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Modeling Table III.11. Optimised size and energy binary interaction parameters for the CO2/alkane mixtures. With polar term Without polar term System ηij � ξij ηij � ξij CO2 – C8H18 1.02 0.930 1.04 0.823 CO2 – C10H18 1.03 0.883 1.06 0.757 CO2 – C7H14 1.01 0.945 1.03 0.819 CO2 – C6H6 1.02 0.957 1.03 0.869 CO2 – C7H8 1.02 0.928 1.04 0.834 It was demonstrated that the soft-SAFT EoS is able to correctly correlate and predict the phase diagrams of CO2/perfluoroalkanes and CO2/alkane mixtures including linear, cyclic and aromatic compounds. The objective of the comparison between CO2/perfluoroalkane vs CO2/alkane mixtures was to study the influence of the quadrupole moment on these mixtures. From the results obtained it seems that, within the soft-SAFT context, the quadrupole moment has an important effect only when describing the CO2/aromatic perfluoroalkanes mixtures. - 151 -
III.4.4. VLE and LLE of Alkane and Perfluoroalkane Mixtures Modeling A significant amount of experimental data is available for perfluoroalkane + alkane systems but, even so, the thermodynamic behaviour of these systems is not completely understood. Althought both alkanes and perfluoroalkanes are nonpolar species and thus it would be expected that their mixtures behave almost ideally, in fact they display large positive deviations from ideality (Hildebrand and Scott, 1950). The first attempts to account for this anomalous behaviour appeared in the early 50s just after the publication of the experimental data for symmetric perfluoralkane + alkane mixtures (Hildebrand et al., 1950; Simons and Dunlap, 1950 and Simons and Mausteller, 1952) showing substantial regions of liquid-liquid immiscibility. To that date it was believed that such mixtures would be completely miscible in all proportions and that the regular solution theory would also describe these mixtures, at least in a qualitatively way. In 1958 Scott (Scott, 1958) reviewed the various explanations proposed and concluded that none of the suggestions accounted fully for the anomalous behaviour of all systems investigated. Among the various explanations were the interpenetration between neighboring C-H groups giving an abnormally strong hydrocarbon-hydrocarbon interaction energy leading to the failure of the geometric combining rule proposed by Simons and Dunlap (1950), an empirical shift in the solubility parameter, δ, for hydrocarbons in order to fit the data proposed by Hildebrand (1950), corrections to the regular solution theory to include the effect of volume changes, that occur on mixing proposed by Simons and Dunlap (1950) and modification of regular solution theory to take into account size and ionization potential differences between the two components proposed by Reed (1955). The author concluded that none of these explanations could account for the behaviour of all of the anomalous systems. In the early 70s Dantzler and Knobler (1971) measured the second virial coefficients of n-alkanes, perfluoro-n-alkanes, and their mixtures and concluded that the anomalous behavior of alkane + perfluoroalkane systems was due to the failure of the geometric mean rule to describe the unusually weak hydrocarbon-fluorocarbon attractive interaction. They discussed possible reasons for such a weak unlike interaction between the two components: noncentral forces, large ionization potential differences, and large size differences, concluding that the observed deviation from the geometric-mean prediction was most likely due to the latter. This explanation had previously been suggested by Dyke - 152 -
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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
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III.1. Introduction Modeling Most c
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Modeling The pioneering work of Wer
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III.2. Soft-SAFT Model Modeling A S
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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 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: Modeling Finally, Figure III.24 pre
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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