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Modeling behavior of CO2/n-alkane and CO2/n-perfluoroalkane mixtures, obtaining good agreement for the CO2/n-alkane mixtures but only a fair agreement for the CO2/perfluorohexane mixture (the only experimental CO2/perfluoroalkane mixture available). Better results would probably be obtained if the binary parameters were fitted to the perfluoroalkane mixture specifically. No electrostatic interactions were explicitly included. These studies are continued in this work, with the advantage that now, more experimental data is available to help to elucidate the questions that are still under discussion. Two main conclusions are expected to be achieved with this work namely, the influence of the structure on the solubility of carbon dioxide in perfluoroalkanes, which was already addressed in Part II, and the influence of electrostatic contributions to the global properties of systems containing at least one component with a quadrupole moment. This last point will be discussed in this section and for that purpose, a polar term was added to the original soft-SAFT EoS (Equation III.3) to account for electrostatic contributions as explained in Section III.3.2. When the quadrupole moment is explicitly taken into account, two more parameters have to be considered, the quadrupolar moment Q and xp, defined as the fraction of segments in the chain that contain the quadrupole. Three of the compounds studied in this work have a quadrupole moment: carbon dioxide, perfluorobenzene and perfluorotoluene. Experimental values for the quadrupole moment in carbon dioxide (Vrabec et al., 2001) and perfluorobenzene (Vrbancich and Ritchie, 1980) are available in the literature. No reference was found regarding the quadrupole in perfluorotoluene but, knowing that the quadrupole moment for benzene is similar to that of toluene (Casas et al., 2003) and that of perfluorobenzene although with a symmetric sign (Vrbancich and Ritchie, 1980), it is legitimate to admit that the quadrupole in perfluorotoluene will be similar to that in perfluorobenzene and with the same sign. Regarding the molecular parameter xp, it was fixed to 1/3 for carbon dioxide and 1/6 for perfluorobenzene and perfluorotoluene mimicking the molecules as three and six segments with a quadrupole in one of them. Therefore, with xp and Q fixed, only the usual m, σ and ε parameters need to be adjusted for the molecule presenting a quadrupole moment. They were readjusted in the usual way by fitting vapor pressure and saturated liquid densities to experimental. The parameters for carbon dioxide, perfluorobenzene and perfluorotoluene with and without the quadrupole moment included are presented in Table III.7. Also in the table is given the absolute - 137 -
Modeling average deviation (AAD) between experimental liquid coexisting densities and vapor pressures of carbon dioxide, perfluorobenzene and perfluorotoluene given by the soft- SAFT EoS, with and without the inclusion of the quadrupole moment on the molecule. In both cases, vapour pressures and liquid densities are fitted to experimental data with an AAD inferior to 3 % and 0.5 % respectively. For perfluoro-n-octane and perfluoromethylcyclohexane the parameters that will be used are in Table III.1. Table III.7. soft-SAFT molecular parameters for CO2 and perfluoroalkanes with and without quadrupole Component m σ (Å) ε/kBB (Κ) Q (C.m 2 ) AAD (%) Pvap AAD (%) Density CO2 2.681 2.534 153.4 -- 0.25 0.44 CO2 1.571 3.184 160.2 4.4 x 10 -40 0.50 0.90 C6F6 3.148 3.647 253.6 -- 3.61 0.19 C6F6 3.253 3.602 245.5 5.0 x 10 -40 2.39 0.30 C7F8 3.538 3.764 253.0 -- 3.11 0.52 5.0 x 10 -40 C7F8 3.636 3.723 246.5 2.63 0.40 Figures III.13, III.14 and III.15 show a comparison between the experimental data for the systems CO2/perfluorobenzene, CO2/perfluorotoluene and CO2/perfluoro-n-octane with predictions from the soft-SAFT equation with and without the quadrupole term, at three different temperatures, 293.15, 323.15 and 353.15 K. Symbols correspond to the experimental data; dashed lines show calculations with soft-SAFT without the quadrupole, while the full lines represent calculations with the polar term. No binary parameters were fitted in these cases and so the lines are full predictions from the pure component parameters. It can be observed that the quadrupole has a significant influence on the description of the phase behaviour of the mixtures involving aromatic compounds. Polar soft-SAFT is able not only to provide an overall better agreement, but it also captures the changes in the curvature as a function of temperature. As before, the results given by the soft-SAFT EoS are compared with the ones given by the Peng-Robinson EoS represented in the figures by the lighter full lines. In the case of the CO2/aromatic compounds, especially for the CO2/perfluorobenzene mixture, the results given by the Peng-Robinson EoS are much better than could be expected when using such a simple equation. - 138 -
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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
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II.6. Liquid - Liquid Equilibrium I
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0 τ β Δ1 2Δ1 [ 1+ B τ + B τ +
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References Experimental Methods, Re
Page 105 and 106: Experimental Methods, Results and D
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 and 146: Modeling the assumptions made by th
Page 147 and 148: Modeling between oxygen and perfluo
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: Modeling CO2 binary mixtures using
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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