Molecular Weight and Functionality of Polyurethane (Part 1)

The molecular weight of a polymer is the average of the various molecular weights of its molecules. It includes the number-average molecular weight (Mn), which is averaged based on the number of molecules, and the weight-average molecular weight (Mw), which is averaged based on the mass of the molecules. In laboratories, molecular weight is typically measured using end-group analysis or vapor pressure osmometry, both yielding the number-average molecular weight.

The general formula for Mn is:

Mn = ∑niMi / ∑ni  (11-18)

If the equivalent value (E) and functionality (f) of a polymer are known, then:

Mn = E × f (11-19)

For polyether or polyester polyols with known hydroxyl value (OH) and functionality (F), formula (11-19) can be rewritten as:

Mn = (1000 × 56.1 × F) / OH (11-20)

Example:

For a polyether triol with a hydroxyl value of 55.8 mgKOH/g:

Mn = (1000 × 56.1 × 3) / 55.8 = 3016.1

In polyurethane production, blended polyether polyols are often used to achieve optimal product performance. Therefore, accurate calculation of the average molecular weight of polyol mixtures is crucial.

The general form for the number-average molecular weight of a mixture:

Mnm = (NjMj + NkMk) / (Nj + Nk) (11-21)

If the molecular weights and mass fractions of each component are known:

Mnm = (Mnj × Mnk) / (Mnk × A + Mnj × (1 - A)) (11-22)

Example: For PU microcellular elastomers (e.g., shoe soles), using 80% polyether polyol (Mn = 3000) and 20% polyester polyol (Mn = 1000):

Mnm = (3000 × 1000) / (1000 × 0.8 + 3000 × 0.2) = 2142.8

If the hydroxyl values, functionalities, and mass fractions of two polyols are known, the number-average molecular weight of their blend is calculated using:

Mnm = (1000 × 56.1 × Fj × Fk) / (OHj × Fk × A + OHk × Fj × (1 - A)) (11-23)

Where:

Fj – Functionality of compound j

Fk – Functionality of compound k

OHj – Hydroxyl value of compound j

OHk – Hydroxyl value of compound k

A – Mass fraction of compound j

1 – A – Mass fraction of compound k

In the polyurethane industry, polyol analysis reports typically include hydroxyl values and functionalities, making formula (11-23) more practical than formula (11-22).

Example:

For a prepolymer synthesis using 70% polyether diol (OH = 100) and 30% polyester diol (OH = 56):

Fj = 2; Fk = 2; A = 0.7; 1 - A = 0.3

Mnm = (1000 × 56.1 × 2 × 2) / (100 × 2 × 0.7 + 56 × 2 × 0.3) = 1292.6

The general formula for weight-average molecular weight (Mw) is:

Mw = ∑iWiMi / ∑iWi (11-24)

Where Wi – Mass of component i; Mi – Molecular weight of component i.

Alternatively, using number of molecules:

Mw = ∑iNiMi² / ∑iNiMi (11-25)

For a polyol blend, the weight-average molecular weight is simpler to calculate:

Mwm = Mwj × A + Mwk × (1 - A) (11-26)

Note: In formula (11-26), Mw must be used. Mn or OH values are not valid substitutes.