Group Contribution Method To Predict Boiling Points and Flash Points

ARTICLE pubs.acs.org/EF

Group Contribution Method To Predict Boiling Points and Flash Points of Alkylbenzenes Justin M. Godinho,† Chung-Yon Lin,† Felix A. Carroll,*,† and Frank H. Quina‡ † ‡

Department of Chemistry, Davidson College, Davidson, North Carolina 28035, United States Instituto de Química, Universidade de S~ao Paulo (USP), CP 26077, S~ao Paulo 05513-970, Brazil

bS Supporting Information ABSTRACT: Boiling point numbers (YBP) of alkylbenzenes are predicted directly from the molecular structure with the relationship YBP = Ari + 1.726 + 2.779C + 1.716M3 + 1.564M + 4.204E3 + 3.905E
0.329D + 0.241G + 0.479V + 0.967T + 0.574S. Here, Ari is a parameter that depends upon the substitution pattern of the aromatic ring, while the remainder of the equation is the same as that reported earlier for calculating the YBP values of alkanes. The boiling points (TB) of the alkylbenzenes are then calculated from the relationship TB (K) =
16.802YBP2/3 + 337.377YBP1/3
437.883. For a data set consisting of 130 alkylbenzenes having 7
40 carbon atoms, the average absolute deviation between the literature and predicted TB values was 1.67 K and the R2 of the correlation was 0.999. In addition, YBP values calculated with this method can be used to predict the flash points of the alkylbenzenes.

’ INTRODUCTION The alkylbenzenes comprise a major category of liquid hydrocarbons, with applications ranging from petroleum products to reagents for the synthesis of diverse organic compounds. Two of the most important physical properties of alkylbenzenes are their normal boiling points (TB) and flash points (TFP). The boiling points guide the selection of reaction conditions when the alkylbenzenes are used as starting materials and also the choice of isolation methods when they are products of reactions. The flash points provide a measure of the fire hazard associated with the storage and use of these compounds at various temperatures. Boiling points are generally available, if only at reduced pressure, for compounds that have been reported in the literature. However, a chemist planning the synthesis of a new compound must rely on physical property prediction methods to estimate the boiling point of the synthetic target. On the other hand, experimental flash points are often unavailable even for known compounds, and they are certainly not available for compounds that have yet to be synthesized. Even when experimental TB and TFP data can be found, there may be discrepancies in the values from different sources, thus requiring the chemist to make judgments about the reliability of the data. For all of these reasons, methods for the correlation, evaluation, and prediction of TB and TFP values of alkylbenzenes continue to be of interest. One of the fundamental information-organizing themes in organic chemistry is the concept of homology, and students learn early that the boiling points of a series of homologous compounds increase regularly with the number of repeat units in the structures. This regular variation in boiling points is not linear, however. For example, Figure 1 shows the curvature in a plot of reported boiling points (•) of the n-alkylbenzenes from toluene to n-tetratriacontylbenzene. Because of this curvature, methods to predict TB values from simple structure counts typically have been applicable over only a small range of molecular sizes. Methods covering a wider range of molecular sizes usually incorporate a series r 2011 American Chemical Society

of parameters that, taken together, can model this curvature. Such methods may be based on complex multiparametric or neural network methods requiring computed electronic properties or graph theoretical connectivity functions.1 Recently, we reported a new group contribution method for predicting TB values of alkanes from structure, and it combines very good accuracy with ease of use. Improving upon a method originally proposed by Kinney,2,3 we introduced YBP (boiling point number) as a new measure of the boiling points of the paraffins. The relationship between boiling points and YBP values is shown in eq 1.4 TB ðKÞ ¼
16:802YBP 2=3 þ 337:377YBP 1=3
437:883

ð1Þ In turn, the YBP values of alkanes could be calculated directly from structure as shown in eq 2. YBP ¼ 1:726 þ 2:779C þ 1:716M3 þ 1:564M þ 4:204E3 þ 3:905E þ 5:007P
0:329D þ 0:241G þ 0:479V þ 0:967T þ 0:574S

ð2Þ

Here, C is the number of carbon atoms in the longest chain, M3 is the number of methyl substituents on carbon 3 of this chain (counting from either end), M is the number of methyl substituents at other positions, E3 and E are the number of corresponding ethyl substituents, P is the number of propyl substituents, D is the number of 2,2-dimethyl groupings (again counting from either end), G is the number of geminal substitutions at other positions, V is the number of vicinal alkyl relationships, T is the number of instances of two methyl substituents on both carbons Received: July 28, 2011 Revised: September 27, 2011 Published: October 13, 2011 4972

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Table 1. Contribution of Different Substitution Patterns to YBP Values substitution pattern

Ariv

mono

1.313

ortho meta

0.970 0.658

para

1.095

1,2,3

1.947

1,2,4

1.784

1,3,5

1.196

same as in eq 2. Therefore, we changed eq 2 only by introducing the parameter Ari, which measures the effect of various types of aromatic units on the YBP value of an alkylbenzene relative to that of an alkane with the same number of carbon atoms. The result is given in eq 4. YBP ¼ Ari þ 1:726 þ 2:779C þ 1:716M3 þ 1:564M Figure 1. Nonlinear relationship of literature TB values (b, left axis) and linear relationship of literature YBP values (O, right axis) with the number of carbon atoms in a series of n-alkylbenzenes having 1
34 aliphatic carbons. The solid line shows the best-fit linear correlation of the YBP values.

1 and 3 of a three-carbon segment along the main chain, and S is the square of the ratio of the total number of carbons to the number of carbons in the longest chain. The correlation of boiling points predicted by this method with those obtained from the literature had a R2 of 0.999 for a set of acyclic alkanes containing 6
30 carbons.4 Because of the success of this method in predicting the boiling points of alkanes, we have now extended this approach to the prediction of TB values of alkylbenzenes. The results provide a convenient and highly accurate method to predict both the boiling points and the flash points of this category of organic compounds.

’ METHOD AND RESULTS From literature sources, we obtained the boiling points of 130 linear and branched alkylbenzenes containing 7
40 carbon atoms and having 1
3 alkyl groups on the aromatic ring.5 We then determined the experimental YBP values for these compounds from eq 3, where a =
16.802, b = 337.377, and c =
437.883.4 As shown in Figure 1, these YBP values are quite linear with the number of methylene units in a series of nalkylbenzenes spanning a very large range of aliphatic chain lengths. " YBP ¼


b þ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#3 b2
4aðc
TBP Þ 2a

ð3Þ

Next, we sought to modify eq 2, which was developed specifically for alkanes, so that the YBP values of alkylbenzenes could also be calculated directly from molecular structure. We felt that this new equation should resemble eq 2 as closely as possible because the structural components that contribute to YBP values for alkanes should contribute in the same way to the YBP values of the aliphatic portion of the alkylbenzenes. That is, not only the structural parameters but also their coefficients should be the

þ 4:204E3 þ 3:905E þ 5:007P
0:329D þ 0:241G þ 0:479V þ 0:967T þ 0:574S

ð4Þ

Other than the new parameter Ari, all of the parameters and coefficients in eq 4 are identical to those in eq 2. However, we did slightly alter the interpretation of some of the parameters to reflect the differences in the geometry and in the electronic nature of an aromatic compound in comparison to an alkane. First, when both the total number of carbons and the number of carbons in the longest chain are counted, the aromatic ring was always counted as six carbons. Thus, for a monosubstituted compound, C is the number of carbon atoms in the main chain of the alkyl group plus six for the ring carbons. For a disubstituted compound, C is six plus the sum of the number of carbons in the two main chains of the substituents. For a trisubstituted compound, C is six plus the sum of the carbons in the two longest main chains; the third substituent (ethyl or methyl in our data set) on the ring is counted as M or E. Second, the data suggested that the effect of the 2,2-dimethyl grouping on an aliphatic chain is lost when the tert-butyl group is attached to the aromatic ring. Therefore, we counted a tert-butyl substituent on the aromatic ring as G and not D. Similarly, when attached to the benzylic carbon of a three-carbon chain, a methyl substituent was counted as M (and not as M3) and an ethyl group was counted as E (and not as E3). We also found it necessary to include some structure-specific adjustments to Ari for compounds having two methyl groups ortho or meta on the aromatic ring, as well as for compounds having a methyl group either ortho or meta to an ethyl group.6 Specifically, we added 0.920 to the Ari value for ortho substitution when the two substituents were both methyl groups and added 0.477 when one group was methyl and the other was ethyl. Similarly, we added 0.432 to the Ari value for meta substitution when the two groups were both methyl and added 0.172 when one was methyl and the other was ethyl. These values are empirical, but we will discuss a possible rationalization for them below. We used the Solver add-in of Microsoft Excel to determine the values of Ari for different patterns of aromatic substitution that produced the lowest average absolute deviation (AAD) between YBP values calculated from literature boiling points with eq 3 and 4973

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Energy & Fuels those predicted from structure using eq 4. The resulting values of Ari are shown in Table 1. Although entirely empirical at this stage, these Ari values can be interpreted as the net result of a complex interplay of the steric and electronic differences between an alkylaromatic and an acyclic alkane with the same number of carbon atoms.7 All of the values are positive, indicating that the aromatic ring adds more to the YBP value than would six aliphatic carbons. One factor contributing to this effect could be the planarity of the aromatic ring, which enables greater intermolecular interaction of the aromatic portions of the alkylbenzenes than would be possible with a nonplanar analogue. The smaller Ari values of disubstituted compounds than monosubstituted compounds could result from steric hindrance to the intermolecular attraction of the aryl groups, although the much lower Ari value for meta disubstitution than for ortho or para disubstitution suggests an electronic effect as well. Such steric effects should be offset somewhat by the greater planarity of a compound having more substituents on the aromatic ring in comparison to an isomer having fewer substituents on the ring, and this may be the reason that the Ari values of trisubstituted structures are larger than for mono- or disubstituted structures. This reasoning also applies to the adjustments to Ari values for small alkyl groups ortho or meta on the aromatic ring. In disubstituted alkylbenzenes, ortho and (to a lesser extent) meta alkyl substituents produce a molecular dipole moment.8 Therefore, these substitution patterns produce stronger intermolecular attraction, but this enhancement can be lost if the substituents are large enough to provide a steric barrier to intermolecular association of the aryl groups in orientations favored by the local polarity. As an example of the application of eq 4, consider the calculation of YBP for (1,1,2-trimethylpropyl)benzene. There is one alkyl substituent on the aromatic ring; therefore, Ari = 1.313. There are three carbons in the longest chain of this substituent; therefore, those three carbons plus six for the aromatic ring make C = 9. The alkyl chain has three methyl substituents; therefore, M = 3. The two methyl groups on C1 of the propyl substituent are geminal; therefore, G = 1 (these two methyl groups on C1 are not counted as M3 because C1 is a benzylic position). The vicinal relationships of the two methyl groups on C1 with the one methyl substituent on C2 make V = 2. The S parameter is calculated as the square of [12 (the total number of carbons) divided by 9 (3 carbons in the longest alkyl chain plus 6 for the aromatic ring)], which is 1.778. For this compound, therefore, YBP = 1.313 + 1.726 + (9  2.779) + (3  1.564) + 0.241 + (2  0.479) + (1.778  0.574) = 34.96. The value calculated from the literature boiling point and eq 3 is 35.17. As another illustration of the method, consider 4-ethyl-1,2-dimethylbenzene. The Ari value for 1,2,4-trialkylbenzene in Table 1 is 1.784. There is an adjustment to this value of 0.920 because the two methyl groups on the ring are ortho, and there is a further adjustment of 0.172 because a methyl group and the ethyl group are meta. Therefore, Ari = (1.784 + 0.920 + 0.172) = 2.876. The longest chain is counted by summing 1 for the methyl group on C1 of the ring, 6 for the aromatic ring, and 2 for the ethyl group on C4 of the ring. Therefore, C = 9. The total number of carbons is 10; therefore, S = (10/9)2 = 1.234. The second methyl group on the ring makes M = 1. Therefore, YBP = 2.786 + 1.726 + (9  2.779) + (1  1.564) + (1.23  0.574) = 31.89. The value calculated from the literature boiling point and eq 3 is 31.88. Additional examples of the method are provided in the Supporting Information.

ARTICLE

Figure 2. Correlation of literature boiling points of 130 alkylbenzenes with values predicted using YBP values calculated from structure via eq 4. The diagonal line represents perfect correlation of literature TB values.

We used eq 4 to calculate YBP values of the 130 alkylbenzenes from their structures. When these YBP values were used to predict TB values with eq 1, a very good correlation was obtained (Figure 2). Here, R2 = 0.999, the standard error is 2.23 K, and the AAD between literature and predicted TB values is 1.67 K.

’ DISCUSSION The results reported here compare quite favorably to those obtained using other boiling point prediction methods. As noted earlier, previous methods for calculating TB values from simple structure counts have limited accuracy. With the present data set, the simple Joback
Reid method produced very large errors (AAD = 35 K).9 Kinney also had reported a method for predicting TB values of alkylbenzenes from structure, and it gave an AAD of 7 K for the compounds in our data set.6 A more recent group contribution method for the prediction of boiling points of organic compounds in general produced an AAD of 9.4 K for a set of 112 aromatic hydrocarbons.10 Some of the more complex boiling point prediction methods give better results than previous group contribution methods. A six-variable linear model incorporating molecular connectivity and computed values of electron density surfaces was developed to predict the boiling points of hydrocarbons in general. For a set of 44 alkylbenzenes containing up to 15 carbon atoms, this approach gave an AAD of 7.32 K.11 A general group contribution method based on counts of molecular fragments plus a steric factor, with consideration of group interactions, gave an AAD of 6.02 K for a set of 177 aromatic compounds.12 A method relating physicochemical properties to molecular connectivity indices produced a standard deviation of 5.82 K for a set of 47 alkylbenzenes.13 A linear multivariate regression model based on connectivity descriptors for diverse organic compounds gave a standard error of 4.51 K for 69 alkylbenzenes.14 A method incorporating group contributions and topological parameters developed to estimate TB values of hydrocarbons in general gave an AAD of 4.39 K for a group of 117 benzene derivatives.15 A bond orbital-connection matrix method produced an AAD of 4974

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both D and T = 0; therefore, eq 6 reduces to eq 7. NFP ¼ 0:987YBP þ 0:536

Figure 3. Correlation of flash points of 75 alkylbenzenes calculated using YBP values from eq 4 with literature TFP values. The diagonal line represents a perfect correlation of predicted and reported values, and the data points are sized to indicate the standard error of the correlation.

2.70 K for a set of 41 alkylbenzenes having up to 16 carbons and up to 3 substituents on the aromatic ring.7 A support vector regression method based on topological indices gave an AAD of 1.46 K for a set of 41 compounds that were also in our data set.16 By comparison, the AAD of the TB values predicted with eq 4 for these same 41 compounds was 1.39 K. Thus, the simple method reported here produces a better correlation than these other methods. Furthermore, these other methods require input parameters that can be tedious to calculate without specialized software. In contrast, eq 4 requires only parameters that are obvious from molecular structure; therefore, the method reported here can be used quite easily by any chemist. The YBP values calculated with eq 4 may also be used to predict the flash points (TFP) of alkylbenzenes. The flash point of a liquid is the lowest temperature at which the vapor
air mixture above the liquid can be ignited. Therefore, flash points are the most frequently cited measure of the fire hazard associated with the storage and use of flammable compounds. Experimental flash points of alkylbenzenes are less available, however, than experimental boiling points. Therefore, many methods have been developed to estimate TFP values, often using as inputs molecular connectivity indices or theoretical descriptors, such as computed properties of an electron density surface.17
20 Recently, we introduced the flash point number, NFP, as a new descriptor of the flammability hazards of organic compounds. The relationship of flash points and NFP values is shown in eq 5.21 TFP ðKÞ ¼ 23:369NFP 2=3 þ 20:010NFP 1=3 þ 31:901

ð5Þ

There is a strong relationship between NFP and YBP values of hydrocarbons, as shown in eq 6.22 NFP ¼ 0:987YBP þ 0:176D þ 0:687T þ 0:712B
0:176

ð6Þ Here, D is the number of olefinic double bonds in the structure, T is the number of triple bonds in the structure, and B is the number of aromatic rings in the structure. For alkylbenzenes, B = 1 and

ð7Þ

We used eq 7 and YBP values calculated with eq 4 to calculate the NFP values of the compounds in our data set, and then we used those NFP values in eq 5 to predict their flash points. We obtained a good correlation between these predicted TFP values and the reported TFP values of 75 alkylbenzenes boiling below 550 K for which reported flash points could be found.5 Equation 5 was developed with a data set of linear and branched alkanes having boiling points up to 589 K and flash points of 438 K or lower,22 and there was an increasing deviation between reported and predicted TFP values for alkylbenzenes boiling above 550 K. Equation 5 works reasonably well for alkylbenzenes boiling below 550 K, as shown in Figure 3. The R2 of the correlation was 0.974, and the AAD was 2.79 K. This correlation compares quite favorably to that of other methods for predicting hydrocarbon flash points from structure, which usually give AADs of 6
12 K.23,23 Therefore, calculation of YBP values with eq 4 provides a way to estimate the flash points of alkylbenzenes from structure more easily and more accurately than is possible with other flash point prediction methods.

’ CONCLUSION The simple method for predicting the boiling points of alkylbenzenes presented here compares favorably in accuracy to neural network and multiple linear regression methods requiring connectivity or topological parameters. Furthermore, the YBP values calculated with eq 4 can be used to predict the flash points of alkylbenzenes. We are currently developing similar correlations for other families of organic compounds. ’ ASSOCIATED CONTENT

bS

Supporting Information. List of alkylbenzenes along with their literature boiling points and references, YBP values, counts of the structural parameters used in eq 4, reported flash points and references, predicted TFP values, and further examples of the application of the method reported here. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Telephone: 704-894-2544. Fax: 704-894-2709. E-mail: fecarroll@ davidson.edu.

’ ACKNOWLEDGMENT Financial and fellowship support from Davidson College and Conselho Nacional de Desenvolvimento Científico e Tecnologico are gratefully acknowledged. Frank H. Quina is affiliated with the Brazilian National Institute for Catalysis in Molecular and Nanostructured Systems (INCT-Catalysis) and with NAPPhotoTech, the USP Research Consortium for Photochemical Technology. ’ REFERENCES (1) For a discussion and leading references, see Katritzky, A. R.; Kuanar, M.; Slavov, S.; Hall, C. D.; Karelson, M.; Kahn, I.; Dobchev, D. A. Chem. Rev. 2010, 110, 5714. 4975

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(2) Kinney, C. R. J. Am. Chem. Soc. 1938, 60, 3032. (3) Kinney, C. R. Ind. Eng. Chem. 1940, 32, 559. (4) Palatinus, J. A.; Sams, C. M.; Beeston, C. M.; Carroll, F. A.; Argenton, A. B.; Quina, F. H. Ind. Eng. Chem. Res. 2006, 45, 6860. (5) The compounds, their boiling points and flash points, and literature references are provided in the Supporting Information. (6) A method for predicting Y values of alkylbenzenes by Kinney also incorporated this kind of parameter: Kinney, C. R. Ind. Eng. Chem. 1941, 33, 791. (7) See, for example, Gao, S.; Cao, C. J. Mol. Struct.: THEOCHEM 2006, 728, 5. (The AAD value reported here was calculated from data in Table 7 of this reference.) (8) Altshuller, A. P. J. Phys. Chem. 1954, 58, 392. (9) Joback, K. G.; Reid, R. C. Chem. Eng. Commun. 1987, 57, 233. (10) Cordes, W.; Rarey, J. Fluid Phase Equilib. 2002, 201, 409. (11) Wessel, M. D.; Jurs, P. C. J. Chem. Inf. Comput. Sci. 1995, 35, 68. (The AAD value reported here was calculated from data in Table 1 of this reference.) (12) Nannoolal, Y.; Rarey, J.; Ramjugernath, D.; Cordes, W. Fluid Phase Equilib. 2004, 226, 45. (13) Jain, D. V. S.; Singh, S.; Gombar, V. K. Indian J. Chem. 1988, 27, 923. (14) Ghavami, R.; Najafi, A.; Hemmateenejad, B. Can. J. Chem. 2009, 87, 1593. (15) Li, H.; Higashi, H.; Tamura, K. Fluid Phase Equilib. 2006, 239, 213. (16) Yang, S.; Lu, W.; Chen, N.; Hu, Q. J. Mol. Struct.: THEOCHEM 2005, 719, 119. (The AAD value reported here was calculated from data in Table 1 of this reference.) (17) Suzuki, T.; Ohtaguchi, K.; Koide, K. J. Chem. Eng. Jpn. 1991, 24, 258. (18) Gharagheizi, F.; Alamdari, R. F. QSAR Comb. Sci. 2008, 27, 679. (19) Patel, S. J.; Ng, D.; Mannan, M. S. Ind. Eng. Chem. Res. 2009, 48, 7378. (20) (a) Katritzky, A. R.; Petrukhin, R.; Jain, R.; Karelson, M. J. Chem. Inf. Comput. Sci. 2001, 41, 1521. (b) Katritzky, A. R.; StoyanovaSlavova, I. B.; Dobchev, D. A.; Karelson, M. J. Mol. Graphics Modell. 2007, 26, 529. (21) Carroll, F. A.; Lin, C.-Y.; Quina, F. H. Energy Fuels 2010, 24, 392. (22) Carroll, F. A.; Lin, C.-Y.; Quina, F. H. Energy Fuels 2010, 24, 4854. (23) Carroll, F. A.; Lin, C.-Y.; Quina, F. H. Ind. Eng. Chem. Res. 2011, 50, 4796.

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