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Flash Points of Organosilicon Compounds: How Data for Alkanes Combined with Custom Additive Fragments Can Expedite the Development of Predictive Models Didier Mathieu* CEA, DAM, Le Ripault, F-37260 Monts, France S Supporting Information *
ABSTRACT: An especially simple approach to the evaluation of flash point (FP) from additive fragment contributions is outlined. Being based on a square root expression derived from the examination of n-alkanes data, it avoids the need for nonlinear fitting procedures and for trial-and-error optimization of the analytical relationship between FP and molecular descriptors. Furthermore, in spite of a specially small number of additive contributions, the method can be applied to most organic molecules. For organosilicon compounds, it exhibits some advantages compared to previously available procedures, while providing very similar performances, with an average absolute deviation from experiment close to 12 K, a determination coefficient R2 = 0.89 and only one error >40 K.
1. INTRODUCTION Correlations of physical properties of fluids with their composition are valuable aids to practicing engineers and chemists.1 Theory provides useful relationships between these properties, but it is usually not possible to derive explicit expressions in terms of molecular quantities (so-called descriptors) easily amenable to molecular computation. For instance, according to explosion theory, flash point (FP) can in principle be obtained as the numerical solution of an algebraic equation involving other properties of the fluid, as well as various parameters of the experimental setup.2 Alternatively, FP can be estimated on the basis of the Clausius−Clapeyron equation, using the vaporization enthalpy, boiling point, and flammability limit of the fluid as input.3 However, empirical relationships between FP and molecular descriptors are often preferred as they do not depend on the availability of intermediary properties. In view of developing such predictive tools, it is interesting to note that the FP is closely related to the corresponding vapor pressure4,5 and may be very accurately estimated using as only input boiling point6,7 and possibly vaporization enthalpy8 or number of carbons.9 These findings suggest that the FP depends primarily on intermolecular interactions in the liquid phase, rather than on the ability of the vaporized compound to enter into combustion regime in air. As a consequence, it should be possible to estimate FP from simple molecular descriptors. In the present context of growing societal concern for safety issues, it comes as no surprise that plenty of relationships aimed at predicting FP from molecular structure are currently being developed10−25 and several reviews published.26−28 Extensive experimental data are available from academic databases such as DIPPR29 or The Chemical Database30 and also from many vendor catalogs, commercial Web sites, and material safety data sheets.31−37 Although new predictive models should ideally take advantage of this data, this is made difficult by the fact that only raw FP values are often reported, despite the fact that © 2012 American Chemical Society
differences in experimental methods and apparatuses may influence these values by tens of degrees, notwithstanding the significant uncertainties and many errors encountered in these compilations.16 In this context, there is a significant risk that an empirical model is flawed owing to some ill-defined parameters whose values primarily depend on erroneous data. Therefore, it is especially important to keep the number of adjustable parameters as small as possible. On the other hand, it is difficult to figure out the limitations of empirical models. For instance, a systematic assessment of available methods to predict FP values for a data set of 230 organosilicon compounds reveals that none of them is satisfactory.18 Considering the growing needs of semiconductor industries regarding FP estimation for such species, the author in this work developed two new prediction methods focused on Si-containing molecules. The first one is obtained using a standard QSPR approach.18 As subsequently pointed out by the authors,19 it exhibits some significant drawbacks inherent to this empirical methodology, including the lack of physical meaning of many descriptors and the need for specialized and costly software to compute their values. Furthermore, it does not provide any insight to chemists regarding the influence of molecular moieties on FP values. Therefore, an alternative method based on the structure group contribution (GC) approach was subsequently implemented.19 As it stands, this procedure provides a useful tool to chemical engineers in semiconductor industries. Nevertheless, as outlined below, it exhibits some undesirable features with regard to physical consistency, number of empirical parameters required, and future developments toward arbitrary organic compounds. The present work shows that further progress can be easily obtained through an alternative additivity approach which Received: Revised: Accepted: Published: 14309
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exhibits two key differences with respect to the previous one.19 First, the relationship between FP and the additive contributions is extrapolated from a previous model for n-alkanes that proved especially successful,17 rather than optimized on a trialand-error basis. Second, molecules are split into additive fragments specifically tailored to account for intermolecular interactions.38 This work thus demonstrates how the development of predictive methods may be expedited, taking advantage of (1) successful relationships already available for simple cases and (2) custom fragmentation schemes.
2. MODELING APPROACH 2.1. Previous GC Scheme for Organosilicon Compounds. The above-mentioned GC method of Wang et al.19 takes advantage of a database of 230 organosilicon compounds for which previous prediction methods proves unsuccessful. It is fitted against a subset of this compilation including 184 compounds. It is then validated using an external test set made of the 46 remaining molecules. Like most GC methods, it is based on a sum of additive contributions: f=
∑ νifi i
Figure 1. Dependence of the determination coefficient for the training and test sets on the exponent α in eq 4. (1)
where f i is the constitutive parameter associated with group i and νi is the number of such groups in the molecule studied. Being unsatisfied with a simple linear expression of FP in term of the f i parameters, the authors attempted to relate f to experimental FP data through polynomial expressions. On a trial-and-error basis, they observed that the most reliable predictions (lowest values for the maximum error and average relative error) were obtained using a quadratic expression: FP = a + f − bf 2
carbon atoms.17 Therefore, we keep α = 1/2 in the present study. Equation 3 predicts that FP increases with molecular size, as usually observed experimentally and anticipated from the fact that larger compounds require higher temperatures to vaporize. In contrast, owing to the negative quadratic term involved, eq 2 yields a decrease of FP with molecular size for large systems, including for instance alkyl chains with about forty methylene units or silicon oils with more than 24 −(O−Si(CH3)2)− siloxane units. This is of little practical significance as FP data are usually not available for such heavy compounds that cannot be easily vaporized under ambient conditions. Nevertheless, this feature of eq 2 points to the fact that it might get unreliable as larger molecules are considered. A more significant advantage of eq 3 over the previous polynomial expression stems from the fact that the f i parameters are simply derived from a straightforward multilinear regression so that computed f values match the squares of the experimental flash points. This is especially interesting in view of further extension of the method to additional compounds as this avoids the need for nonlinear optimization techniques, in addition to the tedious trial-and-error determination of the suitable number of terms required in a polynom to get optimal predictions. 2.3. Molecular Fragmentation Scheme. Notwithstanding the fact that eq 3 is used instead of eq 2, the other distinctive feature of the present relationship with respect to the GC method of Wang et al. stems from the groups i employed in eq 1. The fact that boiling point and vaporization enthalpy allow very accurate FP predictions8 suggests that intermolecular forces play a primary role. Therefore, the present work takes advantage of molecular fragments specifically designed to account for intermolecular interactions while keeping the number of parameters as small as possible. The motivations for introducing such groups are detailed in a recent article where it was demonstrated that they are extremely successful to predict sublimation enthalpy, a property that directly depends on the interactions between molecules.38 Therefore, only a brief definition of the groups is provided here.
(2)
where a and b are positive constants. According to the results obtained on the test set, this simple model is especially reliable compared to previous ones. Therefore, it might be worth generalizing to arbitrary molecular compounds. However, it is shown below that straightforward modifications to this approach yield an even better starting point in view of future development. 2.2. Present Model Equation. Instead of resorting to a polynomial expression similar to eq 2, the present approach takes advantage of the previous observation that FP values for n-alkanes increase approximately as the square root of the number of carbon atoms in the molecule.17 Therefore, for organosilicon compounds, eq 2 is replaced by FP = f 1/2
(3)
where f is still obtained according to eq 1. While the exponent 1/2 in eq 3 proves optimal for alkanes, yielding an excellent performance and thus providing confidence to this exponent value, it might be tempting to consider a more general equation: FP = f α
(4)
where α is treated as an adjustable parameter. For the training and test sets used in ref 19, the best correlations are obtained for values of α ranging from 0.3 to 0.5, as shown in Figure 1. They yield much improved results with respect to a linear model (α = 1). However, decreasing α below the alkane value α = 1/2 does not yield any significant improvement and would prevent the use of the previously optimized parameters for sp3 14310
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remaining parameters yielded a negative value for B3-0. Because this value depends on a single compound and may be plagued with statistical (in addition to experimental) uncertainties, B3-0 is finally arbitrarily set to zero. This is reasonable as boron atoms surrounded by three ligands are relatively crowded and should not contribute significantly to intermolecular interactions. A similar assumption was presumably made in ref 19 as no parameter is reported for boron. Finally, the present scheme applied to the organosilicon data set requires only the determination of the 23 + 7 + 2 = 32 parameters listed in Table 1. In principle, they are sufficient to
They consist primarily of so-called atomic fragments made of a single non-hydrogen atom and all attached hydrogen atoms. Different atomic fragments are introduced for atoms with different coordination number nc and/or different numbers of hydrogen neighbors nH. There are assigned a label Xnc-nH where X stands for the atomic symbol of the non-hydrogen atom. For instance, terminal amide groups (CO)NH2 are described in terms of three atomic fragments labeled, respectively, C3-0, O1-0, and N3-2. They differ from standard (>C), (O), and (NH2) groups by the fact that bond orders are ignored. The present nomenclature was first introduced in the original implementation of this fragmentation procedure.39 In addition to atomic fragments, two kinds of structural corrections are introduced. Ring corrections depend on ring size and aromatic character. More specifically, four contributions labeled R3 to R6 are introduced for ring sizes r = 3 to 6, and a single contribution R>6 is introduced for larger rings. Two specific contributions R5a and R6a are used for aromatic rings. Thus, a total of seven parameters is used to account for the role of rings. Finally, two additional corrections denoted Bn (n = 2, 3) are introduced to account for crowding effects associated with the occurrence of elements beyond the first row of the periodic table. More specifically, Bn is defined as the contribution of a first row atoms bonded to n neighbors heavier than neon. No explicit B1 correction is needed, as explained in ref 38. These fragments mostly coincide with those previously introduced on the basis of geometrical considerations for the prediction of crystal volumes.39 Compared with more conventional groups, they allow a dramatic reduction of the number of empirical parameters required with no loss of accuracy.38,39 This feature should be especially advantageous in the present context, as FP compilations are believed to be full of erroneous values, as emphasized by Rowley et al.16 Consequently, as more parameters are used to fit FP data, there is a risk that some of them will exhibit spurious values owing to erroneous reference data. On the other hand, many additivity schemes do not provide any systematic recipe to define the constitutive groups. the latter are then loosely defined after the functional groups accounting for chemical reactivity, such as alcohol, nitrile, or carbonyl. This is the case for the groups used in ref 19, initially introduced to estimate boiling points.40 The flexibility thus afforded in the definition of the groups allows them to be optimized in order to obtain improved fits. Unfortunately, this increases the risk of chance correlations. Wang et al.19 invoke electronegativity differences to motivate the introduction of additional Si-containing groups. In addition, the three highly specific groups NCN, NCO, and NC S are introduced on the basis of symmetry arguments. Unfortunately, their predictive value cannot be assessed as they do not arise in the test set. In this respect, the well-defined and systematic character of the present fragmentation procedure is a further advantage of the present approach.
Table 1. Parameters of the Present Model (See Text for Details) i
f i (K2)
atomic groups C2-0 5095.8 C2-1 34899.7 C3-0 9179.7 C3-1 10473.6 C3-2 11380.7 N1-0 32605.9 N2-0 8607.9 N3-0 3925.1 N3-1 9193.0 N3-2 26436.5 O1-0 12376.1 O2-0 5153.6 O2-1 42113.9 F1-0 2745.3 Cl1-0 20155.2 Br1-0 42683.5 I1-0 48149.5 S1-0 46371.9 S2-0 19729.0 Si4-0 3730.1 Si4-1 11252.1 Si4-2 15097.2 Si4-3 25658.2 ring corrections R3 38567.8 R4 17226.9 R5 8890.3 R5a 18108.2 R6 9699.1 R6a 2533.6 R>6 17096.1 crowding corrections B2 −8600.2 B3 −19539.1
s.d. (K2)
Nocc
0.22 1.23 0.07 0.04 0.06 0.74 0.25 0.05 0.07 1.14 0.11 0.01 1.02 0.02 0.00 0.51 1.02 1.13 1.07 0.02 0.03 0.28 0.16
7 1 31 49 26 2 4 10 4 1 8 67 1 8 67 2 1 1 1 157 26 5 4
1.15 1.02 0.26 2.58 0.09 1.41 0.32
1 1 5 1 9 22 6
0.02 0.76
35 2
handle most Si- or S-containing compounds (except sulfones) and virtually any compound including only the elements C, H, N, O, F, Cl, Br, and I, except for some uncommon moieties such as the isocyano group NC. This is because such groups exhibit atoms with unusual coordination numbers. For instance, the missing fragment to handle isocyano groups is C10. For the present data set, the GC method of ref 19 requires the determination of 41 empirical parameters, including 39 group contributions f i in addition to the polynomial coefficients a and b in eq 2. Despite more numerous parameters, this
3. VALUES OF THE FRAGMENT PARAMETERS Applying the simple fragmentation procedure described in section 2.3 to the data set used in ref 19 yields 37 parameters, including 28 atomic fragments, 7 ring corrections, and 2 crowding corrections. Among the atomic fragments, values for C4-3, C4-2, C4-1, and C4-0 were already obtained in preliminary work on alkanes.17 A preliminary fit of the 33 14311
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with the primary role assigned to intermolecular interactions. In particular, Table 1 shows that fragments involving heavier atoms tend to exhibit larger contributions, whereas the contribution assigned to a non-hydrogen atom systematically decreases with the coordination number and increases as it includes more hydrogen atoms. For instance, focusing on hydrocarbon fragments centered on sp3 carbon atoms, there are two reasons why the associated GC parameters should increase with the number of attached hydrogen atoms. First, the central carbon gets less crowded and thus more available for intermolecular interactions as one of its ligands is substituted with a hydrogen atom. Second, the corresponding group includes an additional hydrogen atom further contributing to intermolecular interactions. In line with these expectations, C4-0 < C4-1 < C4-2 < C4-3. With regard to the group contributions obtained in ref 19, the observed trend is exactly the opposite with (>C (>CH−) > (>CH2) > (−CH3). Similar observations can be made for sp2 carbon atoms and sp3 silicon atoms. For sp carbon atoms, both methods exhibit values of the parameters consistent with expectations. For other groups, especially those associated with sp3 nitrogen atoms, values reported in ref 19 exhibit erratic variations with the number of attached hydrogen atoms, while present parameters are always fully consistent with expectations.
method is less general than the present one, with molecules containing e.g. S, SiH2, or >C< atoms in ring systems or N atoms not in any ring lying beyond its scope. Missing parameters cannot be extrapolated from available values because the latter exhibit no obvious regularities. For instance, in most cases a group contribution decreases as it gets included into a ring, but this is not the case for O and >NH, while the contribution of C< is left virtually unaffected. To make comparisons easier, the present method is fitted and validated using the training and test sets previously employed in ref 19. The values of the 32 additive contributions f i thus obtained, with associated standard deviations (s.d.) and number of occurences Nocc, are reported in Table 1. More precisely, Nocc stands for the number of compounds for which the knowledge of the parameter f i associated with group i is required to estimate the corresponding FP. These parameters complement the previous set of carbon parameters derived in ref 17, namely C4-3 = 10383.6, C4-2 = 10060.1, C4-1 = 7208.0, and C4-0 = 3457.4. It should be noted that both the method described in ref 19 and the present one exhibit ill-defined parameters, whose values depend on a single experimental measurement. For the former, this problem concerns 10 parameters, namely CH, OH, NH2, >NH in ring, N in ring, S and >SiH in ring, I, and the three triatomic groups NCN, NCO, and N CS mentioned above. In the present scheme, it concerns nine parameters, as is clear from Table 1. Within the present approach, considering more extended data sets provides a straighforward solution to this problem, whereas within the GC approach of ref 19, this would require the introduction of many additional parameters. An advantage of the present method stems from the fact that atomic fragments represent contributions to squared FP values and should therefore be positive. As illustrated in the case of the boron parameter B3-0, such physical expectations allow one to point out spurious parameter values and fix underdetermination difficulties. On the other hand, eq 2 indicates that according to the model of ref 19, FP increases with f for most compounds of interest. Therefore, to be consistent with the expected sizedependence of FP, this model should also exhibit only positive group contributions. However, considering the significant contribution associated with the constant term a = 224.54 K, it comes as no surprise that the fit yields negative parameters and thus spurious predictions. For instance, the values of the parameters indicate that inserting N(CH3) into a ring should decrease the FP of the molecule. It is easy to realize that it is not the case. According to experimental flash points reported in ref 30, FP increases from 231 to 276 K on going from cyclopentane to 2-methylpiperidine. The present method predicts an increase from 243 to 273 K. However, ref 19 predicts a decrease from 282 to 259 K. Similarly, the negative contributions derived in ref 19 lead to severely underestimated FP for such compounds as hexahydro-1,2,4-trimethyl 1,2,4triazine (186 K instead of 314 K in ref 33) or hexahydro-1,3,5trimethyl-s-triazine (186 K instead of 323 K in ref 30). The present method does not exhibit such spurious parameters. The values reported in Table 1 are fully consistent with the assumption that FP depends primarily on the ability of a fluid to vaporize. They exhibit the same general trends as corresponding fragment contributions to sublimation enthalpies, with positive values for atomic and ring parameters and negative values for crowding corrections.38 Moreover, the relative values of the atomic parameters are also fully consistent
4. RESULTS The performance of the present method for the training and test sets is illustrated in Figure 2. The few deviations from
Figure 2. FP values calculated using the present method plotted against experiment: (white symbols) training set; (gray symbols) test set.
experiment by several tens of kelvin are to be expected in view of experimental uncertainties for present organosilicon compounds. In fact, predicted FP values are quite similar to those reported in ref 19, as demonstrated by the significant correlation between the residuals of the two methods shown in Figure 3. This is no surprise since both models express FP as a concave increasing function of a sum of additive group parameters. Reference 19 reports an especially good fit against the training set, with all deviations from experiment lying between 14312
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from a small number of compounds associated with large errors. Let us have a look at the most severe overestimations, starting with the most significant one (+48 K) observed for hexadecyltrichlorosilane C16H33SiCl3. For this compound, no FP value can be found in established compilations such as DIPPR nor in any freely available online source. The second most significant deviation is observed for n-amyltrichlorosilane C5H11SiCl3. The FP value of 339 K obtained for this compound, although +36 K above the value used in previous modeling studies, it is in excellent agreement with the value of 340 K reported in the Chemical Database.30 As for the value of 385 K calculated for vinyl tris(2-methoxyethoxy)silane, it is +32 K above the value of 353 K used for the fit but in excellent agreement with the closed cup value of 386 K reported in the Aldrich catalog.32 Finally, despite the fact that the contribution of boron is neglected in the present scheme, the FP of tris(trimethylsiloxy)boron is overestimated by +31 K, in line with the unrealistic negative value of −20784.0 K2 required for B3-0 in order to obtain a perfect match. As a matter of fact, the most significant errors of the present model proves to be negative. The most significant one concerns ClCH2SiCl3. For this compound, the calculated FP value of 293 K is 49 K below the experimental value of 342 K used for the fit. On the other hand, it is in good agreement with the closed cup value of 288 K reported elsewhere.37 For 2362-10-9, the calculated value of 298 K is 48 K below the value of 346 K stored in the database, but only 35 K below the closed cup value reported in ref 32. Similarly, for dimethoxydimethylsilane, the presently calculated value of 275 K is 41 K below the reference value, but in good agreement with the closed cup value of 279 K reported in ref 32. In contrast, the deviation from experiment for Si(CH3)3F goes from −44 to −49 K as the closed cup value of 243 K from ref 32 is used instead of the present reference value of 238 K. For chloromethylchlorodimethylsilane, no alternative could be found to the reference value of 295 K, which is 38 K above the calculated value. For methyltrimethoxysilane, the deviation from experiment improves from −38 to −32 K as the value of 278 K from ref 36 is used instead of the present reference value of 284 K. In contrast, for 681-84-5, the deviation goes from −37 to −45 as the reference value of 294 K is substituted by the value of 302 K reported in ref 33. In view of experimental uncertainties, it is clearly not easy to provide a thorough validation of FP predictive schemes for silicon compounds. To make up for the relatively small size of the present data set, FP values derived using the present method for additional compounds are hereafter compared to data reported in various online compilations. It should be kept in mind that such values can be unreliable16 and probably do not necessarily always correspond to experimental values for the pure compound. In such cases, data that differ very
Figure 3. Comparison of residuals (deviations from experiment) obtained using either the present method or the model described in ref 19 to estimate FP data: (white symbols) training set; (gray symbols) test set.
−31 and +33 K. As expected from the smaller number of adjustable parameters involved, a slight decrease of the fit quality is observed on going from this earlier model to the present one, with the determination coefficient R2 decreasing from 0.9330 to 0.9077, while the average absolute deviation (AAD) increases from 8.91 to 12.5 K. The present AAD could be further reduced through a nonlinear optimization of the parameters so as to minimize the quadratic deviations between observed and calculated FP values, since the linear regression minimizes corresponding deviations for squared flash point values instead. However, this would only yield a small improvement of the statistics while departing from the simplicity of the present parametrization procedure. In fact, when it comes to predictions for the external test set, the present model proves about as reliable as the one reported in ref 19. On going from this former method to the present one, the determination coefficient increases from 0.8868 to 0.8883 and the AAD goes from 11.15 to 12.4 K. Therefore, the predictive ability of the present model is very satisfactory, especially considering its simplicity. Indeed, as especially clear from the review of very recent works provided a few months ago by Lee et al.,25 even state-of-the-art methodologies resorting to extended pools of descriptors and advanced regression techniques never provide AAD values below 10 K for test sets. To date, lower AAD values can only be obtained by considering models specific to restricted classes of compounds and involving boiling point or other experimental data.25,28 An examination of individual fitted values reveals that the lower fit quality presently obtained for the training set stems
Table 2. FP Data for Compounds Not in the Wang et al. Data Seta compound
CAS RN
tris(cyclohexylamino)methylsilane chlorotris(methylsilyl)silane diphenylsilanediol phenyltris(dimethylsiloxy)silane
15901-40-3 5565-32-2 947-42-2 18027-45-7
calc (K)b 493 359 445 392
(+10) (+55) (+5) (−2)
ref 19b 466 322 451 382
exp (K) (−4) (+18) (+11) (−12)
383d 304f 327d 360e
470c 575c 440c 394c
a
Values calculated using the present method (calc) and the Wang et al. method19 are compared to experiment (exp). bDeviations from the closest corresponding experimental values are reported in parentheses. cReference 33. dReference 34. eReference 31. fReference 32. 14313
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present results demonstrate the interest of the simple additive fragments presently used. While it fills the gap between simple atomic additivity schemes and more popular group decomposition methods involving extensive parameter fitting, this fragmentation procedure yields quite good performance. As they stand, both methods considered in this article are still likely to yield unreliable predictions for some compounds, as they involve ill-defined parameters whose values depend on a very limited amount of experimental data. Because the present method is based on a small set of additive fragments, it is especially straighforward to remedy to this deficiency through an extension of the training set. However, the reliability of experimental data at hand is clearly an obstacle to further progress. Relationships between FP and other properties such as boiling points and vaporisation enthalpies should prove very useful to cure the databases. Empirical relationships focused on consistent chemical series might also lead to new reference FP values, extrapolated from homologous compounds rather than measured. Alternatively, more theoretically grounded equations could lead to satisfactory fits involving relatively few parameters and possibly leading to more reliable predictions.
significantly from the values derived using the present method are especially doubtful, as illustrated in what follows. Table 2 reports FP predictions for organosilicon compounds not included in the Wang et al. data set. For tris(cyclohexylamino)methylsilane, two very different values of 383 and 470 K are reported. The values of 466 and 493 K obtained respectively using the Wang et al. and the present method indicate that the lower value is probably erroneous. Dramatic inconsistencies are also reported for chlorotris(methylsilyl)silane, with two experimental values of 304 and 575 K bracketing the calculated values of 322 and 359 K. Another significant discrepancy between reported experimental data is for diphenylsilanediol, with FP values of 440 and 327 K. This latter value appears to be underestimated in view of the calculated values of 451 and 445 K. Similarly, for phenyltris(dimethylsiloxy)silane, calculations also support the highest of the two experimental values reported. All in all, both models considered in this study appear to yield similar performance for organosilicon compounds. A practical advantage of the present one stems from its wider scope. Table 3 reports the results obtained for 7 organosilicon
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Table 3. Calculated (calc) and Experimental (exp) FP Data for Compounds beyond the Scope of the Wang et al. Methoda compound
CAS RN
calc (K)
bis(trimethylsilyl)acetamide N-(1,3-dimethylbutylidene)-3(triethoxysilyl)-1propanamine 2-butanone,O,O′,O″(methylsilylidyne)trioxime azidotrimethylsilane 2-(trimethylsilyl)benzotriazole 2-(trimethylsilyl)-1,3-dithiane 1-silacyclohexa-2,5-diene
10416-59-8 116229-43-7
321 420
285 317c 404
+4 +16
22984-54-9
419
363 422d
−3
4648-54-8 32137-73-8 13411-42-2 81200-77-3
291 380 319 277
279 296e 382 369 291
−5 −2 −50 −14
exp (K)
devb
ASSOCIATED CONTENT
* Supporting Information S
Table summarizing experimental and calculated FP values in kelvin, as well as the corresponding numbers of fragments, for the training set and test set used in ref 19. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
a
Unless specified otherwise, experimental values are from ref 31. Minimal deviations between calculations and experiment. cReference 32. dReference 33. eReference 34.
b
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compounds beyond the scope of the Wang et al. method. The AAD obtained if experimental values closest to calculated results are systematically used is about 13.5 K, i.e. not significantly higher than the AAD of 11.15 K reported in ref 19. The significant underestimation by 50 K of the FP of 2(trimethylsilyl)-1,3-dithiane might be explained by the fact the calculation involves the S2-0 parameter whose value depends on a single measurement, as indicated in Table 1.
5. CONCLUSION The model developed in this work provides a practical tool for engineers needing to estimate flash points for organosilicon compounds. With an average absolute deviation from experiment close to 12%, it provides no obvious reliability improvement with respect to the method reported in ref 19. However, it appears more attractive in view of future development of such methods, being much easier to parametrize, more consistent with physical expectations, and more amenable to rigorous validation owing to the constraint that additive atomic contributions should be positive. Furthermore, it may be applied to a much broader range of compounds while requesting fewer adjustable parameters. On the other hand, 14314
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