The Molecular Weight and Functionality of Polyurethanes (Part 2)

Functionality refers to the number of reactive groups in a polymer molecule that can participate in a chemical reaction. Understanding the functionality of various polymers is highly beneficial for selecting appropriate raw materials and synthesizing desired products. For example, elastomers generally use difunctional compounds, while foam products require polyfunctional compounds.

The general formula for functionality is:

F = Mn / E  (11-27)

Where:

Mn — number-average molecular weight

E — equivalent value

In practice, the commonly provided parameters are the hydroxyl value (OH number) and Mn of polyether polyols. Thus, formula (11-2) can be used:

E = (1000 × 56.1) / OH

Substituting into equation (11-27) gives:

Fa = (Mn × OH) / (1000 × 56.1)  (11-28)

Example:

The Desmophen 3900 polyether from Bayer lists Mn = 4800 and a hydroxyl value of 32 mgKOH/g, but does not provide a functionality value. We can calculate it using formula (11-28):

F = (4800 × 32) / (1000 × 56.1) = 2.7

Note: The Mn used in this formula must be measured by gas permeation chromatography, not by end-group analysis, or the F value may deviate significantly.

Equation (11-28) also allows indirect functionality determination from a polymer's hydroxyl value and Mn.

For mixed polyols, it's best to directly measure both the number-average molecular weight and hydroxyl value, and calculate using:

Fm = (Mnm × OHm) / (1000 × 56.1)  (11-29)

If the functionalities and hydroxyl values of each component are known, the functionality of the blend (by weight fraction) can be calculated as:

Fm = (OHm × Fi × Fk) / (OHi × Fk × a + OHk × Fi × (1 – a))  (11-30)

Where:

OHm — hydroxyl value of the mixture

Fi — functionality of component 1

Fk — functionality of component 2

OHi — hydroxyl value of component 1

OHk — hydroxyl value of component 2

A — mass fraction of component 1

1 – A — mass fraction of component 2

OHm can also be calculated from the hydroxyl values of the two components:

OHm = OHi × A + OHk × (1 –A)  (11-31)

Example:

If 62.5% of a polyether triol with OH = 58 mgKOH/g is blended with 37.5% of a polyether diol with OH = 114 mgKOH/g, the average functionality of the blend is:

First calculate OHm:

OHm = 58 × 0.625 + 114 × 0.375 = 79 (mgKOH/g)

Then apply equation (11-30):

Fm = (79 × 3 × 2) / (58 × 2 × 0.625 + 114 × 3 × 0.375) = 2.36

When blending polyols, we often encounter cases where the molecular weights of two polyols are known and a target average molecular weight is desired. To determine the required proportions, use:

α = (Mnj / Mnm) × [(Mnk – Mnm) / (Mnk – Mnj)]  (11-32)

Example:

Polyether A has Mn = 1990, polyether B has Mn = 1009, and we want a blend with Mn = 1500:

α = 1990 / 1500 × (1009 – 1500) / (1009 – 1990) = 0.664

Polyether B proportion:

1 – α = 0.336

If the functionalities and hydroxyl values of polyols are known, equation (11-32) can be adapted to:

α = (Fi / Mnm) × [(1000 × 56.1 × Fk – Mnm × OHk) / (OHi × Fk – OHk × Fi)]  (11-33)

For weight-average molecular weights, α can be calculated using:

α = (Mwm – Mwk) / (Mwi – Mwk)  (11-34)

Example:

To blend a diol (OH = 55.4 mgKOH/g) and triol (OH = 57.2 mgKOH/g) to achieve Mn = 2500:

Given:

Fi = 2, OHi = 55.4

Fk = 3, OHk = 57.2

Mnm = 2500

Then:

α = 2 / 2500 × [(1000 × 56.1 × 3 – 2500 × 57.2) / (55.4 × 3 – 57.2 × 2)] = 0.391 → 39.1%

Second component:

1 – α = 60.9%