How to Calculate the Required Amount of Isocyanate for Flexible PU Foam?

In polyurethane chemistry, various active hydrogen compounds consume a certain amount of isocyanates. Based on the principle of equivalent reactions, accurately calculating the required isocyanate amount for each component in a formulation is a common practice in polyurethane synthesis. The following are simplified formulas used for such calculations.

1. For polyether or polyester polyols:

Ws=(EsWpI2)/Ep

Where:

Ws: Required amount of isocyanate

Wp: Amount of polyether or polyester

Es: Equivalent weight of the isocyanate

Ep: Equivalent weight of the polyether or polyester

I₂: Molar ratio of NCO to OH (i.e., the isocyanate index)

[Example]
In producing flexible polyurethane foam, 50g of a tri-functional polyether (with a hydroxyl value of 56 mgKOH/g) reacts with toluene diisocyanate (TDI) at an index of 1.05. The required TDI amount (Ws) is calculated as follows:

Given:Es= 87; Wp= 50; I₂ = 1.05

Ep= (1000 × 56.1) / 56 ≈ 1000

Then:
Ws= (87 × 50 × 1.05) / 1000 = 4.6g

It should be noted that this is the theoretical amount of isocyanate required for reacting with the polyether. In actual synthesis, the purity (ρs) of the isocyanate must also be considered. The formula is therefore adjusted to:

Ws= (EsWsI2/Epρs)  (2)

2. For amine-based compounds:

Ws=(EsWpI3)/Epρs  (3)

[Example]
In polyurethane foam rubber synthesis, the crosslinking agent MOCA is commonly used. If 10g of MOCA is used, the corresponding TDI amount is:

Given:Es= 133.5 (for MOCA); Wp(Wa) = 10g; Ep(Ea)= 87; ρs= 98%; I₃ = 1.05

Then:
Ws= (87 × 10 × 1.05) / (133.5 × 0.98) = 6.98g

In production, MOCA is often dissolved in polyether to form a binary blend. The formula is then modified to:

Ws=(EsWp/Ep+EsWa/Ea)*(I4/ρs)=(Wp/Ep+Wa/Ea)(EsI4/ρs)  (4)

Where:

I₄: Total isocyanate index for the mixture

ρs: Isocyanate purity

3. For water in the reaction system:

Water also consumes isocyanate—especially in flexible foam formulations using water as a blowing agent. The formula is:

Ws=(EsWqI2)/Enρs  (5)

4. Converting hydroxyl and acid values into the equation:

As polyethers and polyesters are generally specified by their hydroxyl and acid values, the formulas can be adapted as:

Ws=(EsWpOHpI2)/(1000*56.1) 

or 

Ws=EsWpI2(OHp+Ap)/(1000*56.1)

Where:

OHp : Hydroxyl value； Ap : Acid value