Diffusion/Reaction Limited Aggregation Approach for Microstructure Evolution and Condensation Kinetics during Synthesis of Silica-Based Alcogels

Abstract

A base-catalysed methyltrimethoxysilane (MTMS) colloidal gel formation was implemented as a cellular automaton (CA) system, specifically diffusion and/or reaction-limited aggregation. The initial characteristic model parameters were determined based on experimental synthesis of MTMS-based, ambient-pressure-dried aerogels. The applicability of the numerical approach to the prediction of gels’ condensation kinetics and their structure was evaluated. The developed model reflects the kinetics properly within the investigated chemical composition range (in strongly reaction-limited aggregation conditions) and, to a slightly lesser extent, the structural properties of aggregates. Ultimately, a relatively simple numerical model reflecting silica-based gel formation was obtained and verified experimentally. The CA simulations have proved valid for understanding the relation between the initial chemical composition and kinetics constants of MTMS-based synthesis and their impact on secondary particle aggregation process kinetics.

Analysis of the microstructural connectivity and compressive behavior of particle aggregated silica aerogels

“…Borzȩcka et al. [6] have recently demonstrated how the probability parameter, based on the Arrhenius equation, can show the relationship between synthesis parameters and model parameters, such as translating the time of gelation into the probability of an effective collision. The implementation of this study is as follows: the particle–cluster connection will be formed with a probability of $$p_s$$ upon reaching the $$\epsilon _{\text{crit}}$$, while the cluster–cluster connection is established only if more than 50% of potential connections between two clusters are formed (see also Figure 1).…”

“…Although this mesoscale atomistic model is able to capture the structural and mechanical properties, the atomistic nature does not allow for modeling of the sol-gel process, which involves condensation reactions. Currently, the following approaches for sol-gel representation are gaining more attention [1,6]: (i) algorithm based on the Smoluchowski equation [7,8], (ii) Langevin dynamics [9,10], (iii) percolation theory and cluster aggregation models [11][12][13]. Among these, percolation theory and cluster aggregation have provided significant insights into the internal gel structure [6,8], correlating synthesis parameters with microstructure [13].…”

“…Although this mesoscale atomistic model is able to capture the structural and mechanical properties, the atomistic nature does not allow for modeling of the sol–gel process, which involves condensation reactions. Currently, the following approaches for sol–gel representation are gaining more attention [1, 6]: (i) algorithm based on the Smoluchowski equation [7, 8], (ii) Langevin dynamics [9, 10], (iii) percolation theory and cluster aggregation models [11–13]. Among these, percolation theory and cluster aggregation have provided significant insights into the internal gel structure [6, 8], correlating synthesis parameters with microstructure [13].…”

“…More recently, Borzecka et al. [6] have developed a 3D diffusion‐limited (DLCA) and reaction‐limited (RLCA) aggregation model to study the kinetic curves. They obtained the relationship between porosity and collision probability, which is validated by both experimental and numerical results.…”