Polymer Ontology

FLOW ALGEBRA
POLYMER ONTOLOGY
Kireth Semantic Library | Flow Algebra v1.1
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/chemical-entities/polymer-ontology.html
Status: Scientific synthesis; source webpage not independently verified.
Date: 2026-10-12

01. PURPOSE
Represent polymers, repeat units, chain topology, synthesis, structure, properties, and transformations with typed, testable relationships.

02. DOMAIN
Physical Entities > Chemical Entities > Polymer Ontology.

03. FORMAL SIGNATURE
Ontology P = (E, R, A, C, I, V), where E is entities, R relationships, A attributes, C constraints, I inference rules, and V validation tests.

04. ENTITY TYPES
Polymer, Macromolecule, Monomer, RepeatUnit, PolymerChain, Copolymer, Homopolymer, Oligomer, Crosslink, Branch, Network, PolymerBlend, Additive, Solvent, Catalyst, Initiator, PolymerSample, PolymerisationProcess, DegradationProcess, Measurement, ProvenanceRecord.

05. CLASSIFICATION
Polymer may be natural, synthetic, or semi-synthetic.
Polymer may be thermoplastic, thermoset, or elastomer by observed behaviour; these categories are not necessarily mutually exclusive in all contexts.
Polymer may be amorphous, semicrystalline, or predominantly crystalline under specified conditions.

06. IDENTITY AND SCOPE
A polymer substance is a population of molecules; a polymer chain is one molecular instance.
Distinguish repeat-unit identity, chain sequence, chain length, molecular-weight distribution, and specimen conditions.

07. TYPED RELATIONSHIPS
HAS_REPEAT_UNIT(Polymer, RepeatUnit)
DERIVED_FROM(Polymer, Monomer)
CONTAINS_CHAIN(PolymerSample, PolymerChain)
HAS_BRANCH(PolymerChain, Branch)
CROSSLINKED_BY(PolymerChain, Crosslink)
FORMED_BY(Polymer, PolymerisationProcess)
BLENDED_WITH(Polymer, Polymer)
HAS_PROPERTY(PolymerSample, PropertyMeasurement)
DEGRADES_BY(Polymer, DegradationProcess)
MEASURED_UNDER(Measurement, Conditions)
SUPPORTED_BY(Assertion, ProvenanceRecord)

08. POLYMERISATION
Chain-growth polymerisation: growth occurs at active centres by monomer addition.
Step-growth polymerisation: functional groups react between species across a range of sizes.
Examples include radical, ionic, coordination, condensation, and ring-opening routes; mechanisms must be specified rather than assumed from a label.

09. COMPOSITION
Homopolymer: derived from one monomer species (subject to accepted chemical nomenclature).
Copolymer: derived from more than one monomer species.
Copolymer architectures include random/statistical, alternating, block, and graft; a statistical sequence does not necessarily mean an equiprobable random sequence.

10. TOPOLOGY
Linear, branched, star, comb, cyclic, dendritic, and crosslinked/network structures.
Topology affects melt flow, solubility, mechanical response, and degradation.

11. DEGREE OF POLYMERISATION
DP_n = number-average count of constitutional repeat units per chain.
For a chemically uniform repeat unit and negligible end-group contributions: DP_n approximately M_n / M_repeat.
For copolymers, use an appropriate composition-weighted repeat-unit mass and disclose assumptions.

12. MOLECULAR WEIGHT STATISTICS
M_n = sum_i(N_i M_i) / sum_i(N_i).
M_w = sum_i(N_i M_i^2) / sum_i(N_i M_i).
Dispersity D = M_w / M_n >= 1 for positive masses and a well-defined distribution.
Never confuse polymer sample molar-mass averages with the mass of an individual chain.

13. CHAIN CONFORMATION
End-to-end distance, radius of gyration, persistence length, and entanglement depend on architecture, solvent, temperature, and molecular mass.
For an ideal freely jointed chain: <R^2> = N b^2, with N independent segments of length b.
This ideal-chain equation is not universally valid for real chains.

14. THERMAL PROPERTIES
Glass-transition temperature Tg characterises a kinetic transition in amorphous regions.
Melting temperature Tm concerns crystalline regions; amorphous polymers lack a crystalline melting transition.
Thermal decomposition and oxidation must be distinguished from reversible thermal transitions.

15. MECHANICAL PROPERTIES
Young's modulus E = d sigma / d epsilon in the linear elastic regime under specified test conditions.
Viscoelasticity depends on time, frequency, temperature, and strain history.
Creep: strain response under sustained stress; stress relaxation: stress response under fixed strain.

16. TRANSPORT AND SOLUBILITY
Diffusion and permeation depend on molecular size, free volume, temperature, morphology, and interactions.
Fick's first law under its assumptions: J = -D grad(c).
Solubility and swelling are not equivalent; crosslinked networks can swell without dissolving.

17. CRYSTALLINITY
Crystalline fraction is method- and sample-dependent.
Report whether derived from DSC, XRD, density, or another method; do not treat values from different methods as automatically interchangeable.

18. STEREOCHEMISTRY
Tacticity: isotactic, syndiotactic, or atactic arrangements for suitable stereogenic repeat-unit sequences.
Cis/trans configuration and chain stereochemistry may change crystallisation and mechanical behaviour.

19. CHEMICAL INTERACTIONS
Covalent backbone bonding, intermolecular hydrogen bonding, dispersion forces, ionic associations, and coordination can influence polymer properties.
Do not label hydrogen bonds as covalent backbone links.

20. DEGRADATION
Mechanisms: hydrolysis, oxidation, photodegradation, thermal scission, biodegradation, and mechanical chain scission.
Rate depends on polymer chemistry, environment, geometry, and additives.
Biodegradable is not synonymous with rapidly degradable in every environment.

21. RECYCLING AND END OF LIFE
Mechanical recycling, chemical recycling, reuse, incineration with energy recovery, and disposal are distinct processes.
Recyclability claims require process and locality context.

22. BIOPOLYMERS
Examples: cellulose, proteins, nucleic acids, natural rubber.
Biobased origin and biodegradability are independent properties.

23. COMMON SYNTHETIC EXAMPLES
Polyethylene, polypropylene, polystyrene, PET, PVC, nylon, PTFE, and silicone polymers.
Each example requires a chemically accurate repeat-unit and processing context.

24. POLYMER NETWORKS
Crosslink density affects swelling, elasticity, solvent response, and thermal behaviour.
Rubber elasticity idealisation: G approximately nu_e R T under appropriate network assumptions.

25. CHARACTERISATION
SEC/GPC estimates molar-mass distributions subject to calibration or detection model.
NMR probes chemical structure and composition.
FTIR identifies characteristic vibrational features.
DSC probes thermal transitions; TGA probes mass changes under heating.
XRD probes order; rheometry probes viscoelastic response.

26. PROCESSING
Extrusion, injection moulding, compression moulding, casting, fibre spinning, and additive manufacturing.
Processing history can alter crystallinity, orientation, residual stress, and properties.

27. CONSERVATION
For a closed chemical system, elemental atom counts and total mass are conserved within applicable classical chemistry approximations.
Reaction stoichiometry must include byproducts where applicable.

28. INFERENCE RULES
IF a polymer is crosslinked into a percolating network THEN classify it as a network polymer, provided connectivity is demonstrated.
IF M_w and M_n are valid positive averages THEN dispersity >= 1.
IF a sample shows Tg THEN infer an amorphous-phase transition, not necessarily that the entire polymer is amorphous.
IF polymer contains two distinct monomer-derived units THEN it may be classified as a copolymer, subject to repeat-unit definitions.
IF a property changes with temperature THEN require measurement conditions before cross-study comparison.

29. NON-INFERENCE SAFEGUARDS
Do not infer biodegradability from natural origin alone.
Do not infer high crystallinity solely from high stiffness.
Do not infer thermoset classification solely from high molecular mass.
Do not infer molecular identity solely from a trade name.
Do not infer measured values from generic polymer family labels.

30. WORKED EXAMPLE: MOLAR-MASS DISTRIBUTION
Sample contains 2 chains at 10 kg/mol and 1 chain at 20 kg/mol.
M_n = (2*10 + 1*20)/3 = 13.333 kg/mol.
M_w = (2*10^2 + 1*20^2)/(2*10 + 1*20) = 15 kg/mol.
D = 15/13.333 = 1.125.
Validation: D >= 1 and M_w >= M_n.

31. WORKED EXAMPLE: POLYETHYLENE
Monomer: ethene CH2=CH2.
Repeat unit: [-CH2-CH2-].
For a chain with n idealised repeat units, repeat-unit contribution to molar mass is n * 28.05 g/mol approximately.
Account for end groups for accurate finite-chain mass.

32. WORKED EXAMPLE: THERMAL RESPONSE
Given Tg = 80 C and measurement T = 25 C, a primarily amorphous region may be glassy on the experimental timescale.
This does not establish brittleness without loading-rate, morphology, and formulation information.

33. VALIDATION CONSTRAINTS
V1: All entities have unique stable identifiers within the dataset.
V2: Every property measurement includes units and measurement method.
V3: Temperature-dependent properties include temperature and relevant timescale.
V4: M_n > 0; M_w >= M_n for a valid mass distribution.
V5: Monomer-to-repeat-unit mappings preserve chemical stoichiometry.
V6: All empirical claims carry provenance and uncertainty where applicable.
V7: Crosslink assertions distinguish covalent from physical associations.
V8: Theoretical models identify their assumptions and applicability domain.

34. SEMANTIC EQUIVALENCE
polymer chain ~= macromolecular chain when both denote a single covalently linked polymer molecule in context.
number-average molar mass == M_n.
weight-average molar mass == M_w.
polydispersity index is a legacy term often used for dispersity D; prefer D.
polymer != monomer; polymer sample != individual polymer chain.

35. CONFIDENCE
Confidence is attached to individual assertions, not assigned uniformly to an entire ontology.
Formal identities: confidence high when assumptions are satisfied.
Empirical measurements: confidence depends on calibration, reproducibility, uncertainty, and provenance.
Unverified site-specific details: confidence not assessed.

36. FLOW_HASH
Algorithm: SHA-256 over canonical UTF-8 normalised flow content.
Value: COMPUTE_AT_INGESTION (not fabricated).
Canonicalisation: normalise line endings and defined whitespace before hashing.

37. UPDATE_MODEL
Version: 1.1.
On source revision: compare definitions, relationships, constraints, measurements, and provenance.
Preserve prior versions and record changed assertions and timestamps.
Require review when new evidence contradicts existing classification.

38. AI_CONSUMPTION
mode: typed_semantic_reasoning
inputs: polymer_identity, composition, topology, conditions, measurement, provenance
outputs: validated_entities, relationships, derived_properties, constraints, uncertainty
reasoning: rule_based_with_explicit_assumptions
hallucination_guard: do_not_invent_measurements_or_source_claims
citation_policy: attach_provenance_to_empirical_claims

39. PROVENANCE
Source URL identifies the intended Kireth Research ontology page.
This document is a scientific synthesis and does not claim to reproduce unseen page text.
Authors: Mark Higgins — Sky (Recursive AI).

40. COMPLETENESS CHECK
Sections expected: 40.
Sections present: 40.
Required blocks: definitions, entities, relationships, equations, inference, validation, semantic equivalence, confidence, FLOW_HASH, UPDATE_MODEL, AI_CONSUMPTION.
END FLOW ALGEBRA — POLYMER ONTOLOGY