Computational study on reaction enthalpies of urethane-forming reactions.
Reaction of alcohols with isocyanates to form urethanes is the basis of the polyurethane industry  with annual sales in the tens of billions of dollars. The simulation of thermosets formed in these reactions includes generating solutions under the constraints of dozens of differential equations under material balance, energy balance, and constitutive relationships. The many equations and the large number of oligomers with their isomers result in a problem-solving environment where the number of number of model parameters greatly exceed what can be reasonably obtained from fitting parameters to experimental data.
Heuristics such as those provided in Table 1 provide a starting point for simulations. These heuristics allowed for the proof-of-concept by comparison of simulation results on temperature and foam height profiles to justify further efforts to increase accuracy and provide increasingly useful results.
Use of [X.sub.p] and [X.sub.s]
The reaction parameters of polyols are predominantly influenced by the fraction of primary, secondary, and hindered-secondary hydroxyl groups. This characterization reduces the number of parameters needed to characterize a polyol's reactivity and provides useful insight into how a polyol will react in a formulation--these are more meaningful that Arrhenius parameters to most researchers in the area.
In addition, impacts of catalysts are expected to be less dependent on the actual polyol and more dependent on the impact of primary, secondary, and hindered-secondary alcohols. Early work on simulation by Ghoreishi et al. has extended this approach of characterizing reactivity base on type of hydroxyl moiety to the characterizing of the impact of catalysts on reactivity [2-4, 6]. This approach has utility for extrapolating the performance of a catalyst from one polyol to another.
The utility of the simulation approach resides in using physical properties and fitted parameters to pure components (such as the fraction of primary alcohol) to perform simulation on the multitudes of useful combinations of the components in formulations/recipes. For fitting parameters such as the fraction of primary versus secondary alcohol content, fitting parameters to experimental data can be performed with confidence due to the reactivity of the primary alcohols being more than an order of magnitude greater than the reactivity of the secondary alcohols. These parameters that can be readily determined by fitting to experimental data could be characterized as "first tier" fitted parameters.
A "second tier" of parameters that are not as readily obtained by curve fitting emerge, but are needed to improve the accuracy of simulation, especially when extrapolating results outside the range where accuracy has been verified. Example second tier parameters include:
* Impact of polymer size on moiety reactivity (Flory's assumption is not impact).
* Variations of heat of reaction with primary, secondary, and hindered secondary alcohol groups.
* Generalizations that can be made on the impact of catalysts (e.g. is the reduction in activation energy the same for reactions with secondary alcohols as with primary alcohols).
This article is on an approach that uses molecular modeling to determine the sensitivity of parameters to these second tier variations in molecules. When the molecular modeling indicates little variation in parameters, the simulation results are put forward as verification that the first order approximations are adequate. When the molecular modeling indicates that parameters (e.g. heat of reaction) vary by more than about 1%, verification of the variations is pursued so as to improve the accuracy of the simulation.
Reaction enthalpies and rate constants for isocyanate-alcohol reactions catalyzed by tertiary amines were modeled by Chang and Chen  and Baker and Holdsworth ; they reported relative rate constants with respect to different catalyzed conditions. Baser and Khakhar developed theoretical models for physical blowing agent blown rigid polyurethane foam formation  and water-blown polyurethane foams . All the above models are based on an assumption that the reactivity of two molecules having different chain lengths (or molecular weights) are the same as long as they have the same type of functional groups. They reported the enthalpy of isocyanate-polyol reaction as a constant regardless of location of functional groups, molecular size and chain length.
Other research showed the relationship between reaction enthalpy/rate constant and chain length. Lovering and Laidler  performed thermochemical studies on alcohol-isocyanate reactions. They reacted isocyanate with n-butanol, s-butanol, and i-butanol, respectively and measured the heats of reaction using a differential microcalorimeter of the Tian-Calvet type. It was found that the heat of reaction decreased in the order normal > iso > secondary.
More detailed studies on the impact of molecule size on reactivity are available with other chemistries. Figure 1 shows the plot of esterification rate constant, kA versus average polymer chain length, N for C[H.sub.3]C[H.sub.2]OH + H(C[H.sub.2])NCOOH , the reaction rate was linearly decreasing as the chain length number increasing from 1 to 3 and it tended to a constant after the chain length number reaching 4 or more. The phase transition and viscoelastic transition of polymer may influence the reaction of polymer chain [13, 14], but in this study the structure of polymer chain was assumed stable.
Zhao et al. [3, 4, 6] and Ghoreishi et al.  have initiated an approach to simulate near-adiabatic foam-forming reactions that included catalysis impact and treat polyols as fraction of primary, secondary and hindered-secondary hydroxyl. Large differences in Arrhenius parameters allowed experimental data to be used to identify parameters specific to primary, secondary, and hindered secondary hydroxyl groups. However, the uncertainty of the fitted parameters for enthalpies of reaction relative to data did not justify the use of different values for the heats of reaction. The introduction of computation study on this topic can provide more information on how sensitive the heats of reaction are to alcohol moiety isomers.
Several computational studies have been performed on the general characteristics of urethane formation reactions [15-19]. Early mechanistic studies on urethane formation suggest that the alcoholysis reaction occurs either via a concerted mechanism or stepwise mechanism. In the concerted mechanism, the addition of alcohol is carried out across the N=C bond of isocyanate and immediately results in the product (Scheme la). In the stepwise path, the additional of the alcohol across the C=0 bond of isocyanate yields an enol intermediate, which can tautomerize via a proton transfer to give the urethane product (Scheme lb). The free energy profiles calculated by Coban and Konuklar  showed that the concerted path is more likely to occur than the stepwise route. Therefore the concerted path structures were used for calculations in this study.
Urethane reactions have been extensively studied with PM3 semi-empirical method [20, 21], as well as ab initio calculations [22, 23], The most extensive semi-empirical studies are (B3LYP/6-31 + G(d,p)) of Coban and Konuklar , They used density functional theory (DFT) calculations to calculate rate constant ratios ([k.sub.1]/[k.sub.2]) in which [k.sub.1] is the rate constant of the first alcohol attack on the diisocyanate molecule and [k.sub.2] is the rate constant of the second alcohol attack on the diisocyanate molecule. Raspoet et al.  compared experimental data and theoretical results obtained by ab initio MO calculations. They found the bulk solvent effect, which is treated by a polarizable continuum model (PCM), does not affect the preference of the alcohol to attach across the N=C bond as pointed out by the gas-phase values.
The present work is a computational study of the alcoholysis reaction during polyurethane foaming process. Different aromatic isocyanates (2,4-TDI, 2,6-TDI, 2,4-MDl, 4,4-MDI) were considered to react with 1-butanol, 2-butanol, and tert-butanol; and so, to calculate the reaction enthalpies. Impact of functional group location, molecular size and chain length on reaction enthalpies were evaluated based on the computational results. The impact of conformations will not be discussed in this work because it can be neglected comparing with the impact of molecular sizes and configurations. Computational results were used to improve the database of kinetic and thermodynamic parameters used in simulation studies [2-4, 6].
The Gaussian 09 package was used to speed up calculations compared with those using Slater-type orbitals, a choice made to improve performance on the limited computing capacities of then-current computer hardware for Hartree-Fock calculations. The computations were performed on the HPC resources at the University of Missouri Bioinformatics Consortium (UMBC). Chemical structures were optimized at the B3LYP level using a 6-31G(d,p) basis set in the gas phase. Chemical geometries were input and the structures were subjected to vibrational frequency analysis toward their characterization as local minima. Throughout this article, calculated bond length are given in angstroms, calculated bond angles in degrees, total enthalpies in hartrees, and zero point energies and calculated relative enthalpies, unless otherwise stated, in kJ/mol.
The solvent effects were studied using a single-point Integral-Equation-Formalism Polarizable Continuum Model (IEFPCM) to make calculations in toluene (which is used as a solvent in some of the experimental studies to avoid over heat) and benzene. Hartree-Fock and MP2 were also calculated using 631G(d,p) basis set to verify accuracy of the results. SPARTAN, GAMESS, and MOPAC calculations will be performed in the future study to verify the results obtained by Gaussian.
The general computation procedures can be summarized as five steps:
1. Draw chemical structures (reagents and products)
2. Optimized chemical geometries
3. Calculate total electronic and thermal enthalpies using Gaussian
4. Calculate relative enthalpies corrected by ZPEs
5. Compare reaction enthalpies of all reactions
Simulations were performed on the reactants, transition states, and products. Figure 2 shows the molecular models and how the reaction enthalpy was calculated from the reactants and products. The usual way to calculate enthalpies of reaction is to calculate heats of formation, and take the appropriate sums and difference. [H.sub.total] is used for the total enthalpy, [[epsilon].sub.ZPE] is used for the zero point energy and the reaction enthalpy [[DELTA].sub.r][H.sup.0] can be calculated by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[FORMULA NOT REPRODUCIBLE IN ASCII.]
In general, convergence was questionable or not possible on the transition states, and so, it is not possible to report impacts on activation energies from this work. Useful results were obtained to allow enthalpies of reaction to be estimated; these are reported in the discussion. When simulation results predicted more than 5% variation in parameters that could be experimentally measured, experimental data were collected. In the case of heats of reaction, the simulation heats of reaction were used as a basis to curve-fit the Arrhenius parameters. Experimental methods have been previously published [3, 4, 6].
RESULTS AND DISCUSSION
Location and Molecular Size of Isocyanate Groups
Figure 3 presents examples of isocyanates used in this study. The impact of isocyanate group location on reaction enthalpy was evaluated by reacting isocyanate functional groups on different locations with the same alcohol groups. MDI was compared with TDI to evaluate the impact of molecular size on reaction enthalpy.
Table 2 lists total electronic and thermal enthalpies and zero-point vibrational energies of all the reactants and products based on B3LYP/6-31G(d,p) geometries. Notation 2 means the reacted isocyanate was on carbon 2 and notation 4 means the reacted isocyanate was on carbon 4 based on the convention that the 1 carbon is where the methyl group attaches to the aromatic ring. The corresponding relative enthalpies (heats of reaction) were reported in Table 3.
In Table 3, the comparison between HDI, 2,4-TDI and 2,4-MDI results show that larger isocyanate molecules lead to lower enthalpies of reaction. Isocyanate group on four carbons are less sterically hindered than on either two or six carbons. The heat released from reaction with the less sterically hindered isocyanate is noticeably larger.
Location of Hydroxyl Groups
To evaluate the impact of hydroxyl group location (e.g. primary versus secondary) molecular modeling was performed using isomers of pentanol. Total electronic and thermal enthalpies and zero-point vibrational energies are provided in Table 4. The corresponding relative enthalpies were reported in the table.
Both TDI and MDI results show relative magnitudes of heats of reaction in the sequence: 1-pentanol > 2-pentanol > 3-pentanol > tert-pentanol. Primary hydroxyl groups have larger energy potential than secondary, and then secondary has larger energy potential than tertiary. This result does not agree with the assumption used in other kinetics modeling [2, 4, 6, 9, 10] in which only one reaction enthalpy was used for all alcohol-isocyanate reactions.
The trends with the alcohols follow the trends of the isocyanates where the lower steric hindrance of reactive moieties leads to larger heats of reaction. This is consistent with unreacted moieties having less steric hindrance with respective higher energy states; this leads to the release of more energy when the molecules are bound to the urethane configuration.
Chain Length of Hydroxyl Groups
To evaluate the use of Floy's assumption that the reactivity of a moiety can be approximated as independent of the size of the molecule to which the moiety is attached, the heats of reaction for a series of n-alcohols were estimated as reported in Table 5.
Figure 4 graphically summarizes the results of Table 5. The results show that heat of reaction is not dependent on the chain length number of the molecule attached to the hydroxyl group.
The solvent effects were studied using a single-point Integral-Equation-Formalism Polarizable Continuum Model (IEFPCM) to make calculations in toluene (which is used as a solvent in some of the experimental studies to avoid over heat) and benzene. Table 6 reports the solvent effects.
The Results show that the presence of solvent does not have significant impact on reaction enthalpies which matches the conclusion found by Raspoet et al. . In his work as for prototypes, PCM calculations were performed in both aqueous and methanol solution, which lead, after all, to similar results. On the whole, the role of the surroundings was found to be less decisive than the specific action of a catalytic cluster. And in fact, the considered reactions had been shown not to be greatly influenced by the presence of a continuum that does not modify the conclusions emerging from the study carried out for the gas phase species. Based on these, it is assumed that the results with toluene as a solvent are accurate enough to evaluate the reaction enthalpies.
Comparison With Different Models. A primary finding of the molecular simulation results is that the steric hindrance and neighboring molecule effects of reactive moieties on monomers can cause heats of reaction to change up to 17% for urethane-forming reactions. In view of this, the simulation values are compared with literature values and new experimental data in the following paragraphs.
Table 7 shows the comparison between computational results and other results from previous literatures for 4,4-MDI which is the most commonly used isocyanate in the industry. Ghoreishi et al. [2-4, 6] results were from previous simulation development. Baser and Khakhar [9, 10] solved differential equations to model the fundamental kinetics in polyurethane foaming reaction. Lovering and Laidler  gathered these results experimentally by using a differential microcalorimeter of the Tian-Calvet type. Since Lovering's data was measured in 1961, Zhao and Baser's data seem to be more reliable to be references. The polyols used in their studies have significantly high content of hinder-secondary (tertiary) alcohol, hence their values locate very close to tertiary result of Gaussian values.
The Gaussian values straddle the values of both Zhao et al. and Baser providing a level of confidence that the Gaussian values are both reasonable and provide an increased sensitivity to the moiety isomer. The water reaction enthalpy from this study is quite similar to that from Baser and the average gel reaction enthalpy. The deviation between average computational results and literature values is about 5%.
Table 8 presents the reaction enthalpy calculation of isocyanate-amine reaction. Only the HD1 product result was presented because the calculations of MDI and TDI did not converge.
Values as recommended based on this comprehensive analysis are summarized in Table 9. Hindered-secondary alcohol is assumed to have the same reaction enthalpy as tertiary. PMD1 molecules are too large to be computed successfully in Gaussian, and as an approximation are estimated to be 3% less than that of MDI. This assumption is based on the conclusion that heat of reaction decreases as the chain length of isocyanate group increasing when the chain length number is less than 3 .
Simulation results from different modeling were compared with experimental data in Fig. 5. Temperature profiles of pentanol reactions were cut off at 100[degrees]C because the evaporation of toluene impacted results above this temperature. To increase the amount of data collected before reaching 100[degrees]C, toluene was used as a solvent at 20% by mass of the mixture.
Due to volatility issues of pentanol, data was also collected using diethylene glycol. Acetophenone was selected as a solvent due to a higher boiling point and better compatibility than toluene. Figure 6 compares experimental temperature profiles and modeling results of isocyanate-DEG reaction in presence of acetophenone as a solvent. Table 9 recommended heat of reaction for PMDI and primary alcohols (-82.0 kJ/mol) were used in new models (solid lines) to compare with the previously reported values of Zhao et al. (72.0 kJ/mol).
The Table 9 value has a clearly better fit in the absence of acetophenone solvent and at 10% solvent. At higher solvent loadings the lower reaction enthalpy indicated by experimental data may due to the evaporation of solvent due to the combination of longer times and higher fractions of acetophenone.
The new data support that recommended values of Table 9 including the distinction between primary, secondary, and tertiary alcohol reagents.
Verification by Other Calculation Methods
The computation of reaction between 2,4-TDI and 1-Butanol was repeated by Hartree-Fock and MP2 method using a 6-31G(d,p) basis set. The molecules were too large to be successfully calculated in higher level basis sets and QM methods. Table 10 reports total electronic and thermal enthalpies, zero-point vibrational energies and corresponding relative enthalpies from three different methods.
DFT (B3LYP) and MP2 almost have the same results and Hartree-Fock result has a deviation about 4%. This indicates that the computational results are repeatable and consistent.
Molecular configurations for a range of reactants and products in polyurethane foaming reaction were optimized at the B3LYP level using a 6-31G(d,p) basis set in the gas phase. Total electronic and thermal enthalpies and zero-point vibrational energies were computed by Gaussian 09 package on a supercomputer from UMBC. The gas phase results were compared with calculations with solvents with the solvent causing only minor decreases (1.2%) in the heats of reaction. The corresponding relative enthalpies were calculated based on ZPE correction and reported in kJ/mol.
Where possible, computational results were compared using different computational methods as a first pass on verifying accuracy of simulations. When variations between different reagent isomers were large, the values were compared with experimental data and values reported in literature. Values of heats of reaction vary by up to 17%, relative values based on hydroxyl isomers (primary vs. tertiary). Recommended values for use were made based on experimental observations and these deviations.
Based on the reaction enthalpy results, the following is concluded on heats of reaction: (1) isocyanate groups on carbon 4 have larger energy potentials than that on carbon 2 and larger isocyanate molecules have lower enthalpy. (2) Primary hydroxyl groups have larger energy potentials than secondary (about 4% larger), and secondary have larger energy potentials than tertiary (about 15%). (3) The heat of reaction is not dependent on the chain length number of the molecule attached to the hydroxyl group. (4) The presence of solvent decreases the reaction enthalpy slightly with the large molecules self-solvating capability reducing the impact of solvents. (5) Heats of reaction for water-isocyanate reactions were between the two values reported in the literature and provided a basis for recommending values for use.
These studies verify that computational chemistry is a useful tool to estimate changes in reactions due to isomeric variations of reagents or moiety locations on reagent molecules. In a similar manner, simulation of urethane-forming reactions is useful to bridge the gap between fundamental computational chemistry calculations and practical applications.
The authors thank University of Missouri Bioinformatics Consortium (UMBC) for providing the HPC resources to run the computations and technical support for running jobs on the supercomputer. The authors also thank Homayoon Rafatijo, a PhD student from Chemistry Department in University of Missouri, for providing guidance on Gaussian 09 program.
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Yusheng Zhao, Galen J. Suppes
Department of Chemical Engineering, University of Missouri-Columbia, Columbia, Missouri 65211
Correspondence to: Yusheng Zhao; e-mail: firstname.lastname@example.org Contract grant sponsor: United Soybean Board.
Published online in Wiley Online Library (wileyonlinelibrary.com).
TABLE 1. Heuristics for initial efforts in simulating urethane-foaming reactions. Polyols: * Polyols consist of different ratios of primary ([X.sub.p]), secondary ([X.sub.s]), and hindered-secondary hydroxyl ([X.sub.HS]) where the same type of hydroxyl in different polyols have the same reaction rate constants ([k.sub.0])  * The heat of reaction is assumed to be the same for independent of [X.sub.p], [X.sub.S], and [X.sub.HS]. * Flory's assumption is assumed to hold where the reactivity a hydroxyl group is independent of the size of molecule to which the hydroxyl group is attached. * Catalytic reaction rate constants ([k.sub.0]) are unique to the catalyst [3, 4]. Catalysts: * Catalysts will not react with any components in the system. * The structure and reactivity of catalysts will not change during the reaction process. * Catalysts will reduce activation energy ([DELTA]E) relative to noncatalytic reaction. * Catalysts have no impact on heat of reaction ([DELTA]H). * There is no interaction between the catalysis impact from two or more catalysts. Others: * Use of step growth mechanisms as elementary processes can be used to obtain reaction rate expressions for the reactivity of moieties. * All isocyanate groups have the same reactivity. * Other additives (surfactant and fire retardant) have no catalysis impact on reactions. * Foam has a lower heat transfer coefficient than solid resin. * Foam height (density) can be estimated by assuming ideal gas behavior, a modified Raoult's law equilibrium and an overall efficiency in gas cell formation . TABLE 2. Calculated total corrected (Hartree) and zero-point vibrational (ZPE, kJ/mol) energies for studies on isocyanate locations and molecular sizes. Sum of electronic and thermal Enthalpies ZPE HDI -571.839728 519.4 2,4-TDI -606.395275 353.8 2,6-TDI -606.394843 353.7 2,4-MDI -837.364638 568 4,4-MDI -837.364904 568 1-Butanol -233.533899 360.7 2-Butanol -233.540773 359.1 Water -76.394588 56.1 C[O.sub.2] -188.565756 30.4 HDI ZPE HDI + 1-butanol -805.373627 880.1 1-Butanol urethane -805.411671 892.9 HDI + 2-butanol -805.380501 878.5 2-Butanol urethane -805.417679 892.2 HDI + water -648.234316 575.5 Amine -459.698169 555.5 Amine + C[O.sub.2] -648.263925 585.9 2,4-TDI ZPE 2,4-TDI + 1 -butanol -839.929174 714.5 1-Butanol urethane2 -839.965776 727.9 1-Butanol urethane4 -839.967315 727.4 2,4-TDI + 2-butanol -839.936048 712.9 2-Butanol urethane2 -839.971769 726.6 2-Butanol urethane4 -839.97332 726.1 2,4-TDI + water -682.789863 409.9 Amine2 -494.260608 389.6 Amine4 -494.260276 388.7 Amine2 + C[O.sub.2] -682.826364 420 Amine4 + C[O.sub.2] -682.826032 419.1 2,6-TDI ZPE 2,6-TDI + I-butanol -839.928742 714.4 1-Butanol urethane2 -839.96124 727.6 2,6-TDI + 2-butanol -839.935616 712.8 2-Butanol urethane2 -839.967266 726.3 2,6-TDI + water -682.789431 409.8 Amine2 -494.259986 389.8 Amine2 + C[O.sub.2] -682.825742 420.2 2,4-MDI ZPE 2,4-MDI + 1-butanol -1070.898537 928.7 I-Butanol urethane2 -1070.93286 942 1-Butanol urethane4 -1070.935916 941.6 2,4-MDI + 2-butanol -1070.905411 927.1 2-Butanol urethane2 -1070.938823 940.9 2-Butanol urethane4 -1070.941948 940.2 2,4-MDI + water -913.759226 624.1 Amine2 -725.227689 603.8 Amine4 -725.229052 603.1 Amine2 + C[O.sub.2] -913.793445 634.2 Amine4 + C[O.sub.2] -913.794808 633.5 4,4-MDI ZPE 4,4-MDI + 1-butanol -1070.898803 928.7 1-Butanol urethane4 -1070.935949 941.7 4,4-MDI + 2-butanol -1070.905677 927.1 2-Butanol urethane4 -1070.941951 940.4 4,4-MDI + water -913.759492 624.1 Amine4 -725.229134 603 Amine4 + C[O.sub.2] -913.79489 633.4 TABLE 3. Calculated relative enthalpies (kJ/mol) of isocyanate-alcohol reactions, all corrected by ZPE. HDI 2,4-TDI 2,6-TDI 2.4-MDI 4,4-MDI Isocyanate + 1-butanol 0 0 0 0 0 1-Butanol urethane2 -82.7 -72.1 -76.8 1-Butanol urethane4 -87.1 -87.2 -85.2 -84.5 Isocyanate + 2-butanol 0 0 0 0 0 2-Butanol urethane2 -80.1 -69.6 -73.9 2-Butanol urethane4 -83.9 -84.7 -82.8 -81.9 Isocyanate 4 + water 0 0 0 0 0 Amine2 4 + C[O.sub.2] -85.7 -84.9 -79.7 Amine4 4 + C[O.sub.2] -67.3 -85.8 -84.0 -83.6 Using the reference states of zero enthalpy for the reagents, the non-zero values as reported are heats of reaction. TABLE 4. Calculated total corrected (Hartree), zero/point vibrational (ZPE, kJ/mol) energies and relative enthalpies (kJ/mol) for study on impact of hydroxyl locations. Sum of electronic and thermal Enthalpies ZPE HDI -571.839728 519.4 2,4-TDI -606.395275 353.8 4,4-MDI -837.364904 568 1-Pentanol -272.820618 435.6 2-Pentanol -272.827374 434.3 3-Pentanol -272.827249 434.1 Tert-pentanol -272.830000 432.3 Sum of electronic Calculated and thermal relative enthalpies ZPE enthalpies HDI (Hartree) (kJ/mol) (kJ/mol) HDI + 1-pentanol -844.660346 955 0 1-Pentanol urethane -844.698309 968 -86.7 HDI + 2-Pentanol -844.667102 953.7 0 2-Pentanol urethane -844.704307 966.5 -84.9 HDI + 3-pentanol -844.666977 953.5 0 3-Pentanol urethane -844.703379 966.6 -82.5 HDI + Tert-pentanol -844.669728 951.7 0 Tert-pentanol urethane -844.702554 964.4 -73.5 Sum of electronic Calculated and thermal relative enthalpies ZPE enthalpies 2,4-TDI (Hartree) (kJ/mol) (kJ/mol) 2,4-TDI + 1 -pentanol -879.215893 789.4 0 1-Pentanol urethane4 -879.254034 802.3 -87.2 2,4-TDI + 2-pentanol -879.222649 788.1 0 2-Pentanol urethane4 -879.259948 800.9 -85.1 2,4-TDI + 3-pentanol -879.222524 787.9 0 3-Pentanol urethane4 -879.258996 800.9 -82.8 2,4-TDI + tert-pentanol -879.225275 786.1 0 Tert-pentanol urethane4 -879.258207 798.4 -74.2 Sum of electronic Calculated and thermal relative Enthalpies ZPE enthalpies 4,4-MDI (Hartree) (kJ/mol) (kJ/mol) 4,4-MDI + 1-pentanol -1110.185522 1003.6 0 1-Pentanol urethane -1110.222663 1016.6 -84.5 4,4-MDI + 2-pentanol -1110.192278 1002.3 0 2-Pentanol urethane -1110.228568 1015.1 -82.5 4,4-MDI + 3-pentanol -1110.192153 1002.1 0 3-Pentanol urethane -1110.227643 1015.3 -80 4,4-MDI + tert-pentanol -1110.194904 1000.3 0 Tert-pentanol urethane -1110.226724 1013 -70.8 TABLE 5. Calculated total corrected (Hartree), zero/point vibrational (ZPE, kJ/mol) energies, and relative enthalpies (kJ/mol) for study on impact of hydroxyl group chain length. Sum of electronic and thermal Enthalpies ZPE 4,4-MDI -837.364904 568 Methanol -115.668313 135 Ethanol -154.960831 210.5 1 -Propanol -194.247438 285.6 1-Butanol -233.533899 360.7 1-Pentanol -272.820618 435.6 l-Hexanol -312.107241 510.6 Sum of electronic Calculated and thermal relative enthalpies enthalpies 4,4-MDI (Hartree) ZPE (kJ/mol) (kJ/mol) 4,4-MDI + Methanol -953.033217 703 0 Methanol Urethane -953.070704 717.6 -83.8 4,4-MDI + Ethanol -992.325735 778.5 0 Ethanol Urethane -992.362932 791.8 -84.4 4,4-MDI + 1-Propanol -1031.612342 853.6 0 1-Propanol Urethane -1031.649436 866.7 -84.3 4,4-MDI + 1-Butanol -1070.898803 928.7 0 1-Butanol Urethane -1070.935949 941.7 -84.5 4,4-MDI + 1-Pentanol -1110.185522 1003.6 0 1-Pentanol Urethane -1110.222663 1016.6 -84.5 4,4-MDI + 1-Hexanol -1149.472145 1078.6 0 1-Hexanol Urethane -1149.509327 1091.4 -84.8 TABLE 6. Calculated total corrected (Hartree), zero-point vibrational (ZPE, kJ/mol) energies, and relative enthalpies (kJ/mol) for study on impact of solvent effects. Calculated Sum of electronic and ZPE relative thermal enthalpies (kJ/ enthalpies (Hartree) mol) (kJ/mol) 2,4-TDl -606.395275 353.8 1 -Butanol -233.533899 360.7 2,4-TDI + 1-Butanol -839.929174 714.5 0 1 -Butanol Urethane4 -839.967315 727.4 -87.2 2,4-TDI (T) -606.398038 353.3 1-Butanol (T) -233.536108 360.4 2,4-TDI + 1-butanol (T) -839.934146 713.7 0 1-Butanol urethane4 (T) -839.971750 726.3 -86.1 2,4-TDI (B) -606.397921 353.4 1-Butanol (B) -233.536013 360.4 2,4-TDI + 1-butanol (B) -839.933934 713.8 0 1-Butanol urethane4 (B) -839.971560 726.4 -86.2 TABLE 7. Comparison between molecular modeling results and experimental values reported in literature for reactions of 4,4-MDI with alcohol to form urethane. Reaction Enthalpy Zhao and Baser and Lovering and (kJ/mol) Gaussian Suppes  Khakhar  Laidler  Primary -84.5 -72.0 -74.9 -102.9 Secondary -81.2 -72.0 -74.9 -97.9 Tertiary -70.8 -72.0 -74.9 NR Water -83.6 -66.0 -86.0 NR TABLE 8. Enthalpy calculation of isocyanate-amine reaction. Sum of electronic Calculated and thermal relative enthalpies ZPE enthalpies (Hartree) (kJ/mol) (kJ/mol) HDI -571.839728 519.4 HDLAMINE -459.698169 555.5 HDI + AMINE -1031.537897 1074.9 0 ISO-Amine_product -1031.568419 1087.6 -67.4 TABLE 9. Recommended values for heat of reaction (kj/mol). PMDI MDI TDI HDI Primary -82.0 -84.5 -87.2 -86.7 Secondary -78.8 -81.2 -84.0 -83.7 Tertiary (HS) -68.7 -70.8 -74.2 -73.5 Water -81.1 -83.6 -85.8 -67.3 Amine -67.4 TABLE 10. Calculated total corrected (Hartree), zero-point vibrational (ZPE, kJ/mol) energies, and relative enthalpies (kJ/mol) for 2,4-TDl and 1-butanol reaction. Sum of electronic Calculated and thermal ZPE relative enthalpies (kJ/ enthalpies Method (Hartree) mol) (kJ/mol) B3LYP 2,4-TDI -606.395275 353.8 1-Butanol -233.533899 360.7 2,4-TDI + 1 -butanol -839.929174 714.5 0 1-Butanol urethane4 -839.967315 727.4 -87.2 HF 2,4-TDI -602.803702 378.8 1-Butanol -232.011583 384.5 2,4-TDI + 1 -butanol -834.815285 763.3 0 1-Butanol urethane4 -834.855365 778.1 -90.4 MP2 2,4-TDI -604.654634 355.1 1-Butanol -232.783505 371.2 2,4-TDI + 1-butanol -837.438139 726.3 0 1-Butanol urethane4 -837.475997 738.7 -87.0
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|Author:||Zhao, Yusheng; Suppes, Galen J.|
|Publication:||Polymer Engineering and Science|
|Date:||Jun 1, 2015|
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