Predicting a Wide Range of Fractal Dimensions of Salt-Induced Aggregates in Water Using a Random Forest Model

Authors: HAMMOND, CHRISTIAN - Ohio University; MAMOON, KAREEM - Ohio University; Bradford, Scott; CHE, DANIEL - Ohio University; SHARMA, SUMIT - Ohio University; WU, LEI - Ohio University

Submitted to: Langmuir
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/21/2024
Publication Date: 10/31/2024
Citation: Hammond, C.B., Mamoon, K., Bradford, S.A., Che, D., Sharma, S., Wu, L. 2024. Predicting a Wide Range of Fractal Dimensions of Salt-Induced Aggregates in Water Using a Random Forest Model. Langmuir. 40:23606-23615. https://doi.org/10.1021/acs.langmuir.4c01182.
DOI: https://doi.org/10.1021/acs.langmuir.4c01182

Interpretive Summary: Small particles (known as colloids or nanoparticles) tend to group together and form aggregates in water environments. The structure of these aggregates can be characterized by their fractal dimension. Various machine learning approaches were used to estimate the fractal dimension for two data sets using system inputs. The Random Forest model was found to provide a good prediction of the fractal dimension when considering the ionic strength, normalized hydrodynamic radius of aggregates, the particle concentration, and the primary particle radius. This information is expected to aid researchers and engineers to predict the movement, distribution, and availability of colloid contaminants in the environment.

Technical Abstract: Colloidal contaminants that enter aquatic environments tend to form aggregates with fractal characteristics. The fractal dimensions (df) of these aggregates can range from 1.4 to 2.8 depending on the physical and chemical variables of the aggregating system. While the impact of some variables is well-known, particularly for two limiting aggregation regimes - diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) - the quantitative relationship between these variables and the resulting df of aggregates has not been fully explored, especially in predicting a wide range of df. In this study, we developed a Random Forest (RF) model that can predict the complete range of df of aggregates using four simple physical and chemical parameters of the aggregating system (ionic strength (IS), normalized hydrodynamic radius of aggregates (Rg/Rp), particle concentration (Cp), and primary particle radius (Rp)) as inputs. This model was primarily trained and tested on Data 1, which consists of aggregates formed by micro-sized particles. The generalization analysis of the RF model on the prediction of df of aggregates formed by nano-sized particles (Data 2) shows that a larger dataset is required to accurately develop an RF model that predicts the df of aggregates formed by colloids of varying sizes, ranging from nano to micro scale. For Data 1, we determined that the predicted df in the RF model mainly depends on IS, followed by Rg/Rp, Cp, and Rp. All four inputs are negatively correlated with predicting the df of aggregates. For the expanded dataset (Data 1+Data 2), we found that the predicted df in the RF model is still highly dependent on IS, but the importance of Rp also increased. These predictions align with physical interpretations and existing literature.