Joback method: Difference between revisions

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{{Short description|Thermodynamic model}}

The '''Joback method'''<ref>Joback K.G., Reid R.C., "Estimation of Pure-Component Properties from Group-Contributions", ''Chem. Eng. Commun.'', 57, 233–243, 1987</ref> (often named '''Joback/Reid method''') [[Prediction|predicts]] eleven important and commonly used pure component thermodynamic properties from molecular structure only.

The '''Joback method''', often named '''Joback–Reid method''', [[Prediction|predicts]] eleven important and commonly used pure component thermodynamic properties from molecular structure only. It is named after Kevin G. Joback in 1984<ref>{{cite thesis|last=Joback |first=K. G.|date=1984 |title=A Unified Approach to Physical Property Estimation Using Multivariate Statistical Techniques |url=https://dspace.mit.edu/bitstream/handle/1721.1/15374/12352302-MIT.pdf?sequence=2 |type=MS |publisher=Massachusetts Institute of Technology}}</ref> and developed it further with Robert C. Reid.<ref>Joback K. G., Reid R. C., "Estimation of Pure-Component Properties from Group-Contributions", ''Chem. Eng. Commun.'', 57, 233–243, 1987.</ref> The Joback method is an extension of the [[Lydersen method]]<ref>Lydersen A. L., "Estimation of Critical Properties of Organic Compounds", University of Wisconsin College Engineering, ''Eng. Exp. Stn. Rep.'' 3, Madison, Wisconsin, 1955.</ref> and uses very similar groups, formulas, and parameters for the three properties the Lydersen already supported ([[critical temperature]], [[critical pressure]], critical volume).

Joback and Reid extended the range of supported properties, created new parameters and modified slightly the formulas of the old Lydersen method.

== Basic Principles ==

=== GroupBasic Contributionprinciples Method ===

=== Group-contribution method ===

[[Image:Gruppenbeitragsmethodenprinzip.png|thumb|Principle of a Group Contribution Method]]

The Joback method is a [[group contribution method]]. These kind of methods use basic structural information of a chemical molecule like a list of simple functional groups, adds parameters to these functional groups, and calculates thermophysical and transport properties as a function of the sum of group parameters.

[[Image:Gruppenbeitragsmethodenprinzip.pngsvg|thumb|Principle of a Groupgroup-contribution Contribution Methodmethod]]

Joback assumes that there are no interactions between the groups and therefore only uses additive contributions and no contributions for interactions between groups. Other group contribution methods, especially methods like [[UNIFAC]], which estimate mixture properties like activity coefficients, use both simple additive group parameters and group interaction parameters. The big advantage of using only simple group parameters is the small number of needed parameters. The number of needed group interaction parameters gets very high for an increasing number of groups (1 for two groups, 3 for three groups, 6 for four groups, 45 for ten groups and twice as much if the interactions are not symmetric.).

The Joback method is a [[group -contribution method]]. These kindkinds of methods use basic structural information of a chemical molecule, like a list of simple functional groups, addsadd parameters to these functional groups, and calculatescalculate thermophysical and transport properties as a function of the sum of group parameters.

Joback assumes that there are no interactions between the groups, and therefore only uses additive contributions and no contributions for interactions between groups. Other group -contribution methods, especially methods like [[UNIFAC]], which estimate mixture properties like activity coefficients, use both simple additive group parameters and group -interaction parameters. The big advantage of using only simple group parameters is the small number of needed parameters. The number of needed group -interaction parameters gets very high for an increasing number of groups (1 for two groups, 3 for three groups, 6 for four groups, 45 for ten groups and twice as much if the interactions are not symmetric.).

Nine of the properties are single temperature-independent values, mostly estimated by a simple sum of group contribution plus an addend.

Two of the estimated properties are temperature-dependent: the ideal -gas [[heat capacity]] and the dynamic [[viscosity]] of liquids. The heat -capacity [[polynomial]] uses four4 parameters, and the viscosity equation only 2. In both cases the equation parameters are calculated by group contributions.

=== History ===

The Joback method is an extension of the [[Lydersen method]]<ref>Lydersen A.L., "Estimation of Critical Properties of Organic Compounds", University of Wisconsin College Engineering, ''Eng. Exp. Stn. Rep.'' 3, Madison, Wisconsin, 1955</ref> and uses very similar groups, formulas, and parameters for the three properties the Lydersen already supported ([[critical temperature]], [[critical pressure]], critical volume).

Joback extended the range of supported properties, created new parameters and modified slightly the formulas of the old Lydersen method.

==Model Strengthsstrengths and Weaknessesweaknesses==

===Strengths===

Line 25 ⟶ 22:

The popularity and success of the Joback method mainly originates from the single group list for all properties. This allows one to get all eleven supported properties from a single analysis of the molecular structure.

The Joback method additionally uses a very simple and easy to assign group scheme, which makes the method usable also for people with only basic chemical knowledge.

===Weaknesses===

[[Image:JobackNormalBoilingPointSystematicError.png|thumb|Systematic Errorserrors of the Joback Methodmethod (Normalnormal Boilingboiling Pointpoint)]]

Newer developments of estimation methods<ref>Constantinou L., Gani R., "New Group Contribution Method for Estimating Properties of Pure Compounds", ''AIChE J.'', 40(10), 1697–1710, 1994.</ref><ref>Nannoolal Y., Rarey J., Ramjugernath J., "Estimation of pure component properties Part 2. Estimation of critical property data by group contribution", ''Fluid Phase Equilib.'', 252(1–2), 1–27, 2007.</ref> have shown that the quality of the Joback method is limited. The original authors already stated themselves in the original article abstract: "High accuracy is not claimed, but the proposed methods are often as or more accurate than techniques in common use today."

</ref><ref>Nannoolal Y., Rarey J., Ramjugernath J., "Estimation of pure component properties Part 2. Estimation of critical property data by group contribution", ''Fluid Phase Equilib.'', 252(1–2), 1–27, 2007

</ref> have shown that the quality of the Joback method is limited. The original authors already stated themselves in the original paper: "High accuracy is not claimed, but the proposed method are often as or more accurate than techniques in common use today."

The list of groups don'tdoes not cover many common molecules sufficiently. Especially aromatic compounds are not differentiated from normal ring -containing components. This is a severe problem because aromatic and aliphatic components differ strongly.

The data base Joback and Reid used for obtaining the group parameters was rather small and covered only a limited number of different molecules. The best coverage has been achieved for normal boiling points (438 components), and the worst for heatheats of fusion (155 components). Current developments that can use data banks, like the [[Dortmund Data Bank]] or the DIPPR data base, have a much broader coverage.

The formula used for the prediction of the normal boiling point shows another problem. Joback assumed a constant contribution of added groups in homologous series like the [[alkane]]s. This doesn't describe the real behavior of the normal boiling points correctly.<ref>Stein S. E., Brown R. L., "Estimation of Normal Boiling Points from Group Contributions", ''J. Chem. Inf. Comput. Sci.'' 34, 581–587 (1994).</ref> Instead of the constant contribution, a decrease of the contribution with increasing number of groups must be applied. The chosen formula of the Joback method leads to high deviations for large and small molecules and an acceptable good estimation only for mid-sized components.

== Formulas ==

In the following formulas ''G_i'' denotes a group contribution. ''G_i'' are counted for every single available group. If a group is present multiple times, each occurrence is counted separately.

===Normal Boilingboiling Pointpoint===

<math>T_bT_\text{b}[\text{K}] \, = \, 198.2 + \sum {T_{\text{b},i}}.</math>

===Melting Pointpoint===

<math>T_mT_\text{m}[\text{K}] \, = \, 122.5 + \sum {T_{\text{m},i}}.</math>

===Critical Temperaturetemperature===

<math>T_cT_\text{c}[\text{K}] \, = T_\, T_btext{b} \left[0.584 + 0.965 \sum {T_{\text{c},i}} - \left(\sum {T_{\text{c},i}}\right)^2 \right]^{-1}.</math>

This critical -temperature equation needs a normal boiling point ''T''_b. If an experimental value is available, it is recommended to use this boiling point. It is, on the other hand, also possible to input the normal boiling point estimated by the Joback method. This will lead to a higher error.

===Critical Pressurepressure===

<math>P_cP_\text{c}[\text{bar}] \, = \, \left [{ 0.113 + 0.0032 *\, N_AN_\text{a} - \sum {P_{\text{c},i}} }\right ]^{-2},</math>

where ''N''_Aa: Numberis the number of atoms in the molecular structure (including hydrogens).

===Critical Volumevolume===

<math>V_cV_\text{c}[\text{cm}^{3}/\text{mol}] \, = \, 17.5 + \sum {V_{\text{c},i}}.</math>

===Heat of Formationformation (Idealideal Gasgas, 298 K)===

<math>H_\text{formation}[\text{kJ}/\text{mol}] \, = \, 68.29 + \sum {H_{\text{form},i}}.</math>

===Gibbs Energyenergy of Formationformation (Idealideal Gasgas, 298 K)===

<math>G_\text{formation}[\text{kJ}/\text{mol}] \, = \, 53.88 + \sum {G_{\text{form},i}}.</math>

===Heat Capacitycapacity (Idealideal Gasgas)===

<math>C_P[\text{J}/(\text{mol.}\cdot\text{K})] \, = \, \sum a_i - 37.93 + \left[ \sum b_i + 0.210 \right] T + \left[ \sum c_i - 3.91 \cdot 10^{-4} \right] T^2 + \left[\sum d_i + 2.06 \cdot 10^{-7}\right] T^3.</math>

The Joback method uses a four -parameter polynomial to describe the temperature dependency of the ideal -gas heat capacity. These parameters are valid from 273 &nbsp;K to approx.about 1000 &nbsp;K. This can be extended to 1500K with some degree of uncertainty.

===Heat of Vaporizationvaporization at Normalnormal Boilingboiling Pointpoint===

<math>\Delta H_\text{vap}[\text{kJ}/\text{mol}] \, = \, 15.30 + \sum H_{\text{vap},i}.</math>

===Heat of Fusionfusion===

<math>\Delta H_\text{fus}[\text{kJ}/\text{mol}] \, = \, -0.88 + \sum H_{\text{fus},i}.</math>

===Liquid Dynamicdynamic Viscosityviscosity===

<math>\eta_Leta_\text{L}[\text{Pa.}\cdot\text{s}] \, = M_\, M_wtext{w} e^exp{ \left([ \left(\sum \eta_a - 597.82 \right]) / T) + \sum \eta_b - 11.202\right] },</math>

where ''M''_w: Molecularis the [[molecular Weightweight]].

The method uses a two -parameter equation to describe the temperature dependency of the dynamic viscosity. The authors state that the parameters are valid from the melting temperature up to 0.7 of the critical temperature (''T''_r&nbsp;<&nbsp;0.7).

== Group Contributionscontributions ==

{| class="wikitable"

|-

! Group

! ''T''_c

! ''P''_c

! ''V''_c

! ''T''_b

! ''T''_m

! ''H''_form

! ''G''_form

! ''a''

! ''b''

! ''c''

! ''d''

! ''H''_fusion

! ''H''_vap

! ''η_a''

! a

! ''η_b''

! b

|-

|

| colspan="3" | Critical-state State Datadata

| colspan="2" | Temperatures<br>of Phasephase Transitionstransitions

| colspan="2" | Chemical Caloriccaloric<br>Propertiesproperties

| colspan="4" | Ideal-gas Gasheat Heat Capacitiescapacities

| colspan="2" | Enthalpies<br>of Phasephase Transitionstransitions

| colspan="2" | Dynamic Viscosityviscosity

|-

Line 131 ⟶ 126:

|-

| -CH−CH₃

| 0.0141

| −0.0012

Line 149 ⟶ 144:

|-

| -CH−CH₂-−

| 0.0189

| 0.0000

Line 167 ⟶ 162:

|-

| >CH-CH−

| 0.0164

| 0.0020

Line 181 ⟶ 176:

| 0.749

| 1.691

| -322−322.15

| 1.187

Line 203 ⟶ 198:

|-

| <nowiki>=CH</nowiki>₂<nowiki><</nowiki>

| 0.0113

| −0.0028

Line 221 ⟶ 216:

|-

| =CH−

| <nowiki>=CH-</nowiki>

| 0.0129

| −0.0006

Line 257 ⟶ 252:

|-

| <nowiki>=C=</nowiki>

| 0.0026

| 0.0028

Line 275 ⟶ 270:

|-

| <nowiki>≡CH</nowiki>

| 0.0027

| −0.0008

Line 293 ⟶ 288:

|-

| ≡C−

| <nowiki>≡C-</nowiki>

| 0.0020

| 0.0016

Line 314 ⟶ 309:

|-

| -CH−CH₂-−

| 0.0100

| 0.0025

Line 332 ⟶ 327:

|-

| >CH-CH−

| 0.0122

| 0.0004

Line 368 ⟶ 363:

|-

| =CH−

| <nowiki>=CH-</nowiki>

| 0.0082

| 0.0011

Line 407 ⟶ 402:

|-

| -F−F

| 0.0111

| −0.0057

Line 425 ⟶ 420:

|-

| -Cl−Cl

| 0.0105

| −0.0049

Line 443 ⟶ 438:

|-

| -Br−Br

| 0.0133

| 0.0057

Line 461 ⟶ 456:

|-

| -I−I

| 0.0068

| −0.0034

Line 482 ⟶ 477:

|-

| -OH−OH (alcohol)

| 0.0741

| 0.0112

Line 500 ⟶ 495:

|-

| -OH−OH (phenol)

| 0.0240

| 0.0184

Line 518 ⟶ 513:

|-

| -O-−O− (nonringnon-ring)

| 0.0168

| 0.0015

Line 536 ⟶ 531:

|-

| -O-−O− (ring)

| 0.0098

| 0.0048

Line 554 ⟶ 549:

|-

| >C=O (nonringnon-ring)

| 0.0380

| 0.0031

Line 590 ⟶ 585:

|-

| O=CH-CH− (aldehyde)

| 0.0379

| 0.0030

Line 608 ⟶ 603:

|-

| -COOH−COOH (acid)

| 0.0791

| 0.0077

Line 626 ⟶ 621:

|-

| -COO-−COO− (ester)

| 0.0481

| 0.0005

Line 644 ⟶ 639:

|-

| <nowiki>=O (other than above)</nowiki>

| 0.0143

| 0.0101

Line 665 ⟶ 660:

|-

| -NH−NH₂

| 0.0243

| 0.0109

Line 719 ⟶ 714:

|-

| >N-N− (nonringnon-ring)

| 0.0169

| 0.0074

Line 737 ⟶ 732:

|-

| -N−N= (nonringnon-ring)

| 0.0255

| -0.0099

Line 755 ⟶ 750:

|-

| -N−N= (ring)

| 0.0085

| 0.0076

Line 773 ⟶ 768:

|-

| <nowiki>=NH</nowiki>

| n.&nbsp;a.

| n.&nbsp;a.

Line 791 ⟶ 786:

|-

| -CN−CN

| 0.0496

| −0.0101

Line 809 ⟶ 804:

|-

| -NO−NO₂

| 0.0437

| 0.0064

Line 830 ⟶ 825:

|-

| -SH−SH

| 0.0031

| 0.0084

Line 848 ⟶ 843:

|-

| -S-−S− (nonringnon-ring)

| 0.0119

| 0.0049

Line 866 ⟶ 861:

|-

| -S-−S− (ring)

| 0.0019

| 0.0051

Line 885 ⟶ 880:

|}

== Example Calculationcalculation ==

[[Image:AcetonGruppen.PNG]]

[[Acetone]] (Propanonepropanone) is the simplest [[ketone]] and is separated into three groups in the Joback method: two [[methyl group]]s (-CH−CH₃) and one ketone group (C=O). Since the methyl group is present twice, its contributions have to be added twice.

{| class="wikitable"

|

| colspan="2" | <center>-CH−CH₃ </center>

| colspan="2" | <center>>C=O (nonringnon-ring)</center>

|

|

Line 906 ⟶ 901:

| Group value

| <math>\sum G_i</math>

| Estimated Valuevalue

| Unit

|-

| ''T''_c

| <div align="right">2</div>

| <div align="right">0.0141</div>

Line 920 ⟶ 915:

|-

| ''P''_c

| <div align="right">2</div>

| <div align="right">−1.20E−03</div>

Line 930 ⟶ 925:

|-

| ''V''_c

| <div align="right">2</div>

| <div align="right">65.0000</div>

Line 937 ⟶ 932:

| <div align="right">192.0000</div>

| <div align="right">209.5000</div>

| <div align="right">cm3mL/mol</div>

|-

| ''T''_b

| <div align="right">2</div>

| <div align="right">23.5800</div>

Line 950 ⟶ 945:

|-

| ''T''_m

| <div align="right">2</div>

| <div align="right">−5.1000</div>

Line 960 ⟶ 955:

|-

| ''H''_formation

| <div align="right">2</div>

| <div align="right">−76.4500</div>

Line 970 ⟶ 965:

|-

| ''G''_formation

| <div align="right">2</div>

| <div align="right">−43.9600</div>

Line 980 ⟶ 975:

|-

| ''C''_pap: ''a''

| <div align="right">2</div>

| <div align="right">1.95E+01</div>

Line 989 ⟶ 984:

|-

| ''C''_pbp: ''b''

| <div align="right">2</div>

| <div align="right">−8.08E−03</div>

Line 998 ⟶ 993:

|-

| ''C''_pcp: ''c''

| <div align="right">2</div>

| <div align="right">1.53E−04</div>

Line 1,007 ⟶ 1,002:

|-

| ''C''_pdp: ''d''

| <div align="right">2</div>

| <div align="right">−9.67E−08</div>

Line 1,016 ⟶ 1,011:

|-

| ''C''_p

| colspan="5" | <div align="right">at ''T'' = 300 &nbsp;K</div>

| <div align="right">75.3264</div>

| <div align="right">J/(mol*·K) </div>

|-

| ''H''_fusion

| <div align="right">2</div>

| <div align="right">0.9080</div>

Line 1,032 ⟶ 1,027:

|-

| ''H''_vap

| <div align="right">2</div>

| <div align="right">2.3730</div>

Line 1,038 ⟶ 1,033:

| <div align="right">8.9720</div>

| <div align="right">13.7180</div>

| <div align="right">29.0180180</div>

| <div align="right">kJ/mol</div>

|-

| ''η_a''

| <div align="right">2</div>

| <div align="right">548.2900</div>

Line 1,051 ⟶ 1,046:

|-

| ''η_b''

| <div align="right">2</div>

| <div align="right">−1.7190</div>

Line 1,060 ⟶ 1,055:

|-

| ''η''

| colspan="5" | <div align="right">at ''T'' = 300 &nbsp;K</div>

| <div align="right">0.0002942</div>

| <div align="right">Pa ·s</div>

|}

Line 1,072 ⟶ 1,067:

== External links ==

* [https://www.chemeo.com/predict?smiles=CCCC Online molecular drawing and property estimation tool with the Joback method]

* [http://ddbonline.ddbst.de/OnlinePropertyEstimation/OnlinePropertyEstimation.exe Online property estimation with the Joback method]

[[Category:Physical chemistry]]

[[Category:Thermodynamic models]]