Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics

Fluctuations and scaling in models for particle aggregation

We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to diffuse up to \ell steps. Therefore the second model incorporates more fluctuations than the first, but still less than usual (Full Diffusion) models of deposition and diffusion on a crystal surface. We study the time dependence of the average densities of atoms and islands and the island size distribution. The Sequential Diffusion model displays a nontrivial steady-state regime where the island density increases and the island size distribution obeys scaling, much in the same way as the standard Full Diffusion model for epitaxial growth. Our results also allow to gain insight into the role of different types of fluctuations.Comment: 25 pages. Minor changes in the main text and in some figures. Accepted for publication in Surface Scienc

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion systemwith cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface

Novel diffusion mechanism on the GaAs(001) surface: the role of adatom-dimer interaction

Employing first principles total energy calculations we have studied the behavior of Ga and Al adatoms on the GaAs(001)-beta2 surface. The adsorption site and two relevant diffusion channels are identified. The channels are characterized by different adatom-surface dimer interaction. Both affect in a novel way the adatom migration: in one channel the diffusing adatom jumps across the surface dimers and leaves the dimer bonds intact, in the other one the surface dimer bonds are broken. The two channels are taken into account to derive effective adatom diffusion barriers. From the diffusion barriers we conclude a strong diffusion anisotropy for both Al and Ga adatoms with the direction of fastest diffusion parallel to the surface dimers. In agreement with experimental observations we find higher diffusion barriers for Al than for Ga.Comment: 4 pages, 2 figures, Phys. Rev. Lett. 79 (1997). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Surface and interstitial Ti diffusion at the rutile TiO2(110) surface

Diffusion of Ti through the TiO2 (110) rutile surface plays a key role in the growth and reactivity of TiO2. To understand the fundamental aspects of this important process, we present an analysis of the diffusion of Ti adspecies at the stoichiometric TiO2(110) surface using complementary computational methodologies of density functional theory corrected for on-site Coulomb interactions (DFT+U) and a charge equilibration (QEq) atomistic potential to identify minimum energy pathways. We find that diffusion of Ti from the surface to subsurface (and vice versa) follows an intersticialcy exchange mechanism, involving exchange of surface Ti with the 6-fold coordinated Ti below the bridging oxygen rows. Diffusion in the subsurface between layers also follows an interstitialcy mechanism. The diffusion of Ti is discussed in light of continued attempts to understand the re-oxidation of non-stoichiometric TiO2(110) surfaces

Nothing moves a surface: vacancy mediated surface diffusion

We report scanning tunneling microscopy observations, which imply that all atoms in a close-packed copper surface move frequently, even at room temperature. Using a low density of embedded indium `tracer' atoms, we visualize the diffusive motion of surface atoms. Surprisingly, the indium atoms seem to make concerted, long jumps. Responsible for this motion is an ultra-low density of surface vacancies, diffusing rapidly within the surface. This interpretation is supported by a detailed analysis of the displacement distribution of the indium atoms, which reveals a shape characteristic for the vacancy mediated diffusion mechanism that we propose.Comment: 4 pages; for associated movie, see http://www-lion.leidenuniv.nl/sections/cm/groups/interface/projects/therm

Long-timescale simulations of H2_2O admolecule diffusion on Ice Ih(0001) surfaces

Long-timescale simulations of the diffusion of a H$_2$O admolecule on the (0001) basal plane of ice Ih were carried out over a temperature range of 100 to 200 K using the adaptive kinetic Monte Carlo method and TIP4P/2005f interaction potential function. The arrangement of dangling H atoms was varied from the proton-disordered surface to the perfectly ordered Fletcher surface. A large variety of sites was found leading to a broad distribution in adsorption energy at both types of surfaces. Up to 4 % of the sites on the proton-disordered surface have an adsorption energy exceeding the cohesive energy of ice Ih. The mean squared displacement of a simulated trajectory at 175 K for the proton-disordered surface gave a diffusion constant of 6$\cdot$10$^{-10}$ cm$^2$/s, consistent with an upper bound previously reported from experimental measurements. During the simulation, dangling H atoms were found to rearrange so as to reduce clustering, thereby approaching a linear Fletcher type arrangement. Diffusion on the perfectly ordered Fletcher surface was estimated to be significantly faster, especially in the direction along the rows of dangling hydrogen atoms. From simulations over the range in temperature, an effective activation energy of diffusion was estimated to be 0.16 eV and 0.22 eV for diffusion parallel and perpendicular to the rows, respectively. Even a slight disruption of the rows of the Fletcher surface made the diffusion isotropic.Comment: 24 pages, 8 figures, 1 tabl

Oblique evaporation and surface diffusion

The special structure of obliquely evaporated films has its origin in shadowing phenomena during film growth. Because of shadowing, the film consists of bundles of inclined columns with the bundles being aligned perpendicularly to the vapour incidence direction. The column inclination angle lies between the film normal and the vapour incidence direction. Different models found in literature relating process parameters and film structure are discussed. It is found that surface diffusion plays an important role, especially with regard to the difference between random and directional surface diffusion. The latter is induced by the oblique evaporation process. A quantitative expression is given for the relation between process conditions and surface diffusion including the influence of substrate temperature, rate and contamination with residual gasses. Using these models and adding our new calculations, the relation between surface diffusion and film structure is discussed in detail and found to be consistent with measurements published in the literature

Adsorption of pentachlorophenol onto activated carbon in a fixed bed : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology in Environmental Engineering at Massey University

The adsorption of pentachlorophenol (PCP) from water onto granular activated carbon (GAC) was studied. Equilibrium and kinetic behaviour was studied, and the results used to predict fixed bed adsorber behaviour. Batch equilibrium tests showed that the adsorption capacity of activated carbon for PCP is best represented by the Freundlich isotherm, with constants of K = 95 and 1/n = 0.18. Batch adsorption kinetics experiments were conducted in a spinning basket reactor. Surface diffusion and external film transfer coefficients were determined by fitting the homogeneous surface diffusion model (HSDM) to the experimental batch adsorption data. A surface diffusion coefficient value of 2.26 x 10-9cm/s was calculated using this method, which was similar to surface diffusion coefficients for similar compounds found by other investigators. Using equilibrium and kinetic parameters, the HSDM was used to predict bench scale fixed bed adsorber breakthrough curves at varying flow rates. A correlation was used to calculate the film transfer coefficient. There was a good agreement between the experimental breakthrough curves and those predicted by the model. By varying parameters in the model it was found that the adsorption rate in the PCP-activated carbon system was primarily limited by surface diffusion. The homogeneous surface diffusion model was shown to be effective in predicting breakthrough of PCP and could conceivably be used to predict full scale adsorber performance or to aid pilot plant studies