Resin Calculations

Resin calculations serve to determine the following for a resin formulated with a given composition: • Theoretical final properties, • The amount of reaction water produced, • Potential gelation risk. Furthermore, such calculations are invaluable in reformulating resins to modify certain properties and in formulating new resins. The importance of equivalent weights is considerable here. This is because it is necessary to know the equivalent weight of each raw material when performing formula calculations.

Equivalent Weight:

The equivalent weight of a substance is obtained by dividing the molecular weight of that substance by its functionality. For example, isophthalic acid HOOC(C6H4)COOH has a molecular weight of 166. Since it has 2 functional groups, its functionality is 2. Accordingly, equivalent weight = 166/2 = 83. Similarly, trimellitic anhydride (TMA) has a molecular weight O3C2(C6H3)COOH = 192. It has 3 functional groups. Equivalent weight: 192/3 = 64. The anhydride formation here reacts like 2 functional groups. The precision in the equivalent weight term depends on the type of functionality. When a substance has more than one active functionality, the equivalent weight expression is replaced precisely by the functionality term. For substances of unknown or mixed composition, equivalent weight is calculated from experimentally determined acid number (A.N) or hydroxyl number (OH.N). The unit of these numbers is mg KOH/g resin. The factor 56,000 appears in the denominator and the formulas are as follows: Equivalent weight can also be calculated from hydroxyl weight percentage (Wt.%OH). For this, the hydroxyl weight percentage must be known.

Equivalent Weights of Functional Acids

Esterification Water and Resin Yield:

The main reaction producing polyester is an esterification reaction. Ideally, the reaction of equivalent amounts of acid groups with hydroxyl groups results in polyester and water. In general, all polyester surface coating resins are formulated with an excess of hydroxyl. Therefore, when the polyesterification reaction is complete, the water released is directly equivalent in amount to the acid value or acid anhydride. Water Released = Water weight released when reaction is complete (5) Water Released = 18.(Acid Equiv.no.) + 12.(TMA Equiv.no.) + 9(Anhyd.Equiv.no.) Calculation (5) summarizes the water weight resulting from each carboxyl functionality source. Each carboxyl releases one equivalent mole of water. Each mole of TMA (functionality 3) releases two moles of water. Each mole of anhydride (functionality 2) releases one mole of water. Calculation of water released is useful in monitoring the progress of the esterification reaction while distillate is being collected and gives the difference between charge weight and yield. Many water-soluble resins are formulated to contain "pendant" carboxyl groups that will be neutralized to achieve water solubility. Such resins give quite high acid numbers (A.N) and release less water in equation (6). The lower the acid value, the greater the amount of water released. A correction factor has been developed for such high-acid resins and is given by the following formula.

Oil Length and Fatty Acids:

Oil Length: Alkyds are formulated according to the amount of oil or fatty acid they contain. They are defined based on their oil length, which determines the percentage of oil in the formulation. These definitions are shown in the table below. If a resin is formulated as a triglyceride, calculation of the oil percentage is simple: oil charge weight / total yield x 100. When formulating a desired oil length, the oil charge weight can be calculated using equation (10). High acid numbers at the end can increase small differences between intended oil length and end oil percentage. This is because equation (10) uses theoretical water output from equation (5). Corrected water released from equation (8) is a lower figure. This difference is less than 1%. Many alkyd resins are formulated using trifunctional polyol and fatty acid instead of oil. To calculate the oil percentage or oil length of a resin formulated with fatty acid, the following formula is used. A useful rule when using fatty acids is to use 5% less fatty acid than oil and add an equivalent amount of polyol. While this estimate is based on glycerol, other triols used in formulations have considerably lower equivalent weights. Changing the triol does not significantly alter the calculated oil length.

Hydroxyl Excess and Preventing Gelation:

Since polyesterification occurs between polyfunctional molecules containing carboxyl and hydroxyl, it results in increasingly longer chains. Monomers with three or more functional groups especially lead to rapid monomer growth. For practical purposes, resins used in surface coatings must have limited molecular size. There are various options for limiting the polyesterification reaction. Commercial drying oil-based resins contain monofunctional fatty acids acting as chain stoppers (terminators), and these keep polymer growth at practical viscosity levels. At the other end of the spectrum are fully synthetic, oil-free resins. These are based on di and trifunctional materials. In these resins, chain growth can be controlled by using excess polyol. Polyol excess ensures formation of quite low molecular weight polymer with hydroxyl termination when all acid groups have reacted. Commercial resin formulators have developed the rule of using increasing amounts of hydroxyl excess as oil length decreases. Since these commercial resins are oil-based, hydroxyl excess is the amount of polyol added minus the hydroxyl that will esterify the acid or anhydride. Since it is known that the amount of polyol required for esterification equals the carboxyl equivalent number, the following equation can be derived. In fatty acid-based alkyds, to determine hydroxyl excess, the fatty acid equivalent and the polyol required to esterify this fatty acid are excluded from this calculation. Many formula developers in high-performance surface coating resin design use hydroxyl excess calculations based on total polyol charge and finished resin base. This formula is similar to equation (14) but includes the fatty acid equivalent and all triols used in the calculation. This calculation can be used to find the required polyol amount when OH excess is given. Patton's Gelation Constant: Patton's K constant or alkyd constant is a useful tool in determining hydroxyl excess, and also controls the gelation tendency of the formulation. The importance of K values lies in their determination of polymer growth, low acid number, and prevention of gelation during processing. The K value is useful for estimating the likelihood of resin gelation during processing as it approaches the intended acid number. The actual gelation tendency of a resin depends on the equipment and glycol loss during processing. For this reason, the calculated K value does not apply everywhere; rather, each resin manufacturer must determine a K value for their own equipment and develop new resin formulas that meet this K value requirement. Isophthalic acid (IPA)-based alkyds are optimally formulated when the K value is approximately 1.04. This value should be variable in some cases. Free acid groups in a finished polymer can act as chain terminators. For this reason, the K value of high-acid resins should be lowered. An experimentally determined value that will reduce the desired K value = .0025 x (acid no. – 8). The third hydroxyl of trimethylolethane or trimethylolpropane is slightly more reactive than that of glycerol, so when glycerol is used, the K value should be increased by an additional 0.01 unit. Since oils, fatty acids, and glycerol contain equivalent amounts of carboxyl and hydroxyl in equivalent quantities, when calculating the K value of oil-based alkyds, each mole of oil is evaluated as 3 moles of fatty acid and 1 mole of triol.

Molecular Weight and Equivalent Weight of Finished Resin:

The calculated molecular weight of a formulation is a guide to its possible viscosity and the solvent diluents needed to achieve desired application characteristics. Equation (18) is based on a simple outline of polymer growth. Therefore, its validity is questionable if the average acid functionality exceeds 2, which would cause a negative denominator. The remaining hydroxyl functionality in the finished resin is frequently used to cure with crosslinking resins (crosslinkers) such as amino resins. The optimal amount of crosslinking resin (crosslinker) to be used is proportional to available hydroxyls. Excess crosslinker can plasticize the film, while insufficient crosslinker leaves unreacted hydroxyls, leading to weakened resistance in the coating. The hydroxyl equivalent weight of a polyester resin is calculated from the experimentally determined hydroxyl number. (ASTM D 1957)

Determination of Glycol Loss

An analysis of gelation constant calculations (Patton's K value) shows that diol excesses are more efficient than triol excesses in reducing gelation tendency. However, many diols or glycols have quite low boiling and freezing points and high water solubility. Therefore, during esterification, some glycol is carried away by distillation. Even a small amount of glycol loss reduces the K value to a gelating extent as the acid number approaches being low. Although careful selection of efficient condensers minimizes glycol loss, some loss should be expected when glycols with low boiling points are used. Methods to compensate for glycol loss are based on determining glycol in the distillate. Some formula developers consider the distillate excess above theoretical water as glycol loss. Experimental work has shown this method is inaccurate for resins with high acid numbers. Furthermore, the reaction must be complete before glycol determination. This condition may be too late to prevent gelation. The most preferred method for determining glycol in the distillate is to use the refractive index of the collected distillate. Total glycol loss is the percentage of glycol in the distillate multiplied by the reaction water calculated in equation (8). Glycol loss = (% glycol in distillate) (Charge Wt. – Y') If a glycol mixture is used, the distillate will contain primarily the glycol with the lowest boiling point. The effect of reflux solvents on the refractive index of the distillate can be calculated in laboratories.

Compensation for Glycol Loss:

Since refractive index is determined quickly, glycol loss amount can be calculated midway through the reaction and the lost glycol amount can be added if time allows for the reaction. Typical glycol loss can be developed when similar resins are produced. Experimental work has shown that glycol loss prediction and type can be determined quite realistically. This forms a basis for the glycol to be added. With this second method, refractive index measurements are performed to determine expected glycol loss. Determination of glycol amount in distillate water using refractive index

Example Calculation:

An oil-free polyester resin can be formulated based on IPA:9, TMP:2, *AA:3 with desired acid number of 5 using neopentyl glycol (NPG). Melamine can also be formulated to cure excess hydroxyl. *AA: Adipic acid The required polyol amount is calculated with 30% excess hydroxyl. From equation (16): 2028 g NPG: 39 equivalent units and 19.5 moles. Equivalent weight of NPG: 52. From equation (17), K value is checked. Desired K=1.04 This indicates that the resin consists largely of low molecular weight fractions and will not dry quickly. The K value is reduced by using 15% excess hydroxyl. 1794 g NPG: 34.5 equivalent units and 17.25 moles. Equivalent weight of NPG: 52. From equation (17), K value is checked and the desired K=1.04 value is achieved. The amount of water released from esterification can be found with the aid of equation (5). Water Released = 18 (18 + 6) + 12 (6) = 504

Theoretical Yield

Corrected Esterification Water:

Corrected Water Released = 4,110 – 3,612 = 498 (8) When all weights are multiplied by 0.2768 (1,000/Y) for 1,000 units of yield, the values are obtained. Mehmet Namık Kayaalp Chemical Engineer Ecelak Boya Kimya Ltd. Şti.

References 1. AMOCO Chemicals, Chicago, Illinois, Bulletin IF-3a 2. D.H.Solomon, The Chemistry of Organic Film Former, 1977 3. Organic Coating Technology-II, H.F.Payne, J.Wiley and Sons Inc.-New York 1960 4. Finished Paint Products, 1974 Selection and Industrial Training Administration Ltd.-London 5. Alkyd Resin Studies, M.Namık Kayaalp Bayraklı Boya A.Ş., 1976