A Detailed Model for the Sintering of Polydispersed Nanoparticle Agglomerates (original) (raw)
Related papers
Monte Carlo Simulation of Particle Coagulation and Sintering
Aerosol Science and Technology, 1994
A Monte Carlo simulation has been developed to describe the gas phase coagulation and sintering of nanoclusters. The cluster-cluster aggregation model is modified to include a finite interparticle binding energy. Particle restructuring and densification (sintering) are incorporated into the model by modifying Kadanoffs algorithm for random particle walks on the surface of the cluster. The effect of sintering on aggregate size distribution and fractal dimension has been investigated in simulations of two-dimensional clusters.
Aerosol Science and Technology, 1993
A simple model describing the evolution of particle molecular to the continuum regime. The model predicmorphology, size, and number concentration by coagutions compare well to those of a detailed two-dimenlation and sintering is presented that neglects the sional sectional model of nonspherical particle dynamspread of the polydispersity of aggregate and primary ics. After a theoretical evaluation of the main sintering particles. The influence of irregular/fractat structure mechanism, the proposed model was applied to laser on the collision kernel is accounted for, from the free synthesis of silicon in an aerosol reactor.
Polydispersity of primary particles in agglomerates made by coagulation and sintering
Journal of Aerosol Science, 2007
The polydispersity of primary particles (PP) in agglomerates is important in a number of applications, including nanocomposites, quantum dots and pigments. A two-dimensional sectional agglomerate and primary particle dynamics (APPD) model for coagulation and sintering is developed conserving the PP number and size distribution once agglomerates are formed. By balancing the complete PP population over all agglomerates, physical and numerical narrowing or broadening of the primary particle size distribution (PPSD) is investigated systematically. Physical narrowing of the PPSD in agglomerates arises by the faster sintering of smaller PP compared to larger ones while numerical narrowing occurs when average PP diameters are employed in the calculation of agglomerate coagulation and sintering. Broadening of the PPSD by numerical diffusion is caused when constant PP spacing is employed, similar to aerosol growth by condensation. Agglomerate and PP dynamics are elucidated during TiO 2 formation by detailed two-dimensional (primary and agglomerate) size distributions. The PPSD can become much narrower than the self-preserving size distribution of agglomerates by Brownian coagulation, especially when hard-agglomerates are formed. ᭧
A model for the sintering of spherical particles of different sizes by solid state diffusion
Acta Materialia, 1998
ÐIn this paper the numerical scheme developed by Pan and Cocks (Acta metall. 43, 1395±1406, 1995) is used to simulate the co-sintering process of two spherical particles of dierent sizes by coupled grain-boundary and surface diusion. The numerical analysis reveals many interesting features of the cosintering process. For example, it is found that the shrinkage between the two particles is not aected sig-ni®cantly by the size dierence of the two particles as long as the dierence is less than 50%. Based on the numerical results, empirical formulae for the characteristic time of the co-sintering process and for the shrinkage rate between the two particles are established. The empirical formulae can be used to develop constitutive laws for early-stage sintering of powder compacts which take into account the eect of particle size distribution. To demonstrate this, a densi®cation rate equation for compacts with bimodal particle size distributions is derived.
Computer Simulations of Nanoparticle Sintering
TechConnect Briefs, 2005
During the vapor-phase synthesis of titanium dioxide (TiO 2) nanoparticles, sintering of the nanoparticles is an important aspect of their behavior and an understanding of this phenomenon is therefore important. In this work, molecular dynamics (MD) simulations of the coalescence of TiO 2 nanoparticles have been carried out. The driving force for sintering of nanoparticles is the reduction in potential energy due to the decrease in surface area. The loss of potential energy manifests itself as an increase in the temperature of the sintering particles. This work concentrates on 3 and 4nm anatase and rutile nanoparticles. Dependence of particle orientation on sintering is reported along with ion mobility studies in the core and neck regions.
Multiparticle Sintering Dynamics: From Fractal-Like Aggregates to Compact Structures
Langmuir, 2011
Multiparticle sintering is encountered in almost all high temperature processes for material synthesis (titania, silica, and nickel) and energy generation (e.g., fly ash formation) resulting in aggregates of primary particles (hard-or sinter-bonded agglomerates). This mechanism of particle growth is investigated quantitatively by mass and energy balances during viscous sintering of amorphous aerosol materials (e.g., SiO 2 and polymers) that typically have a distribution of sizes and complex morphology. This model is validated at limited cases of sintering between two (equally or unequally sized) particles, and chains of particles. The evolution of morphology, surface area and radii of gyration of multiparticle aggregates are elucidated for various sizes and initial fractal dimension. For each of these structures that had been generated by diffusion limited (DLA), clusterÀcluster (DLCA), and ballistic particleÀcluster agglomeration (BPCA) the surface area evolution is monitored and found to scale differently than that of the radius of gyration (moment of inertia). Expressions are proposed for the evolution of fractal dimension and the surface area of aggregates undergoing viscous sintering. These expressions are important in design of aerosol processes with population balance equations (PBE) and/or fluid dynamic simulations for material synthesis or minimization and even suppression of particle formation.
A molecular dynamics study of sintering between nanoparticles
Computational Materials Science, 2009
The paper presents a molecular dynamics study on the interactions between nanoparticles at elevated temperatures. The emphasis is on the comparison between the molecular dynamics model and the continuum model using solid state physics. It is shown that the continuum model is unable to capture the sintering behaviour of nanoparticles. This is not because the continuum theory does not apply at the nano-scale but because the nanoparticles behave in so many different scenarios of the continuum theory that a meaningful model has to predict these scenarios, using the molecular dynamics for example. In the MD simulation, it is observed that the particles reorient their crystalline orientations at the beginning of the sintering and form different types of ''necks" between different particles. This leads to different mechanisms of matter redistribution at the different necks. It is also observed that the particles can switch the mechanism of matter transportation half-way through the sintering process. It would be very difficult, if not impossible, to handle these complexities using the continuum model. However assuming the right scenario, the continuum theory does agree with the MD simulation for particles consisting of just a few thousands atoms.
Additive Manufacturing, 2016
Additive manufacturing (AM) has received a great deal of attention for the ability to produce three dimensional parts via laser heating. One recently proposed method of making microscale AM parts is through microscale selective laser sintering (-SLS) where nanoparticles replace the traditional powders used in standard SLS processes. However, there are many challenges to understanding the physics of the process at nanoscale as well as with conducting experiments at that scale; hence, modeling and computational simulations are vital to understand the sintering process physics. At the sub-micron (m) level, the interaction between nanoparticles under high power laser heating raises additional near-field thermal issues such as thermal diffusivity, effective absorptivity, and extinction coefficients compared to larger scales. Thus, nanoparticle's distribution behavior and characteristic properties are very important to understanding the thermal analysis of nanoparticles in a-SLS process. This paper presents a discrete element modeling (DEM) study of how copper nanoparticles of given particle size distribution pack together in a-SLS powder bed. Initially, nanoparticles are distributed randomly into the bed domain with a random initial velocity vector and set boundary conditions. The particles are then allowed to move in discrete time steps until they reach a final steady state position, which creates the particle packing within the powder bed. The particles are subject to both gravitational and cohesive forces since cohesive forces become important at the nanoscale. A set of simulations was performed for different cases under both Gaussian and log-normal particle size distributions with different standard deviations. The results show that the cohesive interactions between nanoparticles has a great effect on both the size of the agglomerates and how densely the nanoparticles pack together within the agglomerates. In addition, this paper suggests a potential method to overcome the agglomeration effects in-SLS powder beds through the use of colloidal nanoparticle solutions that minimize the cohesive interactions between individual nanoparticles.
Sintering Time for Silica Particle Growth
Aerosol Science and Technology, 2001
The formation and growth of gas-made silica particles by coagulation and sintering is investigated theoretically. A model for the characteristic time for silica sintering is proposed de ning a minimum primary particle diameter above which macroscopic expressions are applied. The value of the minimum primary particle diameter is selected consistently with molecular dynamics simulations. The proposed characteristic sintering time is tested using a monodisperse model for aggregate dynamics by coagulation and sintering. The model predictions are compared with experimental data for silica formation and growth in premixed ames and hot wall aerosol ow reactors by oxidation of hexamethyl-disiloxane (HMDSO) and silicon-tetrachloride (SiCl 4 ).