Supporting Information
Convex Solubility Parameters for Polymers
Jason S. Howell,2 Benjamin O. Stephens,1 David S. Boucher1
1
Department of Chemistry and Biochemistry, 2Department of Mathematics, School of Sciences and
Mathematics, College of Charleston, Charleston, SC 29401 USA
Description of Methods for Computing the Convex Solubility Parameters
Here points in ℝ3 are represented with triples (𝑥, 𝑦, 𝑧).

Method 1: computing the center of mass of the solubility region, treating the surface of the region
with uniform density as an empty shell. This is accomplished by treating each facet (triangle) on
the boundary of the convex hull as a point mass located at the barycenter of the triangle with
mass equal to the area of the triangle. Let 𝑓𝑖 , 𝑖 = 1, … , 𝑡 be an enumeration of boundary facets
of the convex hull. For facet 𝑓𝑘 , let 𝑃𝑘,1 = (𝑥𝑘,1 , 𝑦𝑘,1 , 𝑧𝑘,1 ), 𝑃𝑘,2 = (𝑥𝑘,2 , 𝑦𝑘,2 , 𝑧𝑘,2 ), and 𝑃𝑘,3 =
𝑃𝑘,1 𝑃𝑘,2 and 𝒗𝑘,2 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗
𝑃𝑘,1 𝑃𝑘,3 be the
(𝑥𝑘,3 , 𝑦𝑘,3 , 𝑧𝑘,3 ) be the vertices of the facet and let 𝒗𝑘,1 = ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗
two vectors formed by two edges of the facet. Then the coordinates of the center of mass
(𝑥 ∗ , 𝑦 ∗ , 𝑧 ∗ ) are computed as
1 𝑡
1 𝑡
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖(𝑥1 + 𝑥2 + 𝑥3 )
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖(𝑦1 + 𝑦2 + 𝑦3 )
6
𝑥∗ =
, 𝑦∗ = 6
,
1 𝑡
1 𝑡
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖
2
2
1 𝑡
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖(𝑧1 + 𝑧2 + 𝑧3 )
𝑧∗ = 6
,
1 𝑡
∑𝑘=1‖𝒗𝑘,1 × 𝒗𝑘,2 ‖
2
where ‖𝒗𝑘,1 × 𝒗𝑘,2 ‖ is the magnitude of the cross product of the two vectors.

Method 2: computing the center of mass of the solubility region, treating the region as a solid
with uniform density. Let 𝑅 be the region occupied by the hull in ℝ3 . Then the coordinates of
the center of mass (𝑥 ∗ , 𝑦 ∗ , 𝑧 ∗ ) are computed as
1
1
1
𝑥 ∗ = ∭ 𝑥 𝑑𝑥 𝑑𝑦 𝑑𝑧, 𝑦 ∗ = ∭ 𝑦 𝑑𝑥 𝑑𝑦 𝑑𝑧, 𝑧 ∗ = ∭ 𝑦 𝑑𝑥 𝑑𝑦 𝑑𝑧,
𝑉
𝑉
𝑉
𝑅
𝑅
𝑅
where
𝑉 = ∭ 1 𝑑𝑥 𝑑𝑦 𝑑𝑧,
𝑅
is the volume of 𝑅. The integrals over the convex hull are accomplished by dimensional reduction
using repeated applications of results from vector calculus. First, let 𝑓𝑖 , 𝑖 = 1, … , 𝑡 be an
enumeration of boundary facets of the convex hull 𝑄. Then the Divergence Theorem guarantees
that the integral of the divergence of a function over a volume V can be written as a surface
integral over the boundary 𝜕𝑉 of 𝑉:
∭ ∇ ∙ 𝑔 𝑑𝑉 = ∬ 𝑔 ∙ 𝑛⃗ 𝑑𝐴,
𝑉
𝜕𝑉
where 𝑛⃗ is the outer unit normal vector to the surface 𝜕𝑉. For a convex hull in ℝ3 , the boundary
consists of the union of all of the planar facets of the boundary. Thus computation of the volume
of the convex hull can be written as the sum of surface integrals over the facets:
𝑡
𝑡
∭ 1 𝑑𝑉 = ∑ (∬ ⟨𝑥, 0,0⟩ ⋅ 𝑛⃗𝑖 𝑑𝐴) = ∑ (𝑛⃗𝑖,𝑥 ∬ 𝑥 𝑑𝐴).
𝑄
𝑓𝑖
𝑖=1
𝑓𝑖
𝑖=1
Here 𝑛⃗𝑖,𝑥 represents the 𝑥-component of the outer unit normal of the facet 𝑓𝑖 . As each facet 𝑓𝑖 is
planar, the normal vector is constant along the face and can be pulled out in front of each
boundary integral. Then, the surface integral over each planar facet 𝑓𝑖 is converted to an integral
over the projection Π𝑖 of that facet in the 𝑥𝑦-coordinate plane. For example, suppose the vector
𝑛⃗𝑖 = ⟨𝛼, 𝛽, 𝛾⟩ is the normal vector of the plane containing facet 𝑓𝑖 , and that 𝛾 ≠ 0 so 𝑓𝑖 ≠ Π𝑖 . If
𝛼𝑥 + 𝛽𝑦 + 𝛾𝑧 + 𝜅 = 0 is an equation of the plane containing 𝑓𝑖 , then,1
∬ 𝑥 𝑑𝐴 =
𝑓𝑖
1
∬ 𝑥 𝑑𝑥 𝑑𝑦,
|𝛾| Π𝑖
(see Theorem 2 of Mirtich, ref. 1). Then Green’s Theorem (the two-dimensional analogue of the
Divergence Theorem) can be applied to convert the integral over a region in the 𝑥𝑦-coordinate
plane (in this case a triangle) to a line integral along the boundary (the triangle edges). Let
𝑒𝑖,1 , 𝑒𝑖,2 , 𝑒𝑖,3 be the boundary edges of triangle Π𝑖 , then we have
3
1
1
∬ 𝑥 𝑑𝑥 𝑑𝑦 = ∮ ⟨ 𝑥 2 , 0⟩ ⋅ 𝑚
⃗⃗ 𝑖 𝑑𝑠 = ∑ 𝑚
⃗⃗ 𝑖,𝑗 ∫ 𝑥 2 𝑑𝑠,
2
Π𝑖
∂Π𝑖 2
𝑒𝑖,𝑗
𝑗=1
where 𝑚
⃗⃗ 𝑖,𝑗 is the outer normal (in the 𝑥𝑦-plane) of edge 𝑒𝑖,𝑗 . Since each edge is a single line
segment in the 𝑥𝑦-plane, the line integrals along each edge can be computed by evaluation of a
Bernstein polynomial at the endpoints of the edge (see Theorem 4 of Mirtich, ref. 1).

Method 3: computing the mean coordinates of all points that lie on the boundary of the solubility
region. Let 𝑃𝑘 = (𝑥𝑘 , 𝑦𝑘 , 𝑧𝑘 ), 𝑘 = 1, … , 𝑚 be an enumeration of the vertices on the boundary of
the convex hull. Then the coordinates of the center of mass are computed as
𝑚
𝑚
𝑚
1
1
1
∗
∗
∗
𝑥 = ∑ 𝑥𝑘 , 𝑦 = ∑ 𝑦𝑘 , 𝑧 = ∑ 𝑧𝑘 .
𝑚
𝑚
𝑚
𝑘=1

𝑘=1
Method 4: computing the mean coordinates of all points on the boundary and within the solubility
region. Let 𝑃𝑘 = (𝑥𝑘 , 𝑦𝑘 , 𝑧𝑘 ), 𝑘 = 1, … , 𝑛 be an enumeration of the vertices on the boundary of
the convex hull and the points inside the hull that represent observed good solvents. Then the
coordinates of the center of mass are computed as
𝑛
𝑛
𝑛
1
1
1
∗
∗
∗
𝑥 = ∑ 𝑥𝑘 , 𝑦 = ∑ 𝑦𝑘 , 𝑧 = ∑ 𝑧𝑘 .
𝑛
𝑛
𝑛
𝑘=1

𝑘=1
𝑘=1
𝑘=1
Method 5: computing the center of the largest sphere completely contained within the solubility
region (known as the Chebyshev center of a convex polyhedron). This is accomplished through
solving a linear programming problem (using the simplex method). First, each facet on the
boundary is converted to a linear inequality of the form
𝑎𝑖1 𝑥1 + 𝑎𝑖2 𝑥2 + 𝑎𝑖3 𝑥3 ≤ 𝑏𝑖 , 𝑖 = 1, … , 𝑡.
Let 𝒂𝑖 = [𝑎𝑖1 , 𝑎𝑖2 , 𝑎𝑖3 ]𝑇 and 𝒙𝑖 = [𝑥1 , 𝑥2 , 𝑥3 ]𝑇 so that inequality 𝑖 is represented by 𝒂𝑇𝑖 𝒙𝑖 ≤ 𝑏𝑖 .
The radius 𝑟 and center 𝒙𝑐 of the largest ball completely contained in the set defined by all
inequalities 1, … , 𝑡 is given by the solution of the linear program,
maximize 𝑟
subject to 𝒂𝑇𝑖 𝒙𝑐 + 𝑟‖𝒂𝑖 ‖ ≤ 𝑏𝑖 ,
𝑖 = 1, … , 𝑡.

Method 6: computing the midpoint of the parameter range of each of the coordinates.2 This is
accomplished via the calculation
1
(𝑥 ∗ , 𝑦 ∗ , 𝑧 ∗ ) = (𝑥𝑚𝑎𝑥 − 𝑥𝑚𝑖𝑛 , 𝑦𝑚𝑎𝑥 − 𝑦𝑚𝑖𝑛 , 𝑧𝑚𝑎𝑥 − 𝑧𝑚𝑖𝑛 ).
2
TABLE S1 Solvent Parameters Used for the Calculations of Polyether Sulfone
δD
δH
δP
Solubility
RED1a
1,4-Dioxane
19.0
1.8
7.4
0
1.741
1-Butanol
16.0
5.7
15.8
0
2.056
2-Nitropropane
16.2
12.1
4.1
0
1.215
Acetone
15.5
10.4
7.0
0
1.252
Acetophenone
19.6
8.6
3.7
1
0.962
Benzene
18.4
0.0
2.0
0
2.347
Butyl_acetate
15.8
3.7
6.3
0
1.808
Carbon_tetrachloride
17.8
0.0
0.6
0
2.502
Chlorobenzene
19.0
4.3
2.0
0
1.684
Chloroform
17.8
3.1
5.7
0
1.6
Cyclohexanol
17.4
4.1
13.5
0
1.747
Diacetone_alcohol
15.8
8.2
10.8
0
1.357
Diethyl_ether
14.5
2.9
5.1
0
2.278
Diethylene_glycol
16.6
12
20.7
0
2.496
Dimethyl_formamide
17.4
13.7
11.3
1
0.934
Dimethyl_sulfoxide
18.4
16.4
10.2
0*
1.054
Ethanol
15.8
8.8
19.4
0
2.431
Ethanol_amine
17.0
15.5
21.2
0
2.655
Ethyl_acetate
15.8
5.3
7.2
0
1.57
Ethylene_dichloride
19.0
7.4
4.1
0
1.002
Ethylene_glycol_monobutyl_ether
16.0
5.1
12.3
0
1.736
Ethylene_glycol_monoethyl_ether
16.2
9.2
14.3
0
1.567
Ethylene_glycol_monomethyl_ether 16.2
9.2
16.4
0
1.874
g-Butyrolactone
19.0
16.6
7.4
1
0.999
Isophorone
16.6
8.2
7.4
0
1.001
Methyl_ethyl_ketone
16.0
9.0
5.1
0
1.24
Methyl_isobutyl_ketone
15.3
6.1
4.1
0
1.76
Methyl-2-pyrrolidone
18.0
12.3
7.2
1
0.393
Methylene_dichloride
18.2
6.3
6.1
1
0.997
Nitroethane
16.0
15.5
4.5
0
1.457
Nitromethane
15.8
18.8
5.1
0
1.866
o-Dichlorobenzene
19.2
6.3
3.3
0
1.255
Propylene_carbonate
20.0
18
4.1
0
1.5
Propylene_glycol
16.8
9.4
23.3
0
2.947
Tetrahydrofuran
16.8
5.7
8.0
0
1.265
Toluene
18.0
1.4
2.0
0
2.139
Trichloroethylene
18.0
3.1
5.3
0
1.605
1,4-Dioxane
19.0
1.8
7.4
0
1.741
1-Butanol
16.0
5.7
15.8
0
2.056
2-Nitropropane
16.2
12.1
4.1
0
1.215
Acetone
15.5
10.4
7.0
0
1.252
*Denotes an outlier. aRED from Ref. 3, bRED from Ref. 4, cRED from Ref. 5.
Solvent
RED2b
1.392
1.698
1.433
1.42
0.936
2.007
1.713
2.181
1.505
1.433
1.389
1.34
2.131
1.967
0.958
1
1.962
2.091
1.545
1
1.525
1.372
1.556
1
1.147
1.409
1.776
0.758
1
1.606
1.886
1.165
1.367
2.274
1.246
1.883
1.431
1.392
1.698
1.433
1.42
RED3c
1.493
1.777
1.387
1.371
0.955
2.129
1.741
2.301
1.576
1.483
1.467
1.321
2.183
2.101
0.915
0.996
2.077
2.241
1.547
1.007
1.563
1.395
1.618
0.998
1.094
1.368
1.782
0.655
0.99
1.58
1.899
1.204
1.429
2.457
1.237
1.978
1.485
1.493
1.777
1.387
1.371
TABLE S2 Solvent Parameters Used for the Calculations of Bitumen 1
Solvent
δD
δP
δH
Solubility
1,1,2-Trichloroethane
18.2
5.3
6.8
1,1-Diethoxy ethanol (acetal)
15.2
5.4
5.3
1,2,3,5-Tetramethylbenzene
18.6
0.5
0.5
1,2,4-Trimethylbenzene
18.0
1.0
1.0
1,2-Dimethoxybenzene
19.2
4.4
9.4
1,4-Dichlorobutane
18.3
7.7
2.8
1-Chloropentane
16.0
6.9
1.9
1-Methyl naphthalene
20.6
0.8
4.7
2,2,4-Trimethylpentane
14.1
0.0
0.0
2-Butanol
15.8
5.7
14.5
2-Butyl octanol
16.1
3.6
9.3
2-Ethyl-hexanol
15.9
3.3
11.8
2-Toluidine
19.4
5.8
9.4
3-Methyl-2-butanol
15.6
5.2
13.4
Butyraldehyde
15.6
10.1
6.2
Caprolactone (epsilon)
19.7
15.0
7.4
Chloroform
17.8
3.1
5.7
cis-Decahydronaphthalene
18.8
0.0
0.0
Cyclohexanol
17.4
4.1
13.5
Cyclohexanone
17.8
6.3
5.1
Cyclohexylamine
17.2
3.1
6.5
Cyclopentanone
17.9
11.9
5.2
Dichloromethyl methyl ether
17.1
12.9
6.5
Diethylene glycol monoethyl ether acetate
16.2
5.1
9.2
Diisopropylamine
14.8
1.7
3.5
Ethyl acetate
15.8
5.3
7.2
Ethyl benzene
17.8
0.6
1.4
Ethyl lactate
16.0
7.6
12.5
Ethylene glycol dibutyl ether
15.7
4.5
4.2
Hexadecane
16.3
0.0
0.0
Hexyl acetate
15.8
2.9
5.9
Isopropyl acetate
14.9
4.5
8.2
Lauryl alcohol
17.2
3.8
9.3
Mesityl oxide
16.4
6.1
6.1
Methyl acetate
15.5
7.2
7.6
Methyl benzoate
17.0
8.2
4.7
Methyl ethyl ketone
16.0
9.0
5.1
Methyl oleate
14.5
3.9
3.7
Methylene dichloride
18.2
6.3
6.1
Nitrobenzene
20.0
8.6
4.1
Oleyl alcohol
14.3
2.6
8.0
o-Xylene
17.8
1.0
3.1
Pyrrolidine
17.9
6.5
7.4
Salicylaldehyde
19.4
10.7
14.7
Tetrahydrofuran
16.8
5.7
8.0
Tetrahydronaphthalene
19.6
2.0
2.9
Toluene
18.0
1.4
2.0
Tricresyl phosphate
19.0
12.3
4.5
*Denotes an outlier. aRED from Ref. 3, bRED from Ref. 6.
1
0
1
1
0
1
1*
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0*
0
0
0
0
0*
0
1
0
0
1
1
0
1
1
0
1*
1
1
0
RED1a
RED2b
0.595
1.214
0.873
0.79
1.02
0.515
1
0.955
1.828
2.101
1.327
1.706
1.046
1.969
1.442
1.87
0.56
0.99
1.749
0.479
0.77
1.257
1.549
1.278
1.402
1.159
0.836
1.831
1.009
1.271
1.099
1.501
1.116
0.914
1.339
0.831
1.177
1.412
0.54
0.786
1.699
0.704
0.772
2.15
1.005
0.569
0.659
1.278
0.620
1.177
0.794
0.681
1.059
0.678
1.022
0.959
1.746
2.128
1.276
1.676
1.127
1.979
1.522
2.096
0.445
0.925
1.762
0.54
0.67
1.434
2.08
1.258
1.301
1.126
0.71
1.877
0.945
1.165
1
1.459
1.08
0.906
1.353
0.914
1.245
1.349
0.615
1
1.63
0.544
0.827
2.299
1
0.546
0.524
1.489
TABLE S3 Solvent Parameters Used for the Calculations of Bitumen 2
Solvent
δD
δP
δH
Solubility
1,1,2-Trichloroethane
18.2
5.3
6.8
1
1,1-Diethoxy ethanol (acetal)
15.2
5.4
5.3
0
1,2,3,5-Tetramethylbenzene
18.6
0.5
0.5
1
1,2,4-Trimethylbenzene
18.0
1.0
1.0
1
1,2-Dimethoxybenzene
19.2
4.4
9.4
0
1,4-Dichlorobutane
18.3
7.7
2.8
1
1-Chloro pentane
16.0
6.9
1.9
1*
1-Methyl naphthalene
20.6
0.8
4.7
1
2,2,4-Trimethylpentane
14.1
0
0.0
0
2-Butanol
15.8
5.7
14.5
0
2-Butyl octanol
16.1
3.6
9.3
0
2-Ethyl-hexanol
15.9
3.3
11.8
0
2-Toluidine
19.4
5.8
9.4
0
3-Methyl-2-butanol
15.6
5.2
13.4
0
Benzophenone
19.6
8.6
5.7
1*
Butyraldehyde
15.6
10.1
6.2
0
Caprolactone (epsilon)
19.7
15.0
7.4
0
Chloroform
17.8
3.1
5.7
1
cis-Decahydronaphthalene
18.8
0.0
0.0
1
Cyclohexanol
17.4
4.1
13.5
0
Cyclohexanone
17.8
6.3
5.1
1
Cyclohexylamine
17.2
3.1
6.5
1
Cyclopentanone
17.9
11.9
5.2
0
Diisopropylamine
14.8
1.7
3.5
0
Ethyl acetate
15.8
5.3
7.2
0
Ethyl benzene
17.8
0.6
1.4
1
Ethyl lactate
16.0
7.6
12.5
0
Ethylene glycol dibutyl ether
15.7
4.5
4.2
0*
Ethylene glycol monoethyl ether acetate
16.2
5.1
9.2
0
Hexadecane
16.3
0.0
0.0
0
Hexyl acetate
15.8
2.9
5.9
1
Isopropyl acetate
14.9
4.5
8.2
0
Laurylalcohol
17.2
3.8
9.3
0
Mesityl oxide
16.4
6.1
6.1
0*
Methyl acetate
15.5
7.2
7.6
0
Methyl benzoate
17.0
8.2
4.7
1
Methyl ethyl ketone
16.0
9.0
5.1
0
Methyl oleate
14.5
3.9
3.7
0
Methylene dichloride
18.2
6.3
6.1
1
Nitrobenzene
20.0
8.6
4.1
0
Oleyl alcohol
14.3
2.6
8.0
0
o-Xylene
17.8
1.0
3.1
1
Pyrrolidine
17.9
6.5
7.4
1
Salicylaldehyde
19.4
10.7
14.7
0
Tetrahydrofuran
16.8
5.7
8.0
1*
Tetrahydronaphthalene
19.6
2.0
2.9
1
Toluene
18.0
1.4
2.0
1
Tricresyl phosphate
19.0
12.3
4.5
0
*Denotes an outlier. aRED from Ref. 3, bRED from Ref. 5.
RED1a
RED2b
0.625
1.168
0.81
0.691
1.081
0.661
1.002
0.995
1.748
2.143
1.285
1.69
1.146
1.993
1
1.511
2.102
0.457
0.943
1.783
0.527
0.677
1.425
1.3
1.123
0.722
1.886
0.934
1.263
1.169
1
1.46
1.092
0.896
1.348
0.898
1.231
1.342
0.612
1.003
1.636
0.56
0.828
2.319
1
0.574
0.536
1.485
0.664
1.184
0.608
0.531
0.996
0.758
1.059
0.753
1.6
2.019
1.231
1.586
1.081
1.884
1.012
1.541
2.038
0.445
0.723
1.657
0.642
0.663
1.458
1.224
1.135
0.557
1.817
0.959
1.241
1.025
0.974
1.42
1.044
0.956
1.363
0.991
1.289
1.31
0.689
1
1.549
0.409
0.872
2.185
1.021
0.364
0.388
1.492
TABLE S4 Solvent Parameters Used for the Calculations of Lignin
Solvent
1,1,1-Trichloroethane
1,3-Butanediol
1,4-Dioxane
1-Bromonaphthalene
1-Butanol
1-Chlorobutane
1-Pentanol
1-Propanol
2,2-Dichlorodiethyl ether
2-Ethyl-1-butanol
2-Nitropropane
Acetic acid
Acetic anhydride
Acetone
Acetonitrile
Acetophenone
Aniline
Benzaldehyde
Benzene
Butyl acetate
Butyl lactate
Butyric acid
Butyronitrile
Carbon disulfide
Carbon tetrachloride
Chlorobenzene
Chloroform
Cyclohexane
Cyclohexanol
Cyclohexanone
Cyclohexylchloride
Di(isobutyl) ketone
Diacetone alcohol
Diethyl ether
Diethyl sulfide
Diethylamine
Diethylene glycol
Diethylene glycol monobutyl ether
Diethylene glycol monomethyl ether
Dimethyl
eterethersulfoxide
Dimethylformamide
Dipropylamine
Dipropylene glycol
Ethanol
Ethanolamine
Ethyl acetate
Ethylbenzene
Ethylene glycol
Ethylene glycol monobutyl ether
Ethylene glycol monoethyl ether
δD
δP
δH
16.8
16.6
19.0
20.3
16.0
16.2
15.9
16.0
18.8
15.8
16.2
14.5
16.0
15.5
15.3
19.6
19.4
19.4
18.4
15.8
15.8
14.9
15.3
20.5
17.8
19.0
17.8
16.8
17.4
17.8
17.3
16.0
15.8
14.5
16.8
14.9
16.6
16.0
16.2
18.4
17.4
15.3
16.5
15.8
17.0
15.8
17.8
17.0
16.0
16.2
4.3
10
1.8
3.1
5.7
5.5
4.5
6.8
9.0
4.3
12.1
8.0
11.7
10.4
18.0
8.6
5.1
7.4
0.0
3.7
6.5
4.1
12.4
0.0
0.0
4.3
3.1
0.0
4.1
6.3
5.5
3.7
8.2
2.9
3.1
2.3
12.0
7.0
7.8
16.4
13.7
1.4
10.6
8.8
15.5
5.3
0.6
11.0
5.1
9.2
2.0
21.5
7.4
4.1
15.8
2.0
13.9
17.4
5.7
13.5
4.1
13.5
10.2
7.0
6.1
3.7
10.2
5.3
2.0
6.3
10.2
10.6
5.1
0.6
0.6
2.0
5.7
0.2
13.5
5.1
2.0
4.1
10.8
5.1
2.0
6.1
20.7
10.6
12.6
10.2
11.3
4.1
17.7
19.4
21.2
7.2
1.4
26.0
12.3
14.3
Solubility
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1*
1
1
0
1
1
1
0
0
1*
0
1
RED1a
RED2b
1.518
0.888
1.229
1.278
1.061
1.523
1.147
1.012
1.016
1.173
1.267
1.194
1.003
1.215
1.28
1.113
0.908
1.058
1.608
1.416
1.161
1.345
1.304
1.618
1.71
1.391
1.309
1.787
1.019
1.206
1.442
1.496
1.085
1.621
1.563
1.567
0.826
1.108
1
0.721
0.766
1.65
0.821
0.983
0.775
1.316
1.64
1.001
1.138
0.92
1.5
0.895
1.211
1.254
1.06
1.506
1.143
1.013
1.006
1.169
1.26
1.195
1.006
1.212
1.277
1.096
0.897
1.044
1.582
1.403
1.158
1.337
1.298
1.586
1.683
1.369
1.293
1.761
1.013
1.193
1.424
1.48
1.085
1.605
1.543
1.552
0.836
1.105
1.001
0.727
0.774
1.631
0.831
0.988
0.788
1.306
1.615
1.002
1.134
0.925
TABLE S4 Solvent Parameters Used for the Calculations of Lignin (cont.)
Solvent
δD
δP
δH
Solubility
Ethylene glycol monomethyl ether
16.2
9.2
16.4
1
Furan
17.8
1.8
5.3
0
gamma-Butyrolactone
19.0
16.6
7.4
1
Glycerol
17.4
12.1
29.3
0
Hexane
14.9
0.0
0.0
0
Isoamyl acetate
15.3
3.1
7.0
0
Isobutyl isobutyrate
15.1
2.9
5.9
0
Isooctyl alcohol
14.4
7.3
12.9
0
Isophorone
16.6
8.2
7.4
0
m-Cresol
18.0
5.1
12.9
1
Mesityl oxide
16.4
6.1
6.1
0
Methanol
15.1
12.3
22.3
0
Methyl ethyl ketone
16.0
9.0
5.1
0
Methyl isoamyl ketone
16.0
5.7
4.1
0
Methyl isobutyl carbinol
15.4
3.3
12.3
0
Methyl isobutyl ketone
15.3
6.1
4.1
0
Methylal
15.0
1.8
8.6
0
Morpholine
18.8
4.9
9.2
1
Nitrobenzene
20.0
8.6
4.1
0
Nitroethane
16.0
15.5
4.5
0
Nitromethane
15.8
18.8
5.1
0
o-Dichlorobenzene
19.2
6.3
3.3
0
Propylene carbonate
20.0
18.0
4.1
0
Propylene glycol
16.8
9.4
23.3
0*
Pyridine
19.0
8.8
5.9
1
Styrene
18.6
1.0
4.1
0
Tetrahydrofuran
16.8
5.7
8.0
0
Tetrahydronaphthalene
19.6
2.0
2.9
0
Toluene
18.0
1.4
2.0
0
Trichloroethylene
18.0
3.1
5.3
0
Xylene
17.6
1.0
3.1
0
*Denotes an outlier. aRED from Ref. 3, bRED from Ref. 5.
RED1a
RED2b
0.9
1.39
0.835
1.132
1.929
1.46
1.53
1.238
1.13
0.922
1.278
1.07
1.282
1.424
1.286
1.476
1.492
0.997
1.071
1.259
1.29
1.229
1.027
0.94
0.997
1.444
1.171
1.417
1.562
1.316
1.546
0.906
1.372
0.833
1.128
1.904
1.447
1.516
1.237
1.125
0.917
1.268
1.076
1.274
1.411
1.279
1.464
1.479
0.986
1.054
1.254
1.286
1.21
1.015
0.944
0.987
1.421
1.163
1.392
1.538
1.298
1.524
FIGURE S1 Plots of Hansen Spheres and convex solubility regions of Bitumen 1. (From ref. 3)
FIGURE S2 Plots of Hansen Spheres and convex solubility regions of Bitumen 2. (From ref. 3)
FIGURE S3 Plots of Hansen Spheres and convex solubility regions of Lignin. (From ref. 3)
FIGURE S4 Plots of Hansen Spheres and convex solubility regions of Polyether Sulfone. (From ref. 3)
FIGURE S5 Convex solubility region for Bitumen 1 plotted with centers computed by methods 1-6 and HSPs from
Vebber et al. (ref. 3) The subscript of C in legend corresponds to the method number.
FIGURE S6 Convex solubility region for Bitumen 2 plotted with centers computed by methods 1-6 and HSPs from
Vebber et al. (ref. 3) The subscript of C in legend corresponds to the method number.
FIGURE S7 Convex solubility region for Lignin plotted with centers computed by methods 1-6 and HSPs from
Vebber et al. (ref. 3) The subscript of C in legend corresponds to the method number.
FIGURE S8 Convex solubility region for Polyether Sulfone plotted with centers computed by methods 1-6 and
HSPs from Vebber et al. (ref. 3) The subscript of C in legend corresponds to the method number.
REFERENCES
1 Mirtich, B., J. Graph. Tools 1996, 1, 31-50.
2 Wiśniewski, R.,Śmieszek, E.,Kamińska, E., Progress in Organic Coatings 1995, 26, 265-274.
3 Vebber, G. C.,Pranke, P.,Pereira, C. N., Journal of Applied Polymer Science 2014, 131, 39696.
4 Gharagheizi, F., Journal of Applied Polymer Science 2007, 103, 31-36.
5 Hansen, C. M., 1967. The Technical University of Denmark, Copenhagen, 1967.
6 Redelius, P., Energy & Fuels 2004, 18, 1087-1092.