Molecular dynamics and machine learning insights into Cu-doped silicate-based bioactive glasses: From radial distribution function to ring size distribution

This study integrates molecular dynamics (MD) simulations and machine learning (ML) approaches to investigate the structure–property relationships of copper-doped silicate bioactive glasses (CBGs). CBGs with compositions 60SiO₂–(40–x)CaO–xCuO (mol%, x = 0, 1, 3, 5, 8, 10, 15, 20) were modeled using MD to analyze short- and medium-range structure, network connectivity, and dissolution-related features. Structural analysis revealed stable Si–O tetrahedral coordination with 1.60 Å bond length, and O-Si-O bond angle of 109°, while increasing CuO content modified Si–O–Si linkages and ring structure by widening the Si–O–Si bond angles from 147.9° (C0) to 151.0° (C20). Modifying atoms had consistent bond lengths of 2.37–2.40 Å (Ca–O) and 2.75 Å (Cu–O). In addition, Qⁿ distributions showed shifts from Q² to Q³ species with higher Cu levels, reflecting network reorganization. In contrast, despite the higher molar mass of Cu, bulk density decreased from 2.71 g·cm⁻³ (C0) to 2.56 g·cm⁻³ (C20), due to volume expansion induced by Cu incorporation. To overcome the challenges of conventional ring size distribution (RSD) calculations, an ML framework was developed combining a modified RSD algorithm, radial distribution function (RDF), and a 2D convolutional neural network (2D-CNN). Despite a limited dataset, the CNN achieved low error, strong correlations, and robust predictive capability in predicting the C20 composition RSD. Collectively, this work demonstrated the synergy between atomistic simulations and AI-driven prediction for complexity of CBGs, accelerating the design of functional CBGs with optimized structural properties. These results pave the way for next-generation BG design paradigms, where ML accelerates materials discovery through deep integration with MD simulation.