How to calculate the molecular weight of polyester polyol repeating units?

M(unit)=M(acid)+M(alcohol)−2M(water) (11-51)

Where:

M(unit) — Molecular weight of the polyester repeating unit

M(acid) — Molecular weight of the dicarboxylic acid

M(alcohol) — Molecular weight of the diol

M(water) — Molecular weight of water (18)

Formula (11-51) applies to a single-system reaction involving only one acid and one alcohol. However, in actual production, a mixture of various acids and alcohols is typically used. Therefore, under mixed acid and alcohol synthesis conditions, the average molecular weight of the mixed acids and alcohols must be calculated first using the following formulas:

Average molecular weight of mixed acids or alcohols = (NjMj + NxMx)/(Nj + Nx) (11-52)

If the mass fractions of each component are known, the average molecular weight of the mixed acid (or alcohol) should be calculated using:

Average molecular weight of mixed acid (alcohol) = (MnjMnk)/[MnkA + Mnj(1−A)] (11-53)

Where:

A — Mass fraction of Mnj

(1−A) — Mass fraction of Mnk

Example:

To reduce cost and improve the flowability of the polyester, a formulation using adipic acid, ethylene glycol, and diethylene glycol aims for diethylene glycol to account for 40% of the total diol content.

Using Formula (11-53):

Given that ethylene glycol has a molecular weight of 62 and accounts for 60% of the diol content, while diethylene glycol has a molecular weight of 106 and accounts for 40%, the average molecular weight of the mixed alcohol is:

(62×106)/(106×0.6 + 62×0.4) = 6572 / (63.6 + 24.8) = 74.34

Many people ignore the number-average concept when calculating the average molecular weight of mixed acids or alcohols. They often mistakenly calculate it as:

62×60% + 106×40% = 37.2 + 42.4 = 79.6

This significantly differs from the correct result of 74.34 obtained using Formula (11-53), potentially causing formulation errors.

Once the average molecular weights of the mixed acid and alcohol are known, the theoretical average molecular weight of the polyester polyol repeating unit can be calculated using Formula (11-51).