Carothers equation
E573389
The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Carothers equation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6155561 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Carothers equation Context triple: [Wallace H. Carothers, notableConcept, Carothers equation]
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A.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
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B.
Karplus equation
The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
-
C.
Gibbs–Duhem equation
The Gibbs–Duhem equation is a fundamental thermodynamic relation that links changes in chemical potential, temperature, and pressure for multicomponent systems, ensuring consistency among intensive variables.
-
D.
Flory–Huggins solution theory
Flory–Huggins solution theory is a thermodynamic model that describes the mixing behavior and phase separation of polymer solutions by accounting for the size difference between polymer chains and solvent molecules.
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E.
Butler–Volmer equation
The Butler–Volmer equation is a fundamental relation in electrochemistry that describes how the rate of an electrode reaction (current density) depends on the electrode potential and reaction kinetics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Carothers equation Target entity description: The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
-
A.
Charney equation
The Charney equation is a fundamental quasi-geostrophic equation in atmospheric dynamics that describes large-scale Rossby waves and mid-latitude weather patterns on a rotating planet.
-
B.
Karplus equation
The Karplus equation is an empirical relationship in nuclear magnetic resonance (NMR) spectroscopy that correlates three-bond scalar coupling constants with dihedral angles, enabling the determination of molecular conformations.
-
C.
Gibbs–Duhem equation
The Gibbs–Duhem equation is a fundamental thermodynamic relation that links changes in chemical potential, temperature, and pressure for multicomponent systems, ensuring consistency among intensive variables.
-
D.
Flory–Huggins solution theory
Flory–Huggins solution theory is a thermodynamic model that describes the mixing behavior and phase separation of polymer solutions by accounting for the size difference between polymer chains and solvent molecules.
-
E.
Butler–Volmer equation
The Butler–Volmer equation is a fundamental relation in electrochemistry that describes how the rate of an electrode reaction (current density) depends on the electrode potential and reaction kinetics.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
polymer chemistry equation
ⓘ
scientific law ⓘ |
| appliesTo |
condensation polymerization
ⓘ
linear polymers ⓘ step-growth polymerization ⓘ |
| assumes |
absence of intramolecular cyclization
ⓘ
equal reactivity of functional groups ⓘ stoichiometric balance of functional groups ⓘ |
| educationalUse |
graduate-level polymer science courses
ⓘ
introductory polymer chemistry courses ⓘ |
| expresses | relationship between degree of polymerization and extent of reaction ⓘ |
| field |
macromolecular science
ⓘ
polymer chemistry ⓘ |
| historicalContext | developed in early 20th century ⓘ |
| influence |
development of synthetic polymer theory
ⓘ
understanding of high molecular weight formation requirements ⓘ |
| involvesConcept |
degree of polymerization
ⓘ
functional group conversion ⓘ molecular weight build-up in step-growth systems ⓘ |
| limitation |
does not account for chain branching
ⓘ
does not account for unequal reactivity of functional groups ⓘ less accurate at very high conversions if side reactions occur ⓘ |
| mathematicalForm | X_n = 1 / (1 - p) ⓘ |
| namedAfter | Wallace Hume Carothers NERFINISHED ⓘ |
| relatedConcept |
Flory distribution
NERFINISHED
ⓘ
extent of reaction in polycondensation ⓘ number-average molecular weight ⓘ step-growth polymerization kinetics ⓘ |
| relatesQuantity |
extent of reaction
ⓘ
fractional conversion of functional groups ⓘ number-average degree of polymerization ⓘ |
| symbolDefinition |
X_n is the number-average degree of polymerization
ⓘ
p is the extent of reaction ⓘ |
| typicalApplication |
synthesis of polyamides
ⓘ
synthesis of polycarbonates ⓘ synthesis of polyesters ⓘ |
| usedFor |
designing polymerization conditions
ⓘ
estimating molecular weight from conversion ⓘ predicting average chain length in step-growth polymers ⓘ teaching fundamental concepts of polymerization kinetics ⓘ |
| validWhen |
functional groups are bifunctional
ⓘ
system is ideal step-growth polymerization ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Carothers equation Description of subject: The Carothers equation is a fundamental relation in polymer chemistry that links the average degree of polymerization to the extent of reaction in step-growth polymerizations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.