Dynamics of liquid benzene: a cage analysis

Dynamics of single molecules in liquids, inspected in the picosecond time scale by means of spectroscopic measurements or molecular-dynamics (MD) simulations, reveals a complex behavior which can be addressed as due to local confinement (cage). This work is devoted to the analysis of cage structures in liquid benzene, obtained from MD simulations. According to a paradigm proposed for previous analysis of atomic and molecular liquids [see, for example, A. Polimeno, G. J. Moro, and J. H. Freed, J. Chem. Phys. 102, 8094 (1995)], the istantaneous cage structure is specified by the frame of axes which identifies the molecular configuration at the closest minimum on the potential-energy landscape. In addition, the modeling of the interaction potential between probe molecule and molecular environment, based on symmetry considerations, and its parametrization from the MD trajectories, allows the estimation of the structural parameters which quantify the strength of molecular confinement. Roto-translational dynamics of probe and related cage with respect to a laboratory frame, dynamics of the probe within the cage (vibrations, librations, re-orientational motions), and the restructuring processes of the cage itself are analyzed in terms of selected time self-correlation functions. A time-scale separation between the processes is established. Moreover, by exploiting the evidence of fast vibrational motions of the probe with respect to the cage center, an orientational effective potential is derived to describe the caging in the time scale longer than approximately 0.2 ps.     

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

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

Molecular dynamics study of the liquid-vapor interface of acetonitrile: equilibrium and dynamical properties

The equilibrium and dynamical properties of the liquid-vapor interface of pure acetonitrile are studied by means of molecular dynamics simulations. Both nonpolarizable and polarizable models are employed in the present study. For the nonpolarizable model, the simulations are carried out for two different system sizes and at two different temperatures whereas the simulation with the polarizable model is done for a single system. The inhomogeneous density, anisotropic orientational profile, the width of the interface, and also the surface tension are calculated at room temperature and also at a lower temperature of 273 K. The dynamical aspects of the interface are investigated in terms of the single-particle dynamical properties such as the relaxation of velocity autocorrelation and the translational diffusion coefficients along the perpendicular and parallel directions and the dipole orientational relaxation of the interfacial acetonitrile molecules. The results of the interfacial dynamics are compared with those of the corresponding bulk phases at both temperatures. The convergence of the calculated results with respect to the length of simulation runs and the system size are also discussed.     

Orientational correlations in two-dimensional liquid crystals studied by molecular dynamics simulation

Orientational correlations in Langmuir monolayers of nematic and smectic-C liquid crystal (LC) phases are investigated by molecular dynamics simulation. In both phases, the orientational correlation functions decay algebraically yet with the different exponents of 1.9 and 0.2 for the nematic and the smectic-C monolayers, respectively. The power law decay, i.e., the absence of long-range orientational order, means the both monolayers should be the ideal 2D system with a continuous symmetry, whereas the large difference in the exponents of power law gives rise to the crucial difference in their optical properties; the nematic monolayer is optically isotropic while the smectic-C monolayer exhibits an anisotropy on the length scale of visible light. Since the exponent is inversely proportional to the molecular exchange energy, the averaged molecular interaction in the nematic monolayer should be an order of magnitude smaller than that in the smectic-C monolayer, which is ascribed to the low molecular density and the weak molecular dipole due to the water molecule. The relation between the molecular interaction and the orientational correlation calculated for the 2D LC system offers much information not only about the 2D LCs but also on the bulk system.     

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.     

A first principles molecular dynamics study of lithium atom solvation in binary liquid mixture of water and ammonia: structural, electronic, and dynamical properties

The preferential solvation of solutes in mixed solvent systems is an interesting phenomenon that plays important roles in solubility and kinetics. In the present study, solvation of a lithium atom in aqueous ammonia solution has been investigated from first principles molecular dynamics simulations. Solvation of alkali metal atoms, like lithium, in aqueous and ammonia media is particularly interesting because the alkali metal atoms release their valence electrons in these media so as to produce solvated electrons and metal counterions. In the present work, first principles simulations are performed employing the Car-Parrinello molecular dynamics method. Spontaneous ionization of the Li atom is found to occur in the mixed solvent system. From the radial distribution functions, it is found that the Li(+) ion is preferentially solvated by water and the coordination number is mostly four in its first solvation shell and exchange of water molecules between the first and second solvation shells is essentially negligible in the time scale of our simulations. The Li(+) ion and the unbound electron are well separated and screened by the polar solvent molecules. Also the unbound electron is primarily captured by the hydrogens of water molecules. The diffusion rates of Li(+) ion and water molecules in its first solvation shell are found to be rather slow. In the bulk phase, the diffusion of water is found to be slower than that of ammonia molecules because of strong ammonia-water hydrogen bonds that participate in solvating ammonia molecules in the mixture. The ratio of first and second rank orientational correlation functions deviate from 3, which suggests a deviation from the ideal Debye-type orientational diffusion. It is found that the hydrogen bond lifetimes of ammonia-ammonia pairs is very short. However, ammonia-water H-bonds are found to be quite strong when ammonia acts as an acceptor and these hydrogen bonds are found to live longer than even water-water hydrogen bonds.     

Effects of solute-solvent proton exchange on polypeptide chain dynamics: a constant-pH molecular dynamics study

A method for performing implicit-solvent molecular dynamics simulations at constant pH was applied to a pentapeptide acetyl-Ala-Asp-Ala-Lys-Ala-amide at pH 4. As a reference, molecular dynamics simulations were done for the same peptide with two variants of its fixed protonation patterns expected to dominate at pH 4, i.e., with a protonated and a deprotonated side chain of the Asp residue and the protonated Lys residue in both cases. The dynamic trajectories of the peptide were used to discuss the problem of the significance of the solute-solvent proton exchange phenomena for the dynamics and structural distributions of the polypeptide chain. The Asp-Lys distance was used as a probe of the overall molecular structure of the investigated pentapeptide. To characterize the dynamics, distributions of the "waiting" times for a transition from a "short" distance conformation to a "long" distance conformation were constructed, based on the generated molecular dynamics trajectories. We show that the relaxation time for the transitions, derived from the constant-pH simulations, is very close to the relaxation time characterizing a permanently protonated molecule, although the average protonation probability of the short-distance conformation is close to zero. However, the distribution of the Asp-Lys distances obtained from constant-pH simulations cannot be reproduced as a linear combination of the distributions resulting from the simulations with fixed protonation states.     

Two-dimensional Monte Carlo studies of lipid molecules in a bilayer membrane

We present a new model to study in-plane liquid properties of lipid membranes. The different conformations of lipids are represented by a seven-state system of hard triatomic particles, or triples, of varying lengths which correspond to the different cross-sectional areas of the lipids in the plane of the membrane. Two-dimensional Monte Carlo simulations are performed in both the constant NVT and NPT ensembles. The distribution of states has a strong density dependence and a small temperature dependence over the biologically relevant range. There is no long range orientational order in the systems before freezing. The short range orientational order increases with density. Widom's particle insertion method is used to obtain the excess chemical potential of the system for the seven states. These values, along with the pressure, are in excellent agreement with estimates from scaled particle theory.     

Molecular dynamics simulations of a liquid crystalline molecule in the smectic A and E phases and in vacuum

Molecular dynamics simulations are performed in this work at 393 and 323 K for a mesogenic molecule ( R )-1-methylheptyl 4\[4-(2-allyloxyethoxy)biphenyl-4-carbonyloxy]benzoate in the simulated smectics A and E, respectively, and in a vacuum at 300 K, for a period of 1.0ns. The trajectories obtained from molecular dynamics simulations allow us to investigate the dynamical behaviour of this mesogenic molecule in the simulated smectic phases. This dynamical behaviour of a single molecule is presented using the distributions of dihedral angles and rotational diffusion around the C-axis defined by the simulated cells. Simulation results indicate that, except for the bonds near the end of the spacer segment, the dihedral angles all exhibit a single Gaussian-like distribution in the smectic A and E phases. Fluctuations of a dihedral angle about its mean value are more restricted in the smectics A and E than in those simulated in a vacuum. The average value of the fluctuations of the dihedral angles at the bonds in the spacer is found to be about 2 fold larger than that of fluctuations in the tail of the same molecule in the smectic A and E phases. In the smectic A phase, the distribution of orientations of a molecule about its long axis in a 36 molecule cell in which the outer molecules are fixed is found to have three distinct peaks. This result shows that the orientational fluctuations of single molecules are limited by confinement due to neighbouring molecules, i.e. that the layers have short-range structural correlations. The orientational distributions show larger fluctuations at the ends of the molecules.     

Spontaneous pattern of linear molecules in strongly confined spaces

In this work, we study the tight packing of short linear molecules in confined space by performing molecular dynamic simulations. The short chain-like molecules spontaneously arrange within single-walled carbon nanotubes (SWNTs) and exhibit a variety of chiral and achiral structures, depending on the pore size and molecule length. Simulation results show that the packing structures for these confined short linear molecules are controlled by the competition between positional order and orientational order. For linear molecules with short molecular length, such as the two-site Lennard-Jones molecules, the orientational order gradually decreases as temperature increases, and then the positional order begins to disappear. While for longer molecules, such as four-site Lennard-Jones molecules, the positional order decreases more rapidly than the orientational order as temperature increases. We also investigated the effect of molecular rigidity. For linear molecules with higher rigidity, part of packing structures may slowly rotate as a whole, and the rotation of packing arrangements is found to be induced by the preexisting defects.     

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.     

Relaxation and jump dynamics of water at the mica interface

The orientational relaxation dynamics of water confined between mica surfaces is investigated using molecular dynamics simulations. The study illustrates the wide heterogeneity that exists in the dynamics of water adjacent to a strongly hydrophilic surface such as mica. Analysis of the survival probabilities in different layers is carried out by normalizing the corresponding relaxation times with bulk water layers of similar thickness. A 10-fold increase in the survival times is observed for water directly in contact with the mica surface and a non-monotonic variation in the survival times is observed moving away from the mica surface to the bulk-like interior. The orientational relaxation time is highest for water in the contact layer, decreasing monotonically away from the surface. In all cases the ratio of the relaxation times of the 1st and 2nd rank Legendre polynomials of the HH bond vector is found to lie between 1.5 and 1.9 indicating that the reorientational relaxation in the different water layers is governed by jump dynamics. The orientational dynamics of water in the contact layer is particularly novel and is found to undergo distinct two-dimensional hydrogen bond jump reorientational dynamics with an average waiting time of 4.97 ps. The waiting time distribution is found to possess a long tail extending beyond 15 ps. Unlike previously observed jump dynamics in bulk water and other surfaces, jump events in the mica contact layer occur between hydrogen bonds formed by the water molecule and acceptor oxygens on the mica surface. Despite slowing down of the water orientational relaxation near the surface, life-times of water in the hydration shell of the K(+) ion are comparable to that observed in bulk salt solutions.     

Theoretical Studies of Single Molecule Spectroscopy at Room Temperature

This talk is motivated by recent room-temperature single molecule experiments, which measure the optical spectrum along single molecular trajectories and monitor the molecular dynamics and chemical kinetics of individual reactive systems. These experiments contain new information that requires theoretical models and interpretations. Several aspects of single molecule spectroscopy are analyzed:(1) Event-averaged single molecule quantities are calculated, with the prediction of the echo signal in the joint event probability distribution function^[1]. Similar to the photon echo phenomenon, the single molecule echo signal measures solvent effects on chemical kinetics. (2) The statistics of single molecule blinking events are often correlated to underlying quantum mechanisms. The distribution functions of waiting-time sequences are examined for several quantum processes, including electron transfer, solvent relaxation, laser-induced emission, and single quantum-dot blinking^[2]. (3) Single molecule measurements of heterogeneous diffusion reveal deviations from the Gaussian distribution of Brownian motion. As a quantitative measure, the non-Gaussian indicator decays asymptotically to zero according to 1/t for finite time correlation, but saturates at a plateau value for power-law correlation.     

Subdiffusive dynamics of a liquid crystal in the isotropic phase

The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330 K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the beta-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1 ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures Tc are 244+/-6 and 258+/-6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of Tc we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320 K to a few nanoseconds at 275 K.     

Molecular dynamics simulations of pregelification mixtures for the production of imprinted xerogels

A series of molecular dynamics (MD) simulations of different pregelification mixtures representing intermediate stages of the sol-gel process were set up to gain insight into the molecular imprinting process in xerogels, namely, to assess the template-gel affinity and template self-aggregation. The physical plausibility of the parametrization was checked, confirming the reliability of the simulations. The simulated mixtures differed in the water/methanol ratio (1:3, 5:3, and 5:1) and in the absence/presence of an organic functional group (phenylaminopropyl-) in the silicate species. The simulation results, expressed mainly by the radial distribution functions and respective coordination numbers, showed that the affinity of the template molecule, damascenone (a hydrophobic species), for the gel backbone would not be attained without the tested functional group, phenylaminopropyl-. The affinity, related to the capability to trap the template within the gel network, was derived mostly from the hydrophobic interaction. It was also inferred from MD simulations that lower water contents (methanol-richer mixtures) would facilitate a better dispersion of both the functional group and the template within the final gel, therefore favoring the imprinting process. From the experimental counterparts of the simulated mixtures, a series of imprinted and nonimprinted xerogels were obtained. There was only one xerogel exhibiting the imprinting effect, namely, the one containing the organic group obtained at the lower water/methanol ratio (1:3), in agreement with predictions from the MD simulations. Such congruence demonstrates the ability of MD simulations to provide information regarding the fine aspects of molecular interactions in pregelification mixtures for imprinting.     

Solute rotational dynamics at the water liquid/vapor interface

The rotational dynamics of a number of diatomic molecules adsorbed at different locations at the interface between water and its own vapors are studied using classical molecular dynamics computer simulations. Both equilibrium orientational and energy correlations and nonequilibrium orientational and energy relaxation correlations are calculated. By varying the dipole moment of the molecule and its location, and by comparing the results with those in bulk water, the effects of dielectric and mechanical frictions on reorientation dynamics and on rotational energy relaxation can be studied. It is shown that for nonpolar and weekly polar solutes, the equilibrium orientational relaxation is much slower in the bulk than at the interface. As the solute becomes more polar, the rotation slows down and the surface and bulk dynamics become similar. The energy relaxation (both equilibrium and nonequilibrium) has the opposite trend with the solute dipole (larger dipoles relax faster), but here again the bulk and surface results converge as the solute dipole is increased. It is shown that these behaviors correlate with the peak value of the solvent-solute radial distribution function, which demonstrates the importance of the first hydration shell structure in determining the rotational dynamics and dependence of these dynamics on the solute dipole and location.     

Liquid-vapor interfacial properties of water-ammonia mixtures: dependence on ammonia concentration

The equilibrium and dynamical properties of the liquid-vapor interfaces of water-ammonia mixtures are investigated by means of molecular-dynamics simulations. Altogether, we have simulated seven different systems of different concentration of ammonia. The inhomogeneous density, anisotropic orientational profiles, surface tension, and the pattern of hydrogen bonding are calculated for both water and ammonia molecules in order to characterize the location, width, thermodynamic aspects, and microscopic structure of the liquid-vapor interfaces of each of the water-ammonia systems. The dynamical aspects of the interfaces are investigated in terms of the anisotropic diffusion and dipole orientational relaxation of water and ammonia molecules. The properties of the interfaces are compared with those of the corresponding bulk phases. The present theoretical results are also compared with experimental findings wherever available.     

What can be learned about molecular reorientation from single molecule polarization microscopy?

We have developed a general approach for the calculation of the single molecule polarization correlation function C(t), which delivers a correlation of the emission dichroisms at time 0 and t. The approach is model independent and valid for general asymmetric top molecules. The key dynamic quantities of our analysis are the even-rank orientational correlation functions, the weighted sum of which yields C(t). We have demonstrated that the use of nonorthogonal schemes for the detection of the single molecule polarization responses makes it possible to manipulate the weighting coefficients in the expansion of C(t). Thus valuable information about the orientational correlation functions of the rank higher than the second can be extracted from C(t).     

Hydrogen bonded structure and dynamics of liquid-vapor interface of water-ammonia mixture: an ab initio molecular dynamics study

We have carried out ab initio molecular dynamics simulations of a liquid-vapor interfacial system consisting of a mixture of water and ammonia molecules. We have made a detailed analysis of the structural and dynamical properties of the bulk and interfacial regions of the mixture. Among structural properties, we have looked at the inhomogeneous density profiles of water and ammonia molecules, hydrogen bond distributions, orientational profiles, and also vibrational frequency distributions of bulk and interfacial molecules. It is found that the interfacial molecules show preference for specific orientations so as to form water-ammonia hydrogen bonds at the interface with ammonia as the acceptor. The structure of the system is also investigated in terms of inter-atomic voids present in the system. Among the dynamical properties, we have calculated the diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational spectral diffusion in bulk and interfacial regions. It is found that the diffusion and orientation relaxation of the interfacial molecules are faster than those of the bulk. However, the hydrogen bond lifetimes are longer at the interface which can be correlated with the time scales found from the decay of frequency time correlations.     

Density dependence of the entropy and the solvation shell structure in supercritical water via molecular dynamics simulation

We perform molecular dynamics simulations of supercritical water (SCW) with a wide range of densities along a near critical isotherm using the simple point charge extended (SPC/E) pair potential in order to study the entropy and the solvation shell structure around a central water molecule. It is shown that both the translational and orientational two-particle correlation entropy terms can serve as the metrics of the translational-orientational structural orders in water and it is revealed that the translational structural order is very sensitive to the density variation in the gas-like and liquid-like region, while the orientational structural order is much more dependent upon compression in the medium-density SCW region. The comparison of the magnitudes of the full thermodynamic excess entropy and two-particle correlation entropy confirms the recent findings that the many-body terms other than two-body ones also present significant and non-neglectable contributions to the full excess entropy for the highly anomalous fluids like water. The analysis of entropy terms as a function of intermolecular distance and the orientational distribution functions as well as the three-dimensional spatial distribution functions indicate that the structural order occurs only in a much more diffused first solvation shell due to the elongated hydrogen bonds under supercritical conditions. It is revealed that no obvious second or higher neighbor shells occur in SCW, in contrast with the feature of normal liquid water that the anomalous decrease of translational order upon compression occurs mainly in the second shell.