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 ==

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=== Group-contribution method ===

[[Image:Gruppenbeitragsmethodenprinzip.pngsvg|thumb|Principle of a group-contribution method]]

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

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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 4 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 strengths and weaknesses==

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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 errors of the Joback method (normal boiling point)]]

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 paperarticle abstract: "High accuracy is not claimed, but the proposed methodmethods are often as or more accurate than techniques in common use today."

The list of groups does 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 boiling point===

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

===Melting point===

<math>T_\text{m}[\text{K}] = 99122.5 + \sum T_{\text{m},i}.</math>

===Critical temperature===

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<math>T_\text{c}[\text{K}] = T_\text{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 pressure===

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

where ''N''_a is the number of atoms in the molecular structure (including hydrogens).

===Critical volume===

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<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 about 1000&nbsp;K. This can be extended to 1500K with some degree of uncertainty.

===Heat of vaporization at normal boiling point===

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===Liquid dynamic viscosity===

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

where ''M''_w is the [[molecular weight]].

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! ''H''_fusion

! ''H''_vap

! ''η_a''

! ''η_b''

|-

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

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

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

|-

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|-

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

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

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

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|-

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

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

| <div align="right">−8.08E−03</div>

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|-

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

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

| <div align="right">1.53E−04</div>

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|-

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

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

| <div align="right">−9.67E−08</div>

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|-

| ''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>

|-

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| <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>

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|-

| ''η_b''

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

| <div align="right">−1.7190</div>

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|-

| ''η''

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

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

| <div align="right">Pa ·s</div>

|}

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

[[Category:Physical chemistry]]

[[Category:Thermodynamic models]]