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. Vapor–liquid 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,. . . ).
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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 Clausius–Clapeyron equation, the normal boiling point can be calculated via the ratio of�Hvap and�Svap:
Tb = �Hvap
�Svap(1)
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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 approximatelyn
2/3CH2
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. 1ashows�Hvap (J/(mol K)) at the normal boiling forn-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 (1–4 –CH2– groups),�Hvapincreases 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 ofn-alkanes at the normal boiling point as function of the molecular weight (datataken from Dortmund Data Bank, 2001).
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For the estimation of the normal boiling temperature also knowledge of the entropy change withvaporization is required. Following Trouton’s rule, the molar entropy of vaporization of a non-associatedliquid at standard boiling point is approximately constant, about 82–88 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 V
transamounts to nearly22.414 dm3/mol. In the liquid phase, the available volumeV L
trans 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 V
trans
V Ltrans
)(3)
V Ltransshould decrease with increasing attractive forces (i.e. increasing enthalpy of vaporization) and
be influenced by structural effects.(b) Due to close packing in the liquid phase, a difficult to estimate part of the internal movements can be
confined. This effect is considered to be very small and generally not of further importance. In case of,e.g. cyclohexane andn-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 forTb based on groupcontributions and other easy to obtain quantities will be sought for as a certain correlation between�Hvap
and�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 ofTb on the number of groups in different homol-ogous series will first be compared to the results of methods previously published.
Figs. 2 and 3show the normal boiling points ofn-alkanes andn-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 Lee–Kesler[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 parametersA,BandCand the group contribution parameters were regressed separately,they do not give the best results possible with this type of mathematical expression.
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Fig. 2. Normal boiling points ofn-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 typei, Ci the group contribution of first-order groupi, Mi
the number of second-order groups of typei, andDi is the group contribution of second-order groupi.The second-order groups are only used as a correction to the first-order estimations for a limited number
of special structures.Marrero-Morejon and Pardillo-Fontdevila[5] employed the equation:
Tb = M−0.404∑
NiCi + 156.00 (6)
whereNi is the number of first-order groups of typei, Ci the group contribution of first-order groupi,andM is the molecular weight (g/mol).
Fig. 3. Normal boiling points ofn-alkanols as a function of the number of –CH2– groups.
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In contrary to the other methods, Marrero-Morejon and Pardillo-Fontdevila use bond contributionsinstead of group contributions.
FromFigs. 2 and 3, it can be seen that, although much better than the linear assumption of Joback andReid, neither the logarithmic dependence nor the termM−0.404 are able to describe the dependence ofTb
on chain length in the two homologous series.For the correlation of group contribution parameters Constantinou and Gani as well as Marrero-Morejon
and 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)
wherea, bandcare the adjustable parameters,Ni the number of groups of typei, Ci the group contributionof groupi (K), andn is the number of atoms in the molecule (except hydrogen).
While this expression gives a good description of the dependence ofTb 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 forn-alkanes andn-alkanols are given inFigs. 4 and 5.Definition of the structural groups was approached by an iterative procedure. Starting off from the
groups used in the method by Joback and Reid, the adjustable parametersa, b andc 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.
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Fig. 4. Normal boiling points ofn-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 ofn-alkanols as a function of the number of –CH2– groups together with the results for the proposedmethod.
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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 inTable 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 inTables 1and 3in 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 –C–CO–CO–C– 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 inTable 1, special second-order corrections were applied.A list of these special corrections together with examples is given inTable 3. Table 4contains 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
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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
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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)
–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 acid–COO– HCOO– connected to C (formic
acid ester)HCOO–(C) 46/21 Ethyl formate, phenyl
formate–COO– 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 ε-Caprolactone,crotonolactone
(OC2) (OC2) (epoxide) (OC2) 39/27 Propylene oxide–CO–O–CO– Anhydride connected to two C –CO–O–CO– 76/6 Acetic anhydride, phthalic
anhydride
Sulphur–S–S– –S–S– (disulfide)
connected to two C(C)–S–S–(C) 55/28 Dimethyldisulfide,
1,2-dicyclopentyl-1,2-disulfide–SH –SH connected to C
(thiols)SH–(C) 53/49 1-Propanethiol
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Table 1 (Continued)
Group Description Name ID/PR Occurs
–S– –S– connected to two C (C)–S–(C) 54/50 Methyl ethyl sulfide–S– 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 isothiocyanate
Periodic group 15Nitrogen
NH2– NH2– connected to eitherC or Si
NH2–(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)
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 inTables 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 coefficientsa, b andc 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 componentsj) (8)
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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
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Table 3Second-order contributions for normal boiling points
Name Description ID Occurs
Parapair(s) Paraposition—counted only once andonly if there are nometaor orthopairs
87 p-Xylene
Metapair(s) Metaposition—counted only once andonly if there are noparaor orthopairs
88 m-Xylene
Orthopair(s) Orthoposition—counted only once andonly if there are nometaor parapairs
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 tothen coefficients (in this case, then individual group contributions) leads ton 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 Gauss–Jordan 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 26.6–1 and theresulting matrix is not close to singular.
Once the coefficients are available from the linear regression, the mean absolute deviation inTb and thesquared standard deviation are calculated and their product is returned to the outer loop. Initial estimatesare only required fora, b andc, 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
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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.
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Table 5Deviations of the models for different types of hydrocarbons
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 inTable 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 theConstantinou–Gani 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:
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5.2. Alkanols
Table 6gives 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 ofn-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 inFig. 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
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.
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Fig. 7. Calculated vs. experimental normal boiling points ofn-alkanols.
5.3. Other oxygenated compounds
A comparison of the different models is given inTable 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)
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.
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Table 8Deviations of the models for different types of halogenated hydrocarbons
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 inTable 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).
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Table 9Estimation of the normal boiling temperature (K) of ethylbenzene
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 ofTb is givenfor ethylbenzene, tetraphenylethane andN-methyl pyrrolidon inTables 9–11.
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
432 W. Cordes, J. Rarey / Fluid Phase Equilibria 201 (2002) 409–433
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- andp-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 lettersρ densityΓ (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.
W. Cordes, J. Rarey / Fluid Phase Equilibria 201 (2002) 409–433 433
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