime, but stretched nonexponential time correlation functions do not change shape as the mean relaxation time grows, is presented and favorably compared with experiment. The theory may serve as a starting point for constructing a predictive model of multiple correlated caging and hopping (forward and backward) events of a pair of tagged particles.     

Dynamics in supercooled ionic organic liquids and mode coupling theory analysis

Optically heterodyne-detected optical Kerr effect experiments are applied to study the orientational dynamics of the supercooled ionic organic liquids N-propyl-3-methylpyridinium bis(trifluoromethylsulfonyl)imide (PMPIm) and 1-ethyl-3-methylimidazolium tosylate (EMImTOS). The orientational dynamics are complex with relaxation involving several power law decays followed by a final exponential decay. A mode coupling theory (MCT) schematic model, the Sj?gren model, was able to reproduce the PMPIm data very successfully over a wide range of times from 1 ps to hundreds of ns for all temperatures studied. Over the temperature range from room temperature down to the critical temperature Tc of 231 K, the OHD-OKE signal of PMPIm is characterized by the intermediate power law t(-1.00+/-0.04) at short times, a von Schweidler power law t(-0.51+/-0.03) at intermediate times, and a highly temperature-dependent exponential (alpha relaxation) at long times. This form of the decay is identical to the form observed previously for a large number of organic van der Waals liquids. MCT analysis indicates that the theory can explain the experimental data very well for a range of temperatures above Tc, but as might be expected, there are some deviations from the theoretical modeling at temperatures close to Tc. For EMImTOS, the orientational dynamics were studied on the ps time scale in the deeply supercooled region near its glass transition temperature. The orientational relaxation of EMImTOS clearly displays the feature associated with the boson peak at approximately 2 ps, which is the first time domain evidence of the boson peak in ionic organic liquids. Overall, all the dynamical features observed earlier for organic van der Waals liquids using the same experimental technique are also observed for organic ionic liquids.     

Heterogeneous dynamics and dynamic heterogeneities at the glass transition probed with single molecule spectroscopy

We studied the temperature dependence of the structural relaxation in poly(vinyl acetate) near the glass transition temperature with single molecule spectroscopy from Tg-1 K to Tg+12 K. The temperature dependence of the observed relaxation times matches results from bulk experiments; the observed relaxation times are, however, 80-fold slower than those from bulk experiments at the same temperature. We attribute this factor to the size of the probe molecule. The individual relaxation times of the single molecule environments are distributed normally on a logarithmic time scale, confirming that the dynamics in poly(vinyl acetate) is heterogeneous. The width of the distribution of individual relaxation times is essentially independent of temperature. The observed full width at half maximum (FWHM) on a logarithmic time axis is approximately 0.7, corresponding to a factor of about 5-fold, significantly narrower than the dielectric spectrum of the same material with a FWHM of about 2.0 on a logarithmic time axis, corresponding to a factor of about 100-fold. We explain this narrow width as the effect of temporal averaging of single molecule fluorescence signals over numerous environments due to a limited lifetime of the probed heterogeneities, indicating that heterogeneities are dynamic. We determine a loose upper limit for the ratio of the structural relaxation time to the lifetime of the heterogeneities (the rate memory parameter) of Q<80 for the range of investigated temperatures.     

A mode coupling theory description of the short- and long-time dynamics of nematogens in the isotropic phase

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experimental data are pre-sented on nematogens 4-(trans-4-n-octylcyclohexyl)isothiocyanatobenzene (8-CHBT), and 4-(4-pentyl-cyclohexyl)-benzonitrile (5-PCH) in the isotropic phase. The 8-CHBT and 5-PCH data and previously published data on 4-pentyl-4-biphenylcarbonitrile (5-CB) are analyzed using a modification of a schematic mode coupling theory (MCT) that has been successful in describing the dynamics of supercooled liquids. At long time, the OHD-OKE data (orientational relaxation) are well described with the standard Landau-de Gennes (LdG) theory. The data decay as a single exponential. The decay time diverges as the isotropic to nematic phase transition is approached from above. Previously there has been no theory that can describe the complex dynamics that occur at times short compared to the LdG exponential decay. Earlier, it has been noted that the short-time nematogen dynamics, which consist of several power laws, have a functional form identical to that observed for the short time behavior of the orientational relaxation of supercooled liquids. The temperature-dependent orientational dynamics of supercooled liquids have recently been successfully described using a schematic mode coupling theory. The schematic MCT theory that fits the supercooled liquid data does not reproduce the nematogen data within experimental error. The similarities of the nematogen data to the supercooled liquid data are the motivation for applying a modification of the successful MCT theory to nematogen dynamics in the isotropic phase. The results presented below show that the new schematic MCT theory does an excellent job of reproducing the nematogen isotropic phase OHD-OKE data on all time scales and at all temperatures.