Branka M. Ladanyi

New type of cluster theory for molecular fluids: Interaction site cluster expansion

A new cluster series, called the interaction site cluster expansion, is derived for classical molecular fluids. For a general class of molecular models, the series provides an exact formula for the equilibrium pair correlations between interaction sites on different molecules. In the models considered, each molecule contains m of these interaction sites. The total intermolecular potential between two molecules is the sum of m2 site–site potentials. A site–site potential depends on the separation between the sites only. However, because the sites are not necessarily located at the centers of molecules, the total molecular pair interaction can depend strongly on molecular orientations. Even though the interaction site cluster expansion is exact, the cluster integrals in the series involve the translational coordinates of the interaction sites only. The molecular orientational coordinates are removed by a transformation which introduces intramolecular correlation functions into the series. Thus, the new clus...

The short‐time dynamics of molecular liquids. Instantaneous‐normal‐mode theory

Since the sharply varying forces that control the arrangement of molecules in liquids are themselves intrinsically anharmonic, the natural assumption would be that any picture that regarded molecular motion as harmonic would be at best a rough phenomenological guide. This expectation is, in fact, not a correct one. While the packing forces that determine liquid structure are indeed strongly anharmonic, the short‐time displacements and librations that molecules execute are actually quite harmonic. It is possible to show rigorously that, for short enough (subpicosecond) time intervals, the dynamics of liquids is governed by a set of independent, collective, harmonic modes—the instantaneous normal modes of the liquid. In this paper we illustrate this fact by predicting the translational and rotational dynamics of a model diatomic liquid using the instantaneous normal modes computed by simulation. When compared to the exact molecular‐dynamics results for the same autocorrelation functions, we find that perfec...

New and proper integral equations for site-site equilibrium correlations in molecular fluids

We show that the often used site-site direct correlation function cannot be defined in terms of a sum over a subset of the diagrams in the interaction site cluster series for the equilibrium pair correlation functions of a molecular fluid. However, from an exact topological reduction, we arrive at a new class of site-site direct correct correlation functions that are properly defined in the diagrammatic sense. The class is composed of four topologically distinct functions which are related to each other and the pair correlation function through four coupled Ornstein-Zernike-like equations. These new integral equations are exact and provide a rigorous foundation for integral equation theories of molecular fluids. The formal solutions to the equations are constructed, and the utility of the formulation is illustrated by discussing one example of an approximate closure to the integral equations.

Vibrational spectroscopy and dynamics of water confined inside reverse micelles.

In this work, we combine atomistic molecular dynamics simulations with theoretical vibrational spectroscopy to study the properties of water confined inside bis(2-ethylhexyl)sulfosuccinate (AOT) reverse micelles. This approach is found to successfully reproduce the experimental spectra, rotational anisotropy decays, and spectral diffusion time-correlation functions as a function of micelle size. These results are interpreted in terms of water molecules in different hydrogen bonding environments. One interesting result from our simulation, not directly accessible experimentally, involves the distance from the surfactant headgroup/water interface over which the dynamical properties of water become bulk-like. We find that this distance varies with micelle size, casting doubt on the core/shell model. In particular, the distance increases with decreasing micelle size, and hence decreasing radius of curvature of the interface. We suggest that this arises from curvature-induced frustration. We also find that the dynamics in the smallest micelle studied is extremely slow--relaxation is still incomplete by 1 ns. As in other glassy systems with collective relaxation, our time-correlation functions can be fit to stretched exponentials, in this case with very small exponents.

Structure and dynamics of water confined in silica nanopores

We report the results of molecular simulation of water in silica nanopores at full hydration and room temperature. The model systems are approximately cylindrical pores in amorphous silica, with diameters ranging from 20 to 40 Å. The filled pores are prepared using grand canonical Monte Carlo simulation and molecular dynamics simulation is used to calculate the water structure and dynamics. We found that water forms two distinct molecular layers at the interface and exhibits uniform, but somewhat lower than bulk liquid, density in the core region. The hydrogen bond density profile follows similar trends, with lower than bulk density in the core and enhancements at the interface, due to hydrogen bonds between water and surface non-bridging oxygens and OH groups. Our studies of water dynamics included translational mean squared displacements, orientational time correlations, survival probabilities in interfacial shells, and hydrogen bond population relaxation. We found that the radial-axial anisotropy in translational motion largely follows the predictions of a model of free diffusion in a cylinder. However, both translational and rotational water mobilities are strongly dependent on the proximity to the interface, with pronounced slowdown in layers near the interface. Within these layers, the effects of interface curvature are relatively modest, with only a small increase in mobility in going from the 20 to 40 Å diameter pore. Hydrogen bond population relaxation is nearly bulk-like in the core, but considerably slower in the interfacial region.

Higher order interaction‐induced effects on Rayleigh light scattering by molecular liquids

Molecular dynamics (MD) computer simulation was used to study Rayleigh light scattering (LS) in oxygen and carbon disulfide liquids. Results are presented for one thermodynamic state of oxygen (82 K, 1.215 g/cm3) and two thermodynamic states of CS2 (193K, 1.42 g/cm3 and 293 K, 1.30 g/cm3). The molecular trajectories were generated using Lennard‐Jones atom–atom potential models. LS spectra were calculated using the dipole–induced dipole (DID) model for the interaction‐induced polarizability. The results obtained for the LS intensities, time correlations, and line shapes, using the first‐order perturbation theory for the system polarizability, based on this model, are compared to the exact DID model results. We find that the relative contribution of the higher order DID terms to LS spectra of these liquids can be correlated with the magnitudes of the isolated molecule isotropic and anisotropic polarizabilities. As a result of this, these terms have a very small effect on O2 LS spectra, but that they make a ...

The role of local fields and interparticle pair correlations in light scattering by dense fluids: I. Depolarized intensities due to orientational fluctuations† Supported in part by the National Science Foundation (NSF Grant CHE 76-07384).

The polarized scattering intensity is calculated, in the Einstein-Smoluchowski approximation, for four thermodynamic states of a model diatomic; these are the same states for which the depolarized intensity was calculated in the first article (I) of this series. The polarized intensity is discussed in terms of an ‘effective isotropic polarizability’ α 0 eff and the ratio (α 0 eff/α 0)2, where α 0 is the gas-phase isotropic polarizability, and is both expressed formally and tabulated for the four states. Similarly in (I), depolarized intensities were discussed in terms of the ratio, (γ/Δα)2, where γ is the ‘effective polarizability anisotropy’ and Δα the gas-phase anisotropy. We find that (α 0 eff/α 0)2 lies much closer to unity than does (γ/Δα)2, in agreement with existing experimental data, which indicates that the introduction of effective polarizabilities is relatively unimportant or important, respectively, as polarized or depolarized scattering is considered.

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.

Molecular dynamics study of Rayleigh light scattering from molecular fluids

In this article, we present the results of a molecular dynamics simulation of Rayleigh light scattering (LS) from molecular fluids. We include the orientational and collision induced (CI) contributions to the depolarized LS time correlation and the CI contribution to the isotropic LS time correlation. The intermolecular potential is represented by a two site Lennard‐Jones model. The bond length and potential parameters are chosen to correspond to those of O2 and CO2. We consider two pair polarizability models, one based on the dipole‐induced dipole (DID) interactions between molecular centers and the other on the DID interactions between Lennard‐Jones sites. For both models, we study the variations of the LS time correlations, integrated intensities, and spectral moments with density and temperature. In the case of the more anisotropic CO2, we find that the two models predict very different behavior of the CI part of the Rayleigh LS spectra. The site DID model is found to agree slightly better with the av...

Wave vector dependent dielectric relaxation in hydrogen-bonding liquids : a molecular dynamics study of methanol

Molecular dynamics simulation is used to study e(k,ω), the frequency and wave vector dependent dielectric permittivity of a three‐site model of methanol in which the methyl group is represented as a single site. The effects of induced dipoles are taken into account using perturbation theory and a three‐site molecular polarizability model. The data are analyzed in terms of projected variables which allow us to distinguish between local field factors which renormalize the permanent‐dipole contribution to the permittivity from the ‘‘collision induced’’ dipole relaxation. We find that induced dipoles significantly enhance the static permittivity, mainly through the local field factors. The time correlation functions for the longitudinal and transverse components of the collective dipole moments, evaluated at several of the smallest wave vectors in the system, present rapid oscillations at short times, followed by a nonexponential relaxation regime at intermediate times. At long times, for which the longitudin...