Model gel formation using functionality and conversion. Compare predicted gel point against your target window. Plan experiments confidently with clear outputs and exports included.
This calculator uses a common step-growth gelation approximation based on average functionality:
Assumptions: random branching, equal reactivity, and no strong intramolecular cyclization effects. Real systems may deviate; validate with rheology or sol–gel testing.
Tip: If your conversion is uncertain, run multiple values to map a safe window below pc.
| Scenario | f_avg | p (conversion) | p_c | Interpretation |
|---|---|---|---|---|
| Mostly bifunctional with small brancher | 2.40 | 0.30 | 0.7143 | Below gel point; mixture remains a sol. |
| Higher branching | 3.00 | 0.55 | 0.5000 | At/above gel point; gel network likely forms. |
| Near-threshold design check | 2.80 | 0.45 | 0.5556 | Safety margin remains; monitor conversion drift. |
Gelation threshold marks the shift from finite clusters to a sample-spanning network in step-growth and sol–gel systems. Near this point, viscosity climbs rapidly, elastic response appears, and filtration or pumping becomes difficult. Using a calculated critical conversion p_c gives a practical “do not cross” marker for pot life and processing. Track temperature, catalyst level, and residence time because each can accelerate conversion toward the threshold.
Average functionality f_avg summarizes how many reactive connections molecules can form on average. Adding trifunctional or tetrafunctional branchers raises f_avg and lowers p_c, so gelation occurs earlier. Monofunctional stoppers and excess difunctional content reduce f_avg and delay network formation. In mixture mode, weight or mole fractions must be consistent; the calculator normalizes fractions to prevent arithmetic bias when inputs do not sum to one.
Conversion p represents the fraction of functional groups that have reacted. Compare measured p from titration, spectroscopy, or calorimetry to p_c to interpret batch status. If p is well below p_c, the material should remain a sol with manageable flow. As p approaches p_c, small errors in measurement matter; sampling delays can push p over the line, triggering gel and trapping bubbles or fillers.
Sensitivity checks strengthen decision making. Recompute p_c using plausible ranges for f_avg based on supplier specs, moisture uptake, and equivalent-weight uncertainty. For formulations, vary brancher fraction and observe how strongly p_c moves; large shifts indicate a narrow processing window. Use the margin p_c − p to set control limits, choose sampling frequency, and define maximum hold times. When scaling, account for heat removal differences that raise reaction rate. If you target a specific gel time, adjust catalyst or temperature so predicted p remains below p_c during mixing, then crosses p_c only after application or molding with checks at each stage.
This relation is a screening model that assumes random branching, equal reactivity, and minimal cyclization. Real systems may gel later or earlier due to intramolecular loops, phase separation, diffusion limits, or unequal rate constants. Validate the estimate with rheology (G′/G″ crossover), gel content, or solubility tests at your cure schedule. Use the calculator to compare scenarios, document assumptions, and communicate risk across R&D, production, and quality teams.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.