Joback method

The Joback method[1] (often named Joback/Reid method) predicts eleven important and commonly used pure component thermodynamic properties from molecular structure only.

Basic Principles

Group Contribution Method

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.

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 four 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[2] 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

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

Systematic Errors of the Joback Method (Normal Boiling Point)

Newer developments of estimation methods[3][4] 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 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 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 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 alkanes. This doesn't describe the real behavior of the normal boiling points correctly.[5] 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 Gi denotes a group contribution. Gi are counted for every single available group. If a group is present multiple times each occurrence is counted separately.

Normal Boiling Point

${\displaystyle T_{b}[K]\,=\,198+\sum {T_{b,i}}}$

Melting Point

${\displaystyle T_{m}[K]\,=\,99.5+\ {T_{m,i}}}$

Critical Temperature

${\displaystyle T_{c}[K]\,=\,T_{b}\left[0.584+0.965\sum {T_{c,i}}-\left(\sum {T_{c,i}}\right)^{2}\right]^{-1}}$

This critical temperature equation needs a normal boiling point Tb. 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

${\displaystyle P_{c}[bar]\,=\,\left[{0.113+0.0032*N_{A}-\sum {P_{c,i}}}\right]^{-2}}$

NA: Number of atoms in the molecular structure (including hydrogens).

Critical Volume

${\displaystyle V_{c}[cm^{3}/mol]\,=\,17.5+\sum {V_{c,i}}}$

Heat of Formation (Ideal Gas, 298 K)

${\displaystyle H_{formation}[kJ/mol]\,=\,68.29+\sum {H_{form,i}}}$

Gibbs Energy of Formation (Ideal Gas, 298 K)

${\displaystyle G_{formation}[kJ/mol]\,=\,53.88+\sum {G_{form,i}}}$

Heat Capacity (Ideal Gas)

${\displaystyle C_{P}[J/(mol.K)]\,=\,\sum a_{i}-37.93+\left[\sum b_{i}+0.210\right]T+\left[\sum c_{i}-3.91\cdot 10^{-4}\right]T^{2}+\left[\sum d_{i}+2.06\cdot 10^{-7}\right]T^{3}}$

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 K to approx. 1000 K.

Heat of Vaporization at Normal Boiling Point

${\displaystyle \Delta H_{vap}[kJ/mol]\,=\,15.30+\sum H_{vap,i}}$

Heat of Fusion

${\displaystyle \Delta H_{fus}[kJ/mol]\,=\,-0.88+\sum H_{fus,i}}$

Liquid Dynamic Viscosity

${\displaystyle \eta _{L}[Pa.s]\,=\,M_{w}e^{\left([\sum \eta _{a}-597.82\right]/T)+\sum \eta _{b}-11.202}}$

Mw: Molecular Weight

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 (Tr<0.7).

Group Contributions

Group Tc Pc Vc Tb Tm Hform Gform a b c d Hfusion Hvap a b
Critical State Data Temperatures
of Phase Transitions
Chemical Caloric
Properties
Ideal Gas Heat Capacities Enthalpies
of Phase Transitions
Dynamic Viscosity
Non-ring groups
-CH3 0.0141 −0.0012 65 23.58 −5.10 −76.45 −43.96 1.95E+1 −8.08E−3 1.53E−4 −9.67E−8 0.908 2.373 548.29 −1.719
-CH2- 0.0189 0.0000 56 22.88 11.27 −20.64 8.42 −9.09E−1 9.50E−2 −5.44E−5 1.19E−8 2.590 2.226 94.16 −0.199
>CH- 0.0164 0.0020 41 21.74 12.64 29.89 58.36 −2.30E+1 2.04E−1 −2.65E−4 1.20E−7 0.749 1.691 -322.15 1.187
>C< 0.0067 0.0043 27 18.25 46.43 82.23 116.02 −6.62E+1 4.27E−1 −6.41E−4 3.01E−7 −1.460 0.636 −573.56 2.307
=CH2 0.0113 −0.0028 56 18.18 −4.32 −9.630 3.77 2.36E+1 −3.81E−2 1.72E−4 −1.03E−7 −0.473 1.724 495.01 −1.539
=CH- 0.0129 −0.0006 46 24.96 8.73 37.97 48.53 −8.00 1.05E−1 −9.63E−5 3.56E−8 2.691 2.205 82.28 −0.242
=C< 0.0117 0.0011 38 24.14 11.14 83.99 92.36 −2.81E+1 2.08E−1 −3.06E−4 1.46E−7 3.063 2.138 n. a. n. a.
=C= 0.0026 0.0028 36 26.15 17.78 142.14 136.70 2.74E+1 −5.57E−2 1.01E−4 −5.02E−8 4.720 2.661 n. a. n. a.
≡CH 0.0027 −0.0008 46 9.20 −11.18 79.30 77.71 2.45E+1 −2.71E−2 1.11E−4 −6.78E−8 2.322 1.155 n. a. n. a.
≡C- 0.0020 0.0016 37 27.38 64.32 115.51 109.82 7.87 2.01E−2 −8.33E−6 1.39E-9 4.151 3.302 n. a. n. a.
Ring groups
-CH2- 0.0100 0.0025 48 27.15 7.75 −26.80 −3.68 −6.03 8.54E−2 −8.00E−6 −1.80E−8 0.490 2.398 307.53 −0.798
>CH- 0.0122 0.0004 38 21.78 19.88 8.67 40.99 −2.05E+1 1.62E−1 −1.60E−4 6.24E−8 3.243 1.942 −394.29 1.251
>C< 0.0042 0.0061 27 21.32 60.15 79.72 87.88 −9.09E+1 5.57E−1 −9.00E−4 4.69E−7 −1.373 0.644 n. a. n. a.
=CH- 0.0082 0.0011 41 26.73 8.13 2.09 11.30 −2.14 5.74E−2 −1.64E−6 −1.59E−8 1.101 2.544 259.65 −0.702
=C< 0.0143 0.0008 32 31.01 37.02 46.43 54.05 −8.25 1.01E−1 −1.42E−4 6.78E−8 2.394 3.059 -245.74 0.912
Halogen groups
-F 0.0111 −0.0057 27 −0.03 −15.78 −251.92 −247.19 2.65E+1 −9.13E−2 1.91E−4 −1.03E−7 1.398 −0.670 n. a. n. a.
-Cl 0.0105 −0.0049 58 38.13 13.55 −71.55 −64.31 3.33E+1 −9.63E−2 1.87E−4 −9.96E−8 2.515 4.532 625.45 −1.814
-Br 0.0133 0.0057 71 66.86 43.43 −29.48 −38.06 2.86E+1 −6.49E−2 1.36E−4 −7.45E−8 3.603 6.582 738.91 −2.038
-I 0.0068 −0.0034 97 93.84 41.69 21.06 5.74 3.21E+1 −6.41E−2 1.26E−4 −6.87E−8 2.724 9.520 809.55 −2.224
Oxygen groups
-OH (alcohol) 0.0741 0.0112 28 92.88 44.45 −208.04 −189.20 2.57E+1 −6.91E−2 1.77E−4 −9.88E−8 2.406 16.826 2173.72 −5.057
-OH (phenol) 0.0240 0.0184 −25 76.34 82.83 −221.65 −197.37 −2.81 1.11E−1 −1.16E−4 4.94E−8 4.490 12.499 3018.17 −7.314
-O- (nonring) 0.0168 0.0015 18 22.42 22.23 −132.22 −105.00 2.55E+1 −6.32E−2 1.11E−4 −5.48E−8 1.188 2.410 122.09 −0.386
-O- (ring) 0.0098 0.0048 13 31.22 23.05 −138.16 −98.22 1.22E+1 −1.26E−2 6.03E−5 −3.86E−8 5.879 4.682 440.24 −0.953
>C=O (nonring) 0.0380 0.0031 62 76.75 61.20 −133.22 −120.50 6.45 6.70E−2 −3.57E−5 2.86E−9 4.189 8.972 340.35 −0.350
>C=O (ring) 0.0284 0.0028 55 94.97 75.97 −164.50 −126.27 3.04E+1 −8.29E−2 2.36E−4 −1.31E−7 0. 6.645 n. a. n. a.
O=CH- (aldehyde) 0.0379 0.0030 82 72.24 36.90 −162.03 −143.48 3.09E+1 −3.36E−2 1.60E−4 −9.88E−8 3.197 9.093 740.92 −1.713
-COOH (acid) 0.0791 0.0077 89 169.09 155.50 −426.72 −387.87 2.41E+1 4.27E−2 8.04E−5 −6.87E−8 11.051 19.537 1317.23 −2.578
-COO- (ester) 0.0481 0.0005 82 81.10 53.60 −337.92 −301.95 2.45E+1 4.02E−2 4.02E−5 −4.52E−8 6.959 9.633 483.88 −0.966
=O (other than above) 0.0143 0.0101 36 −10.50 2.08 −247.61 −250.83 6.82 1.96E−2 1.27E−5 −1.78E−8 3.624 5.909 675.24 −1.340
Nitrogen groups
-NH2 0.0243 0.0109 38 73.23 66.89 −22.02 14.07 2.69E+1 −4.12E−2 1.64E−4 −9.76E−8 3.515 10.788 n. a. n. a.
>NH (non-ring) 0.0295 0.0077 35 50.17 52.66 53.47 89.39 −1.21 7.62E−2 −4.86E−5 1.05E−8 5.099 6.436 n. a. n. a.
>NH (ring) 0.0130 0.0114 29 52.82 101.51 31.65 75.61 1.18E+1 −2.30E−2 1.07E−4 −6.28E−8 7.490 6.930 n. a. n. a.
>N-(nonring) 0.0169 0.0074 9 11.74 48.84 123.34 163.16 −3.11E+1 2.27E−1 −3.20E−4 1.46E−7 4.703 1.896 n. a. n. a.
-N= (nonring) 0.0255 -0.0099 n. a. 74.60 n. a. 23.61 n. a. n. a. n. a. n. a. n. a. n. a. 3.335 n. a. n. a.
-N= (ring) 0.0085 0.0076 34 57.55 68.40 55.52 79.93 8.83 −3.84E-3 4.35E−5 −2.60E−8 3.649 6.528 n. a. n. a.
=NH n. a. n. a. n. a. 83.08 68.91 93.70 119.66 5.69 −4.12E−3 1.28E−4 −8.88E−8 n. a. 12.169 n. a. n. a.
-CN 0.0496 −0.0101 91 125.66 59.89 88.43 89.22 3.65E+1 −7.33E−2 1.84E−4 −1.03E−7 2.414 12.851 n. a. n. a.
-NO2 0.0437 0.0064 91 152.54 127.24 −66.57 −16.83 2.59E+1 −3.74E−3 1.29E−4 −8.88E−8 9.679 16.738 n. a. n. a.
Sulfur groups
-SH 0.0031 0.0084 63 63.56 20.09 −17.33 −22.99 3.53E+1 −7.58E−2 1.85E−4 −1.03E−7 2.360 6.884 n. a. n. a.
-S- (nonring) 0.0119 0.0049 54 68.78 34.40 41.87 33.12 1.96E+1 −5.61E−3 4.02E−5 −2.76E−8 4.130 6.817 n. a. n. a.
-S- (ring) 0.0019 0.0051 38 52.10 79.93 39.10 27.76 1.67E+1 4.81E−3 2.77E−5 −2.11E−8 1.557 5.984 n. a. n. a.

Example Calculation

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

 -CH3 >C=O (nonring) Property No. of groups Group value No. of groups Group value ${\displaystyle \sum G_{i}}$ Estimated Value Unit Tc 2 0.0141 1 0.0380 0.0662 500.5590 K Pc 2 −1.20E−03 1 3.10E−03 7.00E−04 48.0250 bar Vc 2 65.0000 1 62.0000 192.0000 209.5000 cm3/mol Tb 2 23.5800 1 76.7500 123.9100 322.1100 K Tm 2 −5.1000 1 61.2000 51.0000 173.5000 K Hformation 2 −76.4500 1 −133.2200 −286.1200 −217.8300 kJ/mol Gformation 2 −43.9600 1 −120.5000 −208.4200 −154.5400 kJ/mol Cpa 2 1.95E+01 1 6.45E+00 4.55E+01 Cpb 2 −8.08E−03 1 6.70E−02 5.08E−02 Cpc 2 1.53E−04 1 −3.57E−05 2.70E−04 Cpd 2 −9.67E−08 1 2.86E−09 −1.91E−07 Cp at T=300 K 75.3264 J/(mol*K) Hfusion 2 0.9080 1 4.1890 6.0050 5.1250 kJ/mol Hvap 2 2.3730 1 8.9720 13.7180 29.018 kJ/mol ηa 2 548.2900 1 340.3500 1436.9300 ηb 2 −1.7190 1 −0.3500 −3.7880 η at T=300 K 0.0002942 Pa s

References

1. ^ Joback K.G., Reid R.C., "Estimation of Pure-Component Properties from Group-Contributions", Chem. Eng. Commun., 57, 233–243, 1987
2. ^ Lydersen A.L., "Estimation of Critical Properties of Organic Compounds", University of Wisconsin College Engineering, Eng. Exp. Stn. Rep. 3, Madison, Wisconsin, 1955
3. ^ Constantinou L., Gani R., "New Group Contribution Method for Estimating Properties of Pure Compounds", AIChE J., 40(10), 1697–1710, 1994
4. ^ 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
5. ^ Stein S.E., Brown R.L., "Estimation of Normal Boiling Points from Group Contributions", J. Chem. Inf. Comput. Sci. 34, 581–587 (1994)