Exploring the importance of quantum effects in nucleation: the archetypical Ne(n) case

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne(8) as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability P(s)(b) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%-20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates k(diss) are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomer dissociation energy due to zero point energy effects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for k(diss) seem to follow a common "corresponding states" behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.     

A stochastic simulation of nonisothermal nucleation

The results of stochastic simulations of growth and evaporation of small clusters in vapor are reported. Energy dependent growth rates are determined from the monomer-cluster collision rate and decay rates are found from a detailed balance, with the equilibrium size and energy distribution of clusters calculated using the capillarity approximation and the equilibrium vapor pressure. These rates are used in simulations of two-dimensional random walks in size and energy space to determine the fraction of clusters in supersaturated vapor of size (i(min)+1) that reach a size i(max). By assuming that clusters of size i(min) are in equilibrium, this fraction can be related to the nonisothermal nucleation rate. The simulated rates show good agreement with the previously published analytical results. In the absence of an inert carrier gas, the nonisothermal nucleation rates are typically between 1% and 5% of the isothermal rates.     

Molecular dynamic simulations of atom-cluster collision processes

Monomer-cluster collisions of Lennard-Jones argon atoms have been studied using molecular dynamics simulation for target cluster sizes of 2, 3, 4, 5, 10, and 20 atoms. Capture probability of monomers by clusters and the lifetimes of the resulting clusters have been calculated as a function of impact parameter and the total energy of the target cluster. Cluster lifetime is further integrated over all impact parameters to obtain the average lifetime for each cluster size and energy. The average lifetime of the smallest aggregates is shown to be short compared to the collision time between monomers and clusters unless the vapor is highly supersaturated. The formation probability of a new cluster decreases steeply if a minimum lifetime is required for the cluster.     

Fragmentation dynamics of ammonia cluster ions after single photon ionisation

A reflecting time of flight mass spectrometer (RETOF) is used to study unimolecular and collision induced fragmentation of ammonia cluster ions. Synchrotron radiation from the BESSY electron storage ring is used in a range of photon energies from 9.08 up to 17.7 eV for single photon ionisation of neutral clusters in a supersonic beam. The threshold photoelectron photoion coincidence technique (TPEPICO) is used to define the energy initially deposited into the cluster ions. Metastable unimolecular decay (µs range) is studied using the RETOF's capacity for energy analysis. Under collision free conditions the by far most prominent metastable process is the evaporation of one neutral NH₃ monomer from protonated clusters (NH₃) _{n ? 2}NH ₄ ⁺ . Abundance of homogeneous vs. protonated cluster ions and of metastable fragments are reported as a function of photon energy and cluster size up ton=10.     

Monomer, clusters, liquid: an integrated spectroscopic study of methanol condensation

We have combined static pressure, spectroscopic temperature, Fourier transform infrared spectroscopy (FTIR), and small angle X-ray scattering (SAXS) measurements to develop a detailed picture of methanol condensing from a dilute vapor-carrier gas mixture under the highly supersaturated conditions present in a supersonic nozzle. In our experiments, methanol condensation can be divided into three stages as the gas mixture expands in the nozzle. In the first stage, as the temperature decreases rapidly, small methanol n-mers (clusters) form, increase in concentration, and evolve in size. In the second stage, the temperature decreases more slowly, and the n-mer concentrations continue to rise. Thermodynamic and FTIR experiments cannot, however, definitively establish if the average cluster size is constant or if it continues to increase. Finally, when the vapor becomes supersaturated enough, liquid droplets form via nucleation and growth, consuming more monomer and reducing the concentration of clusters. At the point where liquid first appears, cluster formation has already consumed up to 30% of the monomer. This is significantly more than is predicted by a model that describes the vapor phase as an equilibrium mixture of methanol monomer, dimer, and tetramer. An energy balance suggests that a significant fraction of the cluster population is larger than the tetramer, while preliminary SAXS measurements suggest that these clusters contain, on average, 6 monomers.     

Pinning of size-selected Pd nanoclusters on graphite

The production of stable cluster arrays on smooth surfaces has several potential technological applications. We report a study of the pinning of size-selected palladium nanoclusters on the graphite surface. The clusters formed during gas aggregation in vacuum are projected with sufficient kinetic energy to create a defect in the graphite surface. The energy necessary to create such an immobilizing defect is investigated as a function of the palladium cluster size. The palladium pinning energy is found to deviate from the simple binary collision model as appropriate to previously reported silver and gold results. This finding is in agreement with the deviation of nickel clusters and points to the influence of the interatomic cluster bonding on the mechanics of the collision.     

A comparison of rigid and flexible water models in collisions of monomers and small clusters

In this study we have investigated the dynamics of small water clusters using microcanonical molecular dynamics simulations. The clusters are formed by colliding vapor monomers with target clusters of two and five molecules. The monomers are sampled from a thermal ensemble at T=300 K and target clusters with several total energies are considered. We compare rigid extended simple point charge water with flexible counterparts having intramolecular harmonic bonds with force constants 10(3) and 10(5) kcal(mol A2). We show that the lifetimes of the clusters formed via collision process are similar for the rigid model and the flexible model with the bigger force constant, if the translational temperatures of the target cluster molecules are equal. The model with the smaller force constant results in much longer lifetimes due to the stabilizing effect caused by the kinetic energy transfer into internal vibration of the molecules. This process may take several hundreds of picoseconds, giving rise to time-dependent decay rates of constant-energy clusters. A study of binary collisions of water molecules shows that the introduction of flexibility to the molecules increases the possibility of dimer formation and thus offers an alternative route for dimer production in vapors. Our results imply that allowing for internal degrees of freedom is likely to enhance gas-liquid nucleation rates in water simulations.     

Attachment cross sections of protonated water clusters

The attachment of water molecules onto size selected protonated water clusters has been experimentally investigated. Absolute attachment cross sections are measured as a function of cluster size, collision energy, and initial cluster temperature. Although thermal evaporation is ruled out in our experiment, attachment cross sections become significantly smaller than hard sphere cross sections as the collision energy increases. This feature is attributed to a transition from adiabatic to nonadiabatic regime. It is shown to be due to a dynamical effect: as the collision duration becomes shorter than the typical time required for collision energy redistribution into clusters internal energy, the attachment probability is reduced. We relate this typical time to the period of the main surface vibrational mode excited by the collisions. This hypothesis is further supported by results obtained with deuterated water clusters.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

IR+vacuum ultraviolet (118 nm) nonresonant ionization spectroscopy of methanol monomers and clusters: neutral cluster distribution and size-specific detection of the OH stretch vibrations

Small methanol clusters are formed by expanding a mixture of methanol vapor seeded in helium and are detected using vacuum UV (vuv) (118 nm) single-photon ionization/linear time-of-flight mass spectrometer (TOFMS). Protonated cluster ions, (CH3OH)(n-1)H+ (n=2-8), formed through intracluster ion-molecule reactions following ionization, essentially correlate to the neutral clusters, (CH3OH)n, in the present study using 118 nm light as the ionization source. Both experimental and Born-Haber calculational results clarify that not enough excess energy is released into protonated cluster ions to initiate further fragmentation in the time scale appropriate for linear TOFMS. Size-specific spectra for (CH3OH)n (n=4 to 8) clusters in the OH stretch fundamental region are recorded by IR+vuv (118 nm) nonresonant ion-dip spectroscopy through the detection chain of IR multiphoton predissociation and subsequent vuv single-photon ionization. The general structures and gross features of these cluster spectra are consistent with previous theoretical calculations. The lowest-energy peak contributed to each cluster spectrum is redshifted with increasing cluster size from n=4 to 8, and limits near approximately 3220 cm(-1) in the heptamer and octamer. Moreover, IR+vuv nonresonant ionization detected spectroscopy is employed to study the OH stretch first overtone of the methanol monomer. The rotational temperature of the clusters is estimated to be at least 50 K based on the simulation of the monomer rotational envelope under clustering conditions.     

Fragmentation cross sections of protonated water clusters

We have measured fragmentation cross sections of protonated water cluster cations (H(2)O)(n=30-50)H(+) by collision with water molecules. The clusters have well-defined sizes and internal energies. The collision energy has been varied from 0.5 to 300 eV. We also performed the same measurements on deuterated water clusters (D(2)O)(n=5-45)D(+) colliding with deuterated water molecules. The main fragmentation channel is shown to be a sequential thermal evaporation of single molecules following an initial transfer of relative kinetic energy into internal energy of the cluster. Unexpectedly, that initial transfer is very low on average, of the order of 1% of collision energy. We evaluate that for direct collisions (i.e., within the hard sphere radius), the probability for observing no fragmentation at all is more than 35%, independently of cluster size and collision energy, over our range of study. Such an effect is well known at higher energies, where it is attributed to electronic effects, but has been reported only in a theoretical study of the collision of helium atoms with sodium clusters in that energy range, where only vibrational excitation occurs.     

Collision energy transfer in collision of NH(4) (+)(NH(3))(n-1) (n=3-9) with ND(3)

An incorporation of ND(3) into protonated ammonia cluster ions NH(4)(+)(NH(3))(n-1) (n=3-9), together with a dissociation of the cluster ions, was observed in the collision of the cluster with ND(3) at collision energies ranging from 0.04 to 1.4 eV in the center-of-mass frame. The branching fractions of the cluster ion species produced in the reactions were obtained as a function of the collision energy. The branching fractions of the incorporation products were successfully explained in terms of the Rice-Ramsperger-Kassel (RRK) theory at collision energies lower than the binding energy of the cluster ion. In addition, the internal energy distributions of the parent cluster ions were determined, and found to be in good agreement with those predicted using the evaporative ensemble model. In incorporations at collision energies lower than the binding energy of the cluster ion, all of the collision energy was transferred to the internal energy of the cluster ions; subsequently, an evaporation of ammonia molecules occurred in an equilibrium process after a complete energy redistribution in the clusters. In contrast, at collision energies higher than the binding energy of the cluster ion, a release of an ammonia molecule from the incorporation products occurred in a nonequilibrium process. The transition from the complex mode to the direct mode in the incorporation was observed at collision energies approximately equal to the binding energy. On the other hand, the collision energy dependence of the cross sections for the dissociation and for a nonreactive collision were estimated by a RRK simulation in which the collision energy transfer was interpreted by using the classical hard-sphere collision model. A relationship between reactivity and reaction modes in the collision of NH(4)(+)(NH(3))(4) with ND(3) is discussed via a comparison of the experimental results with the RRK simulation.     

On the statistical nature of collision and surface-induced dissociation: a theoretical investigation of aluminum clusters

The unimolecular dissociation dynamics of aluminum clusters following collision with either a rare gas atom or a surface is investigated by classical trajectory simulations with model potentials. Two conformers of Al(6) with very distinct shapes, i.e., the spherical O(h) and planar C(2)(h) clusters, are considered in this work. The initial vibrational energy and angular momentum distributions resulting from collision, as well as the energy and angular momentum resolved lifetime distributions, of excited clusters were determined for both collision-induced dissociation (CID) and surface-induced dissociation (SID) processes. The partitioning of excitation energy acquired upon collision was found to depend on the excitation mechanism (CID or SID), as well as on the cluster molecular shape, especially in the case of CID. For both types of processes, the energy and angular momentum resolved excited cluster lifetime distributions were found to decay exponentially, in agreement with statistical theories of chemical reactions, suggesting intrinsic Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. Moreover, the simulated microcanonical rate constants determined from the cluster lifetime distributions are in good agreement with the predictions of the orbiting transition state model of phase space theory (OTS/PST), which further supports the statistical character of cluster CID and SID. Thus, in the CID and SID of highly fluxional systems such as aluminum clusters, the rate of intramolecular vibrational energy redistribution (IVR) is much faster than the dissociation rate, which validates one of the key assumptions, i.e., post-collision statistical behavior, underlying the models that are routinely used to determine cluster binding energies from experimental CID/SID cross sections.     

Hydrogen transfer in excited pyrrole-ammonia clusters

The excited state hydrogen atom transfer reaction (ESHT) has been studied in pyrrole-ammonia clusters [PyH-(NH(3))(n)+hnu-->Py.+.NH(4)(NH(3))(n-1)]. The reaction is clearly evidenced through two-color R2P1 experiments using delayed ionization and presents a threshold around 235 nm (5.3 eV). The cluster dynamics has also been explored by picosecond time scale experiments. The clusters decay in the 10-30 ps range with lifetimes increasing with the cluster size. The appearance times for the reaction products are similar to the decay times of the parent clusters. Evaporation processes are also observed in competition with the reaction, and the cluster lifetime after evaporation is estimated to be around 10 ns. The kinetic energy of the reaction products is fairly large and the energy distribution seems quasi mono kinetic. These experimental results rule out the hypothesis that the reaction proceeds through a direct N-H bond rupture but rather imply the existence of a fairly long-lived intermediate state. Calculations performed at the CASSCF/CASMP2 level confirm the experimental observations, and provide some hints regarding the reaction mechanism.     

Vapor Nucleation and Droplet Growth: Cluster Distribution Kinetics for Open and Closed Systems

A theory based on cluster distribution kinetics for single-monomer addition and dissociation is presented as a framework for homogeneous and heterogeneous vapor nucleation and growth dynamics. For continuous cluster and monomer distributions in a well-mixed non-steady-state flow system, population (mass) balance equations yield moment equations for the cluster mass moments. Nuclei are either homogeneously generated or heterogeneously seeded, and subsequent cluster growth occurs by reversible condensation of vapor monomers. The zeroth moment is the number (or moles) of clusters, the first moment is cluster mass, and the second moment gives cluster-size variance. Solutions are proposed for steady-state flow (open) and non-steady-state batch (closed) systems. Experimental data are interpreted by recognizing that droplets typically observed in nucleation experiments have grown much larger than their nuclei. This allows resolution of the large temperature-dependent discrepancy between experiment and classical nucleation theory. Copyright 2000 Academic Press.     

Simulation of cluster impact fusion

We report molecular dynamics simulations of the impact of TiD clusters on TiD targets. In each cluster collision the total fusion probability seems to be due to a single deuterium deuterium collision. The kinetic energies of incident deuterium atoms gradually level off around the initial cluster energy, but do not reach the high energy tail of a corresponding Maxwell-Boltzmann distribution. Neither any other support for a thermonuclear fusion mechanism was observed. On the contrary, our simulations imply that the enhanced fusion rate is rather due to channeled many atom collision cascade type mechanism.     

The role of dimers in evaporation of small argon clusters

Evaporation of small Lennard-Jones argon clusters has been studied using molecular dynamic simulations. An extensive library of clusters with 4, 5, 6, 11, and 21 atoms has been obtained from an earlier study. Analysis of the evaporation properties of the clusters indicate, that the fraction of dimer evaporations of all evaporation events increases with the total energy of the cluster. The fraction of evaporated dimers from clusters with a constant lifetime is independent of the cluster size for short-lived clusters and increases with cluster size for long-lived clusters. Only a few percent of the clusters which are long lived enough to participate in vapor-liquid nucleation decay by emitting dimers. The mean cluster lifetime as a function of total energy shows the same exponentially decreasing trend for monomer and dimer evaporation channels. The fraction of trimer evaporations is found to be vanishingly small.     

Electron trapping by polar molecules in alkane liquids: cluster chemistry in dilute solution

Experimental observations are presented on condensed-phase analogues of gas-phase dipole-bound anions and negatively charged clusters of polar molecules. Both monomers and small clusters of such molecules can reversibly trap conduction band electrons in dilute alkane solutions. The dynamics and energetics of this trapping have been studied using pulse radiolysis-transient absorption spectroscopy and time-resolved photoconductivity. Binding energies, thermal detrapping rates, and absorption spectra of excess electrons attached to monomer and multimer solute traps are obtained, and possible structures for these species are discussed. "Dipole coagulation" (stepwise growth of the solute cluster around the cavity electron) predicted by Mozumder in 1972 is observed. The acetonitrile monomer is shown to solvate the electron by its methyl group, just as the alkane solvent does. The electron is dipole-bound to the CN group; the latter points away from the cavity. The resulting negatively charged species has a binding energy of 0.4 eV and absorbs in the infrared. Molecules of straight-chain aliphatic alcohols solvate the excess electron by their OH groups; at equilibrium, the predominant electron trap is a trimer or a tetramer, and the binding energy of this solute trap is ca. 0.8 eV. Trapping by smaller clusters is opposed by the entropy that drives the equilibrium toward the electron in a solvent trap. For alcohol monomers, the trapping does not occur; a slow proton-transfer reaction occurs instead. For the acetonitrile monomer, the trapping is favored energetically, but the thermal detachment is rapid (ca. 1 ns). Our study suggests that a composite cluster anion consisting of a few polar molecules imbedded in an alkane "matrix" might be the closest gas-phase analogue to the core of solvated electron in a neat polar liquid.     

钯团簇碰撞沉积钯/银基板的分子动力学模拟

运用分子动力学模拟方法研究了常温下较大的钯团簇以不同初始速度撞击不同硬度基板的微观过程,着重分析了沉积形貌的变化、团簇的嵌入深度和原子的扩散程度、基板碰撞接触区域的温度演变以及碰撞过程中团簇与基板间的能量转化,获得了沉积过程中变形形貌、结构特征及能量转化随团簇尺寸、初始速度及基板材质的变化规律.并进一步探究了第二颗团簇以不同时刻沉积时前一团簇的变形形貌及基板接触区域温度变化的特点,发现短时间间隔下第二颗团簇的沉积更有利于团簇与基板的结合.