What Is the Relationship Between Catalyst Dosage and Polyurethane Foam Properties?

① Introduction to General Polyether Triols for Block Foam

General soft foam characteristics: Moderate hardness; moderate elasticity; moderate elongation and tear properties; relatively high permanent deformation.

Density (d): Mass of substance per unit volume. Denoted as d. Units: kilograms per cubic meter (kg/m³) in SI and Chinese legal units.

m represents mass, V represents volume: d = m/V

Raw material densities:

d(PPG) ≈ 1.0 d(TDI) ≈ 1.25 d(H₂O) ≈ 1.0

Foam density:

d(Foam) = (Total mass of all formulation components - Mass of escaped CO₂) / (Volume of foam struts + Volume of cells)

The first step in formulation design is determining density and factors related to its change. Neglect the mass difference between water/additives and escaped CO₂. Neglect the volume occupied by foam struts.

Cell volume relates to CO₂ and blowing agent quantity.

Foaming Index is denoted as In(F).

In(F) = m(H₂O) + m(MC)/9

Final foam density is:

d(Foam) = [m(PPG) + m(TDI)] / K·In(F)

Dow Chemical, under 22°C room & material temperature and atmospheric pressure foaming, derived an empirical graph from extensive data showing the relationship between foaming index and foam density for standard formulations.

Relationship between Foaming Index and Free-Rise Foam Density

Mathematically, it's a typical inverse function curve, closely resembling:

x • y = 96 or y = 96/x

Therefore, an empirical formula can be derived:

Density × Blowing Index = 96 (Constant)

i.e., d • In(F) = 96

② Relationship between TDI Index and Density

TDI Index: In(TDI) or In(T)

In(T) = [m(TDI) / mo(TDI)] × 100%

Formulation design starts by setting the TDI index, then determining TDI usage. Why does actual TDI usage m(TDI) differ from theoretical mo(TDI)? This relates to the competitiveness of side reactions and their variation with temperature. As shown below:

Curve I: Polyester triol + XDI reaction

Curve II: Crosslinker MOCA + XDI reaction

Curve III: Diphenylurea + XDI reaction

Curve IV: Phenylene dibutyl carbamate + XDI reaction

Low raw material purity requires a higher given index.

High auxiliary usage (e.g., MC, stone powder) requires a higher given index.

Higher system temperature (lower density) requires a higher given index.

Schematic Diagram of Foam Density vs. TDI Index Value

Effect of TDI Index on Foam Density

Note: When In(F) is constant, a higher given In(TDI) causes density to decrease.

Affected by purity, d·In(F) ≈ 96 can be revised to:

d·In(F) ≈ 80 ~92

d·In(F)·In(TDI) ≈ 100

or d·In(F)·In(TDI) ≈ 95~110

③ Brief Introduction to Formulation Design Methods

Method 1: Early Modeling Deduction: Establish complex mathematical models to derive series of relationships (e.g., for H₂O, MC, Si, A33, T9, In(TDI) in the formulation) for design.

Special Recommendation: Center Temperature Calculation Formula

T_max = [1471.3In(TDI) + 1639.2m(H₂O)In(TDI) - 43m(F-11) - 78.1m(MC)] / [46.2 + 3.8In(TDI) + 4.3m(H₂O)In(TDI) + 0.54m(H₂O) + 0.14m(F-11) + 0.3m(MC)] + 22

Useful guidance for beginners, but experienced foam masters might not match a single value.

Method 2: Empirical Analogy: Statistically analyze numerous mature formulations to find patterns, establish non-quantitative relationships, and determine variable value ranges.

④ Example of Empirical Analogy Formulation Design

We present empirical formulas derived from over 30 years of experience and extensive statistical analysis of formulations.

General soft foam densities are artificially segmented:

Ultra-low density: 8--10 kg/m³

Low density: 10--16 kg/m³

Medium-low density: 16--24 kg/m³

Medium density: 24--32 kg/m³

Medium-high density: 32--40 kg/m³

High density: 40--48 kg/m³

Ultra-high density: 48--80 kg/m³

a. Determining TDI Index: Apply the solution set of the Golden Ratio equation.

Ultra-low density: Density increase Δd=1 → TDI index decrease ΔIn(TDI)= -1.618

Low density: Δd=1 → ΔIn(TDI)= -1

Medium-low density: Δd=1 → ΔIn(TDI)= -0.618

Medium & Medium-high density: Δd=1 → ΔIn(TDI)= -0.382

Adjust below In(TDI)=1.05 based on specifics.

b. Determining Blowing Index:

Reference data table provide: 

Can also derive using:

d·In(F) ≈ 96 (suitable for high purity)

d·In(F)·In(TDI) ≈ 100 (tentative, for low purity)

c. Determining Silicone Amount (Using L-580 as example):

m(Si) = 1/2 to 1/3 of m(H₂O)

Low cell requirement: m(Si) = 1/3 m(H₂O) usually sufficient.

High cell requirement or high m(MC) in ultra-low density: m(Si) = 1/2 m(H₂O)

Adjust for different silicone activity (≠L-580) or other system requirements. Systems have processing latitude for silicone amount.

d. Determining Amine/Tin Catalyst Amounts:

Amine-Tin Balance: Not equal amounts, but foam can bear its weight post-reaction with adequate cell opening.

Tin complements amine.

Tin has a processing range (latitude); different amines create different tin latitudes. Multiple Amine-Tin balance points exist per system.

"Balanced Amine-Tin": Amine/Tin difference ≤20g.

"High Amine Low Tin": High amine, difference >20g.

"Low Amine High Tin": Low amine, difference >20g.

System with Similar Reactivity (by Density and Flow Range):

Balance Zone Illustration:

Aa Zone: Low amine, high tin;  Bb Zone: Balanced amine and tin;p Cc Zone: High amine, low tin

⑤ Formulation Examples:

1.Medium Density (24–32 kg/m³)

Polyether triol (OH 56): 100，Water: 3–4，Silicone oil (L-580): 1.0–1.4，Triethylenediamine (A33): 0.18–0.22，Stannous octoate (T9): 0.18–0.22，TDI index: 105–110

2.Medium-High Density (32–48 kg/m³)

Polyether triol (OH 56):100, Water:1~2, Silicone (L-580):0.5~0.8, A33:0.25~0.30, T9:0.12~0.20, In-TDI:100~105

3.High Density (48–80 kg/m³)

Polyether triol (OH 56):100, Water:1~2, Silicone (L-580):0.5~0.8, A33:0.25~0.30, T9:0.12~0.20, In-TDI:100~105

4.Medium-Low Density (16–24 kg/m³)

Polyether triol (OH 56):100, In(F):4~6, m(H₂O):4.0~4.8, m(MC):0~11, Silicone (L-580):1.3~2.0, A33:0.25~0.30, T9:0.25~0.30, In-TDI:110~116

Effect of Water Content in the Formulation on Core Temperature

Effect of TDI Index on Core Temperature (m(H₂O) = 4)

A: In(TDI) = 103;     B: In(TDI) = 108;      C: In(TDI) = 113;      D: In(TDI) = 118

Effect of Foam Block Volume on Core Temperature

b: Foam height 100 cm
a: Foam height 81 cm

Light weight Flexible Foam Formulation for Low and Ultra-Low Densities (8kg/m³ to 16kg/m³)

General-purpose polyether triol (hydroxyl value 56): 100
In(F): 6 ~ 10.5
m(H₂O): 4.8 ~ 6.6
m(MC): 11 ~ 36
Silicone oil L-580 or B8110: 2 ~ 3.5
A33 or SMP: 0.3 ~ 0.5
T9: 0.3 ~ 0.5
In-TDI: 116 ~ 125

In(F) = m(H₂O) + m(MC) — How to distribute?

For low density, calculate In(F) based on: d·In(F)·In(TDI) = 105, to get In(F)

Based on reaction heat: Δm(H₂O) = 13.5·m(MC)
So each unit of water’s reaction heat can be absorbed by 13.5 units of MC.

Plan I:
When m(H₂O) ≥ 4, start adding MC. Based on the above relationships:

 m(H₂O) = 2.4 + 42⁄[d•In(TDI)]
 m(MC) = 567⁄[d•In(TDI)] − 21.6

Plan II:
At higher raw material temperature, when m(H₂O) ≥ 3.5, add MC. Similarly:

 m(H₂O) = 2.1 + 42⁄[d•In(TDI)]
 m(MC) = 567⁄[d•In(TDI)] − 18.9

Foaming Conditions Table

Low-Density Formulation Schemes

Simplified Formula for Core Temperature Estimation:

Tmax = [250·In(TDI) + 320·m(H₂O) − 8·m(MC)] / [8 + m(H₂O)] + Raw Material Temperature

Summary Chart:

DOW Chemical Plot (As Shown Below):