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 %NCO
g/eq
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 OH value
g/eq
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 OH value
x (fn) g/mole
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 56x100 17 %NCO
= 7,5 x OH number %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%
