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.     

Dynamics of surface water in ZrO2 studied by quasielastic neutron scattering

A quasielastic neutron scattering experiment has revealed the dynamics of surface water in a high surface area zirconium oxide in the temperature range of 300-360 K. The characteristic times of the rotational (picoseconds) and translational (tens of picoseconds) components of diffusion motion are well separated. The rotational correlation time shows an Arrhenius-type behavior with an activation energy of 4.48 kJ/mol, which is lower compared to bulk water. The rotational diffusion at room temperature is slower by about a factor of 2 compared to bulk water, whereas the translational diffusion slows down by a factor of 40. In contrast to bulk water, the translational correlation time exhibits an Arrhenius-type temperature dependence with an activation energy of 11.38 kJ/mol. Comparison of different models for jump diffusion processes suggests that water molecules perform two-dimensional jumps at a well-defined, almost temperature-independent distance of 4.21-4.32 A. Such a large jump distance indicates a low molecular density of the layer of diffusing molecules. We argue that undissociated water molecules on an average form two hydrations layers on top of the surface layer of hydroxyl groups, and all the layers have similar molecular density. Quasielastic neutron scattering experiment assesses the dynamics of the outermost hydration layer, whereas slower motion of the water molecules in the inner hydration layer contributes to the elastic signal.     

Solvation dynamics and electric field relaxation in an imidazolium-PF6 ionic liquid: from room temperature to the glass transition

Time-resolved phosphorescence spectra and anisotropy of quinoxaline were measured in an ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM-HFP), in its supercooled state near the glass-transition temperature. The solvation dynamics results are compared with the rotational motion of the probe and with the dielectric behavior of the neat ionic liquid. The dynamics in the viscous state are highly dispersive and show a super-Arrhenius temperature dependence, as typical for glass-forming materials. Combined with room-temperature results, solvation dynamics is observed to follow the structural relaxation times in terms of eta/T for more than 10 decades, from subnanoseconds at room temperature to seconds near the glass-transition temperature T(g). The dielectric modulus relaxation follows this trend only for temperatures T > 1.2T(g) and departs significantly from eta/T in the 1.1T(g) > T > T(g) range. This deviation is reminiscent of the enhanced translational diffusion or fractional Stokes-Einstein behavior observed in many fragile supercooled liquids. Because the electric field relaxation in BMIM-HFP includes dc conductivity, this correlation function involves translational motion and thus displays the effect of enhanced diffusivity. A microscopic model is required for rationalizing the decoupling of solvation dynamics from the longitudinal time scales and the limitation of this effect to the viscous regime with T < 1.2T(g).     

Superdipole liquid scenario for the dielectric primary relaxation in supercooled polar liquids

We propose a dynamic structure of coupled dynamic molecular strings for supercooled small polar molecule liquids and accordingly we obtain the Hamiltonian of the rotational degrees of freedom of the system. From the Hamiltonian, the strongly correlated supercooled polar liquid state is renormalized to a normal superdipole liquid state. This scenario describes the following main features of the primary or alpha-relaxation dynamics in supercooled polar liquids: (1) the average relaxation time evolves from a high temperature Arrhenius to a low temperature non-Arrhenius or super-Arrhenius behavior; (2) the relaxation function crosses over from the high temperature exponential to low temperature nonexponential form; and (3) the temperature dependence of the relaxation strength shows non-Curie features. According to the present model, the crossover phenomena of the first two characteristics arise from the transition between the superdipole gas and the superdipole liquid. The model predictions are quantitatively compared with the experimental results of glycerol, a typical glass former.     

String-like propagation of the 5-coordinated defect state in supercooled water: molecular origin of dynamic and thermodynamic anomalies

We find that at low temperature water, large amplitude (~60°) rotational jumps propagate like a string, with the length of propagation increasing with lowering temperature. The strings are formed by mobile 5-coordinated water molecules which move like a Glarum defect (J. Chem. Phys., 1960, 33, 1371), causing water molecules on the path to change from 4-coordinated to 5-coordinated and again back to 4-coordinated water, and in the process cause the tagged water molecule to jump, by following essentially the Laage-Hynes mechanism (Science, 2006, 311, 832-835). The effects on relaxation of the propagating defect causing large amplitude jumps are manifested most dramatically in the mean square displacement (MSD) and also in the rotational time correlation function of the O-H bond of the molecule that is visited by the defect (transient transition to the 5-coordinated state). The MSD and the decay of rotational time correlation function, both remain quenched in the absence of any visit by the defect, as postulated by Glarum long time ago. We establish a direct connection between these propagating events and the known thermodynamic and dynamic anomalies in supercooled water. These strings are found largely in the regions that surround the relatively rigid domains of 4-coordinated water molecules. The propagating strings give rise to a noticeable dynamical heterogeneity, quantified here by a sharp rise in the peak of the four-point density response function, χ(4)(t). This dynamics heterogeneity is also responsible for the breakdown of the Stokes-Einstein relation.     

Single molecules reveal the dynamics of heterogeneities in a polymer at the glass transition

The notion of heterogeneous dynamics in glasses, that is, the spatial and temporal variations of structural relaxation rates, explains many of the puzzling features of glass dynamics. The nature and the dynamics of these heterogeneities, however, have been very controversial. Single rhodamine B molecules in poly(vinyl acetate) at the glass transition reorient through sudden jumps. With a statistical search for the most likely break points in the logarithm of the ratio of the two perpendicular fluorescence polarizations, we determine the times of these angular jumps. We interpret these jumps as an indication for individual glass rearrangements in the vicinity of the probe molecule. Time-series analysis of the resulting sequence of waiting times between jumps shows that dynamic heterogeneities in the matrix exist, but are short lived. From the correlation of the logarithm of the waiting time between subsequent jumps, we determine an upper limit for the lifetime of heterogeneities in the sample. The correlation time of τ(het) = 32 s is three times shorter than the orientational correlation time of the probe molecule, τ(orient) = 90 s, in the sample at this temperature, but 13 times longer than the structural relaxation time, τ(α) = 2.5 s, estimated for this sample from dielectric experiments. We present a model for glass dynamics in which each rearrangement in one region causes a random change in the barrier height for subsequent rearrangements in a neighboring region. This model, which equates the dynamics of the heterogeneities with the dynamics of the glass itself and thus implies a factor of one between heterogeneity lifetime and structural relaxation time, successfully reproduces the statistics of the experimentally observed waiting time sequences.     

Separable cooperative and localized translational motions of water confined by a chemically heterogeneous environment

We report quasi-elastic neutron scattering experiments at two resolutions that probe timescales of picoseconds to nanoseconds for the hydration dynamics of water, confined in a concentrated solution of N-acetyl-leucine-methylamide (NALMA) peptides in water over a temperature range of 248 K to 288 K. The two QENS resolutions used allow for a clean separation of two observable translational components, and ultimately two very different relaxation processes, that become evident when analyzed under a combination of the jump diffusion model and the relaxation cage model. The first translational motion is a localized beta-relaxation process of the bound surface water, and exhibits an Arrhenius temperature dependence and a large activation energy of approximately 8 kcal mol(-1). The second non-Arrhenius translational component is a dynamical signature of the alpha-relaxation of more fluid water, exhibiting a glass transition temperature of approximately 116 K when fit to the Volger Fulcher Tamman functional form. These peptide solutions provide a novel experimental system for examining confinement in order to understand the dynamical transition in bulk supercooled water by removing the unwanted interface of the confining material on water dynamics.     

An investigation of water dynamics in binary mixtures of water and dimethyl sulfoxide

The motion of water molecules in mixtures of water and d6-dimethyl sulfoxide (DMSO) has been explored through molecular dynamics (MD) simulations using the SPC/E water model (J. Chem. Phys. 1987, 91, 6269) and the P2 DMSO model (J. Chem. Phys. 1993, 98, 8160). We evaluate the self-intermediate scattering functions, FS(Q,t), which are related by a Fourier transform to the incoherent structure factors, S(Q,omega), measured in quasielastic neutron scattering (QNS) experiments. We compare our results to recent QNS experiments on these mixtures reported by Bordallo et al. (J. Chem. Phys. 2004, 121, 12457). In addition to comparing the MD data to the experimental signals, which correspond to a convolution of S(Q,omega) with a resolution function, we examine the rotational and translational components of FS(Q,t) and investigate to what extent simulation results for the single-molecule dynamics follow the dynamical models that are used in the analysis of the experimental data. We find that the agreement between the experimental signal and the MD data is quite good and that the portion of FS(Q,t) due to translational dynamics is well represented by the jump-diffusion model. The model parameters and their composition dependence are in reasonable agreement with experiment, exhibiting similar trends in water mobility with composition. Specifically, we find that water motion is less hindered in water-rich and water-poor mixtures than it is near equimolar composition. We find that the extent of coupling between rotational and translational motion contributing to FS(Q,t) increases as the equimolar composition of the mixture is approached. Thus, the decoupling approximation, which is used to extract information on rotational relaxation from QNS spectra at higher momentum transfer (Q) values, becomes less accurate than that in water-rich or DMSO-rich mixtures. We also find that rotational relaxation deviates quite strongly from the isotropic rotational diffusion model. We explore this issue further by investigating the behavior of orientational time correlations for different unit vectors and corresponding to Legendre polynomials of orders 1-4. We find that the rotational time correlations of water molecules behave in a way that is more consistent with the extended jump rotation model recently proposed by Laage and Hynes (Science 2006, 311, 832).     

2H NMR characterization of phenylene ring flip motion in poly(p-phenylene vinylene) films

Solid-state ²H quadrupole echo nuclear magnetic resonance (NMR) spectra and measurements of ²H spin lattice relaxation times have been obtained for films of poly(p-phenylene vinylene) deuterated in phenylene ring positions (PPV-d₄). NMR line shapes show that all the phenylene rings of PPV undergo 180° rotational jumps about the 1,4 ring axis (“ring flips”) at 225°C. The temperature dependence of the ²H line shapes show that the jump motion is thermally activated, with a median activation energy, E_a = 15 kcal/mol, and a distribution of activation energies of less than ±2 kcal/mol. The jump rate was also determined from the magnitude of the anisotropic T₂ relaxation associated with ²H line shapes and from the curvature of inversion recovery intensity data. The experimental activation energy for jumps is comparable to the intramolecular potential barrier for rotation about phenylene vinylene bonds. ²H NMR provides a method for determining the phenylene-vinylene rotational barrier in pristine PPV, and may potentially be used to study conjugation in conducting films.     

Single particle jumps in a binary Lennard-Jones system below the glass transition

We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events (jumps) where a particle escapes the cage formed by its neighbors. Using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position. We find two kinds of jumps: "reversible jumps," where a particle jumps back and forth between two or more average positions, and "irreversible jumps," where a particle does not return to any of its former average positions, i.e., successfully escapes its cage. For all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur. With increasing temperature, relaxation is enhanced by an increasing number of jumps and growing jump lengths in position and potential energy. However, the waiting time between two successive jumps is independent of temperature. This temperature independence might be due to aging, which is present in our system. We therefore also present a comparison of simulation data with three different histories. The ratio of irreversible to reversible jumps is also increasing with increasing temperature, which we interpret as a consequence of the increased likelihood of changes in the cages, i.e., a blocking of the "entrance" back into the previous cage. In accordance with this interpretation, the fluctuations both in position and energy are increasing with increasing temperature. A comparison of the fluctuations of jumping particles and nonjumping particles indicates that jumping particles are more mobile even when not jumping. The jumps in energy normalized by their fluctuations are decreasing with increasing temperature, which is consistent with relaxation being increasingly driven by thermal fluctuations. In accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position.     

Variable-temperature (17)o NMR studies allow quantitative evaluation of molecular dynamics in organic solids

We report a comprehensive variable-temperature solid-state (17)O NMR study of three (17)O-labeled crystalline sulfonic acids: 2-aminoethane-1-sulfonic acid (taurine, T), 3-aminopropane-1-sulfonic acid (homotaurine, HT), and 4-aminobutane-1-sulfonic acid (ABSA). In the solid state, all three compounds exist as zwitterionic structures, NH(3)(+)-R-SO(3)(-), in which the SO(3)(-) group is involved in various degrees of O···H-N hydrogen bonding. High-quality (17)O NMR spectra have been obtained for all three compounds under both static and magic angle spinning (MAS) conditions at 21.1 T, allowing the complete set of (17)O NMR tensor parameters to be measured. Assignment of the observed (17)O NMR parameters to the correct oxygen sites in the crystal lattice was achieved with the aid of DFT calculations. By modeling the temperature dependence of (17)O NMR powder line shapes, we have not only confirmed that the SO(3)(-) groups in these compounds undergo a 3-fold rotational jump mechanism but also extracted the corresponding jump rates (10(2)-10(5) s(-1)) and the associated activation energies (E(a)) for this process (E(a) = 48 ± 7, 42 ± 3, and 45 ± 1 kJ mol(-1) for T, HT, and ABSA, respectively). This is the first time that SO(3)(-) rotational dynamics have been directly probed by solid-state (17)O NMR. Using the experimental activation energies for SO(3)(-) rotation, we were able to evaluate quantitatively the total hydrogen bond energy that each SO(3)(-) group is involved in within the crystal lattice. The activation energies also correlate with calculated rotational energy barriers. This work provides a clear illustration of the utility of solid-state (17)O NMR in quantifying dynamic processes occurring in organic solids. Similar studies applied to selectively (17)O-labeled biomolecules would appear to be very feasible.     

Quasi-elastic neutron scattering study of dimethyl-sulfoxide-water mixtures: probing molecular mobility in a nonideal solution

The translational and rotational motions of water and dimethyl sulfoxide, [DMSO, (CH(3))(2)SO] have been investigated using quasi-elastic neutron scattering. Water-DMSO mixtures at five DMSO mole fractions, chi(DMSO), ranging from 0 to 0.75, were measured. Hydrogen-deuterium substitution was used to extract independently the water proton dynamics (d-DMSO-H(2)O), the DMSO methyl proton dynamics (h-DMSO-D(2)O) and to obtain background corrections (d-DMSO-D(2)O). The translational diffusion of water slows down significantly compared to bulk water at all chi(DMSO)>0. The rotational time constant for water exhibits a maximum at chi(DMSO)=0.33 that corresponds to the observed maximum of the viscosity of the mixture. Data for DMSO can be analyzed in terms of a relatively slow tumbling of the molecule about its center-of-mass in conjunction with random translational diffusion. The rotational time constant for this motion exhibits some dependence on chi(DMSO), while the translational diffusion constant shows no clear variation for chi(DMSO)>0. The results presented reinforce the idea that due to the stronger associative nature of DMSO, DMSO-water aggregates are formed over the whole composition range, disturbing the tetrahedral natural arrangement of the water molecules. As a consequence adding DMSO to water causes a drastic slowing down of the dynamics of the water molecule, and vice versa.     

Probe dependence of spatially heterogeneous dynamics in supercooled glycerol as revealed by single molecule microscopy

Spatially heterogeneous dynamics in supercooled glycerol over the temperature range 198 K (1.04T(g))-212 K (1.12T(g)) is investigated using widefield single molecule (SM) fluorescence microscopy. Measurements are performed using three different perylenedicarboximide probes to investigate whether probe size and probe-host interactions affect breadth of heterogeneity reported in the glassy host by such SM experiments. Rotational relaxation times of single probe molecules are measured, and for all probes, log-normal distributions of relaxation times are found. No significant change in relaxation time distribution as a function of temperature is evident for a given probe. However, across probes, probe rotational relaxation time is correlated with breadth of heterogeneous dynamics reported. Molecules that undergo changes in dynamics are identified using two complementary approaches that interrogate time scales between 10(3) and 10(6) τ(α), with τ(α) the structural relaxation time of glycerol. Exchange is found on the shortest time scales probed (~30 τ(c), with τ(c) the rotational correlation time of the probe) and is relatively temperature and probe independent. No evidence is found for additional exchange occurring on the longest time scales interrogated. Taken together with the fact that probes that rotate the fastest report the greatest breadth of spatially heterogeneous dynamics in the system, this indicates that exchange times reported from analysis of SM linear dichroism trajectories as described here are upper bounds on the average exchange time in the system.     

Positron annihilation and relaxation dynamics from dielectric spectroscopy and nuclear magnetic resonance: cis-trans-1,4-poly(butadiene)

We report a joint analysis of positron annihilation lifetime spectroscopy (PALS), dielectric spectroscopy (BDS), and nuclear magnetic resonance (NMR) on cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD). Phenomenological analysis of the orthopositronium lifetime τ(3)-T dependence by linear fitting reveals four characteristic PALS temperatures: T(b1)(G)=0.63T(g)(PALS), T(g)(PALS), T(b1)(L)=1.22T(g)(PALS), and T(b2)(L)=1.52T(g)(PALS). Slight bend effects in the glassy and supercooled liquid states are related to the fast or slow secondary β process, from neutron scattering, respectively, the latter being connected with the trans-isomers. In addition, the first bend effect in the supercooled liquid coincides with a deviation of the slow effective secondary β(eff) relaxation related to the cis-isomers from low-T Arrhenius behavior to non-Arrhenius one and correlates with the onset of the primary α process from BDS. The second plateau effect in the liquid state occurs when τ(3) becomes commensurable with the structural relaxation time τ(α)(T(b2)). It is also approximately related to its crossover from non-Arrhenius to Arrhenius regime in the combined BDS and NMR data. Finally, the combined BDS and NMR structural relaxation data, when analyzed in terms of the two-order parameter (TOP) model, suggest the influence of solidlike domains on both the annihilation behavior and the local and segmental chain mobility in the supercooled liquid. All these findings indicate the influence of the dynamic heterogeneity in both the primary and secondary relaxations due to the cis-trans isomerism in c-t-1,4-PBD and their impact into the PALS response.     

Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR T1 measurements

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR T(1) measurements. MD trajectories based on an effective potential are used to calculate the (2)H NMR relaxation time, T(1) via Fourier transform of the relevant rotational time correlation function, C(2R)(t). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of T(1) when an effective charge of ±0.5e is used for the anion and the cation, respectively. The computed C(2R)(t) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the C(2R)(t) is most important to understand frequency and temperature dependencies of T(1) in ILs. On the other hand, the effect of the initial ps relaxation is an increase of T(1) by a constant factor. This is equivalent to an "effective" reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR T(1) analysis, the rotational time correlation function can be modeled analytically in the form of aexp (-t/τ) (Lipari-Szabo model), where the constant a, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and τ represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with a = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since a is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2-3 as a compensation for the neglect of the Lipari-Szabo factor.     

IR and raman study of rotational relaxation of furan and thiophene. II. Correlation functions. Interpretation according to models

The IR and isotropic and anisotropic Raman band profiles of the A₁ fundamental modes of furan and thiophene and their temperature dependence are studied in the liquid phase. The vectorial and tensorial rotational correlation times and correlation functions are derived by deconvolution. We show that, among the various rotational models studied, the Brot-Lassier model (librational motions in a potential well and jumps from one well into another) best describes our experimental data. The orders of magnitude of the times of residence in the wells, times of flight and jump angles, are given.     

Stimulated echoes and two-dimensional nuclear magnetic resonance spectra for solids with simple line shapes

Nuclear magnetic resonance (NMR) experiments on ion conductors often yield rather unstructured spectra, which are hard to interpret if the relation between the actual translational motion of the mobile species and the changes of the NMR frequencies is not known. In order to facilitate a general analysis of experiments on solids with such spectra, different models for the stochastic evolution of the NMR frequencies are considered. The treated models involve random frequency jumps, diffusive evolutions, or approximately fixed frequency jumps. Two-dimensional nuclear magnetic resonance spectra as well as stimulated-echo functions for the study of slow and ultraslow translational dynamics are calculated for Gaussian equilibrium line shapes. The results are compared with corresponding ones from rotational models and with experimental data.     

Adsorption dynamics of water on Pt{110}-(1 x 2)

The dynamics of H(2)O adsorption on Pt{110}-(1 x 2) is studied using supersonic molecular beam and temperature programed desorption techniques. The sticking probabilities are measured using the King and Wells method at a surface temperature of 165 K. The absolute initial sticking probability s(0) of H(2)O is 0.54+/-0.03 for an incident kinetic energy of 27 kJmol. However, an unusual molecular beam flux dependence on s(0) is also found. At low water coverage (theta<1), the sticking probability is independent of coverage due either to diffusion in an extrinsic precursor state formed above bilayer islands or to incorporation into the islands. We define theta=1 as the water coverage when the dissociative sticking probability of D(2) on a surface predosed with water has dropped to zero. The slow falling H(2)O sticking probability at theta>1 results from compression of the bilayer and the formation of multilayers. Temperature programed desorption of water shows fractional order kinetics consistent with hydrogen-bonded islands on the surface. A remarkable dependence of the initial sticking probability on the translational (1-27 kJ/mol) and internal energies of water is observed: s(0) is found to be essentially a step function of translational energy, increasing fivefold at a threshold energy of 5 kJ/mol. The threshold migrates to higher energies with increasing nozzle temperature (300-700 K). We conclude that both rotational state and rotational alignment of the water molecules in the seeded supersonic expansion are implicated in dictating the adsorption process.