Fracture patterns generated by diffusion controlled volume changing reactions

A simple two-dimensional model was developed for the growth of fractures in a chemically decomposing solid. Simulations were carried out under rapid chemical decomposition conditions for which the kinetics of fracture growth is controlled by diffusion of the volatile reaction product or the kinetics of evaporation. The growth of the fracture pattern is self-sustaining due to the volume reduction associated with the decomposition process. Consistent with the theoretical analysis of Yakobson [Phys. Rev. Lett. 67, 1590 (1991)10.1103/PhysRevLett.67.1590], the fracture front propagates with a constant velocity v approximately=k2/3(Dl0)1/3 under evaporation controlled conditions and v approximately=D/l0 under diffusion controlled conditions, where k is the evaporation rate constant, D is the diffusion constant for the volatile reaction product in the solid, and l0 is the critical stable crack length. Under diffusion controlled conditions, the front width w scales as w approximately=(kl0/)D.     

Rates of diffusion controlled reactions for one-dimensionally-moving species in 3D space

ABSTRACT

The asymmetry in diffusion dimensionality between self-interstitial atom (SIA) clusters and vacancies is a fundamental feature of irradiation damage in crystals, leading to a defect buildup imbalance that manifests itself as measurable dimensional and mechanical property changes. It is well known that, while vacancies and mobile vacancy clusters diffuse in a three-dimensional (3D) fashion, SIA clusters perform one-dimensional motion along mostly rectilinear trajectories. Despite this, a complete set of kinetic coefficients, including coagulation reaction rates and sink strengths, does not exist for 1D-moving objects. In this paper, we derive analytical expressions for these coefficients from continuum diffusion theory particularised to 1D motion. Moreover, we carry out kinetic Monte Carlo simulations of numerical replicas of the geometry of diffusing particles and sinks to validate the proposed solutions. Our simulations, which are conducted entirely independently from the analytical derivations, reveal excellent agreement with the proposed expressions, adding confidence to their validity. We compare the 1D and 3D cases and discuss their relevance for kinetic codes for damage accumulation calculations.     

Fusion hindrance in the neck evolution of symmetric nuclear reactions

Fusion hindrance in the radial degree of freedom for massive nuclear reactions is known for a long time. However the present work shows that the fusion hindrance also exists in the neck evolution. We calculate the potential at different distances and different neck parameters by the two-center liquid drop model and then check whether fusion hindrance exists in the neck evolution by examing the sign of slope of potential vs. the neck parameter. The area of fusion hindrance in the neck evolution is shown.     

Analysis of the fusion hindrance in mass-symmetric heavy ion reactions

The fusion hindrance,which is also denominated by the term extra-push,is studied on mass-symmetric systems by the use of the liquid drop model with the two-center parameterization.Following the idea that the fusion hindrance exists only if the liquid drop barrier(saddle point) is located at the inner side of the contact point after overcoming the outer Coulomb barrier,the reactions in which two barriers are overlapped with each other are determined.It is shown that there are many systems where the fusion hi...     

Steric hindrance in cationic and neutral rhodamine 6 G molecules adsorbed on Au nanoparticles

The adsorption of cationic and neutral R6G molecules on Au nanoparticles was elucidated by surface enhanced Raman scattering (SERS). The steric hindrance at hydroethyl amino (‐N(H)Et) groups in R6G was evidenced by the observation that R6G⁺ adsorb on as‐prepared gold nanoparticles (AuNPs) only with electrostatic forces, in contrast to the electrostatic and chemical adsorption of R123⁺ with dihydro amino (‐NH₂) groups on as‐prepared AuNPs. Large steric hindrance at the amino groups in R6G yielded saturated coverage of 700 molecules/AuNP for R6G⁺ significantly fewer than 1000 molecules/AuNP for R123⁺. In addition, neutral R6G⁰ on AuNPs showed markedly enhanced peaks at 1200–1600 cm⁻¹, which were not observed in Raman spectra of R6G⁰ in bulk solution, and also in SERS of R6G⁺ on AuNPs. These bands are attributed to vibrational modes of an outer phenyl ring and ethyl amino groups, which are vertical to a xanthene plane, on the basis of theoretical analysis of molecular vibrations. Thus, Raman scattering of these bands is enhanced under an inclined orientation of R6G⁰ molecules chemisorbed on AuNPs via lone pair electrons at amino groups. Copyright © 2013 John Wiley & Sons, Ltd.     

Lattice theory of diffusion reactions

The problem of diffusion-limited reactions is treated in lattice theory. We calculate the probability that a mobile interstitial by jump diffusion reaches a site of the recombination region around a vacancy (assumed to be given) if it starts at a distanceR _p from the vacancy. We show that the continuum treatment with the recombination region represented by a spherical volume with an effective recombination radiusR _a is a good approximation even for small regions and short diffusion paths. We give an explicit expression forR _a in terms of the Green's function for stationary diffusion. The results for cubic lattices are discussed for recombination regions containing 1 to about 100 sites. As a rule of thumb we find that the effective recombination radiusR _a is equal to the average distance \(\bar R\) of the surface sites from the recombination center.     

Theory of diffusion controlled growth

We present a new theoretical framework for diffusion limited aggregation and associated dielectric breakdown models in two dimensions. Key steps are understanding how these models interrelate when the ultraviolet cutoff strategy is changed, the analogy with turbulence and the use of logarithmic field variables. Within the simplest, Gaussian, truncation of mode-mode coupling, all properties can be calculated. The agreement with prior knowledge from simulations is encouraging, and a new superuniversality of the tip scaling exponent is both predicted and confirmed.     

Growth instability in diffusion controlled polymerization

We report the observation of a sharp transition in the structure of polypyrrole prepared via diffusion controlled polymerization in a quasi-two dimensional electrochemical cell. As the oxidation potential is increased, the fractal dimension drops sharply from values near 2 (compact structures) to 1 as the growth becomes dendritic. At higher potentials, where the polymerization becomes diffusion limited, a continuum of structures is observed as the dendrites become irregular and the fractal dimension increases to 1.74+-0.01. The mean branch angle was also measured and found to decrease from 90° at the point of dendritic growth, to 45° at high potential.     

Positronium quenching reactions and diffusion in solutions

The temperature effect on positronium quenching rates for p-benzoquinone and iodine in several solvents was determined. The quenching rate constantk ₁ follows ak ₁∝1/η relationship better than thek ₁∝T/η one, predicted by ordinary theory. A simple theoretical treatment based on diffusion theory shows that the temperatureT of the solute, positronium, may not be the same as the temperature of the solvent if the positronium is not fully thermalized. This temperature is found to be about twice the room temperature for the solvents investigated. The findings further support the theory that positronium reactions are “diffusion controlled” in liquid solutions. The activation energies of all the positronium reactions studied are either negligible or less than 0.1 eV.     

On kinetics of reactions limited by surface diffusion

An analysis is given of the unsteady-state kinetics of the catalytic reaction limited by surface diffusion of reactants to active sites. The following assumptions are used: the surface is uniform, adsorption/desorption processes are absent, the diffusion coefficient is dependent on coverage. It is shown that the reaction rate is determined primarily by the maximal value of the diffusion coefficient, the dependence of the diffusion coefficient on coverage leads to nonexponential reaction kinetics.     

Advanced diffusion studies with isotopically controlled materials

The use of enriched stable isotopes combined with modern epitaxial deposition and depth profiling techniques enables the preparation of material heterostructures, highly appropriate for self- and foreign-atom diffusion experiments. Over the past decade we have performed diffusion studies with isotopically enriched elemental and compound semiconductors. In the present paper, we highlight our recent results and demonstrate that the use of isotopically enriched materials ushered in a new era in the study of diffusion in solids, which yields greater insight into the properties of native defects and their roles in diffusion. Our approach of studying atomic diffusion is not limited to semiconductors and can be applied also to other material systems. Current areas of our research concern the diffusion in the silicon-germanium alloys and glassy materials such as silicon dioxide and ion conducting silicate glasses.     

Computation of the hindrance factor for the diffusion for nanoconfined ions: molecular dynamics simulations versus continuum-based models

We report the self-diffusion coefficients and hindrance factor for the diffusion of ions into cylindrical hydrophilic silica nanopores (hydrated silica) determined from molecular dynamics (MD) simulations. We make a comparison with the hindered diffusion coefficients used in continuum-based models of nanofiltration (NF). Hindrance factors for diffusion estimated from the macroscopic hydrodynamic theory were found to be in fair quantitative agreement with MD simulations for a protonated pore, but they strongly overestimate diffusion inside a deprotonated pore.     

Anomalous scaling in systems partially controlled by diffusion

We study the nature of anomalous scaling in several systems partially controlled by diffusion. We quantify the departure from Fickian scaling by means of an apparent exponent governing the scaling of long-time behavior with system size. We find that anomalous scaling should be expected whenever complex geometries, higher dimensionality, or time-dependent boundary conditions are encountered.     

Mathematics of diffusion controlled precipitates with time-dependent boundary conditions

The boundary value problem of diffusion controlled precipitation with time-dependent boundary conditions is treated by an extension of the conventional eigenfunction expansion method. In this approach, expansion coefficients and eigenvalues become functions of time and eigenfunctions become functions of space and time. Mathematical techniques to determine the relevant quantities are set forth and the general solution describing precipitate growth under time-dependent conditions is obtained. The general solution is applied to the precipitation of plates and spheres and the growth of radii as a function of time is determined. In the latter case, comparisons are made with conventional methods and the fractional error for a particle to reach half its equilibrium is estimated.