Light scattering from nanoparticle agglomerates

A Simple Model for Gas-Phase Synthesis of Nickel Nanoparticles

“…Here, a population balance model assuming monodisperse agglomerate and primary particles , is extended to account for the evolution of agglomerate fractal-like structure , during Ni particle nucleation, surface growth, coagulation, and sintering of agglomerates by tracking their N , V , and A . The average diameter of primary particles in each agglomerate is and the average number of primary particles in each agglomerate is calculated with eq by dividing the volume of an agglomerate, V / N , with that of a single primary particle, : then the agglomerate mobility diameter, d m , that is often characterized by scanning mobility particle sizer (SMPS) is calculated using d p and n p with and gyration diameter is obtained using d m and n p with and agglomerate mass fractal dimention, D f , that quantifies the fractal-like structure of the agglomerates is obtained by Eqs – are obtained from rigorous discrete element modeling for coagulation and surface growth of different materials and a wide range of process temperatures that are not specific to the conditions simulated in this study. The rate of change of N is where the first and second right-hand side (RHS) terms describe particle nucleation and agglomerate coagulation, respectively, with β the harmonic mean of free molecular, β fm , and continuum, β co , regime collision frequencies: here, β fm is and β co is where 1.82 ± 0.35 describes the impact of polydispersity of agglomerates on their collision frequency from the free molecular to continuum regime, assuming self-preserving size distribution has been attained .…”

A Monodisperse Population Balance Model for Nanoparticle Agglomeration in the Transition Regime

“…The MPBM-derived , , and are in excellent agreement with those obtained by DEM for all investigated here. Therefore, the present MPBM could be used to simulate the coagulation dynamics of organic nanoparticles with rather monodisperse primary particle size distributions [ 3 , 35 ], and also those of metals [ 44 ] and metal oxides [ 22 , 37 ] that attain the self-preserving size distribution by coalescence in practical applications. The MPBM-derived agglomeration dynamics are also in excellent agreement with those obtained by DEM for nanoparticles with d p = 10, 20 and 40 nm ( Supplementary Materials: Figure S1 ).…”

“…Figure 6 illustrates the agglomerate effective density, , as a function of the normalized mobility diameter, , measured for soot particles sampled from premixed ethylene flames with an equivalence ratio (EQR) of 2 (triangles) or 2.4 (squares), and estimated here accounting for the evolving fractal-like agglomerate structure (Equations (1) and (2) [ 10 ], solid line) or assuming a constant agglomerate structure with (broken line) [ 16 ]. Ramified agglomerates are formed at EQR = 2 and 2.4 having average [ 35 ] and 19.6 nm [ 47 ], respectively. The agglomerate increases during coagulation, reducing and from 1.29 to 0.7 (as shown in Figure 3 ).…”

“…The surrounding gas pressure, P , is increased from 1 to 5 bar to simulate conditions close to those in combustion engines [ 6 ]. The geometric standard deviation, , of the initial particle size distribution is also varied from 1 to 1.5 in order to be consistent with the measured soot [ 35 ] and metal oxide [ 22 ] primary particle size distributions.…”

“…Figure 1 shows the DEM-derived geometric standard deviation, , of the d m distribution as a function of the normalized mean, d m / d p , of agglomerates, with primary particles having = 1 (a, b: broken lines), 1.2 (a: dotted line) and 1.5 (a: solid line) coagulating at 1830 K, and P = 1 (a, b: broken lines), 3 (b: dotted line) and 5 bar (b: solid line). Small = 1 and 1.2 are representative for organic nanoparticles (e.g., soot [ 3 , 35 ]), while = 1.5 is common for inorganic nanoparticles (e.g., SiO 2 [ 22 ] and ZrO 2 [ 37 ]) that attain their self-preserving size distribution by coalescence. Regardless of , the of the agglomerate size distribution increases up to 1.7 ± 0.05 in the free molecular regime at , consistent with DEM simulations of agglomeration and surface growth [ 10 ].…”