Growth and Aggregation Regulate Clusters Structural Properties and Gel Time

Abstract

When particles undergo aggregation, very often they form structures that can be described with fractal geometry concepts. The spatial organization of the particles embedded in these aggregates, quantified by means of their fractal dimension, plays a key role in the clusters' diffusion and aggregation process. Fractal dimensions are typically known for some specific, ideal aggregation scenarios, such as for diluted diffusion limited cluster aggregation (DLCA) or reaction limited cluster aggregation (RLCA). The situation becomes significantly more complicated as soon as the initial particle concentration increases and fractal-dimension changing phenomena, such as particle growth, occur. In this frame, the aim of the present work is twofold: (i) to investigate the clusters' spatial organization in a scenario where growth and aggregation occur simultaneously and (ii) to assess the corresponding aggregation kinetics. To this end, an ad hoc Monte Carlo model has been developed. Both DLCA and RLCA regimes have been explored at several initial primary particle concentrations and for different growth rates. The results were discussed in terms of the characteristic times of growth (τ G ) and aggregation (τ A ), as well as the rate at which the structural properties change, v R . It was then possible to propose empirical correlations in the form d m = d m (v R ) and t gel = t gel (τ A , τ G ) to relate the evolution of the mass mobility exponent d m and the gel times to the simultaneously occurring processes of growth and aggregation.

Understanding Time-Dependent Surface-Enhanced Raman Scattering from Gold Nanosphere Aggregates Using Collision Theory

“…1,30,31 Clusters that formed under reactionlimited conditions were shown to depend on the kinetics of monolayer formation (i.e., when surface modification is limited by the number of molecules present in solution or flux to a surface). 1,32 As such, resulting clusters were heterogeneous in size and contained closely spaced primary nanoparticles with a packing density of ∼64%, a value consistent with random packing. 33 In contrast, clusters formed under diffusion-limited conditions were composed of primary nanoparticles coated with a relatively higher SAM density that formed prior to cluster formation.…”

“…33 In contrast, clusters formed under diffusion-limited conditions were composed of primary nanoparticles coated with a relatively higher SAM density that formed prior to cluster formation. 1,31,32 Thus, resulting clusters were largely more homogeneous and contained more loosely packed primary nanoparticles versus those formed under reactionlimited conditions. As a result, primary nanoparticles exhibited a packing density of ∼4−5% of the total cluster volume.…”

“…Previously, the mechanisms associated with cluster formation were both modeled ,, and experimentally evaluated. ,,,, Both thermodynamics (i.e., nanoparticle concentration, analyte concentration, initial nanoparticle surface chemistry, and solution parameters) and kinetics (i.e., nanoparticle functionalization and collision rates) were shown to influence the dynamics of formation and geometries of the resulting clusters. Both reaction-limited and diffusion-limited cluster growth mechanisms were observed for colloidal nanomaterials. ,, Clusters that formed under reaction-limited conditions were shown to depend on the kinetics of monolayer formation (i.e., when surface modification is limited by the number of molecules present in solution or flux to a surface). , As such, resulting clusters were heterogeneous in size and contained closely spaced primary nanoparticles with a packing density of ∼64%, a value consistent with random packing . In contrast, clusters formed under diffusion-limited conditions were composed of primary nanoparticles coated with a relatively higher SAM density that formed prior to cluster formation. ,, Thus, resulting clusters were largely more homogeneous and contained more loosely packed primary nanoparticles versus those formed under reaction-limited conditions.…”

“…Both reaction-limited and diffusion-limited cluster growth mechanisms were observed for colloidal nanomaterials. ,, Clusters that formed under reaction-limited conditions were shown to depend on the kinetics of monolayer formation (i.e., when surface modification is limited by the number of molecules present in solution or flux to a surface). , As such, resulting clusters were heterogeneous in size and contained closely spaced primary nanoparticles with a packing density of ∼64%, a value consistent with random packing . In contrast, clusters formed under diffusion-limited conditions were composed of primary nanoparticles coated with a relatively higher SAM density that formed prior to cluster formation. ,, Thus, resulting clusters were largely more homogeneous and contained more loosely packed primary nanoparticles versus those formed under reaction-limited conditions. As a result, primary nanoparticles exhibited a packing density of ∼4–5% of the total cluster volume …”

Monte Carlo Aggregation Code (MCAC) Part 2: Application to soot agglomeration, highlighting the importance of primary particles

“…current simulations found in the literature as classified based on the above mentioned Knudsen numbers. Agglomeration has been commonly studied in the continuum flow regime for diffusion limited agglomeration (DLCA + Stokes drag) [3,4]. Pierce et al [1] studied the DLCA with an Epstein drag.…”