A population balance framework for nucleation, growth, and aggregation

Nucleation, growth, and aggregation for particulate systems are explored by distribution kinetics and population balances to build a new framework for understanding a range of natural and manufacturing phenomena. Nucleation is assumed to follow classical homogeneous theory or to be caused by heterogeneous nuclei added to the solution. Growth due to monomer addition from solution to clusters, and aggregation between clusters are both represented by integrals of the cluster distribution. When growth and aggregation rate coefficients are independent of cluster size, the population balance equations are readily solved by the moment method. Equations for steady-state well-mixed flow and unsteady-state closed (batch) vessels have relatively straightforward solutions. By incorporating solute (monomer) depletion, the results afford reasonable behavior for the cluster number and mass concentration. The monomer addition terms are shown to be consistent with (and a generalization of) conventional differential growth and growth dispersion expressions.     

Adsorption of Some Atmospherically Important Molecules onto Large Water Clusters: SO2, SO3, HCl,and ClONO2

The adsorption of a range of atmospherically important molecules (SO₂, SO₃, HCl, and ClONO₂) on large water clusters have been studied using a supersonic molecular beam expansion to generate water clusters containing 50–450 water molecules. SO₂ and HCl were found to stick with low efficiency to the water cluster, retaining their chemical identity. In contrast, both SO₃ and ClONO₂ undergo heterogeneous reactions on the surface of the water cluster forming, respectively, H₂SO₄ and HOCl with HNO₃. For SO₃, calculations show that the large barrier that exists in the gas-phase to the reaction of SO₃ with water is removed for water clusters of a sufficient size because of stabilization of the transition state by solvation. For ClONO₂, the barrier to reaction is much larger and cannot be removed by solvation for any size cluster. In this case, it is likely that reaction takes place on the water cluster by the ionic dissociation of ClONO₂ in a similar manner to that observed for ClONO₂ on ice films.     

Effect of the Growth Treatment on Two-Stage Nucleation Experiments

Numerical simulations are presented that document the strong effect of a previously underappreciated portion of two-stage thermal treatments used in the study of nucleation processes: the "heat-up" process whereby samples are heated from "nucleation" conditions to "growth" conditions. The simulations indicate that two limiting regimes exist, dependent on (a) the cluster size distribution of as-quenched glasses, (b) the temperatures used for nucleation and growth, and (c) the rates of heating and cooling: (1) all clusters larger than the critical size at growth conditions ( n ^*_gr) will grow to macroscopic size (the "standard" case); and (2) all clusters larger than the critical size at nucleation conditions ( n ^*_nuc) will grow to macroscopic size. In addition, cases in which the "effective critical size" ( n ^*_eff) is intermediate between n ^*_gr and n ^*_nuc can also occur. Cases in which n ^*_eff < n ^*_gr is manifested during nucleation experiments as an abrupt boost in crystal number density during the heat-up from nucleation to growth conditions, as all clusters larger than n ^*_eff are rapidly "flushed" past n ^*_gr. For the system studied herein, this can lead to a 10⁶-fold increase in final number density within seconds to a few minutes. Finally, the importance of structural relaxation for this process is demonstrated by examining a case in which the nucleation temperature is below the nominal glass transition temperature.     

The Formation of Clusters with Reactive Species Precursors to Aerosol Formation in the Ammonia—Sulfur Dioxide System

Reactions between ammonia and sulfur dioxide are known to form aerosols, but no information on the precursors to particle formation are available in the literature. Herein, the first results on the formation of clusters containing both ammonia and sulfur dioxide are presented. Clusters produced by expansion through a dual nozzle into vacuum have been investigated using a molecular beam mass spectrometer technique. Interestingly, under similar expansion conditions, NH₃ incorporation into SO₂ clusters is more extensive than SO₂ into NH₃ clusters. In contrast to findings from the stoichiometry of the solid precipitate of the aerosol, the cluster distributions fail to reveal clusters of any stoichiometry as particularly abundant or stable, except for NH⁺ ₄·NH₃·SO₂.     

Electronic structures and reactivities of monometallic and bimetallic clusters of Au and Cu

The variation of the Au 4f binding energy of Au clusters with the cluster size has been established by measuring the binding energies of clusters whose size distributions were independently determined by HREM and STM. The binding energy increases significantly when the cluster size is less than 2 nm. Au-Cu bimetallic clusters of the composition Cu₃Au have been deposited for the first time on carbon substrates. The shifts in the core level binding energies of the bimetallic clusters show the effect of alloying in the case of large clusters, but show effects of both alloying and cluster size in the case of the small clusters. The interaction of CO with Cu₃Au clusters is stronger than with a bulk Cu metal. The interaction of CO with small Cu clusters also seems to be stronger than with bulk Cu or with large Cu clusters.     

Catalysts by design: genesis and CO hydrogenation of novel Pd carbonyl clusters in zeolite 5A

The potential of catalyst synthesis by design is demonstrated by comparing Pd/5A to Pd/NaY. While supercage dimensions are similar for both zeolites, the diameter of the supercage windows not only determines the Pd nuclearity of entrapped Pd carbonyl clusters, but also restricts their growth under CO hydrogenation conditions. While Pd₁₃(CO) _x clusters prevail in zeolite Y as a result of migration and coalescence of primary Pd carbonyl clusters after CO exposure at room temperature, cluster growth in zeolite 5A is confined to Pd₆(CO) _x . Under the conditions of syngas conversion, small Pd clusters are stabilized in the supercages of 5A, in contrast to the agglomeration of Pd particles to size larger than 60 Å in NaHY. The catalytic activity of Pd/5A is twice that of Pd/NaHY. The selectivities of CO hydrogenation on both catalysts are also drastically different: on Pd/5A, methanol and dimethylether are the sole products besides methane, but on Pd/NaHY, production of C₂₊ hydrocarbons is significant.     

Synthesis of Titanium Dioxide Aerosol Gels in a Buoyancy-Opposed Flame Reactor

Aerosol gels are a novel class of materials with potential to serve in various energy and environmental applications. In this work, we demonstrate the synthesis of titanium dioxide (TiO₂) aerosol gels using a methane-oxygen coflow diffusion flame reactor operated in down-fired configuration (fuel flow in the direction opposite to buoyancy forces). Titanium tetraisopropoxide was fed as a precursor to the flame under different operating conditions. Control of the monomer size and crystalline phase of TiO₂ gel particles was achieved by adjusting the flame operating conditions, specifically the flame temperature, which was shown to significantly influence the phase transformation and rate of particle growth and sintering. The resulting materials were characterized for their physical and optical properties. Results showed that the TiO₂ aerosol gels had effective densities in the range 0.021–0.025 g/cm³, which is 2 orders of magnitude less than the theoretical mass density of TiO₂. The monomer size distribution, crystalline phase, and UV-Vis absorbance spectra of the gels showed distinct characteristics as a function of flame temperature.

Copyright © 2015 American Association for Aerosol Research     

不同烧成程度对熟料岩相结构的影响

对某水泥厂存在"欠烧"和"过烧"情况的两种熟料进行岩相分析,并结合其化学分析探索主要成分变化规律及形成原因。分析表明:欠烧状态下熟料结构多孔、且孔洞尺寸大,C2S簇和f-CaO簇呈较近距离分布;而过烧状态下熟料结构致密,C3S矿物之间分布一些f-CaO单晶体或小尺寸的簇,周围没有可与之反应的C2S矿物。     

Structure sensitivity of CO oxidation over model Au/TiO2 2 catalysts

Model catalysts of Au clusters supported on TiO₂ thin films were prepared under ultra-high vacuum (UHV) conditions with average metal cluster sizes that varied from ~2.5 to ~6.0 nm. The reactivities of these Au/TiO₂ catalysts were measured for CO oxidation at a total pressure of 40 Torr in a reactor contiguous to the surface analysis chamber. Catalyst structure and composition were monitored with Auger electron spectroscopy (AES) and scanning tunneling microscopy and spectroscopy (STM/STS). The apparent activation energy for the reaction between 350 and 450 K varied from 1.7 to 5 kcal/mol as the Au coverage was increased from 0.25 to 5 monolayers, corresponding to average cluster diameters of 2.5–6.0 nm. The specific rates of reaction ((product molecules) × (surface site)^-1 × s^-1 were dependent on the Au cluster size with a maximum occurring at 3.2 nm suggesting that CO oxidation over Au/TiO₂(001)/Mo(100) is structure sensitive. This revised version was published online in July 2006 with corrections to the Cover Date.     

Metallic States at the Edges of MoS2 Clusters

In this work we suggest that certain structures present in real commercial catalysts maybe related to low dimensional structures and present a theoretical study of two MoS₂ clusters (one made of 61 atoms and the second one made of 68 atoms). The 61 atoms cluster has 7 sulfur atoms decorating at the top of sulfur (S) layer in order to analyze the effects produced on the electronic properties. The first cluster yielded semiconductor behavior with a forbidden energy gap E _g of the order of 0.11 eV, while the second cluster decorated with seven S atoms yielded metallic behavior. A careful analysis to the partial density of states (PDOS) indicate that the contributions to the total DOS in the vicinity of the Fermi level, from the seven S atoms located at the surface is negligible, they serve only as promoters to the metallic behavior to the system.     

The initial stages of multicomponent particle formation during the gas phase combustion synthesis of mixed SiO2/TiO2

The ability to properly scale the synthesis of advanced materials through combustion synthesis routes is limited by our lack of knowledge regarding the initial stages of particle formation. In flame aerosol reactors, the high temperatures, fast reaction rates, and flame chemistry can all play a critical role in determining the properties of the resulting nanomaterials. In particular, multicomponent systems pose a unique challenge as most studies rely on empirical approaches toward designing advanced composite materials. The lack of predictive capabilities can be attributed to a lack of data on particle inception and growth below 2 nm. Measurements for the initial stages of particle formation during the combustion synthesis of SiO₂ and composite SiO₂/TiO₂ using an atmospheric pressure inlet time-of-flight mass spectrometer are presented. Both positively and negatively charged clusters can be measured and results show the presence of silicic acid species which grow through dehydration, hydrogen abstraction, and interactions with hydroxyl radicals. In the case of composite SiO₂/TiO₂ particle formation, new molecular species containing Ti atoms emerge. Tandem differential mobility analysis-mass spectrometry (DMA-MS) provided further insight into the size-resolved chemistry of particle formation to reveal that at each cluster size, further hydroxyl-driven reactions take place. From this we can conclude that previous assumptions on collisional growth from simple monomer species of SiO₂ and TiO₂ do not sufficiently describe the collisional growth mechanisms for particle growth below 2 nm.

Copyright © 2018 American Association for Aerosol Research     

Production of equal sized atomic clusters by a hot wire

A resistively heated metal wire is shown to be a source of charged atomic clusters consisting of only a few atoms. They are size classified with a differential mobility analyzer, and their relative abundance is determined as a function of size. Ag_nK⁺ clusters are obtained from wires containing silver with traces of potassium to provide the electric charge. First principles calculations reveal that the abundance observed can be fully explained by the energetic and chemical stability of the neutral cluster and K⁺ attachment energy. K⁺ attachment is a non-invasive way of charging, as the observed Ag_nK⁺ cluster properties are similar with respect to the pure Ag_n clusters in terms of energetic and electronic stability and cluster structure. The equally sized clusters are basically available for reactivity, coalescence and deposition studies, and the method is extendable to other materials.     

Deposition of Size-Selected Cu Nanoparticles by Inert Gas Condensation

Nanometer size-selected Cu clusters in the size range of 1–5 nm have been produced by a plasma-gas-condensation-type cluster deposition apparatus, which combines a grow-discharge sputtering with an inert gas condensation technique. With this method, by controlling the experimental conditions, it was possible to produce nanoparticles with a strict control in size. The structure and size of Cu nanoparticles were determined by mass spectroscopy and confirmed by atomic force microscopy (AFM) and scanning electron transmission microscopy (STEM) measurements. In order to preserve the structural and morphological properties, the energy of cluster impact was controlled; the energy of acceleration of the nanoparticles was in near values at 0.1 ev/atom for being in soft landing regime. From SEM measurements developed in STEM-HAADF mode, we found that nanoparticles are near sized to those values fixed experimentally also confirmed by AFM observations. The results are relevant, since it demonstrates that proper optimization of operation conditions can lead to desired cluster sizes as well as desired cluster size distributions. It was also demonstrated the efficiency of the method to obtain size-selected Cu clusters films, as a random stacking of nanometer-size crystallites assembly. The deposition of size-selected metal clusters represents a novel method of preparing Cu nanostructures, with high potential in optical and catalytic applications.     

On the nature of turbulent and fast fluidized beds

Fluidization characteristics have been investigated over the range from bubbling to fast fluidization by using a circulating fluidized bed cold model (riser diameter: 50 mm i.d., riser height: 2 390 mm, powder: fluidized cracking catalyst (FCC) and silica sand). Special focus was placed on the concepts of turbulent and fast fluidization regimes. Based on careful measurements of flow structure and cluster behavior, it is demonstrated that the turbulent fluidization regime is a transition regime between bubbling and fast fluidization. Experimental evidence supports the postulate that in fast fluidization the clusters adjust their size so that the gas drag force acting on them compensates with their gravity.     

Multiresolution analysis on identification and dynamics of clusters in a circulating fluidized bed

A new wavelet‐threshold criterion was developed to distinguish the cluster and the void phases from the transient solids holdup/concentration fluctuation signals when measured in a 108 mm‐i.d. × 5.75 m‐high circulating fluidized bed with FCC particles (d_p = 78 μm, ρ_p = 1,880 kg/m³). An appropriate level of approximation subsignal was systematically specified as a threshold for cluster identification, based on multiresolution analysis (MRA) of wavelet transformation. By the established threshold, the dynamic properties of clusters including the appearance time fraction of clusters F_cl, average cluster duration time τ_cl , cluster frequency f_cl, and local average solids holdup in clusters ε_sc , at different radial and axial positions were determined under the turbulent, transition and fast fluidization flow regimes. The results also describe the dynamic properties of clusters and flow patterns in the splash zone along with the dense bottom region of the circulating fluidized beds. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Influence of ultrasonic dual mode mixing on the morphology,molecular structure and thermo-physical properties of a SiO2-epoxy nanocomposite adhesive

Silica nanoparticles (~15 nm) were introduced in an epoxy adhesive using an ultrasonic dual mode mixing route at different amplitudes to tune the thermo-physical properties. Processing at higher amplitude resulted in a homogeneous distribution of less clustered nanoparticles. Glass transition temperature, thermal stability, and activation energy of nanocomposites processed at 55% of amplitude showed a significant enhancement for a very low nanoparticle content of 0.5 wt%. Incorporation of a higher nanoparticle content from 2 to 5 wt% declines the properties of the composite possibly due to increasing the number of clusters rather than the cluster size which may adversely affect the cross-linking density of the base polymer.     

Wavelet analysis to characterize cluster dynamics in a circulating fluidized bed

A common hydrodynamic feature in heavily loaded circulating fluidized beds is the presence of clusters. The continuous formation and destruction of clusters strongly influences particle hold-up, pressure drop, heat transfer at the wall, and mixing. In this paper fiber optic data is analyzed using discrete wavelet analysis to characterize the dynamic behavior of clusters. Five radial positions at three different axial locations under five different operating conditions spanning three different flow regimes were analyzed using discrete wavelets. Results are summarized with respect to cluster size and frequency.     

A two-dimensional layered cadmium sulfide superlattice constructed from capped-supertetrahedral C1 clusters

A new two-dimensional layered cadmium sulfide framework MSF-5 based on a capped-supertetrahedral C1 cluster [Cd₁₇S₄(SPhMe-4)₂₇(SH)]^2? has been synthesized. MSF-5 possesses a 3-connected 6³–hcb net, in which each C1 cluster connects through Cd–S(PhMe-4)–Cd covalent bonds with three neighboring clusters to form a 2D superlattice with 6-membered rings. The 2D sheets stack over each other to form a 3D network. MSF-5 has high thermal stability and is a wide-gap semiconductor.     

On the active site in H3PW12O40/SiO2 catalysts for fine chemical synthesis

The surface environment and structural evolution of silica supported phosphotungstic acid (H₃PW₁₂O₄₀) catalysts have been investigated as a function of acid loading. H₃PW₁₂O₄₀ clusters are deposited intact upon the silica surface, adopting a Stranksi-Krastanov growth mode forming a two-dimensional adlayer which saturates at 45wt% acid. Intimate contact with the silica support perturbs the local chemical environment of three tungstate centres, which become inequivalent with those in the remaining cluster, suggesting an adsorption mode involving three terminal W==O groups. Above the monolayer, H₃PW₁₂O₄₀ clusters form three-dimensional crystallites with physico-chemical properties indistinguishable from those in the bulk heteropoly acid. These H₃PW₁₂O₄₀/SiO₂ materials are efficient for the solventless isomerisation of α-pinene under mild reaction conditions. Activity scales directly with the number of accessible perturbed tungstate sites at the silica interface; these are the active species.     

Cluster formation mechanisms of titanium dioxide during combustion synthesis: Observation with an APi-TOF

Few studies reported the formation of Ti-containing clusters in the initial stages of TiO₂ flame synthesis. The conversion from synthesis precursor to TiO₂ monomers was commonly assumed to take place through global reaction such as thermal decomposition and/or hydrolysis at high temperatures. More recent studies have been able to identify stable intermediates of Ti-containing monomers, most commonly Ti(OH)₄, as the final step before the formation of TiO₂. However, no larger Ti-containing cluster formation mechanisms or interactions between these monomers have been tracked. To investigate cluster formation pathways of TiO₂ during flame synthesis, Charged clusters were measured in an atmospheric pressure interface time-of-flight (APi-TOF) mass spectrometer. TiO₂ nanoparticles were synthesized by adding titanium tetraisopropoxide (TTIP) precursor to a premixed CH₄/O₂/N₂ flat flame aerosol reactor. Pure TiO₂ clusters were not detected by the APi-TOF. Results from measured mass spectra and mass defect plots show that for positively charged clusters, the abstraction of CH₂ groups occurs simultaneously with the clustering of larger intermediate organometallic species. For negatively charged clusters, NO_x formation pathways in the flame may play a role during the initial stages of TiO₂ formation, since a lot of Ti-containing clusters were attached with nitrate-related species. These research findings provide insights on quantum dot synthesis and molecular doping where rapid dilution of the flame synthesized nanoparticles is needed to better control the particle size and chemical composition. The possible influences of and potential artifacts brought by the dilution system on observing the incipient particle formation in flames were also discussed.

© 2017 American Association for Aerosol Research