Three tools for polyester and alkyd resin work: convert Acid Value / Hydroxyl Value to equivalent weight, calculate and classify oil length, and estimate degree of polymerization from extent of reaction. Alkyds are oil-modified polyesters, so the same underlying equations apply to both.
Core Equations Used Below
Oil Length (%) = Oil Weight ÷ Total Nonvolatile Resin Weight × 100
Xn = (1 + r) ÷ (1 + r − 2rp) | Carothers–Odian equation, r = 1 reduces to Xn = 1 ÷ (1 − p)
1. Acid Value / Hydroxyl Value → Equivalent Weight
Acid Eq. Weight
OH Eq. Weight
2. Oil Length Calculator
Oil Length
3. Degree of Polymerization (Carothers–Odian)
Stoichiometry
Stoichiometric Ratio r
r = —
Extent of Reaction (p)
Derive p from Acid Value Drop
p = —
This is an approximation, not an exact identity: it assumes the resin's mass stays constant through the cook. In reality, each esterification step releases water, so total mass drifts down slightly as the reaction proceeds. The water lost is normally small relative to total resin mass, so this stays a useful working estimate of cook progress — just not a chemically exact value.
Degree of Polymerization (Xn)
Practical Note
Alkyds are oil-modified polyesters — the same acid value / hydroxyl value / degree-of-polymerization math applies to both. Oil length boundaries (short/medium/long) vary somewhat by reference and region; treat the classification here as a common convention, not a fixed standard. Deriving p from an acid value drop is a working approximation, not an exact identity — it assumes constant resin mass through the cook, when in reality each esterification step releases water and mass drifts down slightly as the reaction proceeds. The Carothers–Odian equation itself assumes ideal linear step-growth behavior — real cooks deviate near high extents of reaction, and gelation risk rises sharply as p approaches 1, especially with any trifunctional monomer in the mix (glycerol, pentaerythritol). Watch viscosity buildup directly during a real cook rather than relying on Xn alone as the endpoint signal.
Data Sources & References
- Odian, G. — Principles of Polymerization, 4th Ed., Wiley, 2004
- Patton, T.C. — Alkyd Resin Technology, Interscience, 1962
- Martens, C.R. (Ed.) — Alkyd Resins, Reinhold, 1961
- Solomon, D.H. — The Chemistry of Organic Film Formers, 2nd Ed., Krieger, 1977
Equivalent weight: Eq. Wt = 56100 / Acid or OH Value, or Eq. Wt = 1700 / %OH. Oil length: Oil Length % = Oil Weight / Total Resin Weight x 100. Degree of polymerization: Xn = (1+r) / (1+r-2rp), extent of reaction from acid value: p = 1 - AVt/AV0.
Built by PolymerDNA — more formulation references in the Formulae Masterbook.