ceramics Review The Modified Random Network (MRN) Model within the Configuron Percolation Theory (CPT) of Glass Transition Michael I. Ojovan 1,2   Citation: Ojovan, M.I. The Modified Random Network (MRN) Model within the Configuron Percolation Theory (CPT) of Glass Transition. Ceramics 2021, 4, 121–134. https:// doi.org/10.3390/ceramics4020011 Academic Editors: Ashutosh Goel and Gilbert Fantozzi Received: 25 January 2021 Accepted: 24 March 2021 Published: 29 March 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Materials, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK; m.ojovan@imperial.ac.uk 2 Department of Radiochemistry, Moscow State University Named after M.V. Lomonosov, Leninskie Gory 1, Bd.3, 119991 Moscow, Russia Abstract: A brief overview is presented of the modified random network (MRN) model in glass science emphasizing the practical outcome of its use. Then, the configuron percolation theory (CPT) of glass–liquid transition is concisely outlined, emphasizing the role of the actual percolation thresholds observed in a complex system. The MRN model is shown as an important tool enabling to understand within CPT the reduced percolation threshold in complex oxide systems. Keywords: oxide glasses; molecular structure; modified random network; configuron; percolation; glass transition 1. Introduction The modified random network (MRN) model of glasses proposed first by Greaves [1–4] has been nowadays confirmed by many observations in experiment and modeling. The molecular structure of a glass controls the glass properties—for example, the chemical durability—by establishing the distribution of ion exchange sites, hydrolysis sites, and the access of water to those sites. Therefore, it is imperative to investigate the molecular struc- ture of glass evidencing the details of medium-range order (MRO) of glasses. The MRN model involves two interlacing disordered sub-lattices (regions), one of which contains the well-polymerized silica skeleton (covalent network), while the other is depolymerized and comprises of large concentrations of network modifiers such as alkalis. The first model of glass structure was the continuous random network (CRN) model, which became a classical method of thinking on structures of glasses and melts presenting the molecular structure of oxide glass formers as a topologically disordered network of corner-sharing tetrahedra forming rings and cages [5]. Experiments indicated that the CRN model cannot describe the structure of melts and glasses containing modifying metal cations. The MRN model accounts that the metal cations such as Na + ,K + , Ca 2+ , Mg 2+ break the inter-tetrahedral bonds and segregate into clusters, which gradually grow so that at higher concentrations, they eventually become continuous channels once their concentration reaches the percolation threshold [1–4,6]. Figure 1 is schematically representing the MRN model of an alkali silicate glass structure [7]. The MRN model allows Al-free silicate glasses and melts to be well described, whereas aluminosilicate glasses are different. The Al 3+ in silicates enters mostly in tetrahedral coor- dination in the form of negatively charged AlO 4 − with apical oxygen atoms presenting electrical charge deficits. As a result, the metal cations that are present in the melt compen- sate for this electrical charge deficit as they do in the crystalline state. In most aluminosili- cate glasses for practical uses, the concentration of metal cations provides almost exactly the charge compensation of the AlO 4 − present, this effect being used to bind radioactive hazardous nuclides in nuclear waste immobilization [8]. These effects are accounted by the compensated CRN (CCRN) model [9] by locating compensating metallic ions in the vicinity of AlO 4 − . Thus, the CCRN is essentially a variant of MRN which properly accounts for Ceramics 2021, 4, 121–134. https://doi.org/10.3390/ceramics4020011 https://www.mdpi.com/journal/ceramics