New criteria for cluster identification in continuum systems

Cluster Identification Using Modularity Optimization to Uncover Chemical Heterogeneity in Complex Solutions

Structural heterogeneity is commonly manifested in solutions and liquids that feature competition of different interparticle forces. Identifying and characterizing heterogeneity across different length scales requires multimodal experimental measurement and/or the application of new techniques for the interrogation of atomistic simulation data. Within the latter, the parsing of networks of interparticle interactions (chemical networks) has been demonstrated to be a valuable tool for identifying subensembles of chemical environments. However, chemical networks can adopt a wide variety of topologies that challenge generalizable methods for identifying heterogeneous behavior, and few network analysis algorithms have been proposed for multiscale resolution. In this study, we apply a method of partitioning using the graph theoretic concept of clusters and communities. Using a modularity optimization algorithm, the cluster partition creates subgraphs based on their relative internal and external connectivities. The methodology is tested on two soft matter systems that have significantly different network topologies so as to probe its ability to identify multiple scale features and its generalizability. A binary Lennard-Jones fluid is first examined, where one component causes subgraphs that have high internal network connectivity yet are still connected to the rest of the interparticle network of interactions. The impact of connectivity and edge weighting on the cluster partition is investigated. In the second system, hierarchically organized molecular structures comprised of hydrogen bonded water molecules are identified at a liquid/liquid interface. These structures have a much more sparse network with significantly varied internal connectivity that is a challenge to differentiate from the background hydrogen bonding network of water molecules at the instantaneous interface. The organized macrostructures are effectively isolated from the background network using the cluster partition, and a time-dependent implementation allows us to reveal their reactivity. These studies indicate that cluster partitioning based upon intermolecular network connectivity patterns is broadly generalizable, depending only on user-defined intermolecular connectivity, is operable across different length scales, and is extensible to the study of dynamic phenomena.

Micro-heterogeneity versus clustering in binary mixtures of ethanol with water or alkanes

Snapshots of the difference in complex disorder, with analogy with direct (ethanol–water) and inverse (ethanol–alkanes) emulsions.

Effects of surface-active organic matter on carbon dioxide nucleation in atmospheric wet aerosols: a molecular dynamics study

Organic matter (OM) uptake in cloud droplets produces water-soluble secondary organic aerosols (SOA) via aqueous chemistry. These play a significant role in aerosol properties. We report the effects of OM uptake in wet aerosols, in terms of the dissolved-to-gas carbon dioxide nucleation using molecular dynamics (MD) simulations. Carbon dioxide has been implicated in the natural rainwater as well as seawater acidity. Variability of the cloud and raindrop pH is assumed in space and time, as regional emissions, local human activities and geophysical characteristics differ. Rain scavenging of inorganic SOx, NOx and NH3 plays a major role in rain acidity in terms of acid-base activity, however carbon dioxide solubility also remains a key parameter. Based on the MD simulations we propose that the presence of surface-active OM promotes the dissolved-to-gas carbon dioxide nucleation in wet aerosols, even at low temperatures, strongly decreasing carbon dioxide solubility. A discussion is made on the role of OM in controlling the pH of a cloud or raindrop, as a consequence, without involving OM ionization equilibrium. The results are compared with experimental and computational studies in the literature.

Percolation threshold parameters of fluids

Extensive Monte Carlo simulations on three qualitatively different model supercritical fluids (square-well fluid, Lennard-Jonesium, and primitive water) have been performed to examine percolation threshold parameters for continuum (correlated) models and their relation to general results valid for random lattice models; random-site percolation simple-cubic lattice has therefore been considered as well. Two different bond criteria, the configurational and self-bound ones, defining a cluster have been used. In addition to the percolation threshold occupation probability pc and the percolation threshold fluid density rhoc, the correlation length exponent nu and the wrapping probability at the percolation threshold Rw,c have also been evaluated. It is found that parameters nu and Rw,c exhibit not only strong temperature dependence but also, unlike the case of lattice systems, dependence on the nature of the system considered and the employed definition of the cluster.

Temperature dependence of the colloidal agglomeration inhibition: computer simulation study

There exist experimental evidences that the structure and extension of colloidal aggregates in suspensions change dramatically with temperature. This results in an associated change in the suspension rheology. Experimental studies of the inhibitor applications to control the particle clustering have revealed some unexpected tendencies. Namely, the heating of colloidal suspensions has provoked either extension or reduction of the colloidal aggregates. To elucidate the origin of this behavior, we investigate the influence of temperature on the stabilizing effect of the inhibitor, applying an associative two-component fluid model. Our results of the canonical Monte Carlo simulations indicate that the anomalous effect of the temperature may not be necessarily explained by the temperature dependent changes in the inhibitor tail conformation, as has been suggested recently by Won et al. [Langmuir 21, 924 (2005)]. We show that the competition between colloid-colloid and colloid-inhibitor associations, which, in turn, depends on the temperature and the relative concentrations, may be one of the main reasons for the unexpected temperature dependence of inhibitor efficacy.

Microstructure of neat alcohols

Formation of microstructure in homogeneous associated liquids is analyzed through the density-density pair correlation functions, both in direct and reciprocal space, as well as an effective local one-body density function. This is illustrated through a molecular dynamics study of two neat alcohols, namely, methanol and tert-butanol, which have a rich microstructure: chainlike molecular association for the former and micellelike for the latter. The relation to hydrogen bonding interaction is demonstrated. The apparent failure to find microstructure in water--a stronger hydrogen bonding liquid--with the same tools is discussed.

Accurate modeling of sequential decay in clusters over long time scales: Insights from phase space theory

A general theoretical framework for describing the thermally induced sequential decay in atomic clusters is presented. The scheme relies on a full treatment of individual dissociation steps based on phase space theory (PST), built into a kinetic Monte Carlo (kMC) procedure. This combined PST/kMC approach allows one to follow the evolution of several statistical properties such as the size, the angular momentum, or the temperature of the cluster over arbitrarily long time scales. Quantitative accuracy is achieved by incorporating anharmonicities of the vibrational densities of states, the rigorous conservation of angular momentum via the effective dissociation potential, and a proper calibration of the rate constants. The approach is tested and validated on selected Lennard-Jones clusters in various situations. Several approximations, including a mean-field rate equation treatment, are critically discussed; possible extensions are presented.

Cluster pair correlation function of simple fluids: Energetic connectivity criteria

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.

Percolation of clusters with a residence time in the bond definition: Integral equation theory

We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.

Molecular cluster decay viewed as escape from a potential of mean force

We show that evaporation from a quasistable molecular cluster may be treated as a kinetic problem involving the stochastically driven escape of a molecule from a potential of mean force. We derive expressions for the decay rate, and a relationship between the depth of the potential and the change in system free energy upon loss of a molecule from the cluster. This establishes a connection between kinetic and thermodynamic treatments of evaporation, but also reveals differences in the prefactor in the rate expression. We perform constant energy molecular dynamics simulations of cluster dynamics to calculate potentials of mean force, friction coefficients and effective temperatures for use in the kinetic analysis, and to compare the results with the directly observed escape rates. We also use the simulations to estimate the escape rates by a probabilistic analysis. It is much more efficient to calculate the decay rate by the methods we have developed than it is to monitor escape directly, making these approaches potentially useful for the assessment of molecular cluster stability.