Relationships between the Properties of Families of Materials

Brian K. Peterson*

Computational Modeling Center, Air Products and Chemicals, Inc., Allentown, PennsylVania 18195-1501

A general and useful regularity exists between the properties of families of chemical species: the propertiesof the members of one family are shown to be simply, and approximately linearly, related to the propertiesof analogous materials in similar families. As examples, the phenomenon is shown to enable accurate predictivecorrelations from small amounts of data for the liquid/vapor critical temperatures of several families of organicmolecules and for the normal boiling temperatures of SF5- and CF3-containing compounds.

Introduction

Typical approaches to understanding and predicting thephysical properties of materials relate the properties to structuralor other features of the atoms and molecules comprising thematerial. These approaches include theoretical and computa-tional ones based in quantum and/or statistical mechanics1 andnumerical/statistical ones parametrized by data, such as groupcontribution methods2 and quantitative structure/property rela-tionships.3 Perhaps the simplest method is to use a homologousseries if one exists: the property is related to some single featurethat varies within a family of molecules, and a smooth curvefitting the data is used to predict the property for members forwhich data are missing. Emphasis is usually placed on findingan explicit relationship between molecular structure and theproperty of interest.

We have found a quite general effect that leads in many casesto an alternative method of analysis and prediction and that doesnot require any explicit structure/property relationship. Whena property of members of one family of materials is comparedto the same property of analogues in related families ofmaterials, a simple, usually linear, relationship is found. Weintroduce the effect and prediction method by examples showingthe relationship between the liquid/vapor critical temperaturesand the normal boiling points of different families of compunds.

Critical Points of Organic Compounds

Because of their use in treatments based on the principal ofcorresponding states, critical properties have been cited4 as themost important properties to be able to predict for the analysisof liquid/vapor systems. Relatively few direct measurements ofcritical properties have been made, and so it is important tovalidate the existing data and to develop accurate predictionmethods based on them.

Let us first establish a structural correspondence between twofamilies of materials. A simple and useful correspondence is topair materials that differ by a single functional group. Table S1in the Supporting Information contains evaluated and recom-mended experimental values5-8 of the critical temperatures ofseveral families of organic molecules (R1XR2) containingdifferent functional groups X: ketones (CdO), ethers (-O-),alkanols (C(H)OH), amines (NH), and methyl-branched alkanes(CH2CH3), with R1 and R2 representing either branched or linearalkyl groups. Every such structure from the data set is includedin Table S1 in the Supporting Information if data exist for at

least two of the families. In Figure 1 are shown criticaltemperatures for the ketones on the ordinate and criticaltemperatures for the analogous ethers, alkanols, amines, andalkanes on the abscissa. The plots in Figure 1A-D thereforeconsist of the ordered pairs {Tc(R1OR2), Tc(R1(CdO)R2)},{Tc(R1(C(H)OH)R2), Tc(R1(CdO)R2)}, {Tc(R1NHR2), Tc(R1-(CdO)R2)}, and {Tc(R1C(H)CH3R2), Tc(R1(CdO)R2)}, respec-tively. The lines are the results of linear regression fits to thedata points.

The points in Figure 1A-C are seen to lie near straight lineswith apparent predictive ability. Table 1 contains the results ofthe linear regression fits shown in Figure 1 and also those forevery nontrivial pairing of the five families of compounds.Several features are evident: Tc for any of the polar group-containing families is nearly linearly related to Tc of any of theothers (R2 > 0.99), and a predictive correlation can be made ineach case. The mean unsigned error (MUE) for these regressionsis in the range of 1-3 K, which is a little above the reporteduncertainties in the measurements (0.1-2 K)5-8 and is smallerthan the mean errors reported for group contribution methodsfor Tc, even those that also use a measured boiling point to makethe predictions.9 Correlations between polar compounds andalkanes (such as that shown in Figure 1D) exhibit largerdeviations from linearity and larger scatter than those for theother families with 0.94 < R2 < 0.975 and 4.0 < MUE (K) <11.5. A second-order polynomial provides a better fit (notshown) to the ketone versus alkane data in Figure 1D, but thedeviations are still larger than those for the linear fits for anyof the pairs of polar families.

Several other features of the analysis are of interest. Theobvious outlier shown in Figure 1C, which was not included inthe regression analysis, has an analogue in each of the data setsthat contained the amines, and the same compound was involvedin each instance: N-methyl-1-propanamine, with reported Tc )550 K. Correspondence with the authors10 of the reviewconfirmed that this compound and this property value are notactually associated with one another and that the datum wasincluded inadvertently.

That relatively few data are available for the amines ispartially due to their instability at the critical point.6 Onevalue of correlations such as those shown in Figure 1C isthat more data are available for the more stable families, suchas the ketones. If the amine/ketone relationship holds for theseother analogues, the critical points of more than 30 aminesof structure R1NHR2 can be predicted from just the ketonedata5 without developing a detailed structure/property model.As an example, the predicted Tc of N-methyl-1-propanamine

* To whom correspondence should be addressed. E-mail: petersbk@yahoo.com.

Ind. Eng. Chem. Res. 2010, 49, 3492–34953492

10.1021/ie901721w 2010 American Chemical SocietyPublished on Web 02/24/2010

from the regression fit of the amines to the ketones is 503K. The predictions from the ether and alkanol fits are 507

and 502 K, respectively, demonstrating also that correlationsbased on different families of materials give similarresults.

As is evident in Table 1, the relationship of the ketones andalkanols is more than just linear: there is near-numericalcoincidence. This perhaps reflects the importance of keto-enoltautomerism at the high temperatures characteristic of the criticalpoint, leading to very similar molecular and fluid structures.

A demonstration of the effect discussed here on criticalpressures, Pc, is made difficult by several factors. Among theseare that there are fewer data available than for Tc and that themagnitude of the reported uncertainties is larger (by almost anorder of magnitude) relative to the property values themselvesand to the range of the property values within a given family.However, as for Tc, the relationship of Pc for the ketones5 versusalkanols7 is linear and also is nearly an equality (N ) 8, R2 )0.9981, slope ) 0.9971, and intercept ) 0.0444 MPa). A plot(not shown) of Pc for the ketones5 versus ethers5 (N ) 9)exhibits a useful correlation but shows significantly less scatteraround a quadratic expression (R2 ) 0.9879) than a linear one(R2 ) 0.9537). The reported uncertainties in critical densities,Fc, for these families of materials are of a magnitude similar tothat of the total variation of the property value within a familyand therefore obscure any meaningful trend.

Normal Boiling Temperatures

While we have found simple or linear relationships for a widevariety of other properties and a wide variety of families ofmaterials, we here show just one more example. The pentafluo-rosulfanyl (-SF5) functional group is of recent interest (a)because of its similarity to and differences from the trifluoro-methyl (-CF3) group, (b) because of its potential use inbiochemically active substances,11 and (c) because of newsynthetic techniques for introducing the group to organicmolecules.12 Because there are relatively few known materialscontaining the pentafluorosulfanyl group, its effects on thephysical properties of substances containing it are relativelyunknown. The trifluoromethyl group is present in many moreknown materials, and it would be useful to understand theproperties of the SF5-containing compounds based on knowl-edge of the properties of the CF3-containing compounds. In theliterature, we found 12 pairs of stable compounds, RX, whereR represents a variety of molecular structures and X representseither functional group SF5 or CF3 and for which the normal (1atm) boiling temperatures or vapor-pressure curves werereported. Table S2 in the Supporting Information contains thenormal boiling points, Tb, of the species, and in Figure 2, theboiling temperatures are plotted as the ordered pairs: [Tb(RCF3),Tb(RSF5)].

As in the case of critical temperatures, the normal boilingtemperatures lie remarkably close to a straight line. Thisrelationship holds over the entire temperature range shown withTmax - Tmin > 200 °C. A regression line fit through all of thepoints yields slope ) 0.929, intercept ) 52.0 (°C), a coefficientof determination, R2 ) 0.9983, and MUE ) 2.1 (°C). It isevident that a line fit through several of the points could beused to predict Tb for SF5-containing compounds in cases whereTb is known for CF3-containing analogues. When points to bepredicted are left out of the regression analyses, the averageunsigned prediction error for the 12 SF5 compounds is 2.5 (°C).

It is important to note that there is no simple regularitybetween the members of either of these families by themselves:the R groups contain phenyl, various halides, oxyhalides, andfully or partially halogenated alkanes, alkenes, and alkynes and

Figure 1. Critical temperatures of ketones related to those of analogousethers (A), alkanols (B), amines (C), and alkanes (D).

Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010 3493

yet the points lie near a single straight line. The two functionalgroups that define the families are similar but not so similarthat there is a close numerical correspondence between Tb(RCF3)and Tb(RSF5): they differ by δT ∼ 50 °C.

Summary

We have shown several cases where an interesting effectoccurs: a property of one family of materials is simply relatedto the same property of analogous members of another familyof materials. For similar families, the relationships shown arenearly linear and have little scatter, while for dissimilar families(e.g., polar vs alkanes), there is less useful correlation. Withina family, the members need not be related homologously. Onthe basis of this effect, predictive correlations can be developedwithout positing any specific model for the structure/propertyrelationship, as long as the property value for an analogue isknown. The correlations, or simply the property/property plots,are very effective in aiding the detection of outliers or anomalousdata.

The effect demonstrates that information useful for directlydetermining the value of a property of a material is to be foundnot only within the same family of materials but also in adifferent family of materials and in the relationship betweenthe two families. In future work, we will explore a mathematicaljustification for the effect and the relationship of the correlativemethod based on it to other methods of producing predictivecorrelations.

Acknowledgment

The author thanks Air Products and Chemicals, Inc., forpermission to publish this work.

Supporting Information Available: Tables of evaluatedcritical temperatures from the literature for a series of relatedalkanols, ethers, amines, ketones, and alkanes and also normalboiling temperatures for a series of related SF5- and CF3-containing compounds and literature citations for all of the data.This material is available free of charge via the Internet at http://pubs.acs.org.

Table 1. Properties of Linear Regression Fits for the Critical Temperatures (Tc) of Analogous Ethers, Alkanols, Amines, Alkanes, and Ketonesa

independent variable dependent variable N slope intercept (K) R2 MUE (K) MaxUE (K) MUE (%) MaxUE (%)

ether alkanol 9 0.6910 233.73 0.9938 2.18 3.36 0.38 0.60amineb 4 0.9211 68.77 0.9997 0.94 1.70 0.17 0.31alkane 10 1.0460 3.40 0.9510 8.72 15.32 1.74 3.48ketone 11 0.7115 223.86 0.9926 2.32 6.63 0.40 1.16

alkanol ether 9 1.4382 -333.17 0.9938 3.11 4.93 0.64 1.06amineb 4 1.2759 -212.50 0.9995 1.18 1.79 0.23 0.36alkane 12 1.4329 -306.48 0.9750 6.09 14.07 1.21 3.45ketone 22 1.0040 -2.12 0.9984 1.52 3.18 0.25 0.58

amineb ether 4 1.0854 -74.49 0.9997 1.01 1.85 0.20 0.35alkanol 4 0.7834 166.74 0.9995 0.92 1.40 0.16 0.25alkane 4 1.1396 -79.70 0.9702 11.43 14.85 2.27 2.94ketone 5 0.7844 166.77 0.9987 1.69 2.67 0.29 0.48

alkane ether 10 0.9092 20.58 0.9510 7.76 17.03 1.60 3.12alkanol 12 0.6804 222.94 0.9750 4.10 10.11 0.71 1.61amineb 4 0.8514 83.37 0.9702 9.54 13.28 1.83 2.66ketone 15 0.6778 223.51 0.9408 6.01 14.15 1.03 2.24

ketone ether 11 1.3952 -308.70 0.9926 3.15 9.28 0.64 1.87alkanol 22 0.9945 3.05 0.9984 1.53 3.08 0.25 0.55amineb 5 1.2732 -211.60 0.9987 2.15 3.45 0.41 0.69alkane 15 1.3880 -279.17 0.9408 8.81 19.19 1.71 4.48

a N ) number of observations. R2 ) coefficient of determination. MUE ) mean unsigned error. MaxUE ) maximum unsigned error. b Allcorrelations involving the amines leave out one obvious outlier (see the text).

Figure 2. Normal boiling temperatures of pentafluorosulfanyl- (-SF5) compounds related to those of analogous trifluoromethyl- (-CF3) containing compounds.

3494 Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010

Literature Cited

(1) Leach, A. R. Molecular Modelling: Principles and Applications, 2nded.; Prentice Hall: Upper Saddle River, NJ, 2001.

(2) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties ofGases and Liquids, 5th ed.; McGraw-Hill: New York, 2000.

(3) Katritzky, A. R.; Fara, D. C. How Chemical Structure DeterminesPhysical, Chemical, and Technological Properties: An Overview Illustratingthe Potential of Quantitative Structure-Property Relationships for FuelsScience. Energy Fuels 2005, 19, 922–935.

(4) Daubert, T. E. Strengths and Weaknesses of Predictive Methods forEstimating Thermophysical Properties. J. Chem. Eng. Data 1996, 41, 942–946.

(5) Kudchadker, A. P.; Ambrose, D.; Tsonopoulos, C. Vapor-LiquidCritical Properties of Elements and Compounds. 7. Oxygen CompoundsOther Than Alkanols and Cycloalkanols. J. Chem. Eng. Data 2001, 46:,457–479.

(6) Marsh, K. N.; Young, C. L.; Morton, D. W.; Ambrose, D.;Tsonopoulos, C. Vapor-Liquid Critical Properties of Elements andCompounds. 9. Organic Compounds Containing Nitrogen. J. Chem. Eng.Data 2006, 51, 305–314.

(7) Gude, M.; Teja, A. Vapor-Liquid Critical Properties of Elements andCompounds. 4. Aliphatic Alkanols. J. Chem. Eng. Data 1995, 40, 1025–1036.

(8) Daubert, T. Vapor-Liquid Critical Properties of Elements andCompounds. 5. Branched Alkanes and Cycloalkanes. J. Chem. Eng. Data1996, 41, 365–372.

(9) Yan, X.; Dong, Q.; Hong, X. Reliability Analysis of Group-Contribution Methods in Predicting Critical Temperatures of OrganicCompounds. J. Chem. Eng. Data 2003, 48, 374–380.

(10) Marsh, K. N.; Tsonopoulos, C. Personal communication.(11) Welch, J. T.; Lim, D. S. The Synthesis and Biological Activity of

Pentafluorosulfanyl Analogs of Fluoxetine, Fenfluramine, and Norfenflu-ramine. Bioorg. Med. Chem. 2007, 15, 6659–6666.

(12) Dolbier, W. R., Jr.; Aı̈t-Mohand, S.; Schertz, T. D.; Sergeeva, T. A.;Cradlebaugh, J. A.; Mitani, A.; Gard, G. L.; Winter, R. W.; Thrasher, J. S.A Convenient and Efficient Method for Incorporation of Pentafluorosulfanyl(SF5) Substituents into Aliphatic Compounds. J. Fluorine Chem. 2006, 127,1302–1310.

ReceiVed for reView November 1, 2009ReVised manuscript receiVed January 24, 2010

Accepted February 5, 2010

IE901721W

Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010 3495