Nonadditivity of orientational interactions and perturbation theory for dipole hard spheres

The procedure of approximate summation is applied to a series of many-body perturbation theory for the internal energy of a dipolar hard sphere (DHS) fluid to produce an expression similar to the mean field approximation in the Widom-Rowlinson penetrable sphere model, which is well consistent with the experiment at moderate or high densities. Similar results are obtained from the hindered rotation model generalized for arbitrary density. The critical parameters ρ_c, P _c and T _c of both models are consistent with the data of machine experiments and are close to the parameters of the percolation transition in the DHS system.     

Phase behavior of weakly polydisperse sticky hard spheres: perturbation theory for the Percus-Yevick solution

We study the effects of size polydispersity on the gas-liquid phase behavior of mixtures of sticky hard spheres. To achieve this, the system of coupled quadratic equations for the contact values of the partial cavity functions of the Percus-Yevick solution [R. J. Baxter, J. Chem. Phys. 49, 2770 (1968)] is solved within a perturbation expansion in the polydispersity, i.e., the normalized width of the size distribution. This allows us to make predictions for various thermodynamic quantities which can be tested against numerical simulations and experiments. In particular, we determine the leading order effects of size polydispersity on the cloud curve delimiting the region of two-phase coexistence and on the associated shadow curve; we also study the extent of size fractionation between the coexisting phases. Different choices for the size dependence of the adhesion strengths are examined carefully; the Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] of a mixture of polydisperse colloids and small polymers is studied as a specific example.     

Scalar fundamental measure theory for hard spheres in three dimensions: application to hydrophobic solvation

Hard-sphere mixtures provide one a solvable reference system that can be used to improve the density functional theory of realistic molecular fluids. We show how the Kierlik-Rosinberg's scalar version of the fundamental measure density functional theory of hard spheres [E. Kierlik and M. L. Rosinberg, Phys. Rev. A 42, 3382 (1990)], which presents computational advantages with respect to the original Rosenfeld's vectorial formulation or its extensions, can be implemented and minimized in three dimensions to describe fluid mixtures in complex environments. This implementation is used as a basis for defining a molecular density functional theory of water around molecular hydrophobic solutes of arbitrary shape.     

Second order of perturbation theory correction to the radial distribution function of a liquid with the interaction potential of hard spheres plus a square-well

A liquid with the interaction potential of hard spheres plus a square-well is analyzed using the Monte-Carlo technique. Numerical results for the perturbation theory series over a square-well potential are obtained in the form of the Barker and Henderson discrete representation. Approximating expressions for the correction to a liquid radial distribution function in the second order of perturbation theory are presented. The obtained results allow us to define this correction with a root-mean-square deviation of about 0.007. It is shown that the given approach provides a complete calculation in the second order of perturbation theory, and also the determination of the third order correction to the free energy for a liquid interacting with the potential of the Lennard-Jones type.     

Integral equation theory for hard spheres confined on a cylindrical surface: anisotropic packing entropically driven

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube.     

Molecular dynamics simulations of a hard sphere crystal and reaction-like mechanism for homogeneous melting

Molecular dynamics simulations of a hard sphere crystal are performed for volume fractions ranging from solidification point to melting point. A local bond order parameter is chosen to assign a nature, liquid or solid, to a particle. The probability for a liquid or solid particle to change state presents a typical sigmoid shape as the nature of its neighbors changes. Using this property, I propose a reaction-like mechanism and introduce a small number of rate constants. A mean-field approach to melting and a kinetic Monte Carlo algorithm on a lattice are derived from these chemical processes. The results of these models successfully compare with molecular dynamics simulations, proving that the main properties of melting can be captured by a small number of dynamical parameters.     

Inhomogeneous fluids of colloidal hard dumbbells: fundamental measure theory and Monte Carlo simulations

Recently, a density functional theory for hard particles with shape anisotropy was developed, the extended deconvolution fundamental measure theory (edFMT). We apply edFMT to hard dumbbells, arguably the simplest non-convex shape and readily available experimentally in the form of colloids. We obtain good agreement between edFMT and Monte Carlo simulations for fluids of dumbbells in a slit and for the same system under gravity. This indicates that edFMT can be successfully applied to nearly all colloidal shapes, not just for the convex shapes for which edFMT was originally derived. A theory, such as edFMT, that allows a fast and general way of mapping the phase behavior of anisotropic colloids, can act as a useful guide for the design of colloidal shapes for various applications.     

Clustering in the absence of attractions: density functional theory and computer simulations

We numerically investigate the formation of stable clusters of overlapping particles in certain systems interacting via purely repulsive, bounded pair potentials. In close vicinity of a first-order phase transition between a disordered and an ordered structure, clusters are encountered already in the fluid phase which then freeze into crystals with multiply occupied lattice sites. These hyper-crystals are characterized by a number of remarkable features that are in clear contradiction to our experience with harshly repulsive systems: upon compression, the lattice constant remains invariant, leading to a concomitant linear growth in the cluster population with density; further, the freezing and melting lines are to high accuracy linear in the density-temperature plane, and the conventional indicator that announces freezing, that is, the Hansen-Verlet value of the first peak of the structure factor, attains for these soft systems much higher values than for their hard-matter counterparts. Our investigations are based on the generalized exponential model of index 4 (i.e., Phi(r) approximately exp[-(r/sigma)4]). The properties of the phases involved are calculated via liquid state theory and classical density functional theory. Monte Carlo simulations for selected states confirm the theoretical results for the structural and thermodynamic properties of the system. These numerical data, in turn, fully corroborate an approximate theoretical framework that was recently put forward to explain the clustering phenomenon for systems of this kind (Likos, C. N.; Mladek, B. M.; Gottwald, D.; Kahl, G. J. Chem. Phys. 2007, 126, 224502).     

Perfect wetting along a three-phase line: theory and molecular dynamics simulations

Wetting behavior along a three-phase equilibrium has been obtained by density gradient theory (DGT) and molecular dynamics simulations for a type-II equal size Lennard-Jones mixture. In order to perform a consistent comparison between both methodologies, the molecular parameters of this type of mixture were defined from the global phase diagram of equal size Lennard-Jones mixtures. We have found excellent agreement between predictions from the DGT (coupled to a Lennard-Jones equation for the bulk phases) and simulations results for both the phase and interface behavior, in the whole temperature, pressure, and concentration ranges. For all conditions explored in this work, this type-II mixture shows a three-phase equilibrium composed by a bulk immiscible liquid phase (L1) and a bulk gas phase (G) separated by a second immiscible liquid phase (L2). A similar phase distribution is obtained from the interfacial concentration profile in the whole range of conditions used in this work. This type of structure is a clear evidence that L2 completely wets the GL1 interface. The wetting behavior is also confirmed by the values and evolution of the interfacial tensions. In summary, this kind of type-II mixture does not show wetting transitions and exhibits a permanent perfect wetting in all the thermodynamic conditions explored here.     

Interfacial and coexistence properties of soft spheres with a short-range attractive Yukawa fluid: molecular dynamics simulations

Molecular dynamics simulations have been carried out to obtain the interfacial and coexistence properties of soft-sphere attractive Yukawa (SAY) fluids with short attraction range, κ = 10, 9, 8, 7, 6, and 5. All our simulation results are new. These data are also compared with the recently reported results in the literature of hard-core attractive Yukawa (HAY) fluids. We show that the interfacial and coexistence properties of both potentials are different. For the surveyed systems, here we show that all coexistence curves collapse into a master curve when we rescale with their respective critical points and the surface tension curves form a single master curve when we plot γ* vs. T/T(c).     

Reactions on cell membranes: comparison of continuum theory and Brownian dynamics simulations

Biochemical transduction of signals received by living cells typically involves molecular interactions and enzyme-mediated reactions at the cell membrane, a problem that is analogous to reacting species on a catalyst surface or interface. We have developed an efficient Brownian dynamics algorithm that is especially suited for such systems and have compared the simulation results with various continuum theories through prediction of effective enzymatic rate constant values. We specifically consider reaction versus diffusion limitation, the effect of increasing enzyme density, and the spontaneous membrane association/dissociation of enzyme molecules. In all cases, we find the theory and simulations to be in quantitative agreement. This algorithm may be readily adapted for the stochastic simulation of more complex cell signaling systems.     

A unified theory of adsorption and wetting using the percus yevick equation for hard spheres with surface adhesion

Abstract

The recent analysis by Baxter of the Percus-Yevick model for an assembly of similar spherical particles with hard sphere repulsion plus a delta function attraction is generalised to an arbitrary number of components. We use the solution to study one component gas adsorption onto a planar substrate. The resulting adsorption isotherms exhibit monolayer or multilayer wetting according to the strengths of the interaction parameters. In particular, we find that multilayer wetting will not occur if the adsorbate/adsorbate interaction is sufficiently weak regardless of the strength of the adsorbate/adsorbent interaction. For weak adsorbate/ adsorbate interactions at low gas pressures the adsorption saturates at approximately a monolayer as the adsorbate/adsorbent interaction is increased.     

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 2002, 65, 011106] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also successfully tested against simulations of a hard sphere fluid at relatively low density.     

The dynamical role of solvent on the ICN photodissociation reaction: connecting experimental observables directly with molecular dynamics simulations

The ICN photodissociation reaction is the prototype system for understanding energy disposal and curve crossing in small molecule bond-breaking. The wide knowledge base on this reaction in the gas phase makes it an excellent test case to explore and understand the influence of a liquid solvent on the photo-induced reaction dynamics. Molecular dynamics simulations that include surface-hopping have addressed numerous aspects of how the solvent should influence non-adiabatic transitions and energy flow and ultimately determine product branching for this reaction system. In this paper, we report femtosecond transient absorption work directly combined with new molecular dynamics simulations that make direct connection with the spectroscopic observables. The full spectral evolution after initiating ICN photodissociation at 266 nm in water and ethanol is recorded with unprecedented time resolution, fast enough to see the nascent products emerge before interacting with the solvent cage. Use of a 266 nm pump maximizes the probability of subsequent caging on the upper diabat while launching large rotational energy release for trajectories emerging on the lower diabat. The 2D dataset yields a map of the different products and how they interconvert. In particular, information on the branching ratio and spectral evolution of the product bands is revealed as the products relax their electronic and rotational degrees of freedom. An evolution from rotationally hot gas-phase like CN (sharp band, at 390 nm) to equilibrated and solvated CN radicals (broad, at 326 nm in water and 415 nm in ethanol) is clearly observed in both solvents, and signals assignable to I* are also captured. The non-adiabatic molecular dynamics simulations focus on identifying when trajectories curve cross, filtering the trajectory ensemble into spectroscopically distinct sub-populations and analyzing the rotational energy for the CN product population. The experimental results, taken together with the MD simulations, establish the initial surface crossing probability and suggest multiple passes through the curve crossing region determine the final product yields and provide a source of freshly torqued CN radicals that continues to top up the population of rotationally hot photoproduct over the first few picoseconds.     

‘Exact’ integral equation theory and local formulation for excess thermodynamic properties of hard spheres

A hybrid hard sphere bridge function is proposed, which, in combination with the standard Ornstein–Zernike integral equation, can predict extremely accurately hard sphere compressibility, virial pressure, and correlation function. Second, a local formulation for determination of excess chemical potential is derived out, which, in combination with the present hybrid hard sphere bridge function and OZ integral equation, can predict the excess chemical potential also extremely accurately. The resultant excess entropy is in excellent agreement with that from the Carnahan–Starling equation of state. The present formalism performs excellently over the whole density range, i.e. from zero to freezing density, and is largely superior to a formalism available in the literature.     

Recent applications and developments of charge equilibration force fields for modeling dynamical charges in classical molecular dynamics simulations

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, in our hands those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for small molecules, proteins, lipids, and lipid bilayers and recently have begun work on carbohydrate force fields. The latter area has been relatively untouched by force field developers with particular focus on polarizable, non-additive interaction potential models. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration method for phase-dependent polarizable force fields, lipid molecules, and small-molecule carbohydrates. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields.     

Polydispersions radiation envelope: Influence of particle size and assumed distribution function

Summary The influence of polydispersity, particle size and of assumed distribution on angular dependence of theMie intensity functions in systems with relative refractive indexm = 1.10 was studied theoretically. Two distribution functions were used; Stevenson-Heller-Wallach (SHWD) and logarithmic distribution of negative order (NOLD). It was found, that for highly polydisperse systems the functional dependences obtain also undulative character. By means of NOLD the angular shift of extremes on the curves studied with increasing polydispersity was not observed. The application of this distribution in comparison with SHWD shows more structured angular scattering patterns with increasing particle size and this fact can also be employed in modelling and in distribution analysis of dispersion with higher degree of polydispersity.With 4 figures     

Single particle and pair dynamics in water-formic acid mixtures containing ionic and neutral solutes: nonideality in dynamical properties

A series of molecular dynamics simulations of water-formic acid mixtures containing either an ionic solute or a neutral hydrophobic solute has been performed to study the extent of nonideality in the dynamics of these solutes for varying composition of the mixtures. The diffusion coefficients of the charged solutes, both cationic and anionic, are found to show nonideal behavior with variation of composition, and similar nonideality is also observed for the diffusion and orientational relaxation of solvent molecules in these mixtures. The diffusion coefficient of a neutral hydrophobic solute, however, decreases monotonically with increase in water concentration. We have also investigated some of the pair dynamical properties such as water-water and water-formic acid hydrogen bond relaxation and residence dynamics of water molecules in water and formic acid hydration shells. The lifetimes of water-water hydrogen bonds are found to be longer than those between formic acid carbonyl oxygen-water hydrogen bonds, whereas the lifetimes of formic acid hydroxyl hydrogen-water hydrogen bonds are longer than those of water-water hydrogen bonds. In general, the hydrogen bond lifetimes for both water-water and water-formic acid hydrogen bonds are found to decrease with increase in water concentration. Residence times of water molecules also show the same trend with increase in formic acid concentration. Interestingly, these pair dynamical properties show a monotonic dependence on composition without any maximum or minimum and behave almost ideally with respect to changes in the composition of the mixtures. The present calculations are performed with fixed-charge nonpolarizable models of the solvent and solute molecules without taking into account many-body polarization effects in an explicit manner.