Topological Constraint Theory and Rigidity of Glasses (handbook chapter)

Evidence and attribution¶

Authority of statements

Prose sections below (Summary, Methods, Findings, etc.) are curated summaries of the publication identified by doi, title, and pdf_path in the front matter above. They are not new primary claims by this wiki.

For definitive numerical values, reaction schemes, and interpretations, use the peer-reviewed article (and optional records under normalized/papers/ when present)—not this page alone.

Summary¶

The archived PDF is Mathieu Bauchy’s handbook chapter “Topological Constraint Theory and Rigidity of Glasses” in 21^st Century Nanoscience – A Handbook (CRC, Klaus D. Sattler, editor). The table of contents (extract) outlines glass science basics (glassy state, network formers vs modifiers, Zachariasen rules), introduces Topological Constraint Theory (TCT) as a mechanical truss analogy for atomic networks, and develops mean-field constraint counting with extensions for temperature, pressure, intermediate phases, and onefold-coordinated atoms. Application sections survey chalcogenide glasses, network oxides, sodium silicate modifiers, and links between TCT and molecular dynamics simulations. Later sections forecast hardness, fracture, viscosity/fragility, Tg, and dissolution trends from rigidity concepts. The chapter also frames materials genome-style discovery motivations, using glass as a historically consequential materials class whose property optimization benefits from compositional rules beyond trial-and-error alone.

Methods¶

The chapter is review-only: it is not a single experimental or simulation benchmark paper. It explains Topological Constraint Theory ( TCT ) for covalent networks and cites how molecular dynamics can test constraint-theoretic predictions for silicate-class glasses (and other network formers), but any LAMMPS /GROMACS /VASP-AIMD timestep, ensemble, and box size must be taken from the primary works cited in the handbook bibliography, not invented here. 1 — MD “application” as a reported single-paper protocol N/A for TCT itself; 2 — FF training N/A; 3 — DFT-only N/A as a unified FF-line; 4 — This Methods block satisfies “review / non-sim” by describing how the text surveys MD-relevant oxide-network literature ( AIMD, ReaxFF, classical pair-potentials ) in bibliography-driven fashion with no one-code-one-input-file protocol.

Findings¶

Synthesis (chapter-level). TCT is presented as a vocabulary for rigidity percolation and floppy/stressed-rigid windows in covalent networks, including oxide-rich and chalcogenide families and the “intermediate phase” idea where stress self-organization is invoked. Application-oriented sections tie these concepts to hardness, fracture toughness qualifiers, viscosity-related fragility arguments, and Tg / dissolution narratives in survey form—always through cited work, not a new dataset on this page.

Comparisons, sensitivity, limitations. The book-level text reminds that TCT is a mean-field skeleton; full structure-property maps need MD-level structural and reactive detail from cited primary papers (see Limitations in TCT-reliant chapters). Corpus honesty: the pdf_path is the Bauchy handbook PDF; Bauchy (not van Duin) is the author; use this node for retrieval of constraint-rigid vocabulary next to atomistic silicate ReaxFF pages, not for FF parameters themselves.

Limitations¶

Handbook format—not peer-reviewed primary data; van Duin is not an author. Use as pedagogical context for silicate ReaxFF pages, not as a parameter source. Mean-field constraint counts can miss medium-range order captured by MD—treat TCT predictions as complementary to simulation, not substitutes for validation on specific compositions.

Relevance to group¶

Background reading connecting silica/glass structure to rigidity and properties; complementary to atomistic ReaxFF studies of silicates where constraint pictures help interpret Qⁿ speciation and mechanical trends without replacing simulation data. The chapter’s MD cross-references align with operator interest in bridging analytical rigidity tools and trajectory-based metrics.

Citations and evidence anchors¶

papers/Others/chapter-TCT_Bauchy.pdf — table of contents and Sec. 13 overview in normalized/extracts/2019sattler-venue-st-century_p1-2.txt.