Coarse-Grained Monte Carlo Simulations with Octree Cells for Geopolymer Nucleation at Different pH Values

Abstract

Geopolymers offer a potential alternative to ordinary Portland cement owing to their performance in mechanical and thermal properties, as well as environmental benefits stemming from a reduced carbon footprint. This paper endeavors to build upon prior atomistic computational work delving deeper into the intricate relationship between pH levels and the resulting material's properties, including pore size distribution, geopolymer nucleate cluster dimensions, total system energy, and monomer poly-condensation behavior. Coarse-grained Monte Carlo (CGMC) simulation inputs include tetrahedral geometry and binding energy parameters derived from DFT simulations for aluminate and silicate monomers. Elevated pH values may can alter reactivity and phase stability, or, in the structural concrete application, may passivate the embedded steel reinforcement. Thus, we examine the effects of pH values set at 11, 12, and 13 (based on silicate speciation chemistry), investigating their respective contributions to the nucleation of geopolymers. To simulate a larger system to obtain representative results, we propose the numerical implementation of an Octree cell. Finally, we further digitize the resulting expanded structure to ascertain pore size distribution, facilitating a comparative analysis. The novelty of this study is underscored by its expansion in both system size, more accurate monomer representation, and pH range when compared to previous CGMC simulation approaches. The results unveil a discernible correlation between the number of clusters and pores under specific pH levels. This links geopolymerization mechanisms under varying pH conditions to the resulting chemical properties and final structural state.

Keywords: 3D off-lattice coarse-grained Monte Carlo; alkali silicate solution; aluminosilicates; cluster size distribution; metakaolinite-based geopolymer; nucleation; pH; pore-size distribution.

Figure 1

(a) The total system is divided into eight partitions, each representing a subsystem, following an Octree pattern. (b) Top view of the pH11 system, showing a detailed zoom-in of the interface planes within the octa-three simulation cell structure. Particles positioned at the periphery of each sub-system effectively percolate, connecting the adjacent cells, increasing the interconnectivity behavior of the total system. (c) The final status of the simulation at pH 11. The particles, clusters, and pore distribution are on the left side. Details are illustrated on the right side about the pore size distribution calculation: the dark aquamarine-colored particles represent the coarse-grained monomer particles (no distinction about the type), and the yellow particles represent the pore sizes.

Figure 2

Dimerization reaction based on tetrahedron formation for (A) Si-O-Si and (B) Si-O-Al optimized by the DFT computational approach. Table A1 and Table A2 in Appendix A show bond lengths and angles between atoms. The radius of coarse-grained particles equals the averaged bond length. The two particles touch at a single point, either the center of bonding oxygen, O4 (case (A)) or O11 (case (B)).

Figure 3

The evolution of the structures and cluster formation for the three different geopolymer systems extracted at a certain number of iterations of 0, 40,000, 80,000, and 56,000,000, respectively. The point at which the metakaolin is added to the system is denoted at iteration 0, with pre-equilibration taking place from iteration “8,000,000” to iteration 0. (a–c) (a) Represents the system with a pH of 11, while (b) illustrates the system at pH 12, and finally, (c) depicts the system at pH 13.

Figure 4

Energetic evolution of silicate particles in solution obtained for pH systems of 11, 12, and 13, where metakaolinite is not yet involved.

Figure 5

The equilibrium condition for three different pH systems was obtained through energy minimization computation of the silicate particles (starting at 0 iterations) and metakaolinite for 8 million iterations. The point at which metakaolinite is introduced to the system is denoted at iteration 0. Thus, pre-equilibration takes place for additional “8,000,000” iterations (shown in Figure 3).

Figure 6

The change in the number of aluminate and silicate monomers present in the system during 56 million iterations for the different pHs. Metakaolinite particles are considered monomers only when dissolved according to the dissolution process.

Figure 7

The evolution of the number of silicate monomers present in the system during 56 million iterations. At the start of the simulation (at iteration zero), metakaolinite particles were not included as they were undergoing the dissolution process.

Figure 8

The evolution of cluster formation in the three systems during 56 million iterations.

Figure 9

The change in the number of monomers participating and not participating in the cluster formation during 56 million iterations.

Figure 10

Dissolving process of metakaolinite during 56 million iterations.

Figure 11

Cluster size distribution after 56 million iterations.

Figure 12

Pore analysis at the end of the simulation. Magenta particles are solids.

Figure 13

Pore connectivity. In this graphical representation, an analysis of the interconnections among the pores in each system is viable.

Figure 14

Cluster distribution. The y-axis shows the total number of clusters, and the x-axis describes the number of particles in each cluster. The clusters that have a particle count of 1 are the monomers in the system.