Diffusion-limited Regime Research Articles

Single- and double-walled boron nitride nanotubes: Controlled synthesis and application for water purification

Research interest in boron nitride nanotubes (BNNTs) has increased after the recent success of large-scale BNNT syntheses using high-temperature-pressure laser ablation or high-temperature plasma methods. Nonetheless, there are limits to the application and commercialization of these materials because of the difficulties associated with their fine structural control. Herein, the growth kinetics of BNNTs were systemically studied for this purpose. The growth pressure of the nitrogen feed gas was varied while the growth temperature remained constant, which was confirmed by black body radiation measurements and calculations based on a heat loss model. Changing from the diffusion-limited regime to the supply-limited regime of growth kinetics based on the optimized BNNT synthesis condition afforded the control of the number of BNNT walls. The total amount of BNNTs possessing single and double walls was over 70%, and the BNNT surface area increased to 278.2 m2/g corresponding to small wall numbers and diameters. Taking advantage of the large surface area and high-temperature durability of the material, BNNTs utilized as a recyclable adsorbent for water purification. The efficiency of the BNNTs for capturing methylene blue particles in water was approximately 94%, even after three repetition cycles, showing the potential of the material for application in the filter industry.

Time-Resolved Dynamics of Struvite Crystallization: Insights from the Macroscopic to Molecular Scale.

The crystallization of magnesium ammonium phosphate hexahydrate (struvite) often occurs under conditions of fluid flow, yet the dynamics of struvite growth under these relevant environments has not been previously reported. In this study, we use a microfluidic device to evaluate the anisotropic growth of struvite crystals at variable flow rates and solution supersaturation. We show that bulk crystallization under quiescent conditions yields irreproducible data owing to the propensity of struvite to adopt defects in its crystal lattice, as well as fluctuations in pH that markedly impact crystal growth rates. Studies in microfluidic channels allow for time-resolved analysis of seeded growth along all three principle crystallographic directions and under highly controlled environments. After having first identified flow rates that differentiate diffusion and reaction limited growth regimes, we operated solely in the latter regime to extract the kinetic rates of struvite growth along the [100], [010], and [001] directions. In situ atomic force microscopy was used to obtain molecular level details of surface growth mechanisms. Our findings reveal a classical pathway of crystallization by monomer addition with the expected transition from growth by screw dislocations at low supersaturation to that of two-dimensional layer generation and spreading at high supersaturation. Collectively, these studies present a platform for assessing struvite crystallization under flow conditions and demonstrate how this approach is superior to measurements under quiescent conditions.

Suspended state heteroaggregation kinetics of kaolinite and fullerene (nC60) in the presence of tannic acid: Effect of π-π interactions

The colloidal heteroassociation between natural mineral colloids and engineered nanoparticles (ENPs) can reduce the bioavailability and toxicity of the ENPs. However, the efficacy of this heteroassociation-based entrapment of ENPs depends on the intrinsic material properties of the particles and the physicochemical parameters of the aquatic environment. Natural organic matter (NOM)-induced surface modifications of clay colloids, functionalization of ENPs, and efficiency of counterions as effective coagulants profoundly affect the effectiveness of heteroaggregation-based attenuation of anthropogenic colloids. In this study, tannic acid (TA), a surrogate of NOM, prevented the edge-to-face self-association of sodium-saturated kaolinite (Na-kaolinite) at acidic pH, as evaluated from the transverse proton spin–spin relaxation data (T2). Likewise, fullerene water suspension (FWS) adhesion to Na-kaolinite prevented the self-association of Na-kaolinite and enhanced the colloidal stability. At pH 4 and diffusion-limited aggregation regime salt concentrations, the Na-kaolinite and FWS heteroaggregation rates were lower than the Na-kaolinite homoaggregation rates, and eventually reached a plateau. The higher colloidal stability of the Na-kaolinite and FWS binary mixture than that of Na-kaolinite, regardless of stronger charge screening by Ca2+, reflects steric stabilization. However, at pH 7, the increased electrostatic barrier reduces the feasibility of colloidal heteroassociation between Na-kaolinite and FWS; thus, higher salt concentrations are required to initiate aggregation. Weak adsorption of TA on Na-kaolinite at pH 7 facilitated stronger π-π interactions with FWS. All suspensions exhibited faster aggregate growth at pH 7 than pH 4, possibly due to the stronger cation response at pH 7. In situ atomic force microscopy imaging and line profile plots of Na-kaolinite, TA, and FWS mixture in CaCl2 further corroborated the difference in the heteroaggregation rates observed at the two different pH values. Thus, TA-induced surface functionalization of FWS and the consequent increased electrostatic barrier to heteroassociation with Na-kaolinite may facilitate the environmental mobility of FWS in aquatic media.

The generality of transient compartmentalization and its associated error thresholds

Can prelife proceed without cell division? A recently proposed mechanism suggests that transient compartmentalization could have preceded cell division in prebiotic scenarios. Here, we study transient compartmentalization dynamics in the presence of mutations and noise in replication, as both can be detrimental the survival of compartments. Our study comprises situations where compartments contain uncoupled autocatalytic reactions feeding on a common resource, and systems based on RNA molecules copied by replicases, following a recent experimental study.Using the theory of branching processes, we show analytically that two regimes are possible. In the diffusion-limited regime, replication is asynchronous which leads to a large variability in the composition of compartments. In contrast, in a replication-limited regime, the growth is synchronous and thus the compositional variability is low. Typically, simple autocatalysts are in the former regime, while polymeric replicators can access the latter.For deterministic growth dynamics, we introduce mutations that turn functional replicators into parasites. We derive the phase boundary separating coexistence or parasite dominance as a function of relative growth, inoculation size and mutation rate. We show that transient compartmentalization allows coexistence beyond the classical error threshold, above which the parasite dominates. Our findings invite to revisit major prebiotic transitions, notably the transitions towards cooperation, complex polymers and cell division.

Reversible aggregation of particles with short oligomeric sidechains at the surface studied with Langevin dynamics

We investigate nanoscopic aggregation of asphaltene nanoaggregates by means of Brownian dynamics simulations. Nanoaggregates that represent clusters of 6–10 asphaltene molecules are modelled as spherical particles with an attractive core consisting of polyaromatic hydrocarbons rings and short aliphatic tails that protrude from the surface, as in a spherical brush. As two such nanoaggregates approach each other, the steric repulsion that arises from interactions between the tails, is modelled using Alexander-de Gennes theory and Derjaguin approximation, while the attraction upon contact between polyaromatic cores, caused by van der Waals and other interactions is modelled as a Morse potential. The aggregation occurs when the steric barrier is overcome and the cores come into contact. Our simulations show that, with shallow interaction potentials, that is, with weak attractions and low barriers, the nanoaggregates form small agglomerates with ramified structure that are in metastable equilibrium with uniform solutions. These agglomerates can be described with a fractal dimensions below 1.5, which may represent soluble asphaltenes. The increase in attraction strength promotes aggregation and destabilizes the systems as in the case of dilution with a flocculant, for which several aggregation regimes are observed. Increasing the well-depth and/or barrier for nanoaggregate interaction leads to classical diffusion limited and reaction limited regimes. We find that with high barrier the clusters formed are less close-packed, and may represent the weak gel state typical for bitumen gel.

Rapid Electrostatic Capture of Rod-Shaped Particles on Planar Surfaces: Standing up to Shear.

We compare the electrostatically driven capture of flowing rod-shaped and spherical silica particles from dilute solutions onto a flow chamber wall that carries the opposite electrostatic charge from the particles. Particle accumulation and orientation are measured in time at a fixed region on the wall of a shear flow chamber. Rod-shaped particle aspect ratios are 2.5-3.2 and particle lengths are 1.3 and 2.67 μm for two samples, while sphere diameters were 0.72, 0.96, and 2.0 μm for three samples. At a moderate wall shear rate of 22 s-1, the particle accumulation for both rods and spheres is well described by diffusion-limited kinetics, demonstrating the limiting effect of particle diffusion in the near-wall boundary layer for electrostatically driven capture in this particle shape and size range. The significance of this finding is demonstrated in a calculation that shows that for delivery applications, nearly the same (within 10%) particle volume or mass is delivered to a surface at the diffusion-limited rate by rods and spheres. Therefore, in the absence of other motivating factors, the expense of developing rod-shaped microscale delivery packages to enhance capture from flow in the diffusion-limited simple shear regime is unwarranted. It is also interesting that the captured orientations of the larger rods, 2.6 μm in average length, were highly varied and insensitive to flow: a substantial fraction of rods were trapped in standing and slightly leaning orientations, touching the surface by their ends. Additionally, for particles that were substantially tipped over, there was only modest orientation in the flow direction. Taken together, these findings suggest that on the time scale of near-surface particle rotations, adhesion events are fast, trapping particles in orientations that do not necessarily maximize their favored adhesive contact or reduce hydrodynamic drag.

On the doping concentration dependence and dopant selectivity of photogenerated carrier assisted etching of 4H–SiC epilayers

A comprehensive photogenerated carrier assisted etching investigation is carried out on the Si polar surface of high-quality p- and n-type (0001) 4H–SiC epilayers. The epilayers have intentional or unintentional doping densities in the 1014–1018 cm−3 range. Cyclic voltammetry and chronoamperometry studies under a non-focused above bandgap (280–400 nm) light illumination (≤0.66 Wcm−2) in a highly basic etching medium (1 wt% KOH solution, pH ∼12) complemented by Mott-Schottky characterization reveal a dependence of the etch voltage (within ±1 V) and etch rate (∼20–60 nm/min) on doping concentration and type. Our results demonstrate separate mutually exclusive etch voltage windows (∼± 0.3–0.7 V) in the diffusion-limited regime for a pair of doping concentrations with opposite conductivities to establish smooth preferential etching. These results provide insight in the design and fabrication of higher performance three dimensional SiC homo/hetero-junctions for various applications including photonic crystal cavities.

Growth and morphology control of CH3NH3PbBr3 crystals

We present here an experimental study on the growth of CH3NH3PbBr3 crystals by conventional spin coating and simple drop casting methods. We observed directly that under the diffusion-limited regime, large-size cuboids and pyramid-like single crystals were obtained. Single-crystal X-ray diffraction revealed that these crystals were in the Pm-3m cubic crystalline structure phase, with a refined unit size of 5.93 A. Polycrystals with fractal-like or snowflake-like morphologies were grown by spin coating method, on fluorine-doped tin oxide-coated glass substrates, that we referred to as the attachment kinetics-limited regime. Interestingly enough, with the same technique, cuboids CH3NH3PbBr3 single crystals were obtained on bare glass substrates. These single crystals and polycrystals exhibited a very strong photoluminescence effect. This study paves a way for controlled growth of CH3NH3PbBr3 crystals and their advanced optoelectronic applications.

Volatile loss under a diffusion-limited regime in tektites: Evidence from tin stable isotopes

Tektites are glasses derived from near-surface continental crustal rocks that were molten and ejected from the Earth's surface during hypervelocity meteorite impacts. They are among the driest terrestrial samples, although the exact mechanism of water loss and the behaviour of other volatile species during these processes are debated. Based on the difference in magnitude of the Cu and Zn isotopic fractionations in tektites, and the difference of diffusivity between these elements, it was suggested that volatile loss was diffusion-limited. Tin is potentially well suited to testing this model, as it has a lower diffusivity in silicate melts than both Cu and Zn, but a similar volatility to Zn. Here, we analysed the Sn stable isotopic composition in a suite of seven tektites, representing three of the four known tektite strewn fields, and for which Zn and Cu isotopes were previously reported. Tin is enriched in the heavier isotopes (≥2.5‰ on the 122Sn/118Sn ratio) in tektites, correlated with the degree of Sn elemental depletion in their respective samples as well as with Cu and Zn isotope ratios, implying a common control. While the isotope fractionation of Sn, Cu and Zn is a result of volatility, the magnitude of isotope fractionation is strongly moderated by their relative rates of diffusion in the molten tektite droplets. An Australasian Muong Nong-type tektite analysed has the least Sn depletion and Sn isotope fractionation, consistent with these samples being more proximal to the source and experiencing a shorter time at high temperatures.

Aggregation kinetics of UV irradiated nanoplastics in aquatic environments

Nanoplastics (NPs) derived from degradation of macroplastics and microplastics possess potential threat to aquatic biota and human health. Their fate and transport in aquatic systems are mainly governed by aging processes and aggregation behavior. In this study, we simulated plastic aging process using UV-irradiation and compared the aggregation kinetics of fresh versus aged polystyrene NPs (PSNPs) under aqueous conditions. The results showed that fresh PSNPs had strong negative surface charge and exhibited both reaction- and diffusion-limited aggregation regimes, in agreement with classic Derjaguin−Landau−Verwey−Overbeek (DLVO) theory. Divalent electrolytes were 10–15 times more effective in inducing PSNP aggregation than monovalent electrolytes. The aging process inhibited PSNP aggregation in NaCl solutions by increasing the negative charge on PSNP surface and the organic matter content in solution, while promoted PSNP aggregation in CaCl2 solutions due to interactions between Ca2+ and carboxyl groups formed on aged PSNP surface. Such distinct behaviors were consistent with characterizations by contact angle measurements, potentiometric titration, total organic carbon (TOC) analysis, Fourier Transform Infrared Spectroscopy (FTIR), and X-ray photoelectron spectroscopy (XPS). Hamaker constants obtained from DLVO fitting decreased from 3.5 × 10−21 J for fresh PSNPs to 1.5 × 10−21 J for aged PSNPs. This study indicated that UV-irradiation plays a vital role in governing the fate, transport, and potential hazards of PSNPs in aquatic environments.

Performance assessment of gas-phase toluene removal in one- and two-liquid phase biotrickling filters using artificial neural networks

The main aim of this work is to study gas-phase toluene removal in one- and two-liquid phase biotrickling filters (O/TLP-BTF) and model the BTF performance using artificial neural networks (ANNs). The TLP-BTF was operated for 60 d in the presence of silicone oil at empty bed residence times (EBRTs) of 120, 60, and 45 s, respectively, and toluene concentrations in the range of 0.9–3.1 g m−3. A t-test analysis indicated that increasing the silicone oil volume ratio from 5 to 10% v/v, did not significantly improve the TLP-BTF performance (p-value = 0.65 > 0.05). The results from ANN modeling showed that toluene removal was more negatively affected by the inlet concentration (casual index, CI = −5.63) due to the kinetic limitation. The CI values for inlet concentration (+4.01) and liquid trickling rate (−2.45) indicated that the diffusion-limited regime controlled the removal process in the OLP-BTF.

Identification of hydrogen permeability parameters of membrane materials in an aggregated experiment

The study of the hydrogen permeability of materials for membrane-based separation/purification technologies employs a variety of experimental methods with their own specific features, advantages and shortfalls. The method of penetration with vacuum pumping allows determining the diffusion coefficient from so-called lag time. The accuracy of the estimation depends on the degree of proximity to the DLR (diffusion limited regime) mode. The method of “communicating vessels” is more sensitive to surface processes. The thermal desorption (TDS) technique permits “scanning” the material dynamically across a wide range of temperatures. “Separate” application of these methods leads to a situation where the materials studied are in fact somewhat different (for example, due to different impacts on the surface), and significant differences in parameter estimates ensue. This paper suggests and implements a technique for a combined three-stage ‹‹penetration (with and without vacuum pumping)+TDS›› experiment and the corresponding mathematical toolkit. The informative capacity of the experiments and the accuracy of the estimation of hydrogen permeability parameters (adsorption, dissolution, diffusion and desorption) of the membrane materials under study are thus enhanced.

A multi-technique approach towards the mechanistic investigation of the electrodeposition of Prussian blue over carbon nanotubes film

A detailed and multi-technique study on the kinetics and mechanism of the electrodeposition of Prussian blue (PB) over iron filled-carbon nanotubes (CNTs) thin films is presented here. PB is electrochemically synthesized through a heterogeneous reaction between iron species encapsulated into CNTs and ferricyanide ion in aqueous solution. The reaction was followed by a combination of in-situ or ex-situ measurements through UV–Vis spectroscopy, cyclic voltammetry, Raman spectroscopy and scanning electron microscopy. The analysis of the evolution of a new parameter that we called coverage ratio as well as an innovative way to associate the data extracted from cyclic voltammetry with the electrochemical reaction, are introduced by the first time. Similar response vs. time profiles are obtained from absorbance, charge, current, band intensity in Raman spectra, particle size, and coverage ratio, yet providing different aspects of the growth mechanism. Electrochemical data demonstrates an initial mixed control process related to the iron releases from the CNTs cavities and nucleation, followed by a diffusion limited regime on the growth of PB. Spectroscopic data indicates pseudo-first order kinetics, dependent on ferricyanide concentration, and the rate limited by the iron releases from the CNTs. Both particle size of PB and coverage ratio show a progressive nucleation of PB corroborating the proposed mechanism. Raman data also confirm the PB growth rate over the CNTs walls and evidence of PB/CNT interactions during voltammetric cycles. This multi-technique approach gives insights on different aspects of PB electrodeposition and can be extended to a wide class of different materials.

Crystallization kinetics of clinopyroxene and titanomagnetite growing from a trachybasaltic melt: New insights from isothermal time-series experiments

In order to investigate the role of crystallization kinetics in mafic alkaline systems, textural measurements, mineral compositional changes and diffusion modelling calculations have been carried out on isothermal time-series experiments. The data were obtained at 400 MPa and 1100 °C under anhydrous (nominally 0 wt% H2O) and hydrous (2 wt% H2O added) conditions. A synthetic trachybasaltic melt was first heated up to the superliquidus temperature of 1300 °C and then rapidly cooled at 80 °C/min down to 1100 °C. The final target temperature was kept constant over variable dwell times in the range of 0.5–24 h. Results from textural analysis indicate the attainment of fast crystal growth kinetics at the shortest experimental run duration, with early achievement of stable crystal sizes for clinopyroxene and titanomagnetite. The surface area to volume ratio weakly decreases with increasing dwell time, according to the development of euhedral crystal morphologies. Crystal growth rates are also observed to progressively decrease from 0.5 to 24 h. Due to the effect of fast growth kinetics, the morphological maturation of clinopyroxene progresses by attachment of dendrite branches, infilling and overgrowth phenomena, leading to the formation of well-faced and euhedral crystals. The kinetically-controlled cation exchange (Si + Mg) → (TAl + Fe3+) controls the clinopyroxene compositional variation, expanding the stability of Tschermak component at the expense of diopside. Conversely, titanomagnetite is characterized by an almost constant composition that, however, is enriched in incompatible Al and Mg cations, as typically observed under rapid crystal growth conditions. Titanomagnetite crystals show always euhedral morphology that develops by heterogeneous nucleation on early-formed clinopyroxene dendrites. Overall, the effect of undercooling causes strong supersaturation phenomena in the trachybasaltic melt, resulting in enhanced nucleation kinetics and fast attainment of a high crystallinity. As the dwell time increases, the bulk system tends to minimize the interfacial free energy between crystals and surrounding melt. This results in the progressive replacement of the early dendritic shapes developed in a diffusion-limited growth regime, by the formation of euhedral morphologies typical of interface-limited regimes that still retain the chemical evidences of the dendritic stage as complex zoning patterns in clinopyroxene.

Unveiling the competitive role of etching in graphene growth during chemical vapor deposition

During the growth of graphene via chemical vapor deposition, its recessive process, that is, etching, is often neglected. However, recent experimental studies showed that etching is not only able to give rise to complex morphologies that cannot be achieved by pure growth, but it also can be used to create designed patterns. In this work, we develop a kinetic Monte Carlo model based on the underlying mechanisms and growth kinetics of graphene to predict the formation of various morphologies during growth and etching. The simulation results reproduce a variety of experimentally observed morphologies of graphene domains with six-fold, four-fold and three-fold symmetries. In addition, we propose analytical relations between the gas flow rate in the experiments and the growth and etching parameters used in our simulations. We also present a phase diagram for the domain morphology from the attachment-limited regime to the diffusion-limited regime to guide the control of domain morphology. The present study not only presents a viable model to simulate the morphological evolution of graphene domain, but also provides essential guidance to control graphene pattern formation for specific applications.

Concurrent grain growth and coarsening of two-phase microstructures; large scale phase-field study

A thermodynamically consistent phase-field model is exploited to demonstrate the influence of relative volume fractions and bulk diffusivity on the grain growth phenomena in two-phase polycrystalline systems. For very small and high volume fractions, the simulated morphology consists of a dispersion of isolated minor phase grains embedded in the matrix of major phase grains. At intermediate fractions, the obtained microstructure resembles an interpenetrating network-like structure. The performed large-scale 2-D simulations elucidate the governing mechanisms for the concurrent two-phase growth at low and high volume fractions, and the continuous transition between interface-controlled and diffusion-limited regimes. While the slowest kinetics is observed for the 50/50 volume fraction case, irrespective of the diffusivity, the fastest kinetics is displayed by the pure systems, with a slight difference, which is due to relative interfacial energies. The relative growth rates of the individual phases and the maximum attainable grain size to mean size ratio are observed to follow the well-known trends for isotropic systems. The obtained results for the concurrent growth of a minor phase with various diffusivities, reveal that it is difficult to reconcile all observed behaviors with a universal Zener relation, in contradiction to the previously made claims in the literature. A need for the full-fledged growth law, which takes into consideration the role of the diffusivity, the volume fractions, and the relative interfacial energies in multiphase polycrystalline systems, is pointed out.

Theoretical Study of the Reactivity and Selectivity of Various Free Radicals with Cysteine Residues.

Radicals in biochemical environments can lead to protein damage. Theoretical studies can help us to understand the observed radical selectivity. In this work, the kinetics and thermodynamics of the hydrogen-transfer (HT) and single-electron transfer (SET) reactions between a cysteine derivative and 17 free radicals of biological significance have been theoretically investigated in aqueous and lipid media. With the exception of the reaction with •OCCl3, all SET reactions in aqueous medium have rate constants in the diffusion-limited regime. The γ site of cysteine was found to be the most reactive for the HT reactions with all the radicals, with rate constants in the diffusion limit for •OH, •OCHCl2, and •OCCl3. The HT reactions from the α and γ positions have very similar ΔG° values and even though the β position is the least thermodynamically favored, when the HT from β is exergonic it is a more reactive site than α. The results obtained confirm that the Bell–Evans–Polanyi principle does not apply to the reactions between amino acid residues and free radicals and that reactivity comparisons demand proper kinetic calculations.

Trapping intermediates in metal transfer reactions of the CusCBAF export pump of Escherichia coli

Escherichia coli CusCBAF represents an important class of bacterial efflux pump exhibiting selectivity towards Cu(I) and Ag(I). The complex is comprised of three proteins: the CusA transmembrane pump, the CusB soluble adaptor protein, and the CusC outer-membrane pore, and additionally requires the periplasmic metallochaperone CusF. Here we used spectroscopic and kinetic tools to probe the mechanism of copper transfer between CusF and CusB using selenomethionine labeling of the metal-binding Met residues coupled to RFQ-XAS at the Se and Cu edges. The results indicate fast formation of a protein−protein complex followed by slower intra-complex metal transfer. An intermediate coordinated by ligands from each protein forms in 100 ms. Stopped-flow fluorescence of the capping CusF-W44 tryptophan that is quenched by metal transfer also supports this mechanism. The rate constants validate a process in which shared-ligand complex formation assists protein association, providing a driving force that raises the rate into the diffusion-limited regime.

Deuterium plasma driven permeation behavior in a Chinese reduced activation martensitic/ferritic steel CLF-1

Deuterium (D) plasma-driven permeation (PDP) experiments for a Chinese reduced activation martensitic/ferritic steel CLF-1 have been performed. The effects of implantation flux, sample temperature and ion incident energy have been studied. The steady state PDP flux is found to be proportional to the square root of the implantation flux, indicating that the permeation takes place in recombination-limited regime for the upstream surface and diffusion-limited regime for the downstream surface (RD). The PDP flux and flux ratio (PDP flux/implantation flux) decrease with the increase of ion incident energy, which may be due to the enhancement of D recombination coefficient at the upstream surface.

İtici ve Çekici Etkileşimlerin Basamaklı Yüzeyler Üzerinde Oluşan Basamak Gruplaşmaları Üzerindeki Etkileri

A surface which consists concentric circular monoatomic steps in two dimensions and below its roughening temperature is discussed. Repulsive and attractive interactions between steps on the surface are considered. It is supposed that repulsive and attractive interactions vary as and respectively. Here indicates the terrace width between monoatomic steps. The solution of diffusion equation is achieved in two- dimension by using polar coordinates. While the initial surface evolves, it is supposed that the local mass transfer exists because of the surface diffusion only under the step-flow model. In the study initial surfaces bounded by envelope functions which have the form of are dealt. In the case of only repulsive interaction between steps surfaces evolve properly. When both repulsive and attractive interactions between steps are accepted step bunchings separated by large flat terraces occur on the surface. While the surface morphology and the evolution of the height of surface in time are investigated for all surface structures in Diffusion-Limited (DL) regime, a parameter space of bunching and no bunching regions is derived.