Dynamics of a discotic liquid crystal in the isotropic phase

Optically heterodyne-detected optical Kerr effect (OHD-OKE) experiments are conducted to study the orientational dynamics of a discotic liquid crystal 2,3,6,7,10,11-hexakis(pentyloxy)triphenylene (HPT) in the isotropic phase near the columnar-isotropic (C-I) phase transition. The OHD-OKE signal of HPT is characterized by an intermediate power law t(-0.76+/-0.02) at short times (a few picoseconds), a von Schweidler power law t(-0.26+/-0.01) at intermediate times (hundreds of picoseconds), and an exponential decay at long times (tens of nanoseconds). The exponential decay has Arrhenius temperature dependence. The functional form of the total time dependent decay is identical to the one observed previously for a large number of molecular supercooled liquids. The mode coupling theory schematic model based on the Sjogren [Phys. Rev. A 33, 1254 (1986)] model is able to reproduce the HPT data over a wide range of times from <1 ps to tens of nanoseconds. The studies indicate that the HPT C-I phase transition is a strong first order transition, and the dynamics in the isotropic phase display a complex time dependent profile that is common to other molecular liquids that lack mesoscopic structure.     

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.     

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.     

Diffusion of water in clays on the microscopic scale: modeling and experiment

Diffusion of water in montmorillonite clays at low hydration has been studied on the microscopic scale by two quasi-elastic neutron scattering techniques, neutron spin-echo (NSE) and time-of-flight (TOF), and by classical microscopic simulation. Experiment and simulation are compared both directly on the level of intermediate scattering functions, I(Q, t), and indirectly on the level of relaxation times after a model of atomic motion is applied. Regarding the dynamics of water in Na- and Cs-monohydrated montmorillonite samples, the simulation and NSE results show a very good agreement, both indicating diffusion coefficients of the order of (1-3) x 10(-10) m(2) s(-1). The TOF technique significantly underestimates water relaxation times (therefore overestimates water dynamics), by a factor of up to 3 and 7 in the two systems, respectively, primarily due to insufficiently long correlation times being probed. In the case of the Na-bihydrated system, the TOF results are in closer agreement with the other two techniques (the techniques differ by a factor of 2-3 at most), giving diffusion coefficients of (5-10) x 10(-10) m(2) s(-1). Attention has been also paid to the elastic incoherent structure factor, EISF(Q). Simulation has played a key role in understanding the various contributions to EISF(Q) in clay systems and in clearly distinguishing the signatures of "apparent" and true confinement. Indirectly, simulation highlights the difficulty in interpreting the EISF(Q) signal from powder clay samples used in experiments.     

Fluctuations and micro-heterogeneity in aqueous mixtures

The problem as to why water-water density correlations are systematically overestimated in computer simulation of aqueous mixtures is examined through an extensive molecular dynamics study of mixtures of the extended single point charge water model with a fully miscible weaker version of it, obtained by scaling down the site partial charges by a factor 2/3, thereby eliminating solute-solvent size differences. The study reveals that enhanced water correlations is a genuine physical effect, and are not an artifact of the simulations or the models, as previously suggested in the context of realistic aqueous mixtures. Rather, they correspond to the existence of strongly correlated water domains, for "weak-water" mole fraction x > 0.4, that modulate the spatial decay of the density correlations. These domains produce a prepeak in the structure factor, suggesting that simple aqueous mixture might behave just like micro-emulsions. The overestimated long range water correlations result from incorrect predictions of the asymptote of these correlations, which themselves arise from size limitations of the simulation box. However, by requiring consistency between thermodynamical and structural expressions of the concentration fluctuations, a method to predict the proper decay of the correlation function is obtained herein, inspired by the formal analogy with micro-emulsions. This study provides a new insight for the large values of the experimental Kirkwood-Buff integrals for many aqueous mixtures: these mixtures are in a Lifshitz-type regime, where concentration fluctuations compete with water domain formation.     

Radiative decay of nonstationary system

When a finite quantum system, say a fluorescent molecule is attached to a bulk surface and excited by a short laser pulse, the decay dynamics of the system is modulated by the surface and the signal is enhanced due to the bulk surface. We have considered the decay dynamics of a model of displaced distorted molecule whose excited potential surface is coupled to a continuum and then this first continuum is in turn coupled to a second continuum. In the short time scale there is a coherent exchange of energy between the system molecule and the first continuum states. In the long time scale the energy of the whole system plus first continuum drains out to the final continuum states. A dendrimer nanocomposite with the gold surface shows an enhanced light emission. This can be qualitatively understood from the model we proposed here. We have numerically studied the various potential parameters of the molecule which can affect the signal. When the potential surfaces are flat, the band structure of the first continuum states along with its initial excitation has some nontrivial effect on the profile of the radiative decay.     

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.     

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.     

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.     

Langevin network model of myosin

Langevin mode theory and the coarse-grained elastic network model (ENM) for proteins are combined to yield the Langevin network model (LNM). Hydrodynamic radii of 6 A were assigned to each alpha-carbon on the basis of matching experimental translational and rotational diffusion constants of lysozyme, myoglobin, and hemoglobin with those calculated using a rigid body bead model with hydrodynamic interactions described by the Rotne-Prager tensor. LNM analysis of myosin II indicates that all ENM-like modes are overdamped at water viscosities. The low-frequency LNM modes in the pre-power stroke structure (PDB code: 1VOM) are substantially less mixed than the corresponding modes of the post-power stroke structure (1Q5G). Results from a four-bead model of the myosin "lever arm" indicate that coupling between modes increases as the array departs from linearity and are consistent with the results for 1VOM and 1Q5G. The decay times for all overdamped Langevin modes are shorter than the calculated rotational tumbling times found for lysozyme and myosin.     

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.     

Structural modes of a polymer in the repton model

Using extensive computer simulations, the behavior of the structural modes-more precisely, the eigenmodes of a phantom Rouse polymer-are characterized for a polymer in the three-dimensional repton model and are used to study the polymer dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with (p∕N)(2)A(t), in which p is the mode number, N is the polymer length, and A(t) is a single function shared by all modes. In time, the quantity A(t) causes an exponential decay for the mode amplitude correlation functions for times <1; a stretched exponential with an exponent 1∕2 between times 1 and τ(R) ～ N(2), the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times t > τ(R). Having assumed statistical independence and the validity of a single function A(t) for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.     

Experimental investigation of statistical density function of decaying radioactive sources

The validity of the Poisson and theP(k) modified Poisson statistical density functions of observing k events in a short time interval t=T/n, proposed previously by others, is investigated experimentally in radioactive decay detection for various measuring times, T. The experiments to measure radioactive decay were performed with 89my (T_1/2=16.06 s), using a multichannel analyzer operating in the multiscaling mode. According to the results, Poisson statistics adequately describes the counting experiment for short measuring times (up to T<0.5 T_1/2) and its application is recommended. However, analysis of the data demonstrated, with confidence, that for long measurements (T>1 T_1/2) Poisson distribution is not valid and the modified Poisson function is preferable.     

Complex chemical kinetics in single enzyme molecules: Kramers's model with fractional Gaussian noise

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramers's flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Water motion in reverse micelles studied by quasielastic neutron scattering and molecular dynamics simulations

Motion of water molecules in Aerosol OT [sodium bis(2-ethylhexyl) sulfosuccinate, AOT] reverse micelles with water content w(0) ranging from 1 to 5 has been explored both experimentally through quasielastic neutron scattering (QENS) and with molecular dynamics (MD) simulations. The experiments were performed at the energy resolution of 85 microeV over the momentum transfer (Q) range of 0.36-2.53 A(-1) on samples in which the nonpolar phase (isooctane) and the AOT alkyl chains were deuterated, thereby suppressing their contribution to the QENS signal. QENS results were analyzed via a jump-diffusion/isotropic rotation model, which fits the results reasonably well despite the fact that confinement effects are not explicitly taken into account. This analysis indicates that in reverse micelles with low-water content (w(0)=1 and 2.5) translational diffusion rate is too slow to be detected, while for w(0)=5 the diffusion coefficient is much smaller than for bulk water. Rotational diffusion coefficients obtained from this analysis increase with w(0) and are smaller than for bulk water, but rotational mobility is less drastically reduced than translational mobility. Using the Faeder/Ladanyi model [J. Phys. Chem. B 104, 1033 (2000)] of reverse micelle interior, MD simulations were performed to calculate the self-intermediate scattering function F(S)(Q,t) for water hydrogens. Comparison of the time Fourier transform of this F(S)(Q,t) with the QENS dynamic structure factor S(Q,omega), shows good agreement between the model and experiment. Separate intermediate scattering functions F(S) (R)(Q,t) and F(S) (CM)(Q,t) were determined for rotational and translational motion. Consistent with the decoupling approximation used in the analysis of QENS data, the product of F(S) (R)(Q,t) and F(S) (CM)(Q,t) is a good approximation to the total F(S)(Q,t). We find that the decay of F(S) (CM)(Q,t) is nonexponential and our analysis of the MD data indicates that this behavior is due to lower water mobility close to the interface and to confinement-induced restrictions on the range of translational displacements. Rotational relaxation also exhibits nonexponential decay. However, rotational mobility of O-H bond vectors in the interfacial region remains fairly high due to the lower density of water-water hydrogen bonds in the vicinity of the interface.     

Interpreting single turnover catalysis measurements with constrained mean dwell times

Observation of a chemical transformation at the single-molecule level yields a detailed view of kinetic pathways contributing to the averaged results obtained in a bulk measurement. Studies of a fluorogenic reaction catalyzed by gold nanoparticles have revealed heterogeneous reaction dynamics for these catalysts. Measurements on single nanoparticles yield binary trajectories with stochastic transitions between a dark state in which no product molecules are adsorbed and a fluorescent state in which one product molecule is present. The mean dwell time in either state gives information corresponding to a bulk measurement. Quantifying fluctuations from mean kinetics requires identifying properties of the fluorescence trajectory that are selective in emphasizing certain dynamic processes according to their time scales. We propose the use of constrained mean dwell times, defined as the mean dwell time in a state with the constraint that the immediately preceding dwell time in the other state is, for example, less than a variable time. Calculations of constrained mean dwell times for a kinetic model with dynamic disorder demonstrate that these quantities reveal correlations among dynamic fluctuations at different active sites on a multisite catalyst. Constrained mean dwell times are determined from measurements of single nanoparticle catalysis. The results indicate that dynamical fluctuations at different active sites are correlated, and that especially rapid reaction events produce particularly slowly desorbing product molecules.     

Recombination reactions of oxygen atoms on an anodized aluminum plasma reactor wall, studied by a spinning wall method

We have studied the recombination of O atoms on an anodized Al surface in an oxygen plasma, using a new "spinning wall" technique. With this method, a cylindrical section of the wall of the plasma reactor is rotated and the surface is periodically exposed to an oxygen plasma and then to a differentially pumped mass spectrometer (MS). By varying the substrate rotation frequency (r), we vary the reaction time (t(r)), that is, the time between exposure of the surface to O atoms in the plasma and MS detection of desorbing O(2) (t(r) = 1/2r). As t(r) is increased from 0.7 to 40 ms, the O(2) desorption signal decreases by a factor of 2 for an O-atom flux of 1 x 10(16) cm(-2) s(-1) and by a factor of 6 when the O flux is 1 x 10(17) cm(-2) s(-1). The O(2) signal decay is highly nonexponential, slowing at longer times and reaching zero signal as r --> 0. A model of O-atom recombination is compared with these time-dependent results. The model assumes adsorption occurs at surface sites with a range of binding energies. O can detach from these sites, become mobile, and diffuse along the surface. This leads to desorption of O, reattachment at free adsorption sites, and recombination to form O(2) that promptly desorbs. With several adjustable parameters, the model reproduces the observed shapes of the O(2) desorption decay curves and the lack of detectable desorption of O and predicts a high O-atom recombination coefficient on anodized aluminum.     

Cooperative effects in photon statistics of molecular dimers with spectral diffusion

The two-point fluorescence intensity correlation function g(2)t and the Mandel parameter Mt are calculated for a strongly pumped dimer of two-level molecules undergoing Gaussian-Markovian frequency fluctuations. The effects of detuning and saturation are examined. All fluctuation time scale regimes are explored using a continued fraction solution of the stochastic Liouville equation for the generating function. Bunching and antibunching are observed for slow and fast fluctuations, respectively. The short-time antibunching dip in g(2) and its variation with intermolecular coupling, the exciton annihilation rate, and laser detuning are studied.