Adsorption and nucleation on smooth surfaces

The nucleation and growth of condensate nuclei on smooth surfaces, e.g., an immiscible liquid or a smooth solid, can occur both by the direct addition of molecules from the vapor and from those adsorbed on the substrate. We show how to generalize nucleation theory to allow for the simultaneous occurrence of both mechanisms. The vapor-condensate-substrate interfacial forces, the contact angle, the critical supersaturation, and the coefficient in the adsorption isotherm are different ways of expressing the affinity between vapor molecules and the substrate surface. The critical supersaturations for nucleation on the surface of an immiscible liquid and nucleation on the surface of a perfectly smooth solid are predicted in terms of these parameters and the relationships among them. For most values of these parameters we find that adsorbed molecules are usually far more important to the nucleation process than those in the vapor phase.     

Self-avoiding random walks on the hexagonal lattice

We use the algorithm recently introduce by A. Berretti and A. D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. We find=1.3509±0.0057±0.0023v=0.7580±0.0049±0.0046=0.519±0.082±0.077 where the first error is the systematic one due to corrections to scaling and the second is the statistical error. For the effective coordination number we find=1.84779±0.00006±0.0017 The results support the Nienhuis conjecture=43/32 and provide a rough numerical check of the hyperscaling relationdv=2–. An additional analysis, taking the Nienhuis value of=(2+2^1/2)^1/2 for granted, gives=1.3459±0.0040±0.0008     

Cooperation under institutional incentives with perfect and imperfect observation

Understanding the evolution of cooperation is a challenging topic in various realms. Increasing attention has been paid to exploring the effects of incentives on the emergence of cooperation. Most of the extant studies have implicitly assumed that the cost of incentives is fixed and independent of the individual's payoff. In human societies, taxation is one important source of funds for supporting the government of individuals and nearly involves everyone. Inspired by this phenomenon, we institute an analytic model where the incentives are established based on the tax regime. Individuals play the prisoner's dilemma game and the ones whose payoffs are greater than zero have to contribute a part as taxes to establish an institution to monitor individuals' behaviors and execute incentives. We investigate the emergence of cooperation under the institutional incentives and make a comparative analysis between reward and punishment subject to the perfect and imperfect environment.     

Discretons: Discrete compactons on a hexagonal lattice

We study the formation and interaction of discretons, solitary waves with an almost compact support (tails decaying at a super-exponential rate), on a hexagonal lattice and its spatial extension. Discretons are shown to be robust and their interaction though not entirely, is quite clean.     

Instability of vibrational modes in hexagonal lattice

The phenomenon of modulational instability is investigated for all four delocalized short-wave vibrational modes recently found for the two-dimensional hexagonal lattice with the help of a group-theoretic approach. The polynomial pair potential with hard-type quartic nonlinearity (β-FPU potential with β > 0) is used to describe interactions between atoms. As expected for the hard-type anharmonic interactions, for all four modes the frequency is found to increase with the amplitude. Frequency of the modes I and III bifurcates from the upper edge of the phonon spectrum, while that of the modes II and IV increases from inside the spectrum. It is also shown that the considered model supports spatially localized vibrational mode called discrete breather (DB) or intrinsic localized mode. DB frequency increases with the amplitude above the phonon spectrum. Two different scenarios of the mode decay were revealed. In the first scenario (for modes I and III), development of the modulational instability leads to a formation of long-lived DBs that radiate their energy slowly until thermal equilibrium is reached. In the second scenario (for modes II and IV) a transition to thermal oscillations of atoms is observed with no formation of DBs.     

Computer simulation of water vapor nucleation on charged nanoparticles

The Monte Carlo method is applied to the study of the formation of condensed-phase nuclei from water vapor on electrically charged silver iodide nanocrystals. This study is a continuation of the investigations carried out earlier in [1] with electrically neutral nucleation centers. Nanoparticles with a size of up to 4 nm and flat nanoparticles with a size of up to 10 nm are investigated. The free energy, entropy, and the work of formation of nuclei with a size of up to 6729 molecules are calculated at the atomic level by the bicanonical statistical ensemble (BSE) method at a temperature of 260 K. Thermodynamic stability of nuclei is investigated depending on the size, shape, and charge of nanocrystal nucleation centers, as well as depending on the presence of crystal defects and the degree of spatial localization of charge on the surface of nanoparticles. The excess charge has a crucial effect on the work of formation of a nucleus only in the case of strong spatial localization of the latter near a point crystal defect; however, this effect is restricted to a relatively small size of the nuclei and therefore cannot substantially enhance the ice-forming activity of nanoparticles. A nucleus that grows on the surface of a nanoparticle evolves through three stages that differ in molecule retention mechanism and thermodynamic stability. The charge of a nanoparticle has a small effect on these factors. The leading factor that determines the ice-forming activity of ion nanocrystals is their intrinsic electric field due to the nonuniform distribution of charge within a unit cell of the crystal lattice.     

Thermodynamics of supersaturated vapor nucleation on molecular condensation nuclei

A key problem in the theory of a supersaturated vapor nucleation on molecular condensation nuclei (namely, the work of formation and the equilibrium concentrations of clusters) is considered. To calculate these quantities using the structural models of clusters, which are better suited for this purpose than the classical droplet model, we derive the equation connecting the work of transfer of a molecular condensation nucleus from the gas phase to a homogeneous cluster with a change in the number of contacts between molecules, occurring in the course of this transfer, and with the work of rupture of individual contacts.     

Simulation of supersaturated vapor nucleation on molecular condensation nuclei

The results of model calculations of nucleation of di(2-ethylhexyl)sebacate (DEHS) supersatu-rated vapor on FeO molecules based of the simplest structural models of clusters are considered. The earlier conclusion that the allowance for the escape of a molecular condensation nucleus (MCN) from a cluster weakly affects the results of analysis of nucleation on a MCN is confirmed. It is found that the interaction of electric charges of the FeO molecule and the ester groups of the DEHS molecule plays the important role in the DEHS nucleation. The importance of the strength of the bond between the MCN and the first condensate molecule is established. The strength of this bond considerably affects the coefficient of conversion of the MCN into aerosol particles as well as the form of the dependence of this quantity on the spontaneous condensation background.     

The adsorption-induced thermal step-bunching on the hexagonal lattice system

We present restricted solid-on-solid model coupled with Ising system (RSOS-I model) on the hexagonal system. Without long-range interaction such as elastic interaction, the adsorption-induced thermal step-bunching is obtained by the Monte Carlo calculation on the hexagonal RSOS-I model.     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Specifics of nucleation in superheated water and supersaturated vapor

This work is dedicated to the experimental studying of the nucleation kinetics in superheated water and supersaturated water vapor. A percolation model for the liquid water structure that explains a number of anomalous thermophysical properties of water and water vapor in the metastable region is proposed.     

Numerical simulation of water vapor nucleation on electrically neutral nanoparticles

Atomic-level Monte Carlo simulations are performed to calculate the free energy, entropy, and work of nucleation for clusters of more than 6 × 10³ water molecules growing on silver iodide crystalline particles of size up to 4 nm at a temperature of 260 K. The Hamiltonian of the system includes explicit expressions for hydrogen bonding energy and Coulomb, dispersion, exchange, and polarization interactions. The work of nucleation exhibits complex behavior depending on the nucleation-site size. With increasing nanoparticle size, clusters become less stable and the probability of crystallization increases. Mutual polarization enhances the bonding between a cluster and a crystalline particle. Cluster growth on relatively large nanoparticles involves two stages characterized by two critical sizes: monolayer growth on the surface and growth normal to the surface. Spontaneous microdroplet polarization involving domain formation is found to occur at the crystal surface. The dependence of the ice-forming activity of an aerosol on particulate size observed in experiments is explained by combined effects of several competing factors, the dominant ones being the stabilizing and destabilizing effects of the nanoparticle electric field.     

A partition function model for nucleation on surfaces

Using a procedure to minimize the total Helmholtz free energy of a system composed of an idealized substrate, a collection of surface clusters, and a vapor in contact with the surface, an expression is derived for the concentration of clusters of a given size on the substrate. The result is based on several assumptions about the system, the most important being that the surface clusters do not interact and that the substrate remains intact. The expression for the concentration of surface clusters together with the conventional form for the growth rate of clusters on a surface can be used to calculate surface nucleation rates.     

Self-intersection numbers and random surfaces on the lattice

String theory in four dimensions has the unique feature that a topological term, the oriented self-intersection number, can be added to the usual action. It has been suggested that the corresponding theory of random surfaces would be free from the problem encountered in the scaling of the string tension. Unfortunately, in the usual dynamical triangulation it is not clear how to write such a term. We show that for random surfaces on a hypercubic lattice however, the analogue of the oriented self-intersection number I[σ] can be defined and computed in a straightforward way. Furthermore, I[σ] has a genuine topological meaning in the sense that it is invariant under the discrete analogue of continuous deformations. The resulting random surface model is no longer free and may lead to a non-trivial continuum limit.     

Self-avoiding and planar random surfaces on the lattice

We study models of self-avoiding (SARS) and of planar (PRS) random surfaces on a (hyper-) cubic lattice. If N_γ(A) is the number of such surfaces with given boundary γ and area A, then N_γ(A) = exp(β₀A + o(A)), where β₀ is independent of γ. We prove that, for β > β₀, the string tension is finite for the SARS model and strictly positive for the PRS model and that in both models the correlation length (inverse mass) is positive and finite. We discuss the possibility of the existence of a critical point and of a roughening transition. Estimates on intersection probabilities for random surfaces and connections with lattice gauge theories are sketched.     

原子模拟钛中微孔洞的结构及其失效行为

六角金属由于其各向异性等特点,在塑性变形等过程中容易产生形状和构型都相对复杂的点缺陷团簇.这些团簇之间及其与运动位错等缺陷的相互作用直接影响材料的物理和力学性能.然而对相关问题的原子尺度、尤其是空位团簇的演化和微孔洞的形成乃至裂纹形核扩展等的理解还不全面.本文采用激发弛豫算法结合第一原理及原子间作用势,系统考察了钛中的空位团簇构型及不同构型间的相互转变,给出了不同尺寸空位团簇的稳定和亚稳构型、空位团簇合并分解和迁移的激发能垒等关键参数,发现较小的空位团簇形成稳定构型,较大的空位团簇呈现出空间对称分布趋势进而形成微孔洞;采用高通量分子动力学模拟系统研究了不同尺寸的空位团簇在拉应力作用下对变形过程的影响,发现这些空位团簇可以形成层错,并对微裂纹的形核产生影响.