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.

==Model Strengthsstrengths and Weaknessesweaknesses==

=== 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 Strengths and Weaknesses==

===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't 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 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 heat 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 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.

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.

==Sanity of Believers==

===Nick S.===

== 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.

Never trust Wikipedia.

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_\,text{w} M_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 135 ⟶ 126:

|-

| -CH−CH₃

| 0.0141

| −0.0012

Line 153 ⟶ 144:

|-

| -CH−CH₂-−

| 0.0189

| 0.0000

Line 171 ⟶ 162:

|-

| >CH-CH−

| 0.0164

| 0.0020

Line 185 ⟶ 176:

| 0.749

| 1.691

| -322−322.15

| 1.187

Line 207 ⟶ 198:

|-

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

| 0.0113

| −0.0028

Line 225 ⟶ 216:

|-

| =CH−

| <nowiki>=CH-</nowiki>

| 0.0129

| −0.0006

Line 261 ⟶ 252:

|-

| <nowiki>=C=</nowiki>

| 0.0026

| 0.0028

Line 279 ⟶ 270:

|-

| <nowiki>≡CH</nowiki>

| 0.0027

| −0.0008

Line 297 ⟶ 288:

|-

| ≡C−

| <nowiki>≡C-</nowiki>

| 0.0020

| 0.0016

Line 318 ⟶ 309:

|-

| -CH−CH₂-−

| 0.0100

| 0.0025

Line 336 ⟶ 327:

|-

| >CH-CH−

| 0.0122

| 0.0004

Line 372 ⟶ 363:

|-

| =CH−

| <nowiki>=CH-</nowiki>

| 0.0082

| 0.0011

Line 411 ⟶ 402:

|-

| -F−F

| 0.0111

| −0.0057

Line 429 ⟶ 420:

|-

| -Cl−Cl

| 0.0105

| −0.0049

Line 447 ⟶ 438:

|-

| -Br−Br

| 0.0133

| 0.0057

Line 465 ⟶ 456:

|-

| -I−I

| 0.0068

| −0.0034

Line 486 ⟶ 477:

|-

| -OH−OH (alcohol)

| 0.0741

| 0.0112

Line 504 ⟶ 495:

|-

| -OH−OH (phenol)

| 0.0240

| 0.0184

Line 522 ⟶ 513:

|-

| -O-−O− (nonringnon-ring)

| 0.0168

| 0.0015

Line 540 ⟶ 531:

|-

| -O-−O− (ring)

| 0.0098

| 0.0048

Line 558 ⟶ 549:

|-

| >C=O (nonringnon-ring)

| 0.0380

| 0.0031

Line 594 ⟶ 585:

|-

| O=CH-CH− (aldehyde)

| 0.0379

| 0.0030

Line 612 ⟶ 603:

|-

| -COOH−COOH (acid)

| 0.0791

| 0.0077

Line 630 ⟶ 621:

|-

| -COO-−COO− (ester)

| 0.0481

| 0.0005

Line 648 ⟶ 639:

|-

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

| 0.0143

| 0.0101

Line 669 ⟶ 660:

|-

| -NH−NH₂

| 0.0243

| 0.0109

Line 723 ⟶ 714:

|-

| >N-N− (nonringnon-ring)

| 0.0169

| 0.0074

Line 741 ⟶ 732:

|-

| -N−N= (nonringnon-ring)

| 0.0255

| -0.0099

Line 759 ⟶ 750:

|-

| -N−N= (ring)

| 0.0085

| 0.0076

Line 777 ⟶ 768:

|-

| <nowiki>=NH</nowiki>

| n.&nbsp;a.

| n.&nbsp;a.

Line 795 ⟶ 786:

|-

| -CN−CN

| 0.0496

| −0.0101

Line 813 ⟶ 804:

|-

| -NO−NO₂

| 0.0437

| 0.0064

Line 834 ⟶ 825:

|-

| -SH−SH

| 0.0031

| 0.0084

Line 852 ⟶ 843:

|-

| -S-−S− (nonringnon-ring)

| 0.0119

| 0.0049

Line 870 ⟶ 861:

|-

| -S-−S− (ring)

| 0.0019

| 0.0051

Line 889 ⟶ 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−CH₃3 </center>

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

|

|

Line 910 ⟶ 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 924 ⟶ 915:

|-

| ''P''_c

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

| <div align="right">−1.20E−03</div>

Line 934 ⟶ 925:

|-

| ''V''_c

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

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

Line 941 ⟶ 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 954 ⟶ 945:

|-

| ''T''_m

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

| <div align="right">−5.1000</div>

Line 964 ⟶ 955:

|-

| ''H''_formation

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

| <div align="right">−76.4500</div>

Line 974 ⟶ 965:

|-

| ''G''_formation

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

| <div align="right">−43.9600</div>

Line 984 ⟶ 975:

|-

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

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

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

Line 993 ⟶ 984:

|-

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

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

| <div align="right">−8.08E−03</div>

Line 1,002 ⟶ 993:

|-

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

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

| <div align="right">1.53E−04</div>

Line 1,011 ⟶ 1,002:

|-

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

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

| <div align="right">−9.67E−08</div>

Line 1,020 ⟶ 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 1,036 ⟶ 1,027:

|-

| ''H''_vap

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

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

Line 1,042 ⟶ 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 1,055 ⟶ 1,046:

|-

| ''η_b''

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

| <div align="right">−1.7190</div>

Line 1,064 ⟶ 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 1,076 ⟶ 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]]