A New Method for the Estimation of the Normal Boiling Point of Non-electrolyte Organics

Fluid Phase Equilibria 201 (2002) 409433

A new method for the estimation of the normal boilingpoint of non-electrolyte organic compounds

Wilfried Cordes a, Jrgen Rarey a,b,a DDBST GmbH, Industriestr. 1, 26121 Oldenburg, Germany

b Industrial Chemistry, Carl von Ossietzky University Oldenburg, Fachbereich 9, Postfach 2503, 26111 Oldenburg, GermanyReceived 3 September 2001; accepted 21 February 2002

Abstract

A group contribution method for the estimation of the normal boiling point of non-electrolyte organic compoundswas developed using experimental data for approximately 2500 components stored in the Dortmund Data Bank(DDB). Predictions are based exclusively on the molecular structure of the compound. The results of the new methodare compared to currently-used methods and are shown to be far more accurate. Structural groups were defined in astandardized form and the fragmentation of the molecular structures was performed by an automatic procedure toeliminate any arbitrary assumptions. 2002 Elsevier Science B.V. All rights reserved.

Keywords: Vapor pressure; Model; Method of calculation; Normal boiling temperature; Group contribution

1. Introduction

Pure component vapor pressures of liquid (and solid) compounds are of great importance for manypractical applications in chemical and biochemical engineering as well as for environmental and safetyproblems. Vaporliquid equilibria of mixtures, which are for example employed for the design andsimulation of distillation processes, are usually described on the basis of the pure component vaporpressures of the components in the mixture and a correction term (activity coefficient), which accountsfor the real behavior of the mixture. If an equation-of-state is used for the calculation of the phaseequilibrium, both pure component vapor pressure and real mixture behavior are described by the fugacitycoefficients of the components in the mixture.

While pure component vapor pressures are in most cases accessible by rather simple experimentaltechniques and are available for nearly all components of industrial importance, great effort was investedinto the development of methods for the correlation and prediction of the real behavior of liquid mixtures(Wilson, NRTL, UNIQUAC, UNIFAC, modified UNIFAC, PSRK, . . . ). Corresponding author. Tel.: +49-441-798-3846; fax: +49-441-798-3330.

E-mail address: [email protected] (J. Rarey).

0378-3812/02/$ see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S0378-3812(02)00050-X

410 W. Cordes, J. Rarey / Fluid Phase Equilibria 201 (2002) 409433

However, with the wide availability of computers and software for the simulation of chemical processesand environmental simulations (e.g. compartment models for the estimation of the distribution of chemi-cals in the environment), today we face a great need for physical properties, especially vapor pressures ofa large number of rather exotic compounds (by-products, trace impurities, additives in resign production,pesticides, . . . ), which are not easily available from literature or experiment.

Another evolving application for accurate physical property estimation methods is computer aidedmolecular design (CAMD), which is focused on generating molecular structures for components withspecific properties (vapor pressure, viscosity, polarity, . . . ). During the optimization process, the computerwill generate a large number of structures, for which experimental data are not available and the programhas to rely on the accuracy of the predictive methods employed.

Due to theoretical considerations, physical property estimation usually starts with the estimation ofthe critical point, which is directly linked to the molecular parameters of the intermolecular potential. Atthe critical point, physical properties of components are not yet strongly influenced by the formation ofshort-range structures, which tend to significantly complicate property estimation.

Development of estimation methods for critical data with broad applicability is limited by the fact, thatthe critical point is difficult to determine and that most of the more complex molecules are not stable atthe critical temperature. Currently, reliable data for less than 600 components are available in literature.

Normal boiling points on the other hand are available for a large number of compounds and are ofspecial practical importance, but are influenced significantly by short-range structures in the liquid phase,which are difficult to describe by group contributions. This paper presents a method for the estimation ofnormal boiling points by group contribution based on a large number of experimental data without theneed for experimental or estimated critical data.

2. Available methods for the prediction of normal boiling points

A variety of estimation methods for normal boiling points from molecular structure are available. Abroad overview on these methods was given by Prausnitz et al. [1]. Several methods are restricted toindividual classes of substances, others require the knowledge of molecular descriptors usually obtainedfrom quantum mechanical methods. In this work, we will compare our results with those of Constantinouand Gani [2], Joback and Reid [3], Stein and Brown [4] and Marrero-Morejon and Pardillo-Fontdevila[5]. All of these methods have in common, that they only require the knowledge about the molecularstructure and therefore are comparable. As the original paper of Marrero-Morejon and Pardillo-Fontdevila[5] contains several misprints, in this work, we use the corrected parameters supplied by the authors andpublished by Prausnitz et al. [1].

3. Theoretical considerations

From the ClausiusClapeyron equation, the normal boiling point can be calculated via the ratio ofHvap and Svap:

Tb = HvapSvap

(1)

W. Cordes, J. Rarey / Fluid Phase Equilibria 201 (2002) 409433 411

At the normal boiling point, the total interaction between the molecules in the vapor phase is smallcompared to that in the liquid phase and the enthalpy of vaporization can be approximated by the totalintermolecular interaction in the liquid phase.

In a homologous series, in which the individual members of the series differ by one CH2 group, thevolume of the molecule increases linearly. Because molecules are usually not stiff, but tend to tangle to amore or less spherical form, their outer surface should increase with approximately n2/3CH2 once a certainlength is reached. In case of short chains, however, the gain in entropy is probably not large enough tofavor a spherical form.

As molecular interaction in organic liquids is dominated by nearest neighbor contacts, it should also beproportional to the molecular surface. Fig. 1a showsHvap (J/(mol K)) at the normal boiling for n-alkanesas function of molecular weight together with a correlation using the expression:

Hvap = 4067.5 + 1738.8M0.6248 (2)The exponent of 0.6248 is close the estimated value of 2/3. In case of small chains (14 CH2 groups),Hvap increases linearly with the number of CH2 groups as expected (Fig. 1b). For very large molecules,a mutual contact of the complete outer surface becomes more difficult (increasing free volume) and theincrease of Hvap is less than estimated.

Fig. 1. (a and b) Enthalpy of vaporization of n-alkanes at the normal boiling point as function of the molecular weight (datataken from Dortmund Data Bank, 2001).


For the estimation of the normal boiling temperature also knowledge of the entropy change withvaporization is required. Following Troutons rule, the molar entropy of vaporization of a non-associatedliquid at standard boiling point is approximately constant, about 8288 J/(mol K). Different approaches areavailable for a more sophisticated estimation. Different effects contribute to the entropy of vaporization,e.g.

(a) Generally, external movement (translation) of the molecule is confined to the molar volume minus thevolume occupied by the molecule itself. For an ideal gas, at 1 atm and 273.15 KV Vtrans amounts to nearly22.414 dm3/mol. In the liquid phase, the available volume V Ltrans is usually less than a few percent ofthe total liquid volume. The translational part of the entropy of vaporization can be calculated via

Svap, trans = R ln(V VtransV Ltrans

)(3)

V Ltrans should decrease with increasing attractive forces (i.e. increasing enthalpy of vaporization) andbe influenced by structural effects.

(b) Due to close packing in the liquid phase, a difficult to estimate part of the internal movements can beconfined. This effect is considered to be very small and generally not of further importance. In case of,e.g. cyclohexane and n-hexane, the difference in the entropy of vaporization is only approximately0.4% which is nearly solely due to the increase in molar vapor volume due to the higher boilingtemperature of cyclohexane.

(c) In case of association, the number of particles is changed when going from the liquid phase (nearlycomplete association) to the vapor phase (partial association).

Instead of separately estimating Hvap and Svap, a correlation expression for Tb based on groupcontributions and other easy to obtain quantities will be sought for as a certain correlation betweenHvapand Svap can be expected. If both properties would depend very differently on molecular structure, twosets of group contributions would be required.

In order to accomplish this, the typical dependence of Tb on the number of groups in different homol-ogous series will first be compared to the results of methods previously published.

Figs. 2 and 3 show the normal boiling points of n-alkanes and n-alkanols as a function of chain lengthtogether with the predicted values from different group contribution methods.

Joback and Reid [3] employed a linear relationship between the sum of group increments and theboiling point, which is only adequate to describe the experimental data over a small range of normalboiling temperatures. Because the method is based on a rather limited database of only 438 components,this deficiency may not have become apparent to the authors.

Stein and Brown employed the same linear relationship, but their method is based on a much larger setof data (4426 components from the Aldrich Chemical Catalog [6] and 6584 different compounds fromthe HODOC [7] database, normal boiling temperatures were partly extrapolated from vapor pressure dataat low pressures using the LeeKesler [8] equation). In this case, large systematic deviations becameapparent and the authors applied a correction to the estimated values:

Tb (corrected) = Tb + A+ BTb + CT2b (4)As the polynomial parameters A, B and C and the group contribution parameters were regressed separately,they do not give the best results possible with this type of mathematical expression.


Fig. 2. Normal boiling points of n-alkanes as a function of the number of CH2 groups.

Constantinou and Gani [2] greatly improved the method of Joback and Reid [3] by using a logarithmicdependence of the boiling point on the sum of the group contributions:

Tb = 204.359 ln(

NiCi +

MiDi

)(5)

with Ni is the number of first-order groups of type i, Ci the group contribution of first-order group i, Mithe number of second-order groups of type i, and Di is the group contribution of second-order group i.

The second-order groups are only used as a correction to the first-order estimations for a limited numberof special structures.

Marrero-Morejon and Pardillo-Fontdevila [5] employed the equation:Tb = M0.404

NiCi + 156.00 (6)

where Ni is the number of first-order groups of type i, Ci the group contribution of first-order group i,and M is the molecular weight (g/mol).

Fig. 3. Normal boiling points of n-alkanols as a function of the number of CH2 groups.


In contrary to the other methods, Marrero-Morejon and Pardillo-Fontdevila use bond contributionsinstead of group contributions.

From Figs. 2 and 3, it can be seen that, although much better than the linear assumption of Joback andReid, neither the logarithmic dependence nor the term M0.404 are able to describe the dependence of Tbon chain length in the two homologous series.

For the correlation of group contribution parameters Constantinou and Gani as well as Marrero-Morejonand Pardillo-Fontdevila used only a limited set of data (392 and 507 components, respectively).

4. Development of the new method

From the analysis of the different estimation methods, it is obvious that a significantly better methodcould be developed based on an improved expression for the dependence of the normal boiling pointon the sum of group increments and a significantly larger set of reliable experimental information. Inaddition, all parameters should be regressed simultaneously in order to find the optimum value of theobjective function.

4.1. Group definitions and equations

To describe the normal boiling point for a large number of molecules greatly differing in size thefollowing expression was employed:

Tb =

NiCi

na + b + c (7)

where a, b and c are the adjustable parameters, Ni the number of groups of type i, Ci the group contributionof group i (K), and n is the number of atoms in the molecule (except hydrogen).

While this expression gives a good description of the dependence of Tb on molecular size, it carries theadditional advantage, that via the number of atoms in the molecule, an additional and readily availablequantity more or less independent from the sum of the increments is introduced. The number of atoms orthe molecular weight have been successfully employed by numerous other authors in the past (e.g. Jobackand Reid [3], Marrero-Morejon and Pardillo-Fontdevila [5]) to improve the results of group contributionmethods for various properties.

Correlation of data for 2550 components lead to the following values for the constants:

a = 0.6713, b = 1.4442, c = 59.344 (K)Results for the new model for n-alkanes and n-alkanols are given in Figs. 4 and 5.

Definition of the structural groups was approached by an iterative procedure. Starting off from thegroups used in the method by Joback and Reid, the adjustable parameters a, b and c as well as all thegroup contributions were fitted to the experimental data. The results were then carefully analyzed andthe group definitions were revised in order to take into account special effects, which otherwise led tolarge deviations. This had to be repeated several times. In the second step, all the molecules, which couldnot be fragmented into the structural groups available were reviewed and new groups were defined forall cases in which enough experimental information was available for the correlation of reliable groupparameters.


Fig. 4. Normal boiling points of n-alkanes as a function of the number of CH2 groups together with the results for the proposedmethod.

In this procedure, each redefinition of molecular groups required the re-fragmentation of about 2550components. This was made possible by employing an automatic fragmentation algorithm (AutoInkr)and a data bank with the molecular structures of all components (ChemDB) (Cordes et al. [9]).

In order to perform group fragmentation consistent with the chemical knowledge usually required forthis task, not only the structure of the groups themselves but also their chemical neighborhood had to beincluded in the group definition.

Fig. 5. Normal boiling points of n-alkanols as a function of the number of CH2 groups together with the results for the proposedmethod.


The list of groups, explanations as well as examples for molecules containing these groups are givenin Table 1. The group contributions, the number of components used for regressing these values and themean absolute deviation in temperature for these components are given in Table 2.

In the approach used for the development of the new method specification of the chemical neighbor-hood of a structural group plays a very important part. The correct specification of this neighborhood isespecially critical, because in our approach the fragmentation of molecules is performed by an automaticalgorithm rather than a chemist with his understanding of the electronic structure.

During the development of the method, it became apparent that:

there is no need to distinguish between carbon or silicon as a neighbor atom; very electronegative (N, O, F and Cl) or aromatic neighbors often significantly influence the contribution

of a structural group; it is usually of great importance whether a group is part of a chain, ring or aromatic system.

In addition, strong steric or mesomeric effects significantly worsen the results of the new method. Thisis discussed in detail later on.

In a number of cases, for a computer software, it is not as obvious as for a chemist which group to use.As there are only two flavors of the CH2 group (ring and chain), one could use the chain CH2 group(identification number (ID) 4, priority (PR) 82) for the phenylic carbon in ethylbenzene. In this case, theC(c) (a)-group (phenylic carbon, ID 8, PR 79) would be the correct choice as the neighboring aromatic

carbon is of greater importance than the two hydrogen atoms. To solve this problem, the different groupswere sorted by priority. In case of the automatic algorithm structural groups are matched in the order oftheir respective priority. In this way, it is guaranteed that always the group with the lower priority number(higher priority) is used to estimate the normal boiling point. The priority numbers are given in Tables 1and 3 in order to allow the reader to correctly apply or program the method.

As was also observed by other authors, the short chain alkanols do not fit into the group contributionscheme. For this reason, special groups are used for short-chain (ID 36) and long-chain (ID 34 and 35)alkanols. In some cases a larger group could be but should not be constructed of smaller groups (e.g. thecarbamat-group, the CCOCOC group, . . . ). Some of these groups are given at the end of Table 1as excluded groups with a group ID of 1. Whenever one of these groups is found in a molecule, themethod cannot be applied as no group parameters are available for excluded groups.

4.2. Second-order corrections

In addition to the group increments given in Table 1, special second-order corrections were applied.A list of these special corrections together with examples is given in Table 3. Table 4 contains thesecond-order contributions, the number of components used for regressing these values and the meanabsolute deviation in temperature for these components.

4.3. Database

Normal boiling temperature data for approximately 2800 components are available in the DortmundData Bank (DDB), out of which 2550 components are constructed of the structural groups proposed inthis work. These data were entered since work on the data bank started in 1973 and were extensivelyused, e.g. for the calculation of phase equilibrium data. This is the reason why this set of data may be


Table 1Group definitions (ID, identification number; PR, priority)Group Description Name ID/PR Occurs

Periodic group 17Fluorine

F F connected to C or Si F(C,Si) 19/59 2-Fluoropropane,trimethylfluorosilane

F connected to a C or Sialready substituted withone F or Cl and one otheratom

F(C([F,Cl]))a 22/56 1-Chloro-1,2,2,2-tetra-fluoroethane[R124],difluoromethylsilane

F connected to C or Sialready substituted with atleast one F or Cl and twoother atoms

F(C([F,Cl]))b 21/54 Trichlorofluoromethane[R11],2,2,3,3-tetrafluoropropionicacid

F connected to C or Sialready substituted withtwo F or Cl

F(C([F,Cl]2)) 23/55 1,1,1-Trifluorotoluene,2,2,2-trifluoroethanol,trifluoroacetic acid

F connected to anaromatic carbon

F(C(a)) 24/58 Fluorobenzene,4-fluoroaniline

F on a C=C (vinylfluoride) CF=C 20/57 Vinyl fluoride,trifluoroethene,perfluoropropylene

ChlorineCl Cl connected to C or Si

not already substitutedwith F or Cl

Cl(C,Si) 25/47 Butyl chloride,2-chloroethanol,chloroacetic acid

Cl connected to C or Sialready substituted withone F or Cl

Cl((C,Si)([F,Cl])) 26/46 Dichloromethane,dichloroacetic acid,dichlorosilane

Cl connected to C or Sialready substituted with atleast two F or Cl

Cl((C,Si)([F,Cl]2)) 27/44 Ethyl trichloroacetate,trichloroacetonitrile

Cl connected to anaromatic C

Cl(C(a)) 28/48 Chlorobenzene

Cl on a C=C(vinylchloride)

CCl=C 29/45 Vinyl chloride

COCl COCl connected to C(acid chloride)

COCl 77/13 Acetyl chloride,phenylacetic acid chloride

BromineBr Br connected to a

non-aromatic C or SiBr(C/Si(na)) 30/41 Ethyl bromide,

bromoacetoneBr Br connected to an

aromatic CBr(C(a)) 31/42 Bromobenzene

IodineI I connected to C or Si I(C,Si) 32/39 Ethyl iodide 2-iodotoluene


Table 1 (Continued)Group Description Name ID/PR Occurs

Periodic group 16Oxygen

OH OH for aliphatic chains withone or two C (even if connectedto aromatic fragments, used inparticular for methanol andethanol and their derivatives)

OH short chain 36/64 Ethanol, benzyl alcohol

OH connected to C which hasfour non-hydrogen neighbors(tertiary alcohols)

OH tert 33/63 Tert-butanol, diacetonealcohol

OH connected to C or Sisubstituted with one C or Si in anat least three C or Si containingchain (primary alcohols)

HO((C,Si)H2(C,Si)(C,Si))

35/60 1-Nonanol,tetrahydrofurfuryl alcohol,ethylene cyanohydrin

OH connected to an aromatic C(phenols)

OH (Ca) 37/62 Phenol, methyl salicylate

OH connected to a C or Sisubstituted with two C or Si in aat least three C or Si containingchain (secondary alcohols)

HO((C,Si)2H(C,Si)(C,Si))

34/61 2-Butanol, cycloheptanol

O O connected to two neighborswhich are each either C or Si(ethers)

(C,Si)O(C,Si) 38/66 Diethyl ether, 1,4-dioxane

O in an aromatic ring witharomatic C as neighbors

(C(a))O(a)(C(a)) 65/65 Furan, furfural

CHO CHO connected to C(aldehydes)

CHO(C) 52/29 Acetaldehyde, benzaldehyde

C=O CO connected to two C(ketones)

O=C (C)2 51/30 Acetone, methylcyclopropyl ketone

O=C(O)2 Non-cyclic carbonate O=C(O)2 79/9 Dimethyl carbonateCOOH COOH connected to C COOH(C) 44/18 Acetic acidCOO HCOO connected to C (formic

acid ester)HCOO(C) 46/21 Ethyl formate, phenyl

formateCOO connected to two C(ester)

(C)COO(C) 45/19 Ethyl acetate, vinyl acetate

COO in a ring, C is connectedto C (lactone)

C(c)OO 47/20 -Caprolactone,crotonolactone

(OC2) (OC2) (epoxide) (OC2) 39/27 Propylene oxideCOOCO Anhydride connected to two C COOCO 76/6 Acetic anhydride, phthalic

anhydride

SulphurSS SS (disulfide)

connected to two C(C)SS(C) 55/28 Dimethyldisulfide,

1,2-dicyclopentyl-1,2-disulfideSH SH connected to C

(thiols)SH(C) 53/49 1-Propanethiol



S S connected to two C (C)S(C) 54/50 Methyl ethyl sulfideS in an aromatic ring S(a) 56/51 Thiazole, thiophene

SO2 Non-cyclic sulfoneconnected to two C(sulfones)

(C)SO2(C) 82/12 Sulfolane, divinylsulfone

SCN SCN (thiocyanate) connected to C SCN(C) 81/14 Allyl isothiocyanatePeriodic group 15

NitrogenNH2 NH2 connected to either

C or SiNH2(C,Si) 40/68 Hexylamine, ethylenediamine

NH2 connected to anaromatic C

NH2(Ca) 41/67 Aniline, benzidine

NH NH connected to twoneighbors which are eacheither C or Si (secondaryamines)

(C,Si)NH(C,Si) 42/71 Diethylamine, morpholine

N N connected to threeneighbors which are eacheither C or Si (tertiaryamines)

(C,Si)2 N(C,Si) 43/72 N,N-dimethylaniline,nicotine

=N aromatic =N in afive-membered ring

=N(a)(r5) 66/70 Piperidine, thiazole

=N aromatic =N in asix-membered ring

=N(a)(r6) 67/69 Pyridine, nicotine

CN CN (cyanide)connected to C

CN(C) 57/31 Acetonitrile, 2,2-dicyanodiethyl sulfide

CONH CONH2 (amide) CONH2 50/22 AcetamideCONH (monosubstituted amide) CONH 49/25 N-methylformamide,

6-caprolactamCON (disubstitutedamide)

CON 48/26 N,N-dimethylformamide(DMF)

OCN OCN connected to C orSi (cyanate)

OCN 80/23 Butylisocyanate,hexamethylenediisocyanate

ONC ONC (oxime) ONC 75/24 Methyl ethyl ketoximeNO2 Nitrites (esters of nitrous

acid)O=NO(C) 74/17 Ethyl nitrite, nitrous acid

methyl esterNO2 connected to aliphatic C NO2(C) 68/15 1-NitropropaneNO2 connected toaromatic C

NO2(C(a)) 69/16 Nitrobenzene

NO3 Nitrate (esters of nitric acid) NO3 72/8 N-butylnitrate,1,2-propanediol dinitrate

PhosphorousPO(O)3 Phosphates with three

substituentsPO(O)3 73/5 Triethyl phosphate,

tris-(2,4-dimethylphenyl)phosphate



ArsineAsCl2 AsCl2 connected to C AsCl2 84/11 Ethylarsenic dichloride

Periodic group 14Carbon

CH3 CH3 not connected to either N,O, F or Cl

CH3(ne) 1/75 Decane

CH3 connected to either N, O, For Cl

CH3(e) 2/73 Dimethoxymethane,methyl butyl ether

CH3 connected to an aromaticatom (not necessarily C)

CH3(a) 3/74 Toluene, p-methyl-styrene

CH2 CH2 in a chain C(c)H2 4/82 ButaneCH2 in a ring C(r)H2 9/83 Cyclopentane

CH CH in a chain C(c)H 5/88 2-MethylpentaneCH in a ring C(r)H 10/87 Methylcyclohexane

C C in a chain C(c) 6/90 NeopentaneC in a chain connected to at

least one aromatic carbonC(c) (a) 8/79 Ethylbenzene, diphenylmethane

C in a chain connected to atleast one F, Cl, N or O

C(c) (e) 7/78 Ethanol

C in a ring C(r) 11/89 Beta-pineneC in a ring connected to at

least one aromatic carbonC(r) (Ca) 14/77 Indene, 2-methyl tetralin

C in a ring connected to atleast one N or O which are notpart of the ring or one Cl or F

C(r) (e,c) 12/80 Cyclopentanol, menthol

C in a ring connected to atleast one N or O which are partof the ring

C(r) (e,r) 13/81 Morpholine, nicotine

=C(a) Aromatic =CH =C(a)H 15/76 BenzeneAromatic =C not connected toeither O, N, Cl or F

=C(a) (ne) 16/86 Ethylbenzene, benzaldehyde

Aromatic =C with threearomatic neighbors

(a)=C(a) 2(a) 18/85 Naphthalene, quinoline

Aromatic =C connected toeither O, N, Cl or F

=C(a) (e) 17/84 Aniline, phenol

C=C H2C=C (1-ene) H2C(c)=C 61/33 1-HexeneC=C (both C have at least one

non-H neighbor)C(c)=C(c) 58/38 2-Heptene, mesityl oxide

Non-cyclic C=C connected toat least one aromatic C

C(c)=C(c) (C(a)) 59/35 Isosafrole, cinnamic alcohol

Cyclic C=C C(r)=C(r) 62/36 CyclopentadieneNon-cyclic C=Csubstituted with at leastone F, Cl, N or O

(e)C(c)=C(c) 60/34 Trans-1,2-dichloroethylene,perfluoroisoprene

CC HCC (1-ine) HCC 64/32 1-HeptyneCC CC 63/37 2-Octyne

W. Cordes, J. Rarey / Fluid Phase Equilibria 201 (2002) 409433 421Table 1 (Continued)Group Description Name ID/PR Occurs

SiliconSi Si Si 70/53 ButylsilaneSi Si connected to at least

one O, F or ClSi (e) 71/52 Trichlorosilane,

hexamethyl disiloxane

GermaniumGe Ge connected to four

carbons(C)2 Ge (C)2 86/43 Tetramethylgermane

GeCl3 GeCl3 connected tocarbons

GeCl3 85/7 Fluorodimethylsilyl-(trichlorogermanyl)methane

StanniumSn Sn connected to four

carbons(C)2 Sn (C)2 83/40 Tetramethylstannane

Periodic group 13Bor

B(O)3 Non-cyclic boric acid ester B(O)3 78/10 Triethyl borateExcluded groups

OCON Carbamat OCON 1/1 N-propylcarbamateCO(NH2)2 Urea and derivatives CO(NH2)2 1/2 UreaCCOCOC Neighboring keto groups CCOCOC 1/3 2,3-ButanedioneImidazol Imidazol Imidazol 1/4 Imidazol

Abbreviations: e, very electronegative neighbors (N, O, F, Cl); ne, not very electronegative neighbors (not N, O, F, Cl); a, aromaticatom or neighbor; c, atom or neighbor is part of a chain; r, atom or neighbor is part of a ring.

regarded as very reliable. In addition, molecular structures for approximately 16000 components werestored in form of connection tables, so that the molecules may easily be fragmented into groups by theautomatic procedure described before. The components in the DDB comprise a set of substances forwhich experimental thermophysical data are available in literature and which are therefore of importanceto science or industry. The frequency of occurrence of the individual structural groups and second-ordercorrections in a database of 2550 components is given in Tables 2 and 4, respectively.

4.4. Regression of the group constants

For the simultaneous regression of the model parameters, a special algorithm was developed consistingof an inner and outer regression loop. In the outer loop, the coefficients a, b and c are optimized in orderto minimize the mean absolute deviation in normal boiling temperature times the square of the standarddeviation with the help of a non-linear regression using a simplex algorithm. Using this, rather uncommonobjective function decreases the number of large deviations while leading to a slightly increased meandeviation. The inner loop incorporates a multilinear least squares regression of the equations:

i

Ni,jCi,j = Tb,j (nbj + c) a (for all components j) (8)


Table 2Group contributions, number of components used for regressing these values and mean absolute deviation in temperature forthese components

Group Group Mean Standard Mean Standard Number ofnumber contribution absolute deviation absolute deviation components

(K) error (%) (%) error (K) (K)1 188.555 1.71 2.42 7.42 10.69 14682 282.015 2.3 3.02 9.67 13.11 1993 176.705 2.01 2.78 9.63 13.41 1534 250.119 1.58 2.26 7.24 10.66 9565 260.938 1.48 2 6.83 10.11 3106 273.544 2.15 2.83 8.56 11.37 667 278.135 2.14 3.42 8.97 14.35 8208 210.93 1.5 2.12 7.85 11.71 1249 246.871 2.07 2.77 8.71 11.65 270

10 241.804 1.55 2.11 6.84 9.43 13711 265.032 1.72 2.15 7.47 9.24 3512 264.839 1.95 4.01 8.05 14.93 6713 304.422 2.49 3.26 10.32 13.21 6414 281.964 1.73 2.22 9.07 11.52 2215 245.521 2.32 3.4 11.73 17.5 55816 322.825 2.08 2.99 10.57 15.65 42117 377.988 2.79 3.94 13.88 19.82 24718 386.361 1.68 2.28 9.81 13.89 6519 129.511 1.95 2.72 6.58 9.44 3820 73.5088 2.92 4.31 6.69 9.29 921 65.9125 2.95 5.04 9.58 15.07 13222 111.411 2.36 3.24 7.12 9.63 2123 144.464 3.95 5.7 9.38 12.9 324 21.348 2.35 2.78 9.04 10.85 2525 327.158 2.01 2.89 8.58 12.59 10826 300.288 1.73 2.23 6.66 8.63 4727 275.233 2.79 3.98 10.37 14.3 5528 204.105 2.1 2.75 10.2 13.55 6329 299.52 1.69 2.21 5.87 7.79 3430 427.56 2.23 2.94 8.45 11.31 6531 351.895 1.36 1.85 6.51 8.83 2132 564.102 1.89 2.35 7.71 9.73 2833 401.033 1.97 2.81 8.51 11.66 4334 411.08 1.81 2.43 8.31 11.4 7335 477.583 2.33 3.1 11.04 14.65 6836 515.544 2.47 3.01 10.6 12.65 6537 354.061 3.28 4.05 16.86 21.4 6338 158.793 2.11 3.14 8.91 13.31 28339 861.138 2.18 2.66 8.88 11.24 1540 361.207 2.31 2.97 9.44 12.75 5141 468.458 2.04 2.83 11.29 15.96 3142 259.446 2.18 2.93 9.21 12.04 5843 121.99 2.76 3.54 11.66 15.7 41


Table 2 (Continued)Group Group Mean Standard Mean Standard Number ofnumber contribution absolute deviation absolute deviation components

(K) error (%) (%) error (K) (K)44 1124.49 1.88 2.87 9.67 14.46 6345 697.228 2.16 3.01 10.41 15.38 20346 712.76 1.4 2.11 6.03 9.17 1947 1230.21 4.76 6.46 20.25 27.66 548 1058.87 1.94 2.57 9.28 12.12 1049 1323.88 2.72 3.29 14.71 17.99 850 1479.27 1.78 2.28 8.76 11.21 551 654.008 3.12 4.96 12.98 20.17 8952 626.216 3.24 4.6 14.97 21.69 4253 459.247 1.37 1.71 5.22 6.35 4454 479.985 1.43 1.9 6.14 8.41 3355 874.273 0.94 1.29 3.66 5.09 456 309.872 2.1 2.82 9.27 12.6 1857 804.356 3.05 3.87 14.38 18.51 4158 516.817 1.66 2.27 6.66 9.37 11759 607.968 2.37 2.62 12.51 13.81 1260 521.597 1.74 2.33 6.31 8.58 2961 437.399 1.95 2.71 7.2 9.82 18262 507.998 2.56 3.48 10.59 14.21 7663 556.785 1.19 2.01 4.98 8.34 2364 468.03 1.74 2.24 5.79 7.7 2365 79.2981 2.81 3.88 12.68 17.51 1166 430.782 3.47 4.4 15.37 19.55 1567 282.737 2.64 4.15 12.39 19.82 3668 907.229 10.26 16.5 40.71 65.72 969 775.752 5.59 7.03 28.47 35.49 3770 294.323 1.42 2.19 4.9 7.16 3371 219.416 2.98 4.47 10.47 13.55 7072 964.373 0.93 1.18 3.79 4.85 673 1267.28 2.39 3.02 11.84 14.97 674 532.35 0.62 0.78 1.91 2.43 775 1082.68 1.95 2.51 8.64 10.9 976 1431.22 5.47 6.35 26.53 30.48 777 837.687 1.41 1.8 5.99 7.74 1878 594.43 0.96 1.37 4.14 5.72 779 911.983 0.88 1.08 3.65 4.34 480 671.441 5.5 7.27 24.7 32.57 1481 1002.53 1.85 2.29 8.21 10.26 582 1502.35 2.4 2.95 13.34 16.46 583 525.228 0.33 0.45 1.28 1.76 384 1173.13 0.43 0.59 1.97 2.7 685 1280.52 186 301.028 1


Table 3Second-order contributions for normal boiling points

Name Description ID Occurs

Para pair(s) Para positioncounted only once andonly if there are no meta or ortho pairs

87 p-Xylene

Meta pair(s) Meta positioncounted only once andonly if there are no para or ortho pairs

88 m-Xylene

Ortho pair(s) Ortho positioncounted only once andonly if there are no meta or para pairs

89 o-Xylene

Five-ring A five-membered non-aromatic ring 90 CyclopentaneThree/four-ring A three- or four-membered non-aromatic ring 91 CyclobuteneOne hydrogen Component has one hydrogen 92 NonafluorobutaneNo hydrogen Component has no hydrogen 93 Perfluoro compounds

The main advantage of this algorithm is, that only three parameters need to be regressed using the slownon-linear method while the large number of group increments is calculated from the fast multilinearleast squares regression. The objective function in linear regression is always the mean squared deviationbetween calculated and experimental value. Partial derivation of the objective function with respect tothe n coefficients (in this case, the n individual group contributions) leads to n linear equations. At theminimum of the objective function, all partial derivatives have to be zero. This leads to a set of n equationswith n unknowns, which can readily be solved, e.g. by the well known GaussJordan elimination. Theset of linear equations leads to exactly one solution provided all columns and rows in the coefficientmatrix are linear independent, which can be analyzed by singular value decomposition. In this work, theratio of experimental data (normal boiling temperatures) to adjustable parameters is about 26.61 and theresulting matrix is not close to singular.

Once the coefficients are available from the linear regression, the mean absolute deviation in Tb and thesquared standard deviation are calculated and their product is returned to the outer loop. Initial estimatesare only required for a, b and c, which are regressed in the outer loop. A full regression of 96 parameters(a, b, c, 87 group contributions and six second-order corrections) to 2550 experimental normal boilingtemperatures, thus, requires only a few minutes on a regular PC. We experienced no problems with

Table 4Second-order contributions, number of components used for regressing these values and mean absolute deviation in temperaturefor these components

Groupnumber

Groupcontribution

Meanabsoluteerror (%)

Standarddeviation(%)

Meanabsoluteerror (K)

Standarddeviation(K)

Number ofcomponents

87 37.5096 2.87 4.29 14.31 21.8 8188 3.5994 2.47 3.83 11.79 18.49 7789 44.8024 2.85 3.82 14.53 19.52 7790 27.0458 2.06 2.85 8.88 12.42 13491 39.0849 3.18 5.3 11.14 17.74 5092 131.323 2.34 3.36 7.64 11.69 3693 167.799 3.48 7.18 11.58 24.73 97


local minima. To verify the algorithm, the final parameters were used as starting values for a non-linearregression of all parameters to the experimental data using the commercial GRG2 algorithm (FrontlineSystems, Inc., Incline Village, NV, USA). No further improvement was achieved.

4.5. Test of the predictive capability

In order to test the predictive capability of the method, experimental normal boiling temperatures for126 components not in the database used for regression were compared with the predicted values. Thislead to a mean absolute deviation in temperature of 8.9 K (35.3 K for the Joback method, 13.1 K for Steinand Brown, 14.5 K for Constantinou and Gani, and 12.3 K for Marrero-Morejon and Pardillo-Fontdevila).

5. Results and discussion

The results for the different group contribution methods were carefully analyzed to detect any possibleweaknesses of the new method compared to the other methods and to identify typical components forwhich to expect extraordinary large deviations.

As the most important criterion for the reliability of a model the probability of a prediction failure(extreme deviation between experimental and estimated value) was chosen. Fig. 6 shows a plot of thepart of the data with a deviation larger than a certain temperature versus the deviation in temperature.Calculations are based on a common set of 1863 components, for which the normal boiling point canbe estimated by all models except that of Marrero-Morejon and Pardillo-Fontdevila. Including the latter

Fig. 6. Part of the data with deviations larger than a given temperature.


Table 5Deviations of the models for different types of hydrocarbons

Components Number ofcomponents

This work Joback andReid [3]

Stein andBrown [4]

Constantinouand Gani [2]

Marrero-Morejonand Pardillo-Fontdevila [5]

n-Alkanes 27 6.5 55.7 12.1 18.7 13.6Alkanes (non-cyclic) 166 6.5 26.7 15.2 8.9 7.7Alkanes (cyclic) 65 7.1 8.9 8.6 6.2 17.3Aromatic hydrocarbons 112 9.4 24.3 10.7 15.7 8.3 (70)Alkenes (HC) 167 7.4 9.4 7.7 6.0 17.8 (123)Alkenes (cyclic C=C) (HC) 38 9.4 8.1 8.2 6.7 16.0 (24)Alkines (HC) 33 5.4 13.1 12.1 13.5 3.8 (31)Hydrocarbons 568 7.4 17.7 10.8 9.5 11.6 (457)

HC denotes that the components taken into account only contain the elements C and H. The numbers in brackets for the methodof Marrero-Morejon and Pardillo-Fontdevila specify the number of components to which the method was applicable.

method would have further reduced the number of components in this test significantly. It can be seen,that in case of the new method, only 8% of the data are estimated with a deviation larger than 20 K.The other models range between 17% (Stein and Braun) and 36% (Constantinou and Gani). Only 14components (0.75%) exhibited a deviation larger than 50 K. The other models range between 3.6 and9.7%. The reasons for these failures will be discussed later. First, the behavior of the different models iscompared for different classes of compounds.

5.1. Hydrocarbons

A comparison of the different models is given in Table 5. While the new model yields small deviations(less than 10 K) for all classes of components, in some cases the method of Constantinou and Ganigives slightly better results. This is due to the larger number of parameters. In this work, only fourdifferent types of alkene groups are used compared to six groups plus three second-order groups in theConstantinouGani method. The use of more than twice the number of parameters results in only minorimprovements. The method of Marrero-Morejon and Pardillo-Fontdevila gives, especially good resultsfor alkines. In case of aromatic hydrocarbons, the range of applicability is significantly smaller (70 insteadof 112 components), which may be a reason for the good results.

Especially, large deviations (Tb,exp Tb,calc) were found for the following components:


5.2. Alkanols

Table 6 gives a comparison of the different models for various types of alkanols. For all 343 components,the new model gives the lowest mean deviation. In case of n-alkanols and primary and secondary alkanolsthe method of Stein and Brown gives slightly better results. This is due to the greater flexibility of thepolynomial linearization. As shown in Fig. 7, up to about C7 the increase of normal boiling temperaturewith molecular weight is over-predicted by the new model. Especially, high deviations are found foralkandiols, whereby geminal diols show no special behavior. If the correction function

Tb,corr = Tb,calc + 39.3 5.26nC (nC, number of carbon atoms) (9)

is applied, the mean deviation reduces to 5.2 K (not taking into account ethanediol).

Table 6Deviations of the models for different types of alkanols



Stein andBrown [4]



n-Alkanols 21 10.6 29.8 7.9 11.3 17.5Aliphatic alkanols 110 7.3 23.6 12.1 10.3 15.7 (103)Primary alkanols 36 8.5 20.8 7.1 10.7 15.1Secondary alkanols 35 6.0 27.7 5.3 10.7 14.7Tertiary alkanols 21 6.4 37.9 7.0 18.1 19.1 (14)Alkandiols 15 15.6 (5.2) 28.9 23.3 23.9 14.3Alkanols (HC) 343 7.5 22.5 12.5 10.6 9.9 (301)

HC denotes that the components taken into account only contain the elements C and H in addition to one or more OH-groups.The numbers in brackets for the method of Marrero-Morejon and Pardillo-Fontdevila specify the number of components towhich the method was applicable.


Fig. 7. Calculated vs. experimental normal boiling points of n-alkanols.

5.3. Other oxygenated compounds

A comparison of the different models is given in Table 7. Deviations for the new model are amongstthe lowest achieved by the different models. The method of Marrero-Morejon and Pardillo-Fontdevilagives exceptionally good results for aldehydes.

Table 7Deviations of the models for different types of oxygenated hydrocarbons (except alkanols)Components Number of

componentsThis work Joback and

Reid [3]Stein andBrown [4]



Ethers (HC) 85 4.7 10.7 6.7 11.1 5.0 (82)Epoxides (HC) 9 8.6 19.9 16.2 30.9 6.31 (7)Aldehydes (HC) 17 9.9 9.8 6.3 7.8 3.0 (16)Ketones (HC) 43 6.9 13.3 7.4 8.8 7.0 (38)Non-cyclic carbonates (HC) 4 3.7 25.1 49.7 3.5 5.5 (4)Carboxylic acids (HC) 32 5.7 30.2 6.0 16.4 9.3Esters (not CHO2)(HC) 120 9.2 34.2 9.0 9.6 13.4 (101)

HC denotes that the components taken into account only contain the elements C and H in addition to one or more groupscontaining oxygen. The numbers in brackets for the method of Marrero-Morejon and Pardillo-Fontdevila specify the number ofcomponents to which the method was applicable.


Table 8Deviations of the models for different types of halogenated hydrocarbons



Stein andBrown [4]



Fluorinated saturated hydrocarbons 52 5.4 16.9 64.3 25.6 10.1 (51)Fluorinated hydrocarbons 74 6.7 16.8 50.3 26.6 9.6 (71)Chlorinated saturated hydrocarbons 55 8.5 27.6 12.6 9.3 13.9 (51)Chlorinated hydrocarbons 88 7.7 23.0 12.5 10.1 13.5 (80)Brominated saturated hydrocarbons 31 7.6 16.9 10.3 8.0 14.9 (22)Brominated hydrocarbons 47 8.2 14.6 10.1 8.4 14.6 (33)Iodinated saturated hydrocarbons 17 5.7 14.7 8.8 8.1 13.4 (14)Iodinated hydrocarbons 20 5.9 13.7 8.1 7.2 11.7 (17)

The numbers in brackets for the method of Marrero-Morejon and Pardillo-Fontdevila specify the number of components towhich the method was applicable.

5.4. Halogenated hydrocarbons

A comparison of the different models is given in Table 8. In all cases, the proposed model gives thelowest deviation, which is probably due to a stronger differentiation in the structural groups and the largeset of data used in the regression.

5.5. Isomer differentiation

The method developed here was mainly focused on covering a broad range of components also, e.g.including germanium, silicon, tin and phosphor and very different in size. For non-cyclic saturatedhydrocarbons, only four different groups are used and a correct differentiation between alkane isomerscannot be expected. For a list of 18 different octane-isomers, an average error of 5.1 K was obtained,3.3 K for the method of Constantinou and Gani and 2.7 K for Marrero-Morejon and Pardillo-Fontdevila.The latter two methods use 9, resp. 10 parameters for non-cyclic saturated hydrocarbons.

5.6. Compounds for which large deviations are observed

Although the group contribution approach for the calculation of normal boiling temperatures generallyleads to good results, the assumption of simple additivity is not always valid.

In cases, where a strong inductive effect influences a mesomeric system, the molecule has a ratherhigh dipole moment or polarizability. In these cases, the estimated normal boiling temperature is sig-nificantly too low. Typical examples are: 4-hydroxybenzaldehyde (Tb,est = 583.20 K, Tb = 523.78 K);4-dimethylaminobenzaldehyde (Tb,est = 529.86 K, Tb = 588. K); 4-nitroaniline (Tb,est = 551.53 K,Tb= 607. K); 1,4-dihydroxybenzene (Tb,est = 512.35 K, Tb= 558.5 K); and resorcinol (Tb,est = 554.55 K,Tb = 506.16 K).

Generally, the influence of a larger number of strong I- or M-effects on mesomeric systems may leadto high deviations as in 2,4,6-trinitrotoluene (Tb,est = 624.60 K, Tb = 573.0 K), and 2,4,6-trinitrophenol(Tb,est = 654.12 K, Tb = 597.0 K).


Table 9Estimation of the normal boiling temperature (K) of ethylbenzene

Component: ethylbenzene; number of atoms: 8

Group Atoms Frequency Contribution Total

1 (CH3(ne)) 1 1 188.555 188.5558 ( C(c) (a)) 2 1 210.930 210.9315 (=C(a)H) 48 5 245.521 1227.60516 (=C(a) (ne)) 3 1 322.825 322.825Sum 1949.915

Tb = 1949.91580.6713 + 1.4442 + 59.344 = 414.98 (remark : atom 2 is matched by the group C(c) (a) as the group C(c)H2appears later in the priority list).

Table 10Estimation of the normal boiling temperature (K) of 1,1,2,2,-tetraphenylethane

Component: 1,1,2,2,-tetraphenylethane; number of atoms: 26


8 ( C(c) (a)) 1, 2 2 210.930 421.86015 (=C(a)H) 48, 1014, 1620, 2226 20 245.521 4910.42016 (=C(a) (ne)) 3, 9, 15, 21 4 322.825 1291.300Sum 6623.580

Tb = 6623.580260.6713 + 1.4442 + 59.344 = 699.05.


Table 11Estimation of the normal boiling temperature (K) of N-methyl-pyrrolidon

Component: N-methyl-pyrrolidon; number of atoms: 7


2 (CH3(e)) 7 1 282.015 282.0159 (C(r)H2) 3, 4 2 246.871 493.74213 ( C(r) (e,r)) 2 1 304.422 304.42248 (CON ) 1, 5, 6 1 1058.87 1058.8790 (five-ring) 15 1 27.0458 27.0458Sum 2112.0032

Tb = 2112.003270.6713 + 1.4442 + 59.344 = 470.508.

A phenyl-group can be sterically hindered, so that the electron system in hardly available for inter-molecular interaction as in the case of 1,1,2,2-tetraphenylethane (Tb,est = 699.07 K, Tb = 633.0 K).

Generally, results for molecules showing an extraordinary number of functional groups should be usedonly with great care. This is true for all group contribution methods.

In some cases, the pure component can rather be regarded as a mixture of tautomers. A typical ex-ample is found in case of -alkoxy-ketones: 2-butoxy-3-hexanone (Tb,est = 421.73 K, Tb = 494.44 K);2-butoxy-3-pentanone (Tb,est = 409.06 K, Tb = 475.94 K); and 2-butoxy-3-butanone (Tb,est = 400.62 K,Tb = 456.22 K).

These examples show, that the relatively few cases of high deviations can usually be contributed tosignificant sterical or electronic effects. Yet, these are not easy to integrate into a group contributionmethod, where the only required input for a property estimation should be the molecular structure.

6. Examples

To illustrate the application of the proposed method, detailed procedure for the estimation of Tb is givenfor ethylbenzene, tetraphenylethane and N-methyl pyrrolidon in Tables 911.

7. Conclusion

A group contribution method for the estimation of the normal boiling point of non-electrolyte organiccompounds was developed. The predictions are based exclusively on the molecular structure of thecompound. The results of the new method are in most cases far more accurate and never significantly worse


than previous methods. Structural groups were defined in a standardized form and the fragmentation of themolecular structures was performed by an automatic procedure to eliminate any arbitrary assumptions.

Second-order corrections were limited to those cases, in which larger structures or structural ef-fects could not be defined as structural groups (e.g. o-, m- and p-positions at rings, three-, four- andfive-membered rings and molecules with only one or two hydrogen atoms).

Structural groups were usually defined including the neighboring atoms, thus, implementing knowledgeabout the electronic structure in the respective context.

Currently, the database for normal boiling points is extended. In case where only low pressure dataare available, these are used for extrapolation. Once, a significant amount of new data is available, themethod will be updated and further extended.

In addition, work has started to use the same approach for the prediction of other pure componentproperties.

List of symbolsa, b, c adjustable parametersA, B, C adjustable parametersB second virial coefficientH enthalpyk Boltzmann constantM molar massr distance from center of moleculeR gas constantS entropyT absolute temperatureV volume

Greek letters density (r) function for the intermolecular potential

Subscriptsb boilingest estimatedfree available for translationvap vaporization

SuperscriptsL liquidV vapor

References

[1] J.M. Prausnitz, R.N. Lichtenthaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid Phase Equilibria, 3rd Edition,Prentice-Hall, Upper Saddle River, 1999.


[2] L.R. Constantinou, R. Gani, AIChE J. 40 (10) (1994) 16971710.[3] K.G. Joback, R.C. Reid, Chem. Eng. Commun. 57 (1987) 233243.[4] S.E. Stein, R.L. Brown, J. Chem. Inf. Comput. Sci. 34 (1994) 581587.[5] J. Marrero-Morejon, E. Pardillo-Fontdevila, AIChE J. 45 (3) (1999) 615621.[6] Aldrich Handbook of Fine Chemicals, Aldrich Chemical Co., Milwaukee, WI, 1990.[7] J. Graselli (Ed.), Handbook of Data of Organic Compounds (HODOC), CRC Press, Boca Raton, FL, 1990.[8] B.I. Lee, M.G. Kesler, AIChE J. 21 (1975) 510527.[9] W. Cordes, J. Rarey, F. Delique, J. Gmehling, in: D. Ziessow (Ed.), Software Development in Chemistry, in: Proceedings of

Computer in der Chemie, Vol. 7, Springer, Berlin, 1993.

A new method for the estimation of the normal boiling point of non-electrolyte organic compoundsIntroductionAvailable methods for the prediction of normal boiling pointsTheoretical considerationsDevelopment of the new methodGroup definitions and equationsSecond-order correctionsDatabaseRegression of the group constantsTest of the predictive capability

Results and discussionHydrocarbonsAlkanolsOther oxygenated compoundsHalogenated hydrocarbonsIsomer differentiationCompounds for which large deviations are observed

ExamplesConclusionReferences

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A New Method for the Estimation of the Normal Boiling Point of Non-electrolyte Organics

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