Calculation of catalysts in polyurethane flexible foam formulations

Kinetics of the reaction of hydroxyl compounds with isocyanates – d(-NCO)/dt = K0 × (-NCO) × (-OH)

K1 is the forward reaction rate for the complex formation of isocyanate with hydroxy compounds

K2 is the negative reaction rate of isocyanate complexes with hydroxyl compounds

K3 is the positive reaction rate of the complex with hydroxy compound to generate carbamate with hydroxy compound.

K0=[K1×K3×(-OH)]/[K2+K3×

Arrhenius equation

K=Ae^[-(Ea/RT)]

A: Exponential factor.

e=2.718

Ea: KJ/mol

R=8.31(J/mol.K)

Calculation of the heat of reaction for the formation of urea, polyurethane, diurea, ureidoformate and other groups:

Bond leaving energy(KJ/mol)

C-N 205.1~251.2

C-C 230.2~293.0

C-O 293.0~314.0

N-H 351.6~406.0

C-H 364.9~393.5

O-H 422.8~460.5

C=C 418.6~523.3

C=O 594.1~694.9

Reaction formula.

RNCO+rOH→RNHCOOr

RNCO+HOH→RNHCOOH+RNCO→RNHCONHR+OCO↑

RNHCOOr+RNCO→RNCONHRCOOr

RNHCONHr+RNCO→RNCONHRCONHr

The volume ratio of the gas to the total volume of the polymerization system in the polymerization system (Vg/Vo) has the ability to regulate the temperature: the gas monomer influences the concentration (mol/L) around the heat of polymerization [Q(KJ/L)=Rp(mol/L)*(-H)]. The heat of polymerization is transferred to the gas dispersion medium causing the gas to absorb heat and expand (PV=NR/T). The polymerization system temperature rises abruptly and then the gas comes off and takes away a large amount of heat (approximately linear with Vg/Vo)

The activation energy of amino acid reaction is about 60(mol.K) and that of urea reaction is 17(mol.K) in one-step polyurethane production.

The foam system is easier to implement than the solution system suspension system. The Norrish-Tromastof effect occurs at the beginning of the reaction for dispersion polymerization, which slows down the rate of change of chain growth parameters with time and improves the monodispersity of the product.

Dispersion polymerization is a method of polymerization in which a gas is used to separate the polymerization system into numerous small bubbles so that the polymerized components are transformed into a surface liquid film of foam and a “multifaceted boundary liquid cell” connecting multiple liquid films to form a special dispersed phase.

Gas is used as the dispersion medium in the foam system. The gas is heated and expands and escapes with sudden cooling effect and the negative pressure is generated when the gas escapes to further polymerize the residual monoconcentration of the system, and the evaporation of water molecules and small molecules are accelerated and carried out.

The dispersion effect of gas on the polymerization system is not equal to the real dilution of the monomer.

Non-primary reaction half-life general formula

T=[2^(n-1)-1]/[a×k×(n-1)×A^(n-1)]

Secondary reaction rate constants

A+B→Q+S

Kt=[1/(CA0-CB0)]×ln[(CB0×CA)/(CA0×CB)

CA0×Kt=[1/(1-M)]×ln{[M(1-xA)]/(M-xA)} where M=CB0/CA0

Attachment.

Example of calculating the density of polyurethane soft foam

General polyether triol Ppg:50pop:50tdi-80:42.8hoh:3.17L-580:1a33:0.34sn:0.17

Calculated: 4.34 2.17 6.51 38.2 112% 17% 5.2 1.74 122 Calculated again, 28kg/m3

Example of polyurethane soft foam catalyst calculation.

General polyether triol ppg:90 pop:10 tdi-80::35.5 hoh:2.2 L-580:0.84 black pulp:6

Calculated: A33:0.18 T-9:0.25

A33:0.14 T-9:0.24

A33: 0.13 T-9: 0.35

A33: 0.12 T-9: 0.30

Tolerance and inflection point ……

Calculation of pendant foam flow rate and lifting speed:

Recipe (for example only) PPG:100, TDI:80, HOH:6, SI:1.5, A33:***, SN:***, MC:14.8

Pendant foam round mold diameter 1.25.

Polyether flow rate is 12 kg/min.

Find what is the lifting speed (m/min)

Find the density of the formulation 12 kg per cube. The total weight of the formulation is 173.5 kg. The volume of the formulation is 14.46 cubic meters. Round mold cross-sectional area:1.23 m2.

Set the loss rate at 5%.

Lifting speed: [14.46×12%×(1-5%)]/1.23=1.34m/min.