Molecular dynamics and machine learning insights into Cu-doped silicate-based bioactive glasses: From radial distribution function to ring size distribution
Amirhossein Moghanian, Mohammad Nasr Esfahani, Arang Pazhouheshgar, Sirus Safaee
Abstract
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. • Cu-doped silicate bioactive glasses were modeled via molecular dynamics simulations. • Structural analysis revealed Cu as an effective network modifier in glass structure. • A new machine learning framework predicted ring size distribution from RDF data. • 2D CNN achieved high accuracy with a limited dataset of glass compositions. • Combined MD–ML approach accelerates the design of next-generation bioactive glasses.