The UNIFAC activity coefficient estimation method [36] assumes that the activity of a species can be determined based on interaction parameters of functional groups in a molecule. The activity coefficient of a species is split into two parts, the combinatorial and the residual:
 | (3–1) |
The combinatorial activity coefficient is expressed as:
 | (3–2) |
using the following definitions for each molecule 
:
 | (3–3) |
Area fraction:
 | (3–4) |
Segment fraction:
 | (3–5) |
 | (3–6) |
Van der Waals volume:
 | (3–7) |
Molecular Surface area:
 | (3–8) |
Here 
is number of occurrences of each group 
in the molecule 
and 
is the mole
fraction of the molecule. The R and Q values have been tabulated for each group.
The residual activity coefficient considers interactions between groups, and is defined as follows:
 | (3–9) |
Group residual activity coefficient:
 | (3–10) |
Area fraction of a group:
 | (3–11) |
Here, 
is the mole fraction of a group 
in the mixture, 
is the group residual
activity coefficient, and 
is the group residual in a reference solution containing
only molecules of type 
. The group interaction parameter is given by:
 | (3–12) |
The group energy interaction activity parameters (
) have been tabulated.
The groups in the formulation of the UNIFAC correlation are shown in Table 3.1: The 50 main and 108 secondary groups used in the UNIFAC activity coefficient estimation . This method has been validated for many molecular species, but it does not cover every kind of molecule. An example of a molecule that cannot be generated from this set of groups is allene.
Table 3.1: The 50 main and 108 secondary groups used in the UNIFAC activity coefficient estimation
|
Main |
Secondary |
Name |
Notes |
|---|---|---|---|
|
1 |
1 |
-CH3 |
methyl group |
|
1 |
2 |
-CH2- |
carbon attached to two hydrogen in a chain |
|
1 |
3 |
>CH- |
branching carbon, attached to a single hydrogen |
|
1 |
4 |
>C< |
branching carbon with no hydrogen bonds |
|
2 |
5 |
CH2=CH- |
ethylene group |
|
2 |
6 |
-CH=CH- |
double bonded carbon in a chain |
|
2 |
7 |
CH2=C< |
carbon along chain that is bonded to a =CH2 |
|
2 |
8 |
-CH=C< |
branching group of double bonded carbons, one hydrogen |
|
2 |
70 |
>C=C< |
branching group of double bonded carbons, no hydrogen |
|
3 |
9 |
Aromatic CH |
aromatic carbon with hydrogen attached |
|
3 |
10 |
Aromatic C |
general aromatic carbon |
|
4 |
11 |
Aromatic C-CH3 |
methyl group attached to aromatic carbon |
|
4 |
12 |
Aromatic C-CH2- |
CH2 chain carbon attached to aromatic carbon |
|
4 |
13 |
Aromatic C-CH< |
branching carbon attached to |
|
5 |
14 |
-OH |
alcohol group |
|
6 |
15 |
"CH3OH" |
methanol |
|
7 |
16 |
"H2O" |
water |
|
8 |
17 |
Aromatic C-OH |
aromatic carbon attached to hydroxyl |
|
9 |
18 |
-C(=O)CH3 |
alodine group |
|
9 |
19 |
-C(=O)CH2- |
alodine monomer |
|
10 |
20 |
-CHO |
aldehyde group |
|
11 |
21 |
CH3C(=O)O- |
methyl ester group |
|
11 |
22 |
-CH2C(=O)O- |
methyl ester monomer |
|
12 |
23 |
HC(=O)O- |
formate group |
|
13 |
24 |
CH3O- |
methyl ether group |
|
13 |
25 |
-CH2O- |
methyl ether monomer |
|
13 |
26 |
>CHO- |
branching methyl ether group |
|
13 |
27 |
-CH2O- (THF) |
tetrahydrofuran group, CH2O in the ring. |
|
14 |
28 |
"CH3NH2" |
methylamine |
|
14 |
29 |
-CH2NH2 |
methylamine group C side |
|
14 |
30 |
>CHNH2 |
branching methylamine group C side |
|
15 |
31 |
CH3NH- |
methylamine group N side |
|
15 |
32 |
-CH2NH- |
methylamine monomer |
|
15 |
33 |
>CHNH- |
branching methylamine monomer C side |
|
16 |
34 |
CH3N< |
methylamine monomer N side |
|
16 |
35 |
-CH2N< |
branching methylamine monomer N side |
|
17 |
36 |
Aromatic C-NH2 |
amine attached to aromatic carbon |
|
18 |
37 |
"C5H5N" |
pyridine |
|
18 |
38 |
C5H4N |
pyridine group |
|
18 |
39 |
C5H3N |
pyridine monomer |
|
19 |
40 |
"CH3CN" |
acetonitrile |
|
19 |
41 |
-CH2CN |
acetonitrile group |
|
20 |
42 |
-C(=O)OH |
carboxylic acid group |
|
20 |
43 |
"HC(=O)OH" |
carboxylic acid |
|
21 |
44 |
-CH2Cl |
chloromethyl group |
|
21 |
45 |
>CHCl |
chloromethyl monomer |
|
21 |
46 |
>C(Cl)- |
branching choloromethyl monomer |
|
22 |
47 |
"CH2Cl2" |
dichloromethane |
|
22 |
48 |
-CHCl2 |
dichloromethyl group |
|
22 |
49 |
>CCl2 |
dichloromethyl monomer |
|
23 |
50 |
"CHCl3" |
trichloromethane |
|
23 |
51 |
-CCl3 |
trichloromethyl group |
|
24 |
52 |
"CCl4" |
carbon tetrachloride |
|
25 |
53 |
Aromatic C-Cl |
chlorine attached to aromatic carbon |
|
26 |
54 |
"CH3NO2" |
methyl nitrite |
|
26 |
55 |
-CH2NO2 |
methyl nitrite group |
|
26 |
56 |
>CHNO2 |
methyl nitrite monomer |
|
27 |
57 |
Aromatic C-NO2 |
nitrate attached to aromatic carbon |
|
28 |
58 |
"CS2" |
carbon disulfide |
|
29 |
59 |
"CH3SH" |
methanethiol |
|
29 |
60 |
-CH2SH |
methylthiol group |
|
30 |
61 |
"O=CC1=CC=CO1" |
furfural |
|
31 |
62 |
"OCCO" |
ethylene glycol |
|
32 |
63 |
I |
iodine |
|
33 |
64 |
Br |
bromine |
|
34 |
65 |
HC#C- |
acetyl group |
|
34 |
66 |
-C#C- |
acetyl monomer |
|
35 |
67 |
"CH3S(=O)CH3" |
dimethyl sulfoxide |
|
36 |
68 |
"N#CC=C" |
acrylonitrile |
|
37 |
69 |
Cl-(C=C) |
chlorine, only when bonded to double bonded carbon |
|
38 |
71 |
Aromatic C-F |
Fluorine attached to aromatic carbon |
|
39 |
72 |
"CN(C)C=O" |
dimethyl formamide |
|
39 |
73 |
HC(=O)N(CH2-)(CH2-) |
DMF monomer |
|
40 |
74 |
-CF3 |
trifluoro carbon group |
|
40 |
75 |
>CF2 |
difluorocarbon monomer |
|
40 |
76 |
>CF- |
branching fluorocarbon monomer |
|
41 |
77 |
-C(=O)O- |
ester monomer |
|
42 |
78 |
-SiH3 |
silane group |
|
42 |
79 |
>SiH2 |
silane monomer |
|
42 |
80 |
>SiH- |
branching silane monomer |
|
42 |
81 |
>Si< |
double branching silane monomer |
|
43 |
82 |
"Si=O" |
silica type aldehyde |
|
43 |
83 |
-Si(=O)H |
silica aldehyde group |
|
43 |
84 |
>Si=O |
silica ketone monomer |
|
44 |
85 |
"CN1CCCC1=O" |
methyl pyrrolidone |
|
45 |
86 |
"CCl3F" |
trichlorofluorocarbon |
|
45 |
87 |
-CCl2F |
dichlorofluorocarbon group |
|
45 |
88 |
"C(Cl)(Cl)F" |
dichlorofluorocarbon |
|
45 |
89 |
-CHClF |
chlorofluorocarbon group |
|
45 |
90 |
-CClF2 |
chloro-difluorocarbon group |
|
45 |
91 |
"C(Cl)(F)F" |
chloro-difluorocarbon |
|
45 |
92 |
"CClF3" |
chloro-trifluorocarbon |
|
45 |
93 |
"C(Cl)(Cl)(F)F" |
dichloro-difluorocarbon |
|
46 |
94 |
-C(=O)NH2 |
amide (H,H) group |
|
46 |
95 |
-C(=O)N(CH3)H |
amide (methyl,H) group |
|
46 |
96 |
-C(=O)N(H)CH2- |
amide (h, methyl) monomer |
|
46 |
97 |
-C(=O)N(CH3)CH3 |
amide (methyl,methyl) group |
|
46 |
98 |
-C(=O)N(CH3)CH2- |
amide (methyl methyl) monomer |
|
46 |
99 |
-C(=O)N(CH2-)CH2- |
branching amide (methyl methyl) monomer |
|
47 |
100 |
-OCH2CH2OH |
enthanol ether group |
|
47 |
101 |
-OC(-)HCH2OH |
methanol methyl ether monomer |
|
48 |
102 |
-SCH3 |
thiomethyl group |
|
48 |
103 |
-SCH2- |
thiomethyl monomer |
|
48 |
104 |
-SCH< |
branching thiomethyl monomer |
|
49 |
105 |
"O1CCNCC1" |
mopholine |
|
50 |
106 |
"s1cccc1" |
thiophene |
|
50 |
107 |
s1c(-)ccc1 |
thiophene group |
|
50 |
108 |
s1c(-)c(-)cc1 |
thiophene monomer |