Modelling the effect of acoustic waves on the thermodynamics and kinetics of phase transformation in a solution: Including mass transportation.

Effects of acoustic waves on a phase transformation in a metastable phase were investigated in our previous work [S. R. Haqshenas, I. J. Ford, and N. Saffari, "Modelling the effect of acoustic waves on nucleation," J. Chem. Phys. 145, 024315 (2016)]. We developed a non-equimolar dividing surface cluster model and employed it to determine the thermodynamics and kinetics of crystallisation induced by an acoustic field in a mass-conserved system. In the present work, we developed a master equation based on a hybrid Szilard-Fokker-Planck model, which accounts for mass transportation due to acoustic waves. This model can determine the kinetics of nucleation and the early stage of growth of clusters including the Ostwald ripening phenomenon. It was solved numerically to calculate the kinetics of an isothermal sonocrystallisation process in a system with mass transportation. The simulation results show that the effect of mass transportation for different excitations depends on the waveform as well as the imposed boundary conditions and tends to be noticeable in the case of shock waves. The derivations are generic and can be used with any acoustic source and waveform.

A free energy study of carbon clusters on Ir(111): Precursors to graphene growth.

It is widely accepted that the nucleation of graphene on transition metals is related to the formation of carbon clusters of various sizes and shapes on the surface. Assuming a low concentration of carbon atoms on a crystal surface, we derive a thermodynamic expression for the grand potential of the cluster of N carbon atoms, relative to a single carbon atom on the surface (the cluster work of formation). This is derived taking into account both the energetic and entropic contributions, including structural and rotational components, and is explicitly dependent on the temperature. Then, using ab initio density functional theory, we calculate the work of formation of carbon clusters CN on the Ir(111) surface as a function of temperature considering clusters with up to N = 16 C atoms. We consider five types of clusters (chains, rings, arches, top-hollow, and domes), and find, in agreement with previous zero temperature studies, that at elevated temperatures the structure most favoured depends on N, with chains and arches being the most likely at N<10 and the hexagonal domes becoming the most favourable at all temperatures for N>10. Our calculations reveal the work of formation to have a much more complex character as a function of the cluster size than one would expect from classical nucleation theory: for typical conditions, the work of formation displays not one but two nucleation barriers, at around N = 4-5 and N = 9-11. This suggests, in agreement with existing LEEM data, that five atom carbon clusters, along with C monomers, must play a pivotal role in the nucleation and growth of graphene sheets, whereby the formation of large clusters is achieved from the coalescence of smaller clusters (Smoluchowski ripening). Although the main emphasis of our study is on thermodynamic aspects of nucleation, the pivotal role of kinetics of transitions between different cluster types during the nucleation process is also discussed for a few cases as illustrative examples.

Modelling the effect of acoustic waves on nucleation.

A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory.

Effects of rotational symmetry breaking in polymer-coated nanopores.

The statistical theory of polymers tethered around the inner surface of a cylindrical channel has traditionally employed the assumption that the equilibrium density of the polymers is independent of the azimuthal coordinate. However, simulations have shown that this rotational symmetry can be broken when there are attractive interactions between the polymers. We investigate the phases that emerge in these circumstances, and we quantify the effect of the symmetry assumption on the phase behavior of the system. In the absence of this assumption, one can observe large differences in the equilibrium densities between the rotationally symmetric case and the non-rotationally symmetric case. A simple analytical model is developed that illustrates the driving thermodynamic forces responsible for this symmetry breaking. Our results have implications for the current understanding of the behavior of polymers in cylindrical nanopores.

Efficient choice of colored noise in the stochastic dynamics of open quantum systems.

The stochastic Liouville-von Neumann (SLN) equation describes the dynamics of an open quantum system reduced density matrix coupled to a non-Markovian harmonic environment. The interaction with the environment is represented by complex colored noises which drive the system, and whose correlation functions are set by the properties of the environment. We present a number of schemes capable of generating colored noises of this kind that are built on a noise amplitude reduction procedure [Imai et al., Chem. Phys. 446, 134 (2015)CMPHC20301-010410.1016/j.chemphys.2014.11.014], including two analytically optimized schemes. In doing so, we pay close attention to the properties of the correlation functions in Fourier space, which we derive in full. For some schemes the method of Wiener filtering for deconvolutions leads to the realization that weakening causality in one of the noise correlation functions improves numerical convergence considerably, allowing us to introduce a well-controlled method for doing so. We compare the ability of these schemes, along with an alternative optimized scheme [Schmitz and Stockburger, Eur. Phys. J.: Spec. Top. 227, 1929 (2019)1951-635510.1140/epjst/e2018-800094-y], to reduce the growth in the mean and variance of the trace of the reduced density matrix, and their ability to extend the region in which the dynamics is stable and well converged for a range of temperatures. By numerically optimizing an additional noise scaling freedom, we identify the scheme which performs best for the parameters used, improving convergence by orders of magnitude and increasing the time accessible by simulation.

Phase coexistence in colloidal suspensions: an analytic Poisson-Boltzmann treatment.

We solve the linearized Poisson-Boltzmann equation analytically, subject to justifiable approximations, for a suspension containing a large number of identical spherical macroions under conditions of constant surface charge and zero added salt, in order to investigate the phase behavior of charge-stabilized colloidal suspensions. Our results for the electrostatic part of the Helmholtz free energy lead to an interaction which resembles the intermolecular interaction in the theory of molecular fluids. When combined with the ideal gas free energy of the counterions, this produces a van der Waals loop in the pV diagram, indicating coexistence between phases with different densities, for certain values of the macroion radius and charge. We also derive an expression for the surface potential of the macroions, and clarify the interpretation of the Poisson-Boltzmann equation.

Optimization algorithm for rate equations with an application to epitaxial graphene.

We describe an algorithm that searches the parameter space of rate theories to optimize the associated rate coefficients based on a fit to experimental (or any other) data. Beginning with an initial set of parameters, which may be estimated, partially calculated, or indeed random, the algorithm follows a path, calculating the error at each point, until a minimum error is reached. We illustrate our method by correcting a previously proposed rate theory for the nucleation and growth of graphene on Ru(0 0 0 1) and Ir(1 1 1) to account for the temperature dependence of the graphene island density. This quantity shows an exponential decrease as the temperature is raised, in contrast to the power law decrease predicted by conventional nucleation theory, which indicates that a qualitatively different mechanism is operative for graphene island formation. Other applications of our method are also discussed.

Nucleation theorems applied to the Ising model.

We use Monte Carlo simulations to study a single cluster of "up" spins in a sea of "down" spins in the three-dimensional Ising model. We evaluate the growth and decay rates for clusters of different sizes, identify the critical size for which these rates are equal, and obtain the internal energy of the critical size cluster. The results of the simulations at different temperatures and magnetic fields are used together with the first and second nucleation theorems to predict how the cluster nucleation rate changes when the external magnetic field and the temperature are changed. Our results are in agreement with literature values, but our method requires significantly less computational effort than the simulations reported earlier and avoids the difficult evaluation of free energies.

Mixing of atmospheric gas concentrations.

Atmospheric gas concentrations were measured at 1 s intervals in the upper troposphere during a flight through and near the anvil of a storm. The observed very high correlations between the concentrations of CO and CH4 are interpreted as arising from the mixing of two distinct air masses with differing concentrations of each species, and is due to the nearly identical diffusivities of CO and CH4 in air. We find that the correlations depend on the period over which each concentration measurement was made. Correlations in measurements made over short periods decay with time, while correlations over larger scales remain high. We interpret this using a simple mixing model.