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Tsochev, V.; Petrov, P. Dae Dampf-Flibigkeitagleichgewichtdes Systems Wasser/Formaldehyd. Z . Phys. Chem. ( L e i p i g ) 1973, 252, 337. Tunik, S. P.; Lavrova, 0. A.; Lesteva, T. M. Liquid-Vapor Phase Equilibrium in Formaldehyde-Water-Alcohols Systems. 11. Methods of Treating Data on the Liquid-Vapor Equilibrium in
the Methanol-Formaldehyde-WaterSystem Complicated by a Chemical Reaction. Zh.Fiz. Khim. 1977, 51, 2707.
Received for review October 10, 1991 Revised manuscript received January 30, 1992 Accepted March 24, 1992
Estimation of Autoignition Temperatures of Hydrocarbons, Alcohols, and Esters from Molecular Structure Leanne M. Egolf and Peter C. Jurs* Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802
Computer-assisted methods are used to develop equations relating molecular structural features
to the autoignition temperatures (AITs)of diverse seta of hydrocarbon, alcohol, and ester compounds. The calculated values of AIT correlate well with experimental data (R= 0.94-0.98), and the standard deviations of the regressions closely approach experimental uncertainties. Results obtained in this study provide evidence to support claims that there exist two different mechanisms for the autoignition of hydrocarbon compounds. It is shown that the low-temperature, very structure-based mechanism could be better modeled with structure-based descriptors than the high-temperature, less structure-dependent mechanism could be. Finally, the developed models are examined to gain insight into how various structural features may affect autoignition processes.
Introduction Autoignition temperature (AIT),as shown in Figure 1 (adapted from Hilado (1970)), is defined as the lowest temperature at which a substance will ignite in the absence of a spark or flame. This phenomenon is initiated at elevated temperatures where the oxygen in the air mbegin to interact with the combustible material, resulting in an exothermic oxidation reaction. When the rate of heat production exceeds the rate at which the heat can be dissipated to the surroundings, autoignition occurs. Researchers are constantly striving to better understand the autoignition process in order to control ita behavior in two areas of tremendous practical importance. The first is to establish a more complete and less ambiguous flammability assessment scale. The ability of a substance to spontaneously ignite introduces potential safety hazards for all who handle, transport, and store combustible materials. Since combustibles have proven to be so esaential, it is increasingly imperative that the risks associated with these chemicals be accurately defined. Stringent, while not overly restrictive, regulations must be established. With both goals in mind, safety could be ensured without needlessly discouraging further development and new applications. The second is to optimize the performance of internal combustion engines through identifying or designing more efficient fuels and fuel blends. The efficiency of combustion in a gasoline engine hinges on a delicately timed sequence of events. Normally the desired combustion reaction is initiated when a spark is applied to the fuel as the piston just reaches the top of its compression stroke. With autoignition, though, the fuel ignites prematurelybefore the piston can be fully extended. Consequently, engine power and efficiency are severely reduced, and the car exhibits what is known as engine knock. Control of engine knock (autoignition) has been the subject of much research throughout the years (Kirsch and Quinn, 1985, Morley, 1987; Affens et aL, 1961). A t present, it is known that it is the structural differences in the
combustibles themselves that determine knock tendency (Morrison and Boyd, 1983). Therefore, studies have been geared toward determining how susceptible individual structural features axe to oxidative attack and autoignition. Through this knowledge, combustible compositions can be effectively altered to yield low-knock, high-efficiencyfuels. Studies by earlier investigators provide much valuable insight into the structural significance and AIT trends of hydrocarbons. For instance, numerous sources agree that a high degree of branching helps to stabilize a molecule against spontaneous ignition (Affens et al., 1961; Swarts and Orchin, 1957; Frank and Blackham, 1952). Some researchers believe that the explanation for this lies in the number of methylenes in the molecule (Affens et d,1961). Since methylene groups seem to increase the potential for autoignition, this eventuality can be averted if branching is used to limit the number of such moieties. Not only is the amount of branching important but also the relative location of this branching. Frank and Blackham (1952) as well as Swarta and Orchin (1957) contend that the likelihood of spontaneous ignition increases with the length of the uninterrupted methylene chain. Therefore, to raise the autoignition temperature of paraffins, it seems logical to intersperse branching between any methylenes that are present in the molecule. Other structural features that offer varying degrees of stability to a molecule include cyclic, aromatic, and multiple bond moieties. To summarize, a molecule’s tendency to react has been reported to increase in the following order: aromatics < branched < cyclics < alkenes < alkanes (Swarta and Orchin, 1957). Interestingly, this general structural sequence closely parallels another chemically important sequence: the ease of free radical formation in hydrocarbons. For this reason, it is not surprising that the AIT mechanism is said to proceed by a free radical reaction (Morley, 1987; Frank and Blackham, 1952; Swarts and Orchin, 1957). The ease of free radical formation, and consequently of oxidation, is directly governed by the stability of the radical formed. For aliphatic hydrocarbons, this stability follows the trend
0888-5885/92/2631-1198$03.00/00 1992 American Chemical Society
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Figure 1. Flammability regions for combustible substance/air mixtures.
3O > 2 O > lo> methyl radical (Morrison and Boyd, 1983). Although this trend shows that the most highly branched position, 3O, is the one most easily oxidized, oxidation does not always end in autoignition. In fact, according to Mens et al. (1961), this initial oxidation leads to relatively stable end products (e.g., ketones) which preclude subsequent autoignition. The secondary radicals, by contrast, are not as easily formed, but once the first oxidation has taken place, the less stable products that are formed continue to react until autoignition occurs. One final factor which also has been found to play a role in compound stability and spontaneous ignition processes is steric strain. According to the Engineering Sciences Data Unit (ESDU), those molecules which exhibit greater strain (e.g., small cyclic compounds such as cyclopropane or epoxides) often need less heat to incite autoignition (ESDU, 1982). In most case, these structural trends can be easily recognized in small, homologous chemical classes. However, as the complexity of the molecule increases and one considers compounds containing functionalities, the structure-property relationships become more obscure. Since we believe-despite apparent obstacles-that the molecular structure still holds the key to understanding and controlling autoignition process, a technique designed to reveal underlying relationships must be found. Our answer to this challenge is a structure-based computer software package known as APT (Automated Data Analysis and Pattern Recognition Toolkit) (Stuper et al., 1979; Jurs et aL,1979). Through the ADAFT system utilities, one can quantitatively describe the structural features in a given set of chemical compounds. The resulting numeric representations (known as descriptors) then are explored as a unit, and important interrelationships are identified. Finally, through the methods of multiple linear regression analysis (Neter et al., 1985),groups of Statistically coherent descriptors can be used to estimate a biological or physical property of interest. Applications of ADAPTtechniques are becoming more widespread. Focusing just on recent physical property applications, this technique has been used to successfully study and model normal boiling points of heterocyclic compounds (Stanton et al., 1991), gas chromatography retention indexes (Anker et al., 19901, Henry's law constants (Dunnivant et al., 1992),surface tensions (Stanton and Jurs, 1992), and I3C NMR spectral data (Egolf et al., 1988). The goal of the present work is to see if the ADAPT methodology can be extended to explore and model yet another physical property: autoignition temperature. In addition, it is of interest to investigate whether the developed models can verify or offer new insight into the importance of isolated structural features as they affect
CI
Figure 2. Example compounds from the data set.
the autoignition process. This study represents the first attempt to estimate AITs for such a large and structurally diverse group of chemical compounds.
Experimental Section All computations were performed on a SUN 4/110 workstation using the ADAPT software package (Stuper et al., 1979; Jurs et al., 1979). Data Set. The data set is comprised of 312 heterogeneous compounds containing from 3 to 22 carbons. Some example compounds are shown in Figure 2. Many of these compounds are hydrocarbons, with the remainder having one or more functionalities, such as ether, ester, nitrile, nitro, amine, halogen, alcohol, epoxy, or carbonyl moieties. In addition, the compounds contain linear, branched, cyclic, and/or aromatic architecture. The end results of these structural combinations are manifested in the unique chemical and physical properties associated with each molecule. Therefore, a wide range of AIT values is found to accompany this collection of very diverse compounds. All of the AITs for this study were obtained from a data compilation published by the Design Institute for Physical Property Data (DIPPR, 1989). Although the majority of properties reported in the DIPPR data base have been critically reviewed for consistency and soundness, AIT values have been flagged as unevaluated. Consequently, the experimental uncertainty of these AITs remains unclear. After conducting our own review of references cited by the source, it was concluded that one of the more widely cited and representative test methods was the now-dicontinued ASTM-D2155 procedure (American Society for Testing and Materials, 1976). The experimental uncertainties are loosely defrned in that procedure. On the basis of our interpretations of those definitions, however, attempts will be made to develop models with experimental uncertainties that fall between 2 and 5%. It is important to note that the same sources which reference ASTM-D2155 as their test method go on to caution that any AIT values reported should be considered approximations only (National Fire Protection k i a t i o n , 1991). Knowledge gained in more recent years has prompted researchers to take a closer look at past autoignition studies. The experimental design has been far from ideal. The main objection is with the detection system used to identify the AIT. Visual inspection was chosen to detect the sudden appearance of a flame inside the autoignition vessel. This method is greatly limited by human capabilities. Current information on ignition processes shows that in some cases autoignition actually begins with a nonluminous or barely luminous reaction which is difficult, if not impossible, to detect by the procedures employed here (National Fire Protection Association, 1991). On top of this, testing methods and compiled literature values have not been standardized, and more
1800 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
recent research reveals that AITs are notoriously sensitive to variations in testing conditions. Deviations in pressure, volume and shape of the test vessel, ignition-vessel material, vessel cleanliness, sample purity, combustible/oxygen ratio, and injection rate and uniformity of sample dispersion have proven to alter AIT values significantly (Hilado and Clark, 1972; Swarta and Orchin, 1957; Frank and Blackham, 1954; ESDU, 1982; National Fire Protection Association, 1991). Molecular Modeling. The chemical structures were sketched on a computer graphics terminal and stored on disk as connection tables which represent atom @pea, bond types, and bond connections. Since some physical properties like AITs may depend not only on how the atoms are connected but also on the geometrical distributions of these atoms, accurate 3-D representations were necessary. Therefore, the compounds were modeled using MMZ, a force-field molecular modeling routine (Burkert and Allinger, 1982). This procedure adjusts bond lengths, bond angles, and torsional angles to the specific atomic environment and correcta the structure to an energy-minimizIwl conformation. AMI, a semi-empirical molecular orbital modeling routine (Dewar et al., 19851, was used in a complementary manner to obtain final, optimized geometries for those molecules with structural features not recognized by the MMz program. Descriptor Generation. Once the molecular structures were stored along with their respective autoignition temperatures, descriptor generation began. The success of a structureproperty relationship study often hinges on the researcher’s ability to identify those structural featurea that contribute most to the physical property in question. In this case, autoignition temperature theory directed which characteristics to quantitatively encode. These numeric representations of structure-commonly known as descriptors-were later used to develop the final, interpretable mathematical models. Descriptors fall into three main categories: topological, geometrical, and electronic. Topological descriptors focus on the framework of the molecule and include items like atom counts, bond counts, path counts, and branching information. Geometrical descriptors, which depend on a structure’s 3-D representation, include principal moments of inertia, molecular volume, and surface area. Electronic descriptors are based on the molecular charge distribution. Total positive charges, total negative charges, sum of charges, and charged partial surface area are examples of descriptors that represent this category. The majority of descriptors were generated through the ADAPT software packages. Where chemical theory suggested the study of structural features not available through existing ADAPT programs, new descriptors were calculated using other means and added to the descriptor pool. Four energetic descriptors were computed through the molecular modeling routines: steric strain, ionization potential, heat of formation, and electronic energy. It was thought that these features might quantitate key information on structural strain and radical reaction mechanisms, both of which are reported to direct the ease of autoignition. Since the number and relative location of methylene groups in a molecule appear to play prominent roles in spontaneous ignition processes, two relevant descriptors were developed a count of the total number of methylene units and a count of the methylene units in the longest uninterrupted methylene chain. Lastly, a descriptor introduced by Kier, the flexibility index, was used to encode the degree of flexibility (or rigidity) in a structure (Kier, 1989).
Objective Feature Selection. In order to refine the descriptor pool, objective feature selection was used to weed out those descriptors that provide minimal or redundant information. This process is termed objective since the property of interest (AIT) is ignored and, therfore, has no influence on the screening of structural features. First the decriptors were analyzed separately. Descriptors containing a large number of zero or identical values (290%)were discarded because they probably fail to encode the distinctions in a structure that are responsible for the differences seen in autoignition temperatures. When only information-rich descriptors remained, it was then necessary to examine the group as a whole. One descriptor was eliminated from each pair exhibiting a high pairwise correlation (10.95), thereby greatly reducing information overlap. Software limitations and/or statistical considerations placed further restrictions on the number of descriptors that could be used in model-building routines. Thus, the goal was to identify those subsets of descriptors that might encompass the most AIT information. In some cases reduced pools of descriptors were built on chemical intuition. This method, though subjective, exposed many collectively important groups of variables. A more systematic, descriptor-ranking approach which also proved invaluable was vector space descriptor analysis (vsda), a program based on the Gram-Schmidt orthogonality selection scheme (Ciarlet, 1989). Regression Analysis. Once a reduced descriptor pool has been chosen, regression analysis can begin. It is at this point that equations relating structure and property are developed. The general form for such an equation is n
AITj = bo + C biXij i=I
where AITj is the autoignition temperature of compound j, bo is the y-intercept of the regression line, bi is the coefficient of the ith descriptor x i , and n is equal to the number of descriptors in the final model. Leaps-and-bounds and interactive regression analysis (IRA)were the linear regression routines implemented in this study. Leaps-and-bounds is a highly automated program which self-sufficientlyidentifies top descriptor subsets based on R2criteria (Furnival and Wilson, 1974). The IRA algorithm, on the other hand, is designed to be user-interactive. This routine allows the researcher to watch how a model reacts as new descriptors are added and the old ones removed. Capitalizing on this capability, IRA can be used to explore and refine models suggested by the more automated but lesa internally critical programs like leaps-and-bounds. During the equation-buildingstages, statistical criteria were monitored closely in order to determine the potential strength of any models in progress. These values include partial F-statistics, the overall F-statistic, the multiple correlation coefficient (R),and the standard deviation of the regression ( 5 ) (Neter et al., 1985). In addition, it is statistically desirable to develop equations in which the number of descriptors is kept to a minimum. When only a select group of equations remained, outlier detection, internal validation, and visual inspection were used to evaluate the validity and stability of all final models (Snee, 1977). The specifics of these tests will be discussed more thoroughly in the following sections. Results and Discussion Initially attempts were made to model the data set as a whole. One of the best equations found yielded a cor-
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1801 relation coefficient R of 0.852. The correaponding standard deviation of regression s of 59 K translated to more than a 10% error at the mean of the temperature range. Considering that it is desirable to have a model error that closely approaches the experimental uncertainty, it became apparent that alternate modeling strategies needed to be explored. As discussed earlier, there were concerns that test method inconsistencies between laboratories may have degraded this very sensitive data set to the point of seriously hindering any modeling attempts. However, there was another possibility to investigate. As seen in previous structureproperty studies (Jurs et al., 1989;Anker et al., 1990), it is often the dissimilarity among the compounds themselves that makes a data set difficult, if not impossible, tQ model. Diverse data sets may have to be broken down into d e r , more homogeneous groups of molecules. This tactic enables the physical property to be more effectively modeled, thereby revealing more meaningful structureproperty relationships. One of the most common subsetting schemes-one based on functionality-was chosen for this portion of the study. This approach met with great rewards, as will be seen through three of the largest subsets explored: hydrocarbons, alcohols, and esters. Hydrocarbons. Early attempts to model the hydrocarbon subset met with limited success. At first, all modeling took place using only a limited set of ADAPT descriptors. The best two models generated here yielded R = 0.87 and 8 = 59 K, results very similar to those obtained when modeling the data set as a whole. Since this was only the preliminary stage of modeling, it was hoped that results could be improved as equations were examined and any internal discrepancies were resolved. Normally, in any given data set, compounds will exist which seriously inhibit the modeling process. These compounds are termed outliers. In some cases, there will be a physical reason to explain why a given molecule cannot be adequately expressed with others in its subset. For instance, if one of the compounds in our data set contained five aromatic ringa and no other compound contained over three aromatic rings, the structural information introduced through the five-ring compound may be so unique to its data set that this compound may not be able to be adequately represented with the rest. Unfortunately, sometimes there is no obvious reason why a compound is cited as an outlier. In these cases,outlier removal is based solely on statistical rationale. In order to identify potential outliers, each model was submitted to robust regression analysis (FUU), a statistical outlier detection program based on the least median squares criteria (Rousseeuw and Leroy, 1987). Fifteen compounds were flagged as outliers in the best model; twenty-one in the second best. These results suggest that over 15% of the data should be removed before continuing with model development. However, to discard such an excessive number of compounds would be contrary to the usual practice involved in uncovering structureproperty relationships. Therefore, the outliers were examined to determine if there was a commonality in s t r u m that was not being effectively encoded. No physical explanations were found. This lack of success led to an extensive search of the autoignition temperature literature. It was at this point that five of the seven, n o n - m m descriptors (introduced earlier) were developed. Hydrocarbon autoignition theory concerning radical reactions suggeats that descriptors based on ionization potential, heat of formation, and electronic
energy might improve modeling capabilities. Consequently, three relevant descriptors were generated. After discovering that two persistent outliers, dicyclopentadiene and a-pinene, had excessively large steric strains, it was hypothesized that a steric strain descriptor could encode key autoignition temperature information. The development of this descriptor was supported by the authors of the ESDU compilation (1982)who noted a relationship between structural strain and autoignition temperatures. Lastly, with the belief that the rigidity of a molecule also could encourage the bond breaking that must precede autoignition, a deecriptor that could adequately encode this feature was sought. Kier's flexibility index had such a capacity and thus was added to the descriptor pool. Models generated with this more informationally rich descriptor pool met with mixed results. First, it was interesting to see that the steric strain descriptor was contained in the three best equations. Also, these models showed some improved statistics the best R value was 0.92 with an associated s of 44 K. It was only when these new models were submitted to outlier detection that it was realized that a considerable problem still remained. RRA flagged between 16 and 22 outliers per model, results which closely mimicked the unsatisfactory results encountered earlier. Although the new descriptors were not able to bring more of the outlying compounds into the model, Frank and Blackham (1952),Affens et al. (19611,and Swarts and Ordhin (1957)cite a theory that suggests that the existence of these outliers can be justifield. According to their research, there is not one but rather two different mechanisms by which autoignition of hydrocarbons takes place. Interestingly, these mechanisms are differentiated on the basis of temperature itself. The low-temperaturemechanism (below 573 K), which is highly structure-dependent, involves peroxide intermediates:
-
ROO' + RH ROOH + R' By contrast, the high-temperature mechanism (above 673 K)depends significantly less on molecular structure and proceeds by alkyl radical intermediates: RH + '00' R' + 'OOH RH
+ 'OOH
R' + 'OOH
-
--
R'
+ H2Oz
R'CH=CH2
+ H202
Since the ADAPTmethodology is entirely structure-baaed, it was logical to deduce that compounds that autoignite in the high-temperature regime should be more difficult to model. A re-examination of our results demonstrates the validity of this hypothesis. When the hydrocarbons were sorted on the basis of their experimental autoignition temperatures, it was discovered that 80% of the outliers were compounds with autoignition temperatures above 673 K. This fact seems especially significant when it is noted that there were approximately 20% more compounds in the high-temperature region, and, consequently, one might have expected that mechanism, because it encompassed the majority of compounds, would have had the greater influence over the group as a whole. While there seemed to be sufficient support for the two-mechanism theory, one final piece of structural information, uncovered through further reading, had to be teated to me if it would refute the two-mechanism theory. Thus, the last two n o n - m m descriptors, those that deal with the importance of methylene moieties, were calculated and entered into the descriptor pool at this time. Exciting consequences ensued. One of the descriptors, the number
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