Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness
Abstract
:1. Introduction
2. Materials and Methods
3. Data and Discussion
3.1. The Hansen Solubility Parameters Vector Field
3.1.1. Concepts and Definitions
3.1.2. Interaction Vectors and Free Surface Energy
3.2. Surface Tension of Liquids
- (a)
- The liquid is completely non-polar, and its molecules do not present any special orientation at the interface with air, since its molecules are, like the air molecules, non-polar. The only relevant parameter is δD, as δP = 0 and δH = 0. This is the case, for instance, for hydrocarbons like pentane.
- (b)
- The liquid is polar, but the molecular size is sufficiently large to hide its hydrogen bonds in the inner part of the liquid, preventing them from interacting with air. The electric dipole moment cannot be hidden because it affects the molecule itself. In this case, δH would not be relevant to the air–liquid interaction, while dispersion and polarity would. Figure 2 shows the example of a carboxylic acid like hexanoic acid. The five-atom carbon chain creates a non-polar barrier that would conceal the hydrogen bonds.
- (c)
- The liquid is polar, but the molecular size is very small, and non-polar hydrocarbon chains are not able to hide the hydrogen bonding effect versus the air. In this case, the variables of the three solubility parameters, namely dispersion, polarity, and hydrogen bonding, would be relevant. Figure 2 shows the case of formic acid, a small polar molecule with hydrogen bonds that cannot be concealed.
3.2.1. Surface Tension of Non-Polar Liquids or Polar with Non-Small Molecular Size as Function of the Interaction Vector
3.2.2. Surface Tension of Polar or Non-Polar Liquids with Not-Small Molecular Size as Function of the Interaction Vector
3.3. Surface Free Energy of Solids
3.4. Interfacial Tension between a Solid and a Liquid, or Any Given Two Substances
3.5. Free Surface Energy: General Equation
3.6. Physical Meaning of τ Constant
3.7. Contact Angle and the Solubility Parameters Vector Field
3.8. Contact Angle and Interaction Vectors Angle
4. Conclusions
- (a)
- To link, for the first time, the cohesion energy of substances with their free surface energy, as surface or interfacial tension.
- (b)
- To calculate the surface tension and free energy of thousands of substances by knowing their Hansen solubility parameters, which are easily obtained from the molecular structure of substances. Likewise, it is possible to determine the interfacial tension between them with a simple vector calculation.
- (c)
- To theoretically calculate and accurately estimate contact angles that would, in many cases, be hard to experimentally determine. This vector field model saves experimental work and time.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Nº | Substance | Ref. | σLG, mN/m | δD, MPa1/2 | δP, Mpa1/2 | δH, MPa1/2 | 4δD2+δP2, MPa | σLG,cal., mN/m | Deviation, mN/m |
---|---|---|---|---|---|---|---|---|---|
1 | 1,1,2,2-Tetrabromoethane | 2 | 48.9 | 22.6 | 5.1 | 8.2 | 2069.1 | 51.7 | 2.8 |
2 | 1,2,3-Tribromopropane | 2 | 44.8 | 19.6 | 6.3 | 6.4 | 1576.3 | 39.4 | −5.4 |
3 | 1,3-Diiodopropane | 2 | 46.3 | 19.4 | 5.7 | 4.3 | 1537.9 | 38.4 | −7.9 |
4 | 1,4-Dioxane | 2 | 32.3 | 19.0 | 1.8 | 7.4 | 1447.2 | 36.2 | 3.9 |
5 | 1-Bromonaphthalene | 2 | 43.9 | 20.6 | 3.1 | 4.1 | 1707.1 | 42.7 | −1.2 |
6 | 1-Butanol | 1 | 24.7 | 16.0 | 5.7 | 15.8 | 1056.5 | 26.4 | 1.7 |
7 | 1-Chloro-2-Methylpropane | 2 | 21.3 | 15.6 | 5.0 | 2.9 | 998.4 | 25.0 | 3.7 |
8 | 1-Chloro-3-Methylbutane | 2 | 23.0 | 15.7 | 4.5 | 2.9 | 1006.2 | 25.2 | 2.2 |
9 | 1-Chlorobutane | 2 | 22.5 | 16.2 | 5.5 | 2.0 | 1080.0 | 27.0 | 4.5 |
10 | 1-Chloronaphthalene | 2 | 41.3 | 19.9 | 4.9 | 2.5 | 1608.1 | 40.2 | −1.1 |
11 | 1-Decanol | 2 | 28.1 | 16.0 | 4.7 | 10.0 | 1046.1 | 26.2 | −1.9 |
12 | 1-Methyl Naphthalene | 2 | 38.0 | 20.6 | 0.8 | 4.7 | 1698.1 | 42.5 | 4.5 |
13 | 1-Nitropropane | 2 | 28.9 | 16.6 | 12.3 | 5.5 | 1253.5 | 31.3 | 2.4 |
14 | 1-Octanol | 2 | 27.2 | 16.0 | 5.0 | 11.9 | 1049.0 | 26.2 | −1.0 |
15 | 1-Propanol | 2 | 23.7 | 16.0 | 6.8 | 17.4 | 1070.2 | 26.8 | 3.1 |
16 | 1-Propanol | 1 | 27.5 | 16.0 | 6.8 | 17.4 | 1070.2 | 26.8 | −0.7 |
17 | 2-Chloro-2-Methyl Propane | 2 | 19.1 | 15.6 | 7.6 | 2.0 | 1031.2 | 25.8 | 6.7 |
18 | 2-Phenyl-ethanol | 1 | 41.0 | 19.0 | 5.8 | 7.2 | 1477.6 | 36.9 | −4.1 |
19 | 2-Propanol | 2 | 22.6 | 15.8 | 6.1 | 16.4 | 1035.8 | 25.9 | 3.3 |
20 | 2-Propanol | 1 | 27.0 | 15.8 | 6.1 | 16.4 | 1035.8 | 25.9 | −1.1 |
21 | 3-Methylbutanenitrile | 2 | 25.6 | 15.4 | 9.7 | 4.6 | 1042.7 | 26.1 | 0.5 |
22 | Acetic acid | 1 | 23.0 | 14.5 | 8.0 | 13.5 | 905.0 | 22.6 | −0.4 |
23 | Acetone | 2 | 24.6 | 15.5 | 10.4 | 7.0 | 1069.2 | 26.7 | 2.1 |
24 | Acetone | 1 | 23.3 | 15.5 | 10.4 | 7.0 | 1069.2 | 26.7 | 3.4 |
25 | Acetonitrile | 1 | 28.6 | 15.3 | 18.0 | 15.8 | 1260.4 | 31.5 | 2.9 |
26 | Aniline | 2 | 43.1 | 19.4 | 5.1 | 10.2 | 1531.5 | 38.3 | −4.8 |
27 | Benzene | 2 | 28.2 | 18.4 | 0.0 | 2.0 | 1354.2 | 33.9 | 5.7 |
28 | Benzene | 1 | 28.8 | 18.4 | 0.0 | 2.0 | 1354.2 | 33.9 | 5.1 |
29 | Benzyl Alcohol | 2 | 38.5 | 18.4 | 6.3 | 13.7 | 1393.9 | 34.8 | −3.7 |
30 | Benzyl Benzoate | 2 | 45.4 | 20.0 | 5.1 | 5.2 | 1626.0 | 40.7 | −4.7 |
31 | Bromobenzene | 2 | 35.9 | 19.2 | 5.5 | 4.1 | 1504.8 | 37.6 | 1.7 |
32 | Bromoform | 2 | 40.8 | 21.4 | 4.1 | 6.1 | 1848.7 | 46.2 | 5.4 |
33 | Butanone | 1 | 24.0 | 16.0 | 9.0 | 5.1 | 1105.0 | 27.6 | 3.6 |
34 | Butyronitrile | 2 | 27.6 | 15.3 | 12.4 | 5.1 | 1090.1 | 27.3 | −0.3 |
35 | Carbon Tetrachloride | 2 | 26.3 | 16.1 | 8.3 | 0.0 | 1105.7 | 27.6 | 1.3 |
36 | Chlorobenzene | 2 | 33.0 | 19.0 | 4.3 | 2.0 | 1462.5 | 36.6 | 3.6 |
37 | Chloroform | 2 | 26.9 | 17.8 | 3.1 | 5.7 | 1277.0 | 31.9 | 5.0 |
38 | Cis-Decahydronaphthalene | 2 | 31.0 | 18.8 | 0.0 | 0.0 | 1413.8 | 35.3 | 4.3 |
39 | Cloroform | 1 | 27.2 | 17.8 | 3.1 | 5.7 | 1277.0 | 31.9 | 4.7 |
40 | Cyclohexane | 2 | 24.3 | 16.8 | 0.0 | 0.2 | 1129.0 | 28.2 | 3.9 |
41 | Cyclohexane | 1 | 28.8 | 16.8 | 0.0 | 0.2 | 1129.0 | 28.2 | −0.6 |
42 | Cyclohexanol | 2 | 34.4 | 17.4 | 4.1 | 13.5 | 1227.9 | 30.7 | −3.7 |
43 | Cyclohexanone | 1 | 28.2 | 16.8 | 5.7 | 8.0 | 1161.5 | 29.0 | 0.8 |
44 | Cyclopentanol | 2 | 32.2 | 17.2 | 5.3 | 12.8 | 1211.5 | 30.3 | −1.9 |
45 | Decane | 2 | 23.4 | 15.7 | 0.0 | 0.0 | 986.0 | 24.6 | 1.2 |
46 | Dichloromethane | 1 | 27.0 | 17.0 | 7.3 | 7.1 | 1209.3 | 30.2 | 3.2 |
47 | Dichloromethane | 2 | 25.9 | 17.0 | 7.3 | 7.1 | 1209.3 | 30.2 | 4.3 |
48 | Diethyl ether | 1 | 18.6 | 14.5 | 2.9 | 5.1 | 849.4 | 21.2 | 2.6 |
49 | Diethyl Fumarate | 2 | 31.1 | 16.7 | 5.6 | 7.6 | 1146.9 | 28.7 | −2.4 |
50 | Diethyl Phthalate | 2 | 36.7 | 17.6 | 9.6 | 4.5 | 1331.2 | 33.3 | −3.4 |
51 | Diiodomethane | 2 | 50.1 | 22.0 | 3.9 | 5.5 | 1951.2 | 48.8 | −1.3 |
52 | Dimethyl Formamide | 2 | 36.4 | 17.4 | 13.7 | 11.3 | 1398.7 | 35.0 | −1.4 |
53 | Dipropylene Glycol Monomethyl Ether | 2 | 27.9 | 15.5 | 5.7 | 11.2 | 993.5 | 24.8 | −3.1 |
54 | Dodecane | 2 | 24.9 | 16.0 | 0.0 | 0.0 | 1024.0 | 25.6 | 0.7 |
55 | Ethanol | 2 | 21.7 | 15.8 | 8.8 | 19.4 | 1076.0 | 26.9 | 5.2 |
56 | Ethanol | 1 | 21.6 | 15.8 | 8.8 | 19.4 | 1076.0 | 26.9 | 5.3 |
57 | Ethyl 2-Aminobenzoate | 2 | 39.0 | 18.7 | 8.3 | 7.9 | 1467.7 | 36.7 | −2.3 |
58 | Ethyl Acetate | 1 | 24.9 | 15.8 | 5.3 | 7.2 | 1026.7 | 25.7 | 0.8 |
59 | Ethyl Benzene | 2 | 28.7 | 17.8 | 0.6 | 1.4 | 1267.7 | 31.7 | 3.0 |
60 | Ethyl Bromide | 2 | 23.6 | 16.5 | 8.4 | 2.3 | 1159.6 | 29.0 | 5.4 |
61 | Ethylene Dichloride | 2 | 32.6 | 19.0 | 7.4 | 4.1 | 1498.8 | 37.5 | 4.9 |
62 | Ethylene Glycol Monoethyl Ether | 2 | 28.1 | 16.2 | 9.2 | 14.3 | 1134.4 | 28.4 | 0.3 |
63 | Furfural | 2 | 41.3 | 18.6 | 14.9 | 5.1 | 1605.9 | 40.1 | −1.2 |
64 | Heptane | 2 | 19.7 | 15.3 | 0.0 | 0.0 | 936.4 | 23.4 | 3.7 |
65 | Hexachloro-1,3-Butadiene | 2 | 35.5 | 19.1 | 5.3 | 0.6 | 1487.3 | 37.2 | 1.7 |
66 | Hexadecane | 2 | 27.0 | 16.3 | 0.0 | 0.0 | 1062.8 | 26.6 | −0.4 |
67 | Hexane | 2 | 17.9 | 14.9 | 0.0 | 0.0 | 888.0 | 22.2 | 4.3 |
68 | Iodobenzene | 2 | 39.1 | 19.5 | 6.0 | 6.1 | 1557.0 | 38.9 | −0.2 |
69 | Isopropyl Benzene (Cumene) | 2 | 27.7 | 18.1 | 1.2 | 1.2 | 1311.9 | 32.8 | 5.1 |
70 | Limonene | 1 | 26.4 | 17.2 | 1.8 | 4.3 | 1186.6 | 29.7 | 3.3 |
71 | Mesitylene | 2 | 28.4 | 18.0 | 0.0 | 0.6 | 1296.0 | 32.4 | 4.0 |
72 | Methanol | 2 | 22.3 | 15.1 | 12.3 | 22.3 | 1063.3 | 26.6 | 4.3 |
73 | Methyl Anthranilate | 2 | 43.7 | 19.1 | 8.9 | 8.7 | 1538.5 | 38.5 | −5.2 |
74 | Methyl Ethyl Ketone | 2 | 24.0 | 16.0 | 9.0 | 5.1 | 1105.0 | 27.6 | 3.6 |
75 | m-Nitrotoluene | 2 | 40.8 | 18.9 | 7.3 | 4.0 | 1482.1 | 37.1 | −3.7 |
76 | m-Xylene | 2 | 28.3 | 17.6 | 1.0 | 3.1 | 1240.0 | 31.0 | 2.7 |
77 | N,N-Dimethyl Acetamide | 2 | 36.0 | 16.8 | 11.5 | 9.4 | 1261.2 | 31.5 | −4.5 |
78 | n-Butyl acetate | 1 | 27.8 | 15.8 | 3.7 | 6.3 | 1012.3 | 25.3 | −2.5 |
79 | n-Butylbenzene | 2 | 28.7 | 17.4 | 0.1 | 1.1 | 1211.1 | 30.3 | 1.6 |
80 | n-Heptane | 1 | 19.7 | 15.3 | 0.0 | 0.0 | 936.4 | 23.4 | 3.7 |
81 | Nitrobenzene | 2 | 43.3 | 20.0 | 8.6 | 4.1 | 1674.0 | 41.8 | −1.5 |
82 | Nitroethane | 2 | 31.3 | 16.0 | 15.5 | 4.5 | 1264.3 | 31.6 | 0.3 |
83 | Nitromethane | 2 | 36.0 | 15.8 | 18.8 | 6.1 | 1352.0 | 33.8 | −2.2 |
84 | N-Methyl−2-Pyrrolidone | 2 | 40.2 | 18.0 | 12.3 | 7.2 | 1447.3 | 36.2 | −4.0 |
85 | n-Tetradecane | 2 | 26.1 | 16.2 | 0.0 | 0.0 | 1049.8 | 26.2 | 0.1 |
86 | Octane | 2 | 21.1 | 15.5 | 0.0 | 0.0 | 961.0 | 24.0 | 2.9 |
87 | o-Nitrotoluene | 2 | 40.9 | 19.0 | 7.5 | 4.3 | 1500.3 | 37.5 | −3.4 |
88 | o-Xylene | 2 | 29.5 | 17.8 | 1.0 | 3.1 | 1268.4 | 31.7 | 2.2 |
89 | p-Cymene | 2 | 27.6 | 17.3 | 2.4 | 2.4 | 1202.9 | 30.1 | 2.5 |
90 | Perfluoroheptane | 2 | 12.4 | 12.0 | 0.0 | 0.0 | 576.0 | 14.4 | 2.0 |
91 | Perfluorohexane (PFC 5060) | 2 | 11.4 | 12.1 | 0.0 | 0.0 | 585.6 | 14.6 | 3.2 |
92 | Perfluorooctane | 2 | 13.5 | 12.1 | 0.8 | 0.3 | 586.3 | 14.7 | 1.2 |
93 | Phenyl Isothiocyanate | 2 | 40.9 | 19.4 | 13.9 | 8.5 | 1698.7 | 42.5 | 1.6 |
94 | Propylbenzene | 2 | 28.5 | 17.3 | 2.2 | 2.9 | 1202.0 | 30.1 | 1.6 |
95 | Pyridine | 2 | 37.3 | 19.0 | 8.8 | 5.9 | 1521.4 | 38.0 | 0.7 |
96 | Pyrrole | 2 | 36.1 | 19.2 | 7.4 | 6.7 | 1529.3 | 38.2 | 2.1 |
97 | Quinoline | 2 | 42.6 | 19.8 | 5.6 | 5.7 | 1599.5 | 40.0 | −2.6 |
98 | Tetrachloroethylene | 1 | 28.4 | 18.3 | 5.7 | 0.0 | 1372.1 | 34.3 | 5.9 |
99 | Tetrahydrofuran | 1 | 27.2 | 16.8 | 5.7 | 8.0 | 1161.5 | 29.0 | 1.8 |
100 | Tetrahydrofuran | 2 | 25.8 | 16.8 | 5.7 | 8.0 | 1161.5 | 29.0 | 3.2 |
101 | Toluene | 2 | 27.8 | 18.0 | 1.4 | 2.0 | 1298.0 | 32.4 | 4.6 |
102 | Toluene | 1 | 27.5 | 18.0 | 1.4 | 2.0 | 1298.0 | 32.4 | 4.9 |
103 | Tricresyl Phosphate | 2 | 40.5 | 19.0 | 12.3 | 4.5 | 1595.3 | 39.9 | −0.6 |
104 | Triethanolamine | 5 | 45.9 | 17.3 | 22.4 | 23.3 | 1698.9 | 42.5 | −3.4 |
105 | Undecane | 2 | 24.2 | 16.0 | 0.0 | 0.0 | 1024.0 | 25.6 | 1.4 |
106 | Xylene (isomers) | 1 | 27.8 | 17.7 | 1.0 | 3.1 | 1254.2 | 31.4 | 3.6 |
Nº | Substance | Ref. | σLG, mN/m | δD, MPa1/2 | δP, Mpa1/2 | δH, MPa1/2 | 4δD2+δP2+δH2, MPa | σLG,cal., mN/m | Deviation, mN/m |
---|---|---|---|---|---|---|---|---|---|
107 | 1,5-Pentanediol | 2 | 42.7 | 17.0 | 8.9 | 19.8 | 1627.3 | 40.7 | −2.0 |
108 | Diethylene Glycol | 2 | 44.4 | 16.6 | 12.0 | 20.7 | 1674.7 | 41.9 | −2.5 |
109 | Diethylene Glycol | 4 | 44.4 | 16.6 | 12.0 | 20.7 | 1674.7 | 41.9 | −2.5 |
110 | Dipropylene Glycol | 2 | 33.4 | 16.5 | 10.6 | 17.7 | 1514.7 | 37.9 | 4.5 |
111 | Dipropylene Glycol | 1 | 34.8 | 16.5 | 10.6 | 17.7 | 1514.7 | 37.9 | 3.1 |
112 | Dimethyl sulfoxide | 1 | 42.2 | 18.4 | 16.4 | 10.2 | 1727.2 | 43.2 | 0.9 |
113 | Dimethyl sulfoxide | 3 | 41.8 | 18.4 | 16.4 | 10.2 | 1727.2 | 43.2 | 1.4 |
114 | Dimethylformamide | 3 | 39.1 | 17.4 | 13.7 | 11.3 | 1526.4 | 38.2 | −0.9 |
115 | Ethanolamine | 2 | 48.3 | 17.0 | 15.5 | 21.2 | 1845.7 | 46.1 | −2.2 |
116 | Ethylene Glycol | 2 | 47.3 | 17.0 | 11.0 | 26.0 | 1953.0 | 48.8 | 1.5 |
117 | Formamide | 2 | 57.8 | 17.2 | 26.2 | 19.0 | 2230.8 | 55.8 | −2.0 |
118 | Formic acid | 3 | 31.4 | 14.3 | 11.9 | 16.6 | 1235.1 | 30.9 | −0.5 |
119 | Glycerol | 2 | 64.3 | 17.4 | 12.1 | 29.3 | 2215.9 | 55.4 | −8.9 |
120 | Glycerol | 3 | 63.7 | 17.4 | 12.1 | 29.3 | 2215.9 | 55.4 | −8.3 |
121 | 3-Hydroxymethylpyridine | 2 | 47.4 | 19.2 | 9.6 | 14.5 | 1777.0 | 44.4 | −3.0 |
122 | Water (molecule) | 2 | 72.0 | 15.5 | 16.0 | 42.3 | 3006.3 | 75.2 | 3.2 |
Nº | Substance | σSG, mN/m | δD, MPa1/2 | δP, Mpa1/2 | δH, MPa1/2 | 4δD2+δP2+δH2, MPa | σSG,cal., mN/m | Deviation, mN/m |
---|---|---|---|---|---|---|---|---|
1 | Polyethylene | 33.0 | 17.3 | 1.7 | 2.1 | 1204.5 | 31.3 | −1.7 |
2 | Poly(vinyl chloride) | 40.8 | 18.6 | 5.8 | 9.0 | 1498.5 | 39.0 | −1.8 |
3 | Poly(vinylidene chloride) | 41.6 | 17.6 | 9.1 | 7.8 | 1382.7 | 35.9 | −5.7 |
4 | Poly(vinyl fluoride) | 36.7 | 17.4 | 13.7 | 11.3 | 1526.4 | 39.7 | 3.0 |
5 | Poly(vinylidene fluoride) | 31.4 | 17.0 | 12.1 | 10.2 | 1406.5 | 36.6 | 5.2 |
6 | Poly(tetrafluoroethylene) | 15.0 | 15.1 | 0.9 | 1.7 | 915.7 | 23.8 | 8.8 |
7 | Poly(ethylene terephthalate) | 41.9 | 18.2 | 6.4 | 3.7 | 1379.6 | 35.9 | −6.0 |
8 | Poly(methyl methacrylate) | 40.7 | 17.0 | 4.8 | 5.7 | 1211.5 | 31.5 | −9.2 |
9 | PA66 | 43.5 | 18.7 | 5.2 | 8.4 | 1496.4 | 38.9 | −4.6 |
10 | Polystyrene | 41.3 | 20.5 | 3.1 | 2.6 | 1697.4 | 44.1 | 2.8 |
11 | Polychlorotrifluoroethylene | 26.9 | 14.1 | 2.7 | 5.5 | 832.8 | 21.7 | −5.2 |
12 | Polypropylene | 30.1 | 18.1 | 1.0 | 0.0 | 1311.4 | 34.1 | 4.0 |
13 | Polyisobutylene | 33.6 | 16.9 | 2.5 | 4.0 | 1164.7 | 30.3 | −3.3 |
14 | Poly-α-methyl styrene | 39.0 | 18.5 | 2.4 | 2.4 | 1380.5 | 35.9 | −3.1 |
15 | Poly-n-butyl methacrylate | 31.2 | 15.9 | 5.5 | 5.9 | 1076.3 | 28.0 | −3.2 |
16 | Polycarbonate | 34.2 | 18.4 | 5.9 | 6.9 | 1436.7 | 37.4 | 3.2 |
17 | Polyethylmethacrylate | 35.9 | 17.6 | 9.7 | 4.0 | 1349.1 | 35.1 | −0.8 |
18 | Graphite | 35.0 | 18.0 | 9.3 | 7.7 | 1441.8 | 37.5 | 2.5 |
19 | MoS2 | 34.4 | 18.0 | 9.0 | 6.2 | 1415.4 | 36.8 | 2.4 |
20 | WS2 | 33.1 | 17.0 | 9.5 | 13.2 | 1420.5 | 36.9 | 3.8 |
21 | BN | 30.1 | 18.0 | 7.0 | 7.0 | 1394.0 | 36.2 | 6.1 |
HSPS | HSPL | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Solid | Liquid | σSL, mN/m | δDS, MPa1/2 | δPS, Mpa1/2 | δHS, MPa1/2 | δDL, MPa1/2 | δPL, Mpa1/2 | δHL, MPa1/2 | , MPa | σSL, calc., mN/m | Deviation, mN/m |
PS | Water | 49.4 | 20.6 | 2.5 | 1.5 | 15.5 | 16.0 | 42.3 | 1953.8 | 52.8 | 3.4 |
Formamide | 26.6 | 20.6 | 2.5 | 1.5 | 17.2 | 26.2 | 19.0 | 914.2 | 24.7 | −1.9 | |
Ethylene Glycol | 21.9 | 20.6 | 2.5 | 1.5 | 17.0 | 11.0 | 26.0 | 726.0 | 19.6 | −2.3 | |
Benzyl Alcohol | 0.4 | 20.6 | 2.5 | 1.5 | 18.4 | 6.3 | 13.7 | 183.5 | 5.0 | 4.6 | |
Nitromethane | 8.1 | 20.6 | 2.5 | 1.5 | 15.8 | 18.8 | 5.1 | 369.8 | 10.0 | 1.9 | |
PMMA | Water | 27.0 | 18.5 | 9.0 | 8.4 | 15.5 | 16.0 | 42.3 | 1235.6 | 33.4 | 6.4 |
Formamide | 17.2 | 18.5 | 9.0 | 8.4 | 17.2 | 26.2 | 19.0 | 414.1 | 11.2 | −6.0 | |
Ethylene Glycol | 17.9 | 18.5 | 9.0 | 8.4 | 17.0 | 11.0 | 26.0 | 323.7 | 8.7 | −9.2 | |
Benzyl Alcohol | 5.3 | 18.5 | 9.0 | 8.4 | 18.4 | 6.3 | 13.7 | 36.0 | 1.0 | −4.3 | |
1-Bromonaphtalene | 3.9 | 18.5 | 9.0 | 8.4 | 20.6 | 3.1 | 4.1 | 71.6 | 1.9 | −2.0 | |
Nitromethane | 8.7 | 18.5 | 9.0 | 8.4 | 15.8 | 18.8 | 5.1 | 134.4 | 3.6 | −5.1 | |
PA66 | Water | 15.6 | 19.5 | 6.2 | 14.7 | 15.5 | 16.0 | 42.3 | 921.3 | 24.9 | 9.3 |
Formamide | 9.6 | 19.5 | 6.2 | 14.7 | 17.2 | 26.2 | 19.0 | 438.6 | 11.8 | 2.2 | |
Ethylene Glycol | 10.4 | 19.5 | 6.2 | 14.7 | 17.0 | 11.0 | 26.0 | 175.4 | 4.7 | −5.7 | |
Benzyl Alcohol | 6.0 | 19.5 | 6.2 | 14.7 | 18.4 | 6.3 | 13.7 | 5.7 | 0.2 | −5.8 | |
1-Bromonaphtalene | 1.7 | 19.5 | 6.2 | 14.7 | 20.6 | 3.1 | 4.1 | 126.9 | 3.4 | 1.7 | |
Nitromethane | 9.9 | 19.5 | 6.2 | 14.7 | 15.8 | 18.8 | 5.1 | 304.4 | 8.2 | −1.7 | |
PTFE | Water | 55.8 | 13.6 | 1.7 | 0.0 | 15.5 | 16.0 | 42.3 | 2008.4 | 54.2 | −1.6 |
Formamide | 31.1 | 13.6 | 1.7 | 0.0 | 17.2 | 26.2 | 19.0 | 1013.6 | 27.4 | −3.7 | |
Ethylene Glycol | 27.2 | 13.6 | 1.7 | 0.0 | 17.0 | 11.0 | 26.0 | 809.7 | 21.9 | −5.3 | |
Benzyl Alcohol | 13.6 | 13.6 | 1.7 | 0.0 | 18.4 | 6.3 | 13.7 | 302.8 | 8.2 | −5.4 | |
1-Bromonaphtalene | 13.8 | 13.6 | 1.7 | 0.0 | 20.6 | 3.1 | 4.1 | 217.5 | 5.9 | −7.9 | |
Nitromethane | 8.1 | 13.6 | 1.7 | 0.0 | 15.8 | 18.8 | 5.1 | 338.0 | 9.1 | 1.0 | |
n-Decane | 2.9 | 13.6 | 1.7 | 0.0 | 15.7 | 0.0 | 0.0 | 21.4 | 0.6 | −2.3 | |
n-Hexane | 2.7 | 13.6 | 1.7 | 0.0 | 14.9 | 0.0 | 0.0 | 10.2 | 0.3 | −2.4 | |
Dimethyl sulfoxide | 15.0 | 13.6 | 1.7 | 0.0 | 18.4 | 16.4 | 10.2 | 413.6 | 11.2 | −3.8 | |
PVB | Water | 33.9 | 17.9 | 8.3 | 4.2 | 15.5 | 16.0 | 42.3 | 1534.2 | 41.4 | 7.5 |
Formamide | 18.3 | 17.9 | 8.3 | 4.2 | 17.2 | 26.2 | 19.0 | 540.9 | 14.6 | −3.7 | |
Ethylene Glycol | 20.0 | 17.9 | 8.3 | 4.2 | 17.0 | 11.0 | 26.0 | 486.0 | 13.1 | −6.9 | |
Benzyl Alcohol | 8.4 | 17.9 | 8.3 | 4.2 | 18.4 | 6.3 | 13.7 | 95.6 | 2.6 | −5.8 | |
1-Bromonaphtalene | 3.0 | 17.9 | 8.3 | 4.2 | 20.6 | 3.1 | 4.1 | 56.6 | 1.5 | −1.5 | |
Nitromethane | 9.1 | 17.9 | 8.3 | 4.2 | 15.8 | 18.8 | 5.1 | 128.1 | 3.5 | −5.6 |
Liquid | Solid | θexp. | δD, MPa1/2 | δP, Mpa1/2 | δH, MPa1/2 | θcalc. | |||
---|---|---|---|---|---|---|---|---|---|
Octane | n-Octacosane | 0 | 15.5 | 0.0 | 0.0 | 961.0 | 1143.8 | 8.0 | 0 |
2-Propanol | PMMA | 0 | 15.8 | 6.1 | 16.4 | 1035.8 | 1556.9 | 130.8 | 0 |
Acetone | PMMA | 0 | 15.5 | 10.4 | 7.0 | 1069.2 | 1556.9 | 39.7 | 0 |
Benzyl alcohol | PMMA | 0 | 18.4 | 6.3 | 13.7 | 1393.9 | 1556.9 | 56.4 | 0 |
Bromobenzene | PMMA | 0 | 19.2 | 5.5 | 4.1 | 1504.8 | 1556.9 | 38.1 | 0 |
Ethyl acetate | PMMA | 0 | 15.8 | 5.3 | 7.2 | 1026.7 | 1556.9 | 59.6 | 0 |
Octane | PMMA | 0 | 15.5 | 0.0 | 0.0 | 961.0 | 1556.9 | 206.5 | 0 |
Tetrahydrofuran | PMMA | 0 | 16.8 | 5.7 | 8.0 | 1161.5 | 1556.9 | 37.0 | 0 |
Chlorobenzene | PMMA | 1 | 19.0 | 4.3 | 2.0 | 1462.5 | 1556.9 | 69.6 | 0 |
Dodecane | PMMA | 1 | 16.0 | 0.0 | 0.0 | 1024.0 | 1556.9 | 194.9 | 0 |
Pyridine | PMMA | 1 | 19.0 | 8.8 | 5.9 | 1521.4 | 1556.9 | 6.1 | 0 |
Ethanol | PMMA | 2.5 | 15.8 | 8.8 | 19.4 | 1076.0 | 1556.9 | 176.6 | 0 |
Methanol | PMMA | 3 | 15.1 | 12.3 | 22.3 | 1063.3 | 1556.9 | 272.0 | 0 |
o-xylene | PMMA | 3 | 17.8 | 1.0 | 3.1 | 1268.4 | 1556.9 | 112.9 | 0 |
Hexadecane | PMMA | 4 | 16.3 | 0.0 | 0.0 | 1062.8 | 1556.9 | 189.0 | 0 |
Nitroethane | PMMA | 7 | 16.0 | 15.5 | 4.5 | 1264.3 | 1556.9 | 61.7 | 0 |
Carbon Tetrachloride | PMMA | 8 | 16.1 | 8.3 | 0.0 | 1105.7 | 1556.9 | 87.1 | 0 |
Cyclohexanol | PMMA | 8 | 17.4 | 4.1 | 13.5 | 1227.9 | 1556.9 | 83.2 | 0 |
Carbon Tetrachloride | n-Octacosane | 24 | 17.8 | 0.0 | 0.6 | 1267.4 | 1143.8 | 3.5 | 26 |
Diethylene glycol | PMMA | 35 | 16.6 | 12.0 | 20.7 | 1674.7 | 1556.9 | 192.8 | 35 |
Cyclohexanol | n-Octacosane | 36 | 17.4 | 4.1 | 13.5 | 1227.9 | 1143.8 | 200.0 | 40 |
Bromoform | n-Octacosane | 39 | 21.4 | 4.1 | 6.1 | 1848.7 | 1143.8 | 134.7 | 57 |
Pyridine | n-Octacosane | 39 | 19.0 | 8.8 | 5.9 | 1521.4 | 1143.8 | 129.7 | 48 |
Nitroethane | n-Octacosane | 40 | 16.0 | 15.5 | 4.5 | 1264.3 | 1143.8 | 263.8 | 46 |
Nitrobenzene | n-Octacosane | 45 | 20.0 | 8.6 | 4.1 | 1674.0 | 1143.8 | 129.0 | 53 |
Nitromethane | n-Octacosane | 51 | 15.8 | 18.8 | 6.1 | 1352.0 | 1143.8 | 395.6 | 56 |
Ethylene Glycol | PMMA | 51 | 17.0 | 11.0 | 26.0 | 1953.0 | 1556.9 | 352.9 | 52 |
Formamide | PMMA | 52 | 17.2 | 26.2 | 19.0 | 2230.8 | 1556.9 | 386.2 | 58 |
Glycerol | PMMA | 68 | 17.4 | 12.1 | 29.3 | 2215.9 | 1556.9 | 483.5 | 61 |
Water | PMMA | 71 | 15.5 | 16.0 | 30.3 | 2135.1 | 1556.9 | 588.9 | 63 |
Diethylene glycol | n-Octacosane | 76 | 16.6 | 12.0 | 20.7 | 1674.7 | 1143.8 | 572.9 | 70 |
Dimethyl sulfoxide | n-Octacosane | 76 | 18.4 | 16.4 | 10.2 | 1727.2 | 1143.8 | 381.9 | 64 |
Ethylene Glycol | n-Octacosane | 86 | 17.0 | 11.0 | 26.0 | 1953.0 | 1143.8 | 797.0 | 80 |
Formamide | n-Octacosane | 95 | 17.2 | 26.2 | 19.0 | 2230.8 | 1143.8 | 1047.8 | 88 |
Glycerol | n-Octacosane | 95 | 17.4 | 12.1 | 29.3 | 2215.9 | 1143.8 | 1005.9 | 86 |
Water | n-Octacosane | 106 | 15.5 | 16.0 | 30.3 | 2135.1 | 1143.8 | 1182.0 | 91 |
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Equation | Comments | References |
---|---|---|
Surface free energy, σ; Hildebrand solubility parameter, δ; molar volume, v. | Hildebrand and Scott (1950) [4] | |
σ is the surface tension, and k is a constant depending on the liquids involved: 0.8 for several homologous series, 0.265 for normal alcohols, and 10.3 for n-alkyl benzenes. | Skaarup and Hansen (1967), cited in Hansen (2007) [5] | |
Hansen solubility parameters, δD, δP, and δH; molar volume, v; surface free energy, σ. For non-alcohols, a = b = 0.632. For majority of alcohols, a = 1.000 and b = 0.060. For acids, phenols, and amines, a = 2.000 and b = 0.481. | Beerbower (1971) [6] | |
Like the Beerbower equation, with a = 1 and no δH. It adjusts the surface tension of almost all substances well, but not that of some cyclic compounds, acetonitrile, some carboxylic acids and multifunctional alcohols. | Koenhen and Smolders (1975) [7] | |
Only used for hydrocarbons without permanent dipoles, and adjusts the dispersion component of the surface tension, σD. | Koenhen and Smolders (1975) [7] | |
Surface tension of 498 pure liquids, σL, with the solubility parameters and molar volume. | Abbott and Hansen (2013) [11] | |
Interfacial tension between two phases, is 0.1 mol−1. For non-alcohols, a = b = 0.63, and for majority of alcohols a = 1.000 and b = 0.060. | Large at al. (2017) [8] | |
And other equations. | Does not include molar volume, v. The ratio between δD to δP and δH is 4 to 1. | Neveen AlQasas et al. (2023) [9] |
For two substances, 1 and 2, liquids or solids. When substance 2 is air, because it is a gas, it is assumed that its cohesion energy is very small and . Since this can be used with solids and liquids indistinctly, it is possible to approximately evaluate the contact angles for technical applications. | Masakazu Murase et al. [10] |
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Bailón-Moreno, R.; Bailón-Ruiz, M.Á.; Aljadiri, A.S.A. Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness. Appl. Sci. 2024, 14, 5834. https://doi.org/10.3390/app14135834
Bailón-Moreno R, Bailón-Ruiz MÁ, Aljadiri ASA. Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness. Applied Sciences. 2024; 14(13):5834. https://doi.org/10.3390/app14135834
Chicago/Turabian StyleBailón-Moreno, Rafael, Miguel Ángel Bailón-Ruiz, and Aqeel Shaikhah Arafat Aljadiri. 2024. "Free Surface Energy and Hansen Solubility Parameter Vector Field. Interface Thickness" Applied Sciences 14, no. 13: 5834. https://doi.org/10.3390/app14135834