Neutron scattering study on dynamics of water molecules in MCM-41. 2. Determination of translational diffusion coefficient

Quasielastic neutron scattering (QENS) spectra of water-filled MCM-41 samples (pore diameters: 21.4 and 28.4 Angstrom) were measured over the temperature range 238-298 K and the momentum transfer range 0.31-0.99 A(-1) to investigate the dynamics of confined water molecules. The spectra, which consist mainly of contributions from the translational diffusion of water molecules, were analyzed by using the Lorentzian and the stretched exponential functions. Comparison of the fits indicated that the latter analysis is more reliable than the former one. The fraction of immobile water molecules located in the vicinity of the pore walls, which give an elastic component, was found to be 0.044-0.061 in both pores. The stretch exponent beta was determined as 0.66-0.80. It was shown that the translational diffusion of water molecules in the pores is decelerated by confinement and that the deceleration becomes marked with a decrease in pore size. The ratios of the translational diffusion coefficient D(T) of confined water to that of bulk water at room temperature were within a range of 0.47-0.63.     

Low temperature properties of acetonitrile confined in MCM-41

The effect of confinement on the phase changes and dynamics of acetonitrile in mesoporous MCM-41 was studied by use of adsorption, FT-IR, DSC, and quasi-elastic neutron scattering (QENS) measurements. Acetonitrile molecules in a monolayer interact strongly with surface hydroxyls to be registered and perturb the triple bond in the C[triple bond]N group. Adsorbed molecules above the monolayer through to the central part of the cylindrical pores are capillary condensed molecules (cc-acetonitrile), but they do not show the hysteresis loop in adsorption-desorption isotherms, i.e., second order capillary condensation. FT-IR measurements indicated that the condensed phase is very similar to the bulk liquid. The cc-acetonitrile freezes at temperatures that depend on the pore size of the MCM-41 down to 29.1 A (C14), below which it is not frozen. In addition, phase changes between alpha-type and beta-type acetonitriles were observed below the melting points. Application of the Gibbs-Thomson equation, assuming the unfrozen layer thickness to be 0.7 nm, gave the interface free energy differences between the interfaces, i.e., Deltagamma(l/alpha) = 22.4 mJ m(-2) for the liquid/pore surface (ps) and alpha-type/ps, and Deltagamma(alpha/beta) = 3.17 mJ m(-2) for alpha-type/ps and beta-type/ps, respectively. QENS experiments substantiate the differing behaviors of monolayer acetonitrile and cc-acetonitrile. The monolayer acetonitrile molecules are anchored so as not to translate. The two Lorentzian analysis of QENS spectra for cc-acetonitriles showed translational motion but markedly slowed. However, the activation energy for cc-acetonitrile in MCM-41 (C18) is 7.0 kJ mol(-1) compared to the bulk value of 12.7 kJ mol(-1). The relaxation times for tumbling rotational diffusion of cc-acetonitrile are similar to bulk values.     

Observation of fragile-to-strong liquid transition in surface water in CeO2

A quasielastic neutron-scattering experiment carried out on a backscattering spectrometer with sub-micro eV resolution in the temperature range of 200-250 K has revealed the dynamics of surface water in cerium oxide on the time scale of hundreds of picoseconds. This slow dynamics is attributed to the translational mobility of the water molecules in contact with the surface hydroxyl groups. The relaxation function of this slow motion can be described by a slightly stretched exponential with the stretch factor exceeding 0.9, which indicates almost a Debye-type dynamics. Down to about 220 K, the temperature dependence of the residence time for water molecules follows a Vogel-Fulcher-Tamman law with the glass transition temperature of 181 K. At lower temperatures, the residence time behavior abruptly changes, indicating a fragile-to-strong liquid transition in surface water at about 215 K.     

Molecular dynamics study of translational and rotational diffusion in liquid ortho-terphenyl

NVT molecular dynamics simulations were performed on liquid o-terphenyl as a function of temperature in the range 320-480 K. Computed translational diffusion coefficients displayed the non-Arrhenius behavior expected of a fragile glass-forming liquid and were in good, semiquantitative agreement with experimental results. Rotational correlation functions calculated for various vectors within the molecule exhibited a very short time (0-1 ps) initial decay, followed by a reversal, which corresponds to free reorientation within the "solvent" cage prior to collision with a wall. Rotational correlation times of three orthogonal vectors fixed on the central benzene were close to equal at all temperatures, indicating nearly isotropic overall molecular reorientation. The average correlation times exhibited a non-Arrhenius temperature dependence and were in very good agreement with experimental values derived from 2D and 1H NMR relaxation times. Correlation times of vectors located on the lateral phenyl rings were used to calculate the "spinning" internal rotation diffusion coefficients, which were approximately twice as great as the overall rotational diffusion constants, indicating rapid internal rotation of the phenyl side groups over wide ranges of angle in the liquid.     

Ultrafast excited-state electron transfer at an organic liquid/aqueous interface

Ultrafast excited-state electron transfer has been monitored at the liquid/liquid interface for the first time. Second harmonic generation (SHG) pump/probe measurements monitored the electron transfer (ET) occurring between photoexcited coumarin 314 (C314) acceptor and dimethylaniline (DMA) donor molecules. In the treatment of this problem, translational diffusion of solute molecules can be neglected since the donor DMA is one of the liquid phases of the interface. The dynamics of excited-state C314 at early times are characterized by two components with exponential time constants of 362 +/- 60 fs and 14 +/- 2 ps. The 362 fs decay is attributed to the solvation of the excited-state C314, and the 14 ps to the ET from donor to acceptor. We are able to provide conclusive evidence that the 14 ps component is the ET step by monitoring the formation of the radical DMA cation. The formation time is 16 ps in agreement with the 14 ps decay of C314*. The recombination dynamics of DMA+ plus C314- was determined to be 163 ps from the observation of the DMA+ SHG signal.     

Heterogeneous diffusion in thin polymer films as observed by high-temperature single-molecule fluorescence microscopy

Single-molecule fluorescence microscopy was used to investigate the dynamics of perylene diimide (PDI) molecules in thin supported polystyrene (PS) films at temperatures up to 135 °C. Such high temperatures, so far unreached in single-molecule spectroscopy studies, were achieved using a custom-built setup which allows for restricting the heated mass to a minimum. This enables temperature-dependent single-molecule fluorescence studies of structural dynamics in the temperature range most relevant to the processing and to applications of thermoplastic materials. In order to ensure that polymer chains were relaxed, a molecular weight of 3000 g/mol, clearly below the entanglement length of PS, was chosen. We found significant heterogeneities in the motion of single PDI probe molecules near T(g). An analysis of the track radius of the recorded single-probe molecule tracks allowed for a distinction between mobile and immobile molecules. Up to the glass transition temperature in bulk, T(g,bulk), probe molecules were immobile; at temperatures higher than T(g,bulk) + 40 K, all probe molecules were mobile. In the range between 0 and 40 K above T(g,bulk) the fraction of mobile probe molecules strongly depends on film thickness. In 30-nm thin films mobility is observed at lower temperatures than in thick films. The fractions of mobile probe molecules were compared and rationalized using Monte Carlo random walk simulations. Results of these simulations indicate that the observed heterogeneities can be explained by a model which assumes a T(g) profile and an increased probability of probe molecules remaining at the surface, both effects caused by a density profile with decreasing polymer density at the polymer-air interface.     

Molecular dynamics simulations of atmospheric oxidants at the air-water interface: solvation and accommodation of OH and O3

A comparative study of OH, O3, and H2O equilibrium aqueous solvation and gas-phase accommodation on liquid water at 300 K is performed using a combination of ab initio calculations and molecular dynamics simulations. Polarizable force fields are developed for the interaction potential of OH and O3 with water. The free energy profiles for transfer of OH and O3 from the gas phase to the bulk liquid exhibit a pronounced minimum at the surface, but no barrier to solvation in the bulk liquid. The calculated surface excess of each oxidant is comparable to calculated and experimental values for short chain, aliphatic alcohols. Driving forces for the surface activity are discussed in terms of the radial distribution functions and dipole orientation distributions for each molecule in the bulk liquid and at the surface. Simulations of OH, O3, and H2O impinging on liquid water with a thermal impact velocity are used to calculate thermal accommodation (S) and mass accommodation (alpha) coefficients. The values of S for OH, O3, and H2O are 0.95, 0.90, and 0.99, respectively. The approaching molecules are accelerated toward the liquid surface when they are approximately 5 angstroms above it. The molecules that reach thermal equilibrium with the surface do so within 2 ps of striking the surface, while those that do not scatter into the gas phase with excess translational kinetic energy in the direction perpendicular to the surface. The time constants for absorption and desorption range from approximately 35 to 140 ps, and the values of alpha for OH, O3, and H2O are 0.83, 0.047, and 0.99, respectively. The results are consistent with previous formulations of gas-phase accommodation from simulations, in which the process occurs by rapid thermal and structural equilibration followed by diffusion on the free energy profile. The implications of these results with respect to atmospheric chemistry are discussed.     

High-resolution neutron-scattering study of slow dynamics of surface water molecules in zirconium oxide

We have performed a quasielastic neutron-scattering experiment on backscattering spectrometer with sub-mueV resolution to investigate the slow dynamics of surface water in zirconium oxide using the sample studied previously with a time-of-flight neutron spectrometer [E. Mamontov, J. Chem. Phys. 121, 9087 (2004)]. The backscattering measurements in the temperature range of 240-300 K have revealed a translational dynamics slower by another order of magnitude compared to the translational dynamics of the outer hydration layer observed in the time-of-flight experiment. The relaxation function of this slow motion is described by a stretched exponential with the stretch factors between 0.8 and 0.9, indicating a distribution of the relaxation times. The temperature dependence of the average residence time is non-Arrhenius, suggesting that the translational motion studied in this work is more complex than surface jump diffusion previously observed for the molecules of the outer hydration layer. The observed slow dynamics is ascribed to the molecules of the inner hydration layer that form more hydrogen bonds compared to the molecules of the outer hydration layer. Despite being slower by two orders of magnitude, the translational motion of the molecules of the inner hydration layer may have more in common with bulk water compared to the outer hydration layer, the dynamics of which is slower than that of bulk water by just one order of magnitude.     

Nuclear magnetic relaxation and diffusion study of the ionic liquids 1-ethyl- and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide confined in porous glass

The molecular dynamics of the room-temperature ionic liquid 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (Bmim Tf2N) confined in porous glass is studied by nuclear magnetic resonance (NMR) relaxometry and diffusometry and is compared with the bulk dynamics over a wide temperature range. The molecular reorientation processes for anions and cations alike are found to be significantly affected by the presence of the glass interface at high temperatures. In this respect, the ionic liquid behaves similarly to polar liquids where proton NMR relaxation is governed by reorientations mediated by translational displacements (RMTDs). This process becomes less significant towards lower temperatures when the characteristic translational correlation times of the ions approach a timescale comparable with those of the RMTD process, and the relaxation dispersions in bulk and in confinement become similar below a temperature corresponding to about 1.2T_g, a value where the onset of dynamic heterogeneity has been observed before. The self-diffusion coefficient, on the other hand, is found to be strongly reduced than the bulk within the accessible temperature range of 248 K and above and is significantly slower than expected from the tortuosity effect, suggesting that ion–surface interactions affect the macroscopic properties.     

Temperature dependence of solvation dynamics of probe molecules in methanol-doped ice and in liquid ethanol

We have studied the solvation statics and dynamics of coumarin 343 and a strong photoacid (pK* approximately 0.7) 2-naphthol-6, 8-disulfonate (2N68DS) in methanol-doped ice (1% molar concentration of methanol) and in cold liquid ethanol in the temperature range of 160-270 K. Both probe molecules show a relatively fast solvation dynamics in ice, ranging from a few tens of picoseconds at about 240 K to nanoseconds at about 160 K. At about 160 K in doped ice, we observe a sharp decrease of the dynamic Stokes shift of both coumarin 343 and 2N68DS. Its value is approximately only 200 cm-1 at approximately 160 K compared to about 1100 cm-1 at T >/= 200 K (at times longer than t > 10 ps). We find a good correlation between the inefficient and slow excited-state proton-transfer rate at low-temperature ice, T < 180 K, and the dramatic decrease of the solvation energy, as measured by the dynamic band shift, at these low temperatures. We find that the average solvation rate in ice is similar to its value in liquid ethanol at all given temperatures in the range of 200-250 K. The surprisingly fast solvation rate in ice is explained by the relatively large freedom of the water hydrogen rotation in ice Ih.     

A 13C NMR study of the molecular dynamics and phase transition of confined benzene inside titanate nanotubes

This work investigated the nanoconfinement effect on the molecular dynamics and phase transition of confined benzene inside titanate nanotubes with a uniform inner diameter of approximately 5.3 nm. For 13C-enriched organics, the 13C nuclear spin-spin relaxation was demonstrated as a sensitive tool to differentiate molecular translational motion and reorientation and, thus, was shown to be advantageous over the commonly employed 1H and 2H NMR for studying complex phase diagram, specifically, for separating the phase behavior of translational motion and the phase behavior of molecular reorientation. In such an approach, the melting of translational motion of confined benzene was explicitly observed to take place in a broad temperature range below the bulk melting temperature. The abrupt change of the 13C nuclear spin-spin relaxation time of the confined liquid benzene at about 260 K suggested that nanoconfinement induced two topologically distinct liquid phases.     

Dynamics and thermodynamics of water in PAMAM dendrimers at subnanosecond time scales

Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water: buried water well inside of the dendrimer surface, surface water associated with the dendrimer-water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values: high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times: a fast relaxation ( approximately 1 ps) corresponding to the libration motion of the water and a slow ( approximately 20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is approximately 0.4 ps while the slow relaxation is approximately 14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be approximately 1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11-33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar: 21-45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM-water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions ( approximately 10 cm(-1) for translation, approximately 35 cm(-1) for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer: energy for surface water is approximately 0.1 kcal/mol lower to that in the bulk, and approximately 0.5-0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored: buried water is 0.9-2.2 kcal/mol lower than the bulk while the surface water is 0.1-0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer: 0.4-1.3 kcal/mol higher for buried water and 0.1-0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.     

Rotational motion in liquid water is anisotropic: a nuclear magnetic resonance and molecular dynamics simulation study

Experimental NMR measurements of the deuterium and (17)O T(1) relaxation times in deuterium-enriched liquid water have been performed from 275 to 350 K. These relaxation times can yield rotational correlation times of appropriate molecule-fixed unit vectors if the quadrupole coupling constants and asymmetry parameters are known. We determine the latter from ab initio studies of water clusters and experimental chemical shift measurements. We find that the rotational correlation time for the OD bond vector in D(2)(16)O varies from 5.8 ps at 275 K to 0.86 ps at 350 K, and that the rotational correlation time for the out-of-plane vector of dilute D(2)(17)O in D(2)(16)O varies from 4.4 ps at 275 K to 0.64 ps at 350 K. These results indicate that the rotational motion of water is anisotropic. Molecular dynamics simulations of liquid water are in good agreement with these experiments at the higher temperatures, but the simulation results are considerably faster than experiment at the lower temperatures.     

Vibrational dynamics of ice in reverse micelles

The ultrafast vibrational dynamics of HDO:D(2)O ice at 180 K in anionic reverse micelles is studied by midinfrared femtosecond pump-probe spectroscopy. Solutions containing reverse micelles are cooled to low temperatures by a fast-freezing procedure. The heating dynamics of the micellar solutions is studied to characterize the micellar structure. Small reverse micelles with a water content up to approximately 150 water molecules contain an amorphous form of ice that shows remarkably different vibrational dynamics compared to bulk hexagonal ice. The micellar amorphous ice has a much longer vibrational lifetime than bulk hexagonal ice and micellar liquid water. The vibrational lifetime is observed to increase linearly from 0.7 to 4 ps with the resonance frequency ranging from 3100 to 3500 cm(-1). From the pump dependence of the vibrational relaxation the homogeneous linewidth of the amorphous ice is determined (55+/-5 cm(-1)).     

Surface tensions in NaCl-water-air systems from MD simulations

Surface tensions for liquid-vapor (lv), solid-liquid (sl), and solid-vapor (sv) interfaces are calculated from molecular dynamics simulations of the NaCl-water-air system. Three distinct calculation techniques based on thermodynamic properties are used to describe the multicomponent mixtures. Simulations of each bulk phase (including a liquid saturated solution) and various interfaces are carried out at both NPT and NVT conditions. The thermodynamic relation for energy difference between interface and bulk phases provides an upper bound to the surface tension, while the energy-integral and test area methods provide direct estimates. At 1 atm and 300 K, the best predictions for surface tensions are sigmasv (NaCl-air) of 114 mN m(-1), sigmasl (NaCl- soln) of 63 mN m(-1), sigmalv (soln-air) of 82 mN m(-1), and sigmalv (water-air) of 66 mN m(-1). The calculated surface tensions from simulations have uncertainties between 5 and 10%, which are higher than measurements for the liquid interfaces and lower than the measurement uncertainty for the solid interfaces. The calculated upper bounds for surface tensions of liquid interfaces compare well with experimental results but provide no improvement over existing measurements. However, the bounding values for solid interfaces lower uncertainty by as much as a factor of 10 as compared to the indirect experimental measurements currently available. The energy-integral and test area methods appear to underestimate the surface tension of water by 10%, which is consistent with previous studies using similar model potentials. The calculated upper bounds of surface tension show a weakly positive correlation with pressure in the 0.1-100 atm range for liquid-solid, liquid-vapor, and solid-vapor interfaces.     

Solvation dynamics of DCM in a DPPC vesicle entrapped in a sodium silicate derived sol-gel matrix

Solvation dynamics of 4-(dicyanomethylene)-2-methyl-6(p-dimethylaminostyryl) 4H-pyran (DCM) has been studied in a dipalmitoyl-phosphatidylcholine (DPPC) vesicle entrapped in a sodium silicate derived sol-gel glass. Solvation dynamics in DPPC in a sol-gel glass is described by two components of 350 +/- 50 ps (50%) and 2300 +/- 200 ps (50%) with a total dynamic Stokes shift of 1300 cm(-1). The fast component (350 ps) is similar to the fast component in a DPPC vesicle in bulk water (320 +/- 50 ps). This component may be ascribed to the dynamics of the water molecules inside the water pool of the vesicle. However, the slow component (2300 +/- 200 ps) is about 2.5 times slower compared to the slow component of solvation dynamics of DCM in a DPPC vesicle in bulk solvent (900 +/- 100 ps). The anisotropy decay of DCM in a DPPC vesicle both in sol-gel glass and in bulk water exhibits a very fast initial decay with a large residual anisotropy, which does not decay in approximately 10 ns. The time scale of anisotropy decay is very different from that of solvation dynamics.     

Negative contributions in the velocity correlation function of supercooled liquid water

The translational dynamics of supercooled and normal liquid water is investigated via a specific correlation function DeltaB with the aim of explaining the behavior of the centers of mass velocity correlation function (VCF). DeltaB is divided into diffusive and nondiffusive parts that yield separated contributions to the VCF, namely an Enskog-type diffusive one, modeled by an exponential function, and a nondiffusive one, made up by damped oscillations of a vanishing time integral. In the translational density of states (DOS), the oscillations yield the bands at omega(1) congruent with 50 cm(-1), omega(3) congruent with 240 cm(-1) (the two well-known experimental bands of the Raman spectra) and omega(2) congruent with 160 cm(-1) (the Einstein frequency of the liquid). It is shown that the chief negative lobe of the VCF is mainly due to the DOS component at the lowest frequency omega(1). The study of the relative pair dynamics shows that this lobe is due to the transverse dynamics, while the longitudinal one determines the fast DOS component at omega(3). The presence of a negative tail is highlighted. Its contribution extends beyond the region of the fast dynamics (t<0.7 ps) up to about 1.5 ps and is due to a low-frequency oscillating mode that produces a low-frequency DOS band centered at about omega(0)=20 cm(-1).     

Temperature dependence of solvation dynamics and anisotropy decay in a protein: ANS in bovine serum albumin

Temperature dependence of solvation dynamics and fluorescence anisotropy decay of 8-anilino-1-naphthalenesulfonate (ANS) bound to a protein, bovine serum albumin (BSA), are studied. Solvation dynamics of ANS bound to BSA displays a component (300 ps) which is independent of temperature in the range of 278-318 K and a long component which decreases from 5800 ps at 278 K to 3600 ps at 318 K. The temperature independent part is ascribed to a dynamic exchange of bound to free water with a low barrier. The temperature variation of the long component of solvation dynamics corresponds to an activation energy of 2.1 kcal mol(-1). The activation energy is ascribed to local segmental motion of the protein along with the associated water molecules and polar residues. The time scale of solvation dynamics is found to be very different from the time scale of anisotropy decay. The anisotropy decays are analyzed in terms of the wobbling motion of the probe (ANS) and the overall tumbling of the protein.     

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.     

Molecular dynamics study of anisotropic translational and rotational diffusion in liquid benzene

Equilibrium NPT and NVT molecular dynamics simulations were performed on liquid benzene over an extended range of temperature (from 260 to 360 K) using the COMPASS force field. Densities and enthalpies of vaporization (from cohesive energy densities) were within 1% of experiment at all temperatures. tumbling and spinning rotational diffusion coefficients, D(perpendicular) and D(parallel), computed as a function of temperature, agreed qualitatively with the results of earlier reported experimental and computational investigations. Generally, it was found that D(parallel)/D(perpendicular) approximately 1.4-2.5 and the activation energy for tumbling was significantly greater than for spinning about the C6 axis [Ea(D(perpendicular)) = 8.1 kJ mol(-1) and Ea(D(parallel)) = 4.5 kJ mol(-1)]. Calculated translational diffusion coefficients were found to be in quantitative agreement with experimental values at all temperatures [deviations were less than the scatter between different reported measurements]. In addition, translational diffusion coefficients were computed in the molecule-fixed frame to yield values for Dxy (diffusion in the plane of the molecule) and Dz (diffusion perpendicular to the plane). It was found that the ratio Dxy/Dz approximately 2.0, and that the two coefficients have roughly equal activation energies. This represents the first atomistic molecular dynamics study of translational diffusion in the molecular frame.