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xSolute 5.5E-03 4.5E-03 3.5E-03 2.5E-03 1.5E-03 285 290 295 300 305 310 315 T / K Modeling Figure III.10. Correlation of oxygen solubility data in linear perfluoroalkanes. Symbols represent experimental data: (♦) perfluoro-n-hexane, (■) perfluoro-n-heptane, (▲) perfluoro-n-octane and (●) perfluoro-n-nonane. Lines represent correlation with Peng-Robinson EoS using a medium kij (full lines) and Regular Solution Theory (dashed lines) These results indicate that additional interactions may exist in this mixture, which are not being considered by the previous models. It was already discussed in Part II that, according to the experimental data measured for the solubility of oxygen in linear fluorinated molecules presenting different degrees of substitution on the terminal CF3 groups, the solvation of oxygen seems to be carried out by the end groups of the perfluorocarbons and the existence of strong interactions between the oxygen and the CF3 group on the fluorinated molecules. A literature research on the subject revealed that ab initio calculations of the interaction potentials for the complex CF4-O2 provided evidence for an interaction between the oxygen and the positive carbon nucleus in CF4, with the formation of a very strong complex (Mack and Oberhammer, 1987). Unfortunately no further work was done for other higher fluorinated molecules to conclude if this favourable interaction could also exist between the oxygen molecule and the terminals CF3 groups. Also, through 19 F NMR techniques it was demonstrated that the terminal trifluoromethyl groups have the greatest sensitivity to oxygen when compared with the CF2 groups of molecules as 1Br-perfluoro-n-octane, perfluorotripropylamine and perfluorotributylamine (Shukla et al., 1995). It was then proposed to add the free energy of cross-association - 127 -
Modeling between oxygen and perfluoroalkane molecules to the total energy of the system to test the existence of the preferential interaction between oxygen and the terminal CF3 groups. One of the main advantages of using an equation as the SAFT EoS is that one can taylor the equation to the system under study by introducing or removing terms to the original equation. To model the interaction between solute and solvent, both molecular oxygen and perfluoroalkanes were modelled as associating molecules with two association sites on each. In the case of oxygen, sites represent the two lone pairs of electrons and, in the case of perfluoroalkanes, the two ends of the molecule where the carbon atoms are more exposed (less screened by the fluorine atoms). The magnitude of the site-site interaction between oxygen and perfluoroalkane molecules in the SAFT model depends on the two cross-association parameters, ε/κΒ = 2000 K and k = 8000 Å 3 , which were set constant for all mixtures. In the case of the substituted perfluoroalkanes, 1Br-perfluoro-n-octane and 1Hperfluoro-n-octane were modelled considering that they have only one association site corresponding to the saturated CF3 group while 1H,8H-perfluoro-n-octane was modelled considering that it does not have any association site. The same energy and volume parameters were used to describe the association site when it exists. Binary size, η, and energy, ξ interaction parameters fitted to experimental data for each mixture, are listed in Table III.5. Figure III.11 shows the results obtained for the different systems studied when this model is considered. Figure a compares the results obtained from the soft-SAFT model with and without cross-association for the linear perfluoroalkanes series. Figure b presents the results obtained for the different substituted systems assuming the existence or not of preferential interactions between the oxygen and the CF3 groups on the solvent´s molecules. In both cases agreement with experimental data is very good and the proposed model can correctly describe the different temperature dependences presented by the different systems. - 128 -
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Ana Maria Antunes Dias Universidade
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o júri presidente Prof. Dr. Joaqui
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palavras-chave resumo perfluoroalca
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Contents Notation List of Tables Li
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Notation Abbreviations AAD EoS LCST
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List of Tables Table I.1 Average Bo
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Table III.6 Adjusted Binary Paramet
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Figure II.9 Comparison between corr
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Figure III.8 Temperature-density di
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Figure III.25 Vapor-phase mole frac
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I.1. Fluorine Properties General In
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Table I.2. Physicochemical Properti
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General Introduction order to compa
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General Introduction the numerous a
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General Introduction carbon dioxide
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General Introduction animals. That
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General Introduction Table I.3. Lit
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References General Introduction Ban
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General Introduction Hildebrand, J.
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General Introduction Rowinsky EK. N
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II. Part EXPERIMENTAL METHODS, RESU
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Experimental Methods, Results and D
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Table II.3. (continued) T K ρexp g
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ρ / g.cm-3 1.750 1.730 1.710 1.690
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I. 3. Vapour pressure I.3.1. Biblio
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I.3.2. Apparatus and Procedure Expe
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I.3.3. Experimental Results and Dis
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Table II.8. (continued) T K Pexp kP
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ΔH vap = TΔS vap 2⎛ d ln P ⎞
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I.4. Solubility at atmospheric pres
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x2 (T,P2) 7.0E-03 6.0E-03 5.0E-03 4
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L 2,1 0.70 0.60 0.50 0.40 0.30 285
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P / MPa 6 5 4 3 2 1 0 P / MPa 14 12
Page 95 and 96: II.6. Liquid - Liquid Equilibrium I
Page 97 and 98: Experimental Methods, Results and D
Page 101 and 102: 0 τ β Δ1 2Δ1 [ 1+ B τ + B τ +
Page 103 and 104: References Experimental Methods, Re
Page 111 and 112: III.1. Introduction Modeling Most c
Page 113 and 114: Modeling The pioneering work of Wer
Page 115 and 116: III.2. Soft-SAFT Model Modeling A S
Page 117 and 118: Modeling The equation of state is w
Page 119 and 120: Chain Term Modeling Originally Wert
Page 121 and 122: Modeling The model is easily extend
Page 123 and 124: ( ) ( ) ∑∑∑ 3 2 2 2 2 qq 32π
Page 125 and 126: Modeling HRT is a promising theory,
Page 127 and 128: ( ρ) ρ , 0 ≤ ρ ( ρ) 2 Modelin
Page 129 and 130: III.3. Application to Pure Compound
Page 131 and 132: Modeling From the optimised paramet
Page 133 and 134: T / K 400 350 300 250 200 150 100 5
Page 135 and 136: ln Pvap 1.0E+01 1.0E+00 1.0E-01 1.0
Page 137 and 138: Modeling Table III.2. Absolute Aver
Page 139 and 140: Modeling The correlation coefficien
Page 141 and 142: Pvap (MPa) 4.00 3.50 3.00 2.50 2.00
Page 143 and 144: Modeling The mixture parameters a a
Page 145: Modeling the assumptions made by th
Page 149 and 150: xSolute 5.5E-03 5.0E-03 4.5E-03 4.0
Page 151 and 152: Modeling previous work, dealing wit
Page 153 and 154: Modeling These results confirm that
Page 155 and 156: Modeling CO2 binary mixtures using
Page 157 and 158: Modeling average deviation (AAD) be
Page 159 and 160: P / MPa 14 12 10 8 6 4 2 0 0 0.2 0.
Page 161 and 162: Modeling Figures III.16, III.17 and
Page 163 and 164: Modeling calculations from the orig
Page 165 and 166: Table III.9. References for VLE exp
Page 167 and 168: P / MPa 20 18 16 14 12 10 8 6 4 2 0
Page 169 and 170: Modeling Finally, Figure III.24 pre
Page 171 and 172: III.4.4. VLE and LLE of Alkane and
Page 173 and 174: Modeling number of perfluro-n-alkan
Page 175 and 176: y C6F14 1.0 0.8 0.6 0.4 0.2 0.0 0.0
Page 177 and 178: P / MPa 0.08 0.07 0.06 0.05 0.04 0.
Page 179 and 180: P / MPa 0.12 0.10 0.08 0.06 0.04 0.
Page 181 and 182: Modeling approach based on the meth
Page 183 and 184: Modeling Blas, F. J.; Vega, L. F.,
Page 185 and 186: DIPPR, Thermophysical Properties Da
Page 187 and 188: Modeling Hildebrand, J. H.; Fisher,
Page 189 and 190: Modeling McCabe, C.; Jackson, SAFT-
Page 191 and 192: Modeling Poling, B.; Prauznitz, J.;
Page 193 and 194: Modeling Wertheim, M. S., Fluids wi
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