Self-assembling of chain molecules in low dimensions: A Monte Carlo study

We studied the self-assembling of linear chain molecules in insoluble monolayers due to attractive interactions. We used lattice Monte Carlo simulations in a two-dimensional system. The molecules consist of segments occupying adjacent lattice sites. The head segments are confined to move along a line whereas the chain segments can arrange in a plane above the heads. Only one interaction parameter is applied. At high densities and small interaction energy the system shows percolation behavior. At moderate and small densities it can be characterized by a monotonous cluster size distribution. Self-assembling occurs at small densities for strong attractive interactions. The corresponding cluster size distributions indicate preferred cluster sizes which depend upon density and interaction strength. With increasing density the clusters grow. The internal cluster structure depends on the cluster size and the interaction parameter. The clusters tend to minimize their total energy. Molecules at cluster margins contribute less to the cluster energy and are mainly disordered. They cause that the cluster properties strongly depend on the cluster size. Large clusters only have minimum energy if the molecules in the cluster are in stretched-out conformation. With decreasing interaction strength the clusters get disordered thereby producing less energy-minimized domain boundaries.     

Heterogeneous condensation of the Lennard-Jones vapor onto a nanoscale seed particle

The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed particle is studied using molecular dynamics simulations. Measuring the nucleation rate and the height of the free energy barrier using the mean first passage time method shows that the presence of a weakly interacting seed has little effect on the work of forming very small cluster embryos but accelerates the rate by lowering the barrier for larger clusters. We suggest that this results from a competition between the energetic and entropic features of cluster formation in the bulk and at the heterogeneity. As the interaction is increased, the free energy of formation is reduced for all cluster sizes. We also develop a simple phenomenological model of film formation on a small seed that captures the general features of the nucleation process for small heterogeneities. A comparison of our simulation results with the model shows that heterogeneous classical nucleation theory provides a good estimate of the critical size of the film but significantly overestimates the size of the barrier.     

Properties of spanning water networks at protein surfaces

The formation of a spanning two-dimensional hydrogen-bonded water network at the surface of proteins via a percolation transition enables their biological function. We show in detail how the spanning (percolating) water network appears at the surfaces of model hydrophilic spheres and at the surface of a single protein (lysozyme) molecule. We have found essential correlations of the linear extension, radius of gyration, and position of the center of mass of the largest water cluster with its size. The specific two-peak structure of the probability distribution of the largest cluster size allowed us to study various properties separately for spanning and nonspanning largest clusters. The radius of gyration of the spanning cluster always exceeds the radii of the spheres or the effective radius of the protein. Any spanning cluster envelops essentially more than half of the surface area. The temporal decay of the spanning networks shows a stretched exponential character. Their average lifetime at the percolation threshold is about the lifetime of a water-water hydrogen bond.     

Kinetics of NaCl nucleation in supercritical water investigated by molecular dynamics simulations

At system pressures between 17 MPa and 25 MPa the nucleation and growth of NaCl nanoparticles in water at supercritical conditions was investigated by molecular dynamics simulations at different system temperatures and system densities. Our results show that particle formation takes place within a few hundred picoseconds after the jump from ambient to supercritical conditions. After nucleation a phase of growth by adding monomers is followed by growth via cluster-cluster collisions. We present results on the time development of distributions of cluster sizes, cluster compositions, and cluster temperatures as well as radial distribution functions and nucleation rates.     

甘油对冰晶生长抑制作用的分子动力学模拟

采用分子模拟方法研究了正交晶系冰晶(020)生长面在不同浓度甘油水溶液中的生长情况. 通过统计分析氢键数、 密度分布函数、 均方根偏差和原子间径向分布函数研究了水分子和甘油分子的动态行为. 结果表明, 甘油分子在水溶液中可与水分子形成大量氢键, 这使水分子间的氢键作用受到抑制, 降低了水分子的扩散性, 致使冰晶不易成核和生长; 另外, 一些甘油分子可代替水分子吸附在晶面上, 甚至占据晶格位点, 这种行为打破了冰晶的对称性并且降低了冰晶的生长速率. 因此, 甘油可同时在晶面和液相中抑制冰晶的生长.     

Freezing water in no-man's land

We report homogeneous ice nucleation rates between 202 K and 215 K, thereby reducing the measurement gap that previously existed between 203 K and 228 K. These temperatures are significantly below the homogenous freezing limit, T(H)≈ 235 K for bulk water, and well within no-man's land. The ice nucleation rates are determined by characterizing nanodroplets with radii between 3.2 and 5.8 nm produced in a supersonic nozzle using three techniques: (1) pressure trace measurements to determine the properties of the flow as well as the temperature and velocity of the droplets, (2) small angle X-ray scattering (SAXS) to measure the size and number density of the droplets, and (3) Fourier Transform Infrared (FTIR) spectroscopy to follow the liquid to solid phase transition. Assuming that nucleation occurs throughout the droplet volume, the measured ice nucleation rates J(ice,V) are on the order of 10(23) cm(-3) s(-1), and agree well with published values near 203 K.     

Nucleation of NaCl nanoparticles in supercritical water: molecular dynamics simulations

Formation of NaCl nanoparticles in supercritical water is studied using molecular dynamics simulation method. We have simulated particle nucleation and growth in NaCl-H2O fluids, with salt concentration of 5.1 wt %, in the temperature and density range of 673-1073 K and 0.17-0.34 g/cm(3), respectively. The cluster size distributions, the size of critical nuclei and cluster lifetimes are reported. The size distribution of emerging clusters shows a very strong dependence on the system's density, with larger clusters forming at lower densities. Clusters consisting of approximately 14-24 ions appear critical for the thermodynamic states examined. The local structures of critical clusters are found to be amorphous. The lifetime values for clusters containing more than 20 ions are in the range of 10-50 ps. We have calculated the NaCl nucleation rates, which appear to be on the order of 10(28) cm(-3) s(-1).     

Analysis of nucleation ability of cluster configurations with Monte Carlo simulations of argon

We determine the nucleation ability of argon clusters from Monte Carlo simulations. The nucleation rate appears to be defined by a sole characteristic of the clusters, namely, the stability. The stability is calculated as the ratio of grand canonical growth and decay rates and can be assigned to individual cluster configurations. We study the connection between the stability of the cluster configurations and their volume and total potential energy. Neither the potential energy nor the volume of a cluster configuration has a clear relation to its stability, and thus to the nucleation ability. On the other hand, we show that it is possible to use a specific volume for each cluster size to calculate the work of the cluster formation. These clusters with a unique volume have the same average stability as the full set of clusters. Our simulation method allows us to study the effect of possible deviations from equilibrium in the cluster configuration distributions. We argue that the nucleation process itself can produce a source for such a deviation. We show that even a small deviation from equilibrium in the cluster configuration distribution can lead to a dramatic deceleration of the nucleation rate. Although our simulations may overestimate the magnitude of the effect, they give qualitative estimates for its importance.     

Percolation transition in supercritical water: a Monte Carlo simulation study

Computer simulations of water have been performed on the canonical ensemble at 15 different molecular number densities, ranging from 0.006 to 0.018 A-3, along the supercritical isotherm of 700 K, in order to characterize the percolation transition in the system. It is found that the percolation transition occurs at a somewhat higher density than what is corresponding to the supercritical extension of the boiling line. We have shown that the fractal dimension of the largest cluster and the probability of finding a spanning cluster are the most appropriate properties for the location of the true percolation threshold. Thus, percolation transition occurs when the fractal dimension of the largest cluster reaches 2.53, and the probability of finding a cluster that spans the system in at least one dimension and in all the three dimensions reaches 0.97 and 0.65, respectively. On the other hand, the percolation threshold cannot be accurately located through the cluster size distribution, as it is distorted by appearance of clusters crossing the finite simulated system even far below the percolation threshold. The structure of the largest water cluster is dominated by a linear, chainlike arrangement, which does not change noticeably until the largest cluster becomes infinite.     

Stochastic self-assembly of incommensurate clusters

Nucleation and molecular aggregation are important processes in numerous physical and biological systems. In many applications, these processes often take place in confined spaces, involving a finite number of particles. Analogous to treatments of stochastic chemical reactions, we examine the classic problem of homogeneous nucleation and self-assembly by deriving and analyzing a fully discrete stochastic master equation. We enumerate the highest probability steady states, and derive exact analytical formulae for quenched and equilibrium mean cluster size distributions. Upon comparison with results obtained from the associated mass-action Becker-D?ring equations, we find striking differences between the two corresponding equilibrium mean cluster concentrations. These differences depend primarily on the divisibility of the total available mass by the maximum allowed cluster size, and the remainder. When such mass "incommensurability" arises, a single remainder particle can "emulsify" the system by significantly broadening the equilibrium mean cluster size distribution. This discreteness-induced broadening effect is periodic in the total mass of the system but arises even when the system size is asymptotically large, provided the ratio of the total mass to the maximum cluster size is finite. Ironically, classic mass-action equations are fairly accurate in the coarsening regime, before equilibrium is reached, despite the presence of large stochastic fluctuations found via kinetic Monte-Carlo simulations. Our findings define a new scaling regime in which results from classic mass-action theories are qualitatively inaccurate, even in the limit of large total system size.     

Homogeneous ice nucleation from aqueous inorganic/organic particles representative of biomass burning: water activity, freezing temperatures, nucleation rates

Homogeneous ice nucleation plays an important role in the formation of cirrus clouds with subsequent effects on the global radiative budget. Here we report on homogeneous ice nucleation temperatures and corresponding nucleation rate coefficients of aqueous droplets serving as surrogates of biomass burning aerosol. Micrometer-sized (NH(4))(2)SO(4)/levoglucosan droplets with mass ratios of 10:1, 1:1, 1:5, and 1:10 and aqueous multicomponent organic droplets with and without (NH(4))(2)SO(4) under typical tropospheric temperatures and relative humidities are investigated experimentally using a droplet conditioning and ice nucleation apparatus coupled to an optical microscope with image analysis. Homogeneous freezing was determined as a function of temperature and water activity, a(w), which was set at droplet preparation conditions. The ice nucleation data indicate that minor addition of (NH(4))(2)SO(4) to the aqueous organic droplets renders the temperature dependency of water activity negligible in contrast to the case of aqueous organic solution droplets. The mean homogeneous ice nucleation rate coefficient derived from 8 different aqueous droplet compositions with average diameters of ～60 μm for temperatures as low as 195 K and a(w) of 0.82-1 is 2.18 × 10(6) cm(-3) s(-1). The experimentally derived freezing temperatures and homogeneous ice nucleation rate coefficients are in agreement with predictions of the water activity-based homogeneous ice nucleation theory when taking predictive uncertainties into account. However, the presented ice nucleation data indicate that the water activity-based homogeneous ice nucleation theory overpredicts the freezing temperatures by up to 3 K and corresponding ice nucleation rate coefficients by up to ～2 orders of magnitude. A shift of 0.01 in a(w), which is well within the uncertainty of typical field and laboratory relative humidity measurements, brings experimental and predicted freezing temperatures and homogeneous ice nucleation rate coefficients into agreement. The experimentally derived ice nucleation data are applied to constrain the water activity-based homogeneous ice nucleation theory to smaller than ±1 order of magnitude compared to the predictive uncertainty of larger than ±6 orders of magnitude. The atmospheric implications of these findings are discussed.     

Cooperativity in ordinary ice and breaking of hydrogen bonds

The total interaction energy between two H-bonded water molecules in a condensed phase is composed of a binding energy between them and an energy due to a cooperative effect. An approximate simple expression is suggested for the dependence of the interaction energy between two H-bonded water molecules on the number of neighboring water molecules with which they are H-bonded. Using this expression, the probabilities of breaking a H bond with various numbers of H-bonded neighbors are estimated. These probabilities are used in computer simulations of the breaking of specified fractions of H bonds in an ordinary (hexagonal) ice. A large "piece" of hexagonal ice (up to 8 millions molecules) is built up, and various percentages of H bonds are considered broken. It is shown that 62-63% of H bonds must be broken in order to disintegrate the "piece" of ice into disconnected clusters. This value is only a little larger than the percolation threshold (61%) predicted both by the percolation theory for tetrahedral ice and by simulations in which all H bonds were considered equally probable to be broken. When the percentage of broken bonds is smaller than 62-63%, there is a network of H-bonded molecules which contains the overwhelming majority of water molecules. This result contradicts some models of water which consider that water consists of a mixture of water clusters of various sizes. The distribution of water molecules with unequal probabilities for breaking is compared with the simulation involving equal probabilities for breaking. It was found that in the former case, there is an enhanced number of water monomers without H bonds, that the numbers of 2- and 3-bonded molecules are smaller, and the number of 4-bonded molecules is larger than in the latter case.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Initiation of the ice phase by marine biogenic surfaces in supersaturated gas and supercooled aqueous phases

Biogenic particles have the potential to affect the formation of ice crystals in the atmosphere with subsequent consequences for the hydrological cycle and climate. We present laboratory observations of heterogeneous ice nucleation in immersion and deposition modes under atmospherically relevant conditions initiated by Nannochloris atomus and Emiliania huxleyi, marine phytoplankton with structurally and chemically distinct cell walls. Temperatures at which freezing, melting, and water uptake occur are observed using optical microscopy. The intact and fragmented unarmoured cells of N. atomus in aqueous NaCl droplets enhance ice nucleation by 10-20 K over the homogeneous freezing limit and can be described by a modified water activity based ice nucleation approach. E. huxleyi cells covered by calcite plates do not enhance droplet freezing temperatures. Both species nucleate ice in the deposition mode at an ice saturation ratio, S(ice), as low as ~1.2 and below 240 K, however, for each, different nucleation modes occur at warmer temperatures. These observations show that markedly different biogenic surfaces have both comparable and contrasting effects on ice nucleation behaviour depending on the presence of the aqueous phase and the extent of supercooling and water vapour supersaturation. We derive heterogeneous ice nucleation rate coefficients, J(het), and cumulative ice nuclei spectra, K, for quantification and analysis using time-dependent and time-independent approaches, respectively. Contact angles, α, derived from J(het)via immersion freezing depend on T, a(w), and S(ice). For deposition freezing, α can be described as a function of S(ice) only. The different approaches yield different predictions of atmospheric ice crystal numbers primarily due to the time evolution allowed for the time-dependent approach with implications for the evolution of mixed-phase and ice clouds.     

Effect of Nanoscale Confinement on Freezing of Modified Water at Room Temperature and Ambient Pressure

Understanding the phase behavior of confined water is central to fields as diverse as heterogeneous catalysis, corrosion, nanofluidics, and to emerging energy technologies. Altering the state points (temperature, pressure, etc.) or introduction of a foreign surface can result in the phase transformation of water. At room temperature, ice nucleation is a very rare event and extremely high pressures in the GPa–TPa range are required to freeze water. Here, we perform computer experiments to artificially alter the balance between electrostatic and dispersion interactions between water molecules, and demonstrate nucleation and growth of ice at room temperature in a nanoconfined environment. Local perturbations in dispersive and electrostatic interactions near the surface are shown to provide the seed for nucleation (nucleation sites), which lead to room temperature liquid–solid phase transition of confined water. Crystallization of water occurs over several tens of nanometers and is shown to be independent of the nature of the substrate (hydrophilic oxide vs. hydrophobic graphene and crystalline oxide vs. amorphous diamond‐like carbon). Our results lead us to hypothesize that the freezing transition of confined water can be controlled by tuning the relative dispersive and electrostatic interaction.     

Free energy landscapes for homogeneous nucleation of ice for a monatomic water model

We simulate the homogeneous nucleation of ice from supercooled liquid water at 220 K in the isobaric-isothermal ensemble using the MW monatomic water potential. Monte Carlo simulations using umbrella sampling are performed in order to determine the nucleation free energy barrier. We find the Gibbs energy profile to be relatively consistent with that predicted by classical nucleation theory; the free energy barrier to nucleation was determined to be ~18 k(B)T and the critical nucleus comprised ~85 ice particles. Growth from the supercooled liquid gives clusters that are predominantly cubic, whilst starting with a pre-formed subcritical nucleus of cubic or hexagonal ice results in the growth of predominantly that phase of ice only.     

Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.     

Formation of spanning water networks on protein surfaces via 2D percolation transition

The formation of spanning hydrogen-bonded water networks on protein surfaces by a percolation transition is closely connected with the onset of their biological activity. To analyze the structure of the hydration water at this important threshold, we performed the first computer simulation study of the percolation transition of water in a model protein powder and on the surface of a single protein molecule. The formation of an infinite water network in the protein powder occurs as a 2D percolation transition at a critical hydration level, which is close to the values observed experimentally. The formation of a spanning 2D water network on a single rigid protein molecule can be described by adapting the cluster analysis of conventional percolation studies to the characterization of the connectivity of the hydration water on the surface of finite objects. Strong fluctuations of the surface water network are observed close to the percolation threshold. Our simulations also furnish a microscopic picture for understanding the specific values of the experimentally observed hydration levels, where different steps of increasing mobility in the hydrated powder are observed.