Calculation of catalysts in polyurethane soft foam formulations

Kinetics of the reaction between hydroxyl compounds and isocyanates
-d(-NCO)/dt=K0×(-NCO)×(-OH)
K1 is the forward reaction rate of isocyanate and hydroxyl compound to form a complex
K2 is the negative reaction rate of the complex formed between isocyanate and hydroxyl compound
K3 is the forward reaction rate of the complex and the hydroxyl compound to form the carbamate and the hydroxyl 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 reaction heat of formation of urea, polyurethane, biuret, allophanate and other groups:
Bond dissociation energy (KJ/mol)
C-N205.1~251.2
C-C230.2~293.0
C-O293.0~314.0
N-H351.6~406.0
C-H364.9~393.5
O-H422.8~460.5
C=C418.6~523.3
C=O594.1~694.9
Reaction
RNCO+rOH→RNHCOOr
RNCO+HOH→RNHCOOH+RNCO→RNHCONHR+OCO↑
RNHCOOr+RNCO→RNCONHRCOOr
RNHCONHr+RNCO→RNCONHRCONHr
The volume ratio of the gas in the polymerization system to the total volume of the polymerization system (Vg/Vo) controls the temperature: the gas monomer affects the concentration (mol/L) and controls 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). After the temperature of the polymerization system rises suddenly, the gas escapes and takes away a large amount of heat (approximately in a straight line with Vg/Vo)
When making polyurethane in one step, the reaction activation energy of amino acids is about 60 (mol.K), and the reaction activation energy of urea is 17 (mol.K)
Foam systems are easier to implement than solution systems and suspension systems. In dispersion polymerization, the Norrish-Tromastof effect occurs at the beginning of the reaction, which slows down the change rate of chain growth parameters over time and improves the monodispersity of the product.
Dispersion polymerization is a method that uses gas to separate the polymerization system into countless small foams, so that the polymerization components are converted into a surface liquid film of the foam and a “multi-faceted boundary liquid cell” connecting multiple liquid films to form a special dispersed phase for polymerization.
The foam system uses gas as the dispersion medium. When the gas expands and escapes when heated, the sudden cooling effect and the negative pressure generated when the gas escapes concentrate the remaining monomers in the system and further polymerize them. It accelerates and carries the evaporation of water molecules and the escape of small molecules.
The dispersion effect of gas on the polymerization system is not equal to the real dilution of the monomer.
General formula for half-life of non-first-order reactions
T=[2^(n-1)-1]/[a×k×(n-1)×A^(n-1)]
Second-order reaction rate constant
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:
Calculation example of density of polyurethane soft foam
Universal polyether triol Ppg: 50pop: 50tdi-80: 42.8hoh: 3.17L-580: 1a33: 0.34sn: 0.17
Calculated: 4.342.176.5138.2112%17%5.21.74122 Calculated again, 28kg/cubic meter
Polyurethane soft foam catalyst calculation example
Universal polyether triol ppg: 90pop: 10tdi-80:: 35.5hoh: 2.2L-580: 0.84 Black pulp: 6
Calculated: A33: 0.18T-9: 0.25
A33：0.14T-9：0.24
A33：0.13T-9：0.35
A33：0.12T-9：0.30
Tolerance and turning point…
Calculation of vertical foaming flow rate and lifting speed:
Formula (for example only) PPG: 100, TDI: 80, HOH: 6, SI: 1.5, A33: ***, SN: ***, MC: 14.8
The diameter of the vertical bubble round mold is 1.25.
The polyether flow rate is 12 kg/min.
What is the lifting speed (m/min)
Find the formula density of 12 kilograms per cubic meter. The total formula weight is 173.5 kg. The formula volume is 14.46 cubic meters. Circular mold cross-sectional area: 1.23 square meters.
Assume the loss rate is 5%.
Lifting speed: [14.46×12%×(1-5%)]/1.23=1.34 meters/minute.