Synthesis of Polyurethane Foam Prepolymers (Part Two)

For polyurethane foam elastomers, such as PU microcellular foam, prepolymers are commonly used as a base and undergo crosslinking curing to form a three-dimensional polymer network. The physical and mechanical properties of such polymers are largely influenced by the crosslinking density. In other words, the higher the molecular weight between crosslink points, the better the resilience of the polyurethane elastomer, though the mechanical modulus decreases. Therefore, accurately calculating the crosslink density of these polymers is essential for controlling product performance. The following equation (11-14) is recommended for this purpose:

Mnc = 100 × 24 × Eg × [(Wv + Wg) / (Wv × Eg × D - 100 × 42 × Wg)]  (11-14)

Where:

Mnc Number-average molecular weight between crosslink points

Eg: Equivalent of the crosslinker (molar equivalent)

Wv: Amount of prepolymer used

Wg: Amount of crosslinker used

D: NCO content

[Example]

100 parts of prepolymer with 5.8% NCO content are cured with 11 parts of MOCA. What is the crosslink density of the cured polyurethane casting elastomer?

Given:

Wv = 100 parts; D = 5.8; Wg = 11 parts; Eg = 267/2 = 133.5

Using equation (11-14):

Mnc = 100 × 42 × 133.5 × [(100 + 11) / (100 × 133.5 × 5.8 - 100 × 42 × 11)] = 1992.9

If a specific crosslink density is required in polyurethane synthesis, one needs to determine in advance how much crosslinker to add. By rearranging equation (11-14), the following formula (11-15) can be derived to calculate the required amount of Wg:

Wg = (Eg × Wv) / (100 × 42) × [(Mnc × D - 100 × 42) / (Mnc + Eg)]  (11-15)

[Example]

A prepolymer with 100 parts and a free NCO content of 7.2% is to be cured with MOCA to achieve an elastomer with a molecular weight between crosslink points of 5000. How much MOCA is needed?

Given:

Eg = 133.5; Wv = 100; Mnc = 5000; D = 7.2

Using equation (11-15):

Wg = (133.5 × 100) / (100 × 42) × [(5000 × 7.2 - 100 × 42) / (5000 + 133.5)] = 19.7 parts

It is important to note that equations (11-14) and (11-15) are only applicable to linear prepolymers. For polyurethane foam products with higher branching, calculation of crosslink density must consider the loss of reactive gases and the total number of crosslinking sites of all reactants. For these systems, equation (11-16) should be used to determine molecular weight between crosslink points:

Mnc = (∑nWn - Wj) / ∑n(Wn / En)(Fn - 2)  (11-16)

Where:

Wn: Amount of each reactant excluding gas

Wj: Amount of gas produced

En: Equivalent (mole equivalent) of each reactant excluding gas

Fn: Functionality of each reactant excluding gas