GUIDE TO URETHANE CALCULATIONS 

Equivalent weight

The equivalent weight (eq.wt) tells you how many grams of a product you need to have for one equivalent of reactive groups. For an isocyanate, the reactive group is

 –N=C=0 (NCO), and its concentration is measured by weight percent NCO.

Isocyanate equivalent weight =       4.200    g/eq
                                                   %NCO

For a polyol, the reactive group is –O-H (OH). OH concentration is measured by the OH value (mg KOH/g sample): 

Equivalent weight of a polyol =       56.100     g/eq
                                                  OH value 

Molecular weight of a polyol

The molecular weight (mol.wt.) of a polyol is approximated by the polyol equivalent weight (eq.wt.) multiplied by the nominal functionality (fn). 

Polyol molecular weight = (eq.wt).(fn) =    56.100      x (fn) g/mole
                                                           OH value         

Molecular weight of any diol = (eq.wt.) . (2) g/mole 

Molecular weight of any triol = (eq.wt.) . (3) g/mole 

The average functionality (1.e. the number of functional groups per polymeric chain) of the polyol can be estimated by: 

f(HO) = OH number x Mn
                  56.100 

It is assumed that the functionality must be at least two in order for the resin to contribute to the crosslinking network. The probability of having low molecular weight fractions with no functional groups or only one functional group can have very serious implications.

Molecules with no functional group will act as plasticisers, presumably changing the mechanical properties of the films. Very low molecular weight fractions of this type (dimers, trimers) may even have a sufficiently high vapour pressure during curing to evaporate off (=VOC)

The presence of oligomer molecules with a single functional group will lead to chain termination in crosslinking, which will also affect the mechanical properties of the cured film. Unfortunately, the probability of obtaining oligomers with inadequate functionality increases as the average molecular weight is reduced, necessitating judicious control of the polymerisation process. The fraction of resin that does not have two functional groups can be determined from actual molecular weight curves and statistical considerations. 

Calculation of required isocyanate for reaction

When reacting an isocyanate ith one or more polyols to form a polyurethane, one NCO group reacts with one OH group. When the number of NCO groups equals the number of OH groups, you have a stoichiometric NCO : OH ratio of 1,0.

This ratio is commonly referred to as the index.

To determine the amount of isocyanate required to react with a given polyol blend, you must know the desired index (often 1,0), the isocyanate equivalent weight and the weight fractions (pbw) and equivalent weights of the polyols and any water present in the blend.The following calculations give the stoichiometric ratio between grams of solid polyisocyanate resin and 100 grams of solid polyol resin. 

By given OH number and NCO%: 

OH number  x  17x100  x   42   x   100      = 7,5 x OH number
                       56x100      17       %NCO              %NCO 

By given OH number and NCO eq.weight: 

OH number  x  17x100  x   42   x   NCO eq.  =  OH number  x  NCO eq.
                       56x100      17        %NCO                   56 x 100 

By given OH eq. and %NCO: 

17x100 x   42   x   100 
OH eq.      17       %NCO 

By given OH eq.weight and NCO eq.weight: 

17x100 x   42   x   NCO eq.
OH eq.      17          42 

By given %OH and %NCO: 

%OH  x   42   x   100      =  247  x   %OH
              17       %NCO                  %NCO 

By given %OH and NCO eq.weight:

%OH  x   42   x   NCO eq.
              17           42       

To calculate %OH from OH number : %OH = OH number / 33 

To calculate %OH from OH eq.weight : %OH = 1700 / OH eq.weight 

To calculate OH number from OH eq.weight : OH number = 56.100 / OH eq.weight 

To calculate %NCO from NCO eq.weight : %NCO = 4200 / NCO eq.weight 

To calculate NCO number from %NCO : NCO number = 13,33 x %NCO

Calculations for formuating a prepolymer to a specific NCO 

To calculate e.g. a MDI prepolymer,

N = desired NCO of the prepolymer (expressed as a fraction)

X = eq.weight of the isocyanate

Y = eq.weight of the polyol (or average eq.weight of the polyol blend) 

Total amount of MDI needed =( X + N (X + Y)) / ((42/X) – N) 

Example:

Say you want a 10,0% NCO prepolymer of a MDI with 33,5% NCO with a polyol blend conssting of 95% polyol B (OH number 28) and 5% ethyleneglycol (OH number 1.810) by eq.weight: 

N = 0,10 

X = 4.200 / 33,5 = 125 g/eq. 

Y = (56.100/28)x(0,95) + (56.100/1.810)x(0,05) = 1.905 g/eq. 

Total amount of MDI needed = (125 + (0,10x(125 +1.905)) / ((42/125) – 0,10) = 985 pbw MDI (33,5% NCO) 

So 1.903 pbw polyol B, 1,55 pdw ethyleneglycol, and 985 pbw MDI(33,5% NCO) would be used to produce this prepolymer at 10,0% NCO. 

Converting to weight percents: 

Amount of MDI (33,5% NCO)             = 34,09%

Amount of polyol B                           = 65,86%

Amount of ethyleneglycol                  =   0,05%