Structural and morphological dependence of carbon nanotube arrays on catalyst aggregation

Catalyst aggregation affects the growth of carbon nanotube (CNT) arrays in terms of tubular structures, waviness, entanglement, lengths, and growth density etc., which are important issues for application developments. We present a systematic correlation between the aggregation of catalyst on the SiO₂/Si substrate and the structure and morphology of CNT arrays. The thickness of the catalyst film has a direct effect on the areal density of the catalytic particles and then the alignment of the CNT array. Introducing alumina as buffer layer and annealing the catalyst film at low pressure are two effective approaches to downsize the catalyst particles and then the diameter, wall number of the CNTs. Both the size and areal density of the catalyst also change with the CNT growth in accordance with Ostwald ripening process, with the bottom of the CNT array varying from well-aligned to disordered and adhesion between catalyst particles and the substrate getting enhanced. Strategies including tuning the thickness of the catalyst film, changing buffer layer, controlling on the growth time and the system pressure were used to regulate the aggregation of the catalyst. CNT arrays from disordered to well-aligned, from multi-walled to few-walled and further to single-walled were reproducibly synthesized by chemical vapor deposition of acetylene.     

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 ? 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.     

Surface analysis for catalyst layer (PT/PTFE/C) and diffusion layer (PTFE/C) for proton exchange membrane fuel cells systems (PEMFCs)

X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) studies have been used to analyze the surface of diffusion layer (PTFE/C) and catalyst layer (Pt/C/PTFE) of electrode. Detail analysis of carbon C_1s peak showed that the carbon was of the form of C, C-O, CO, CF, CF₂ and CF₃ with CF₂ is more dominated on the surface compared to CF and CF₃. The oxygen O_1s photoelectron peak showed that the oxygen was of the form of CO and C-O. The platinum was of the form of Pt⁰ with some Pt oxidized to PtO. The scanning electron microscopy was used to observe the dispersion of Teflon in the diffusion layer, the distribution of platinum in the catalyst layer loaded with 0.38 mg Pt/cm² and also the cross section of the membrane electrode assembly. The prepared electrode delivers a superior performance compared with the commercial electrode (E-TEK). The difference in performance between the two electrodes is due to the good localization of the platinum particles.     

Constant flux relation for aggregation models with desorption and fragmentation

We study mass fluxes in aggregation models where mass transfer to large scales by aggregation occurs alongside desorption or fragmentation. Two models are considered: (1) a system of diffusing, aggregating particles with influx and outflux of particles (in-out model); and (2) a system of diffusing aggregating particles with fragmentation (chipping model). Both these models can exist in phases where probability distributions are power laws. In these power law phases, we argue that the two point correlation function should have a certain homogeneity exponent. These arguments are based on the exact constant flux scaling valid for simple aggregation with input. Predictions are compared with Monte Carlo simulations.     

Graphical models for statistical inference and data assimilation

In data assimilation for a system which evolves in time, one combines past and current observations with a model of the dynamics of the system, in order to improve the simulation of the system as well as any future predictions about it. From a statistical point of view, this process can be regarded as estimating many random variables which are related both spatially and temporally: given observations of some of these variables, typically corresponding to times past, we require estimates of several others, typically corresponding to future times.

Graphical models have emerged as an effective formalism for assisting in these types of inference tasks, particularly for large numbers of random variables. Graphical models provide a means of representing dependency structure among the variables, and can provide both intuition and efficiency in estimation and other inference computations. We provide an overview and introduction to graphical models, and describe how they can be used to represent statistical dependency and how the resulting structure can be used to organize computation. The relation between statistical inference using graphical models and optimal sequential estimation algorithms such as Kalman filtering is discussed. We then give several additional examples of how graphical models can be applied to climate dynamics, specifically estimation using multi-resolution models of large-scale data sets such as satellite imagery, and learning hidden Markov models to capture rainfall patterns in space and time.     

On pattern formation in a class of traffic models

We consider a simple microscopic follow-the-leader model of N identical cars on a circular road. In the classical setting, a car is not allowed to reach its leader. If it happens at a particular time t_E, we propose to extend the model beyond this time t_E: The idea is to define a physically reasonable leader for each car. Mathematically, the resulting model is a kind of Filippov system. The objective is to study a long time behavior of the model. In case N=3, we observed several invariant patterns which apparently exhibit spatial-temporal symmetries. We managed to classify and identify two kinds of rotating waves. The classification exploits symbolic dynamical notions.     

Statistical mechanics of red blood cell aggregation: The distribution of rouleaux in thermal equilibrium

When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting ofn cells and havingm branch points; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux withn cells in a system containing a total ofN cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.     

Variational approximations for square lattice models in statistical mechanics

This paper concerns a square lattice, Ising-type model with interactions between the four spins at the corners of each face. These may include nearest and next-nearest-neighbor interactions, and interactions with a magnetic field. Provided the Hamiltonian is symmetric with respect to both row reversal and column reversal, a rapidly convergent sequence of variational approximations is obtained, giving the free energy and other thermodynamic properties. For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. The method provides a new definition of corner transfer matrices.     

Statistical equilibrium states and long-time dynamics for a transport equation

Statistical equilibrium states for a linear transport equation were defined in a previous work. We consider here the two-dimensional case: we show that under some mild assumptions these equilibrium states actually describe the long-time dynamics of the system.     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.     

Long-time integration methods for mesoscopic models of pattern-forming systems

Spectral methods for simulation of a mesoscopic diffusion model of surface pattern formation are evaluated for long simulation times. Backwards-differencing time-integration, coupled with an underlying Newton–Krylov nonlinear solver (SUNDIALS-CVODE), is found to substantially accelerate simulations, without the typical requirement of preconditioning. Quasi-equilibrium simulations of patterned phases predicted by the model are shown to agree well with linear stability analysis. Simulation results of the effect of repulsive particle–particle interactions on pattern relaxation time and short/long-range order are discussed.     

Motion and diffusion of a passive scalar in a two-dimensional fluid

The motion of a particle in two dimensions in a fluid is considered. The fluid flow is given and time independent. The complex fluid velocity potential can be viewed as a conformal transformation and after rescaling the time, the motion of the particle is uniform and rectilinear in the absence of diffusion. When diffusion of the particle also takes place the same ideas lead to a useful self-consistent approximation based on the average motion of the particle.     

Pseudo-binary and pseudo-ternary diffusion couple methods for estimation of the diffusion coefficients in multicomponent systems and high entropy alloys

The benefits of using the pseudo-binary and pseudo-ternary diffusion couple methods in multicomponent inhomogeneous systems are demonstrated by estimating different types of composition-dependent diffusion coefficients. These are important for understanding the basic atomic mechanism of diffusion and complex compositional evolutions. These were otherwise considered impossible during the last many decades. Without any options previously, sometimes the average values over a composition range of random choice were estimated, which are not the material constants but depend on the composition range and also the end member compositions. The steps and analyses for utilising the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing the ideal diffusion profiles fulfilling the concepts behind these methods. Following, the discussion is extended to the systems related to medium (Ni-Co-Cr) and high (Ni-Co-Fe-Mn-Al) entropy alloys. In fact, this is the first report showing a correct experimental method that should be followed for the estimation of the interdiffusion and intrinsic diffusion coefficients in inhomogeneous high entropy alloys. In the end, the limitations of following these methods because of the generation of non-ideal diffusion profiles are discussed based on experimental results. The steps are also suggested to avoid such complications. These methods are easy to adopt for research engineers. Most importantly, these give an opportunity to validate the data estimated following newly proposed numerical methods by different groups with experimentally estimated diffusion coefficients, which were not possible earlier.     

Ultrasound assisted synthesis of performic acid in a continuous flow microstructured reactor

The present work establishes in depth study of ultrasound assisted preparation of performic acid (PFA) in a continuous flow microstructured reactor. The influence of various parameters viz. formic acid: hydrogen peroxide molar ratio, flow rate, temperature and catalyst loading on the PFA formation were studied in a continuous flow microstructured reactor. In a continuous microstructured reactor in the presence of ultrasonic irradiation, the formation of PFA was found to be dependent on the molar ratio of formic acid: hydrogen peroxide, flow rate of reactants, temperature and catalyst loading (Amberlite IR-120H). The optimized parameter values are 1:1 M ratio, 50 mL/h, 40 °C and 471 mg/cm³ respectively. Further, the performance of Amberlite IR-120H catalyst was evaluated for three successive cycles in continuous microstructured reactor. The performance of catalyst was found to be decreased with the usage of the catalyst and is attributed to neutralization of the sulfonic acid groups, catalyst shrinkage, or loss in pore sites. The experimental results revealed that, for an ultrasound assisted synthesis of PFA in continuous microstructured reactor the observed reaction time was even less than 10 min. The observed intensification in the PFA synthesis process can be attributed to the intense collapse of the cavities formed at low temperature during ultrasonic irradiations, which further improved the heat and mass transfer rates with the formation of H₂O₂ during the reaction. The combined use of ultrasound and a continuous flow microstructured reactor has proved beneficial process of performic acid synthesis.     

Example of diffusion in a disordered Lorentz gas

We prove a diffusion law for a disordered Lorentz gas obtained by modification of a model of Gates, Gerst, Kac in Ref. 1, even though the motion is not a Markovian one in the technical sense of the word.     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

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.     

The influence of radiation-induced vacancy on the formation of thin-film of compound layer during a reactive diffusion process

A theoretical approach is developed that describes the formation of a thin-film of AB-compound layer under the influence of radiation-induced vacancy. The AB-compound layer is formed as a result of a chemical reaction between the atomic species of A and B immiscible layers. The two layers are irradiated with a beam of energetic particles and this process leads to several vacant lattice sites creation in both layers due to the displacement of lattice atoms by irradiating particles. A- and B-atoms diffuse via these lattice sites by means of a vacancy mechanism in considerable amount to reaction interfaces A/AB and AB/B. The reaction interfaces increase in thickness as a result of chemical transformation between the diffusing species and surface atoms (near both layers). The compound layer formation occurs in two stages. The first stage begins as an interfacial reaction controlled process, and the second as a diffusion controlled process. The critical thickness and time are determined at a transition point between the two stages. The influence of radiation-induced vacancy on layer thickness, speed of growth, and reaction rate is investigated under irradiation within the framework of the model presented here. The result obtained shows that the layer thickness, speed of growth, and reaction rate increase strongly as the defect generation rate rises in the irradiated layers. It also shows the feasibility of producing a compound layer (especially in near-noble metal silicide considered in this study) at a temperature below their normal formation temperature under the influence of radiation.     

Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

We analyze the different degrees of accuracy of two Monte Carlo methods for the simulation of one-dimensional diffusion processes with homogeneous or spatial dependent diffusion coefficient that we assume correctly described by a differential equation. The methods analyzed correspond to fixed and Gaussian steplengths. For a homogeneous diffusion coefficient it is known that the Gaussian steplength generates exact results at fixed time steps Δt. For spatial dependent diffusion coefficients the symmetric character of the Gaussian distribution introduces an error that increases with time. As an example, we consider a diffusion coefficient with constant gradient and show that the error is not present for fixed steplength with appropriate asymmetric jump probabilities.     

Exploring associations between micro-level models of innovation diffusion and emerging macro-level adoption patterns

A micro-level agent-based model of innovation diffusion was developed that explicitly combines (a) an individual’s perception of the advantages or relative utility derived from adoption, and (b) social influence from members of the individual’s social network. The micro-model was used to simulate macro-level diffusion patterns emerging from different configurations of micro-model parameters. Micro-level simulation results matched very closely the adoption patterns predicted by the widely-used Bass macro-level model (Bass, 1969 [1]). For a portion of the p−q$p-q$ domain, results from micro-simulations were consistent with aggregate-level adoption patterns reported in the literature. Induced Bass macro-level parameters p$p$ and q$q$ responded to changes in micro-parameters: (1) p$p$ increased with the number of innovators and with the rate at which innovators are introduced; (2) q$q$ increased with the probability of rewiring in small-world networks, as the characteristic path length decreases; and (3) an increase in the overall perceived utility of an innovation caused a corresponding increase in induced p$p$ and q$q$ values. Understanding micro to macro linkages can inform the design and assessment of marketing interventions on micro-variables–or processes related to them–to enhance adoption of future products or technologies.