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.
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.