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Modeling of the segments. The strength of the association bond between site α on specie i and site β on specie j depends on the energy ε αiβj and volume of association k αiβj . The dots indicate that other terms can be added in a perturbation manner. A brief description of each of the terms follows: Ideal term The form of A ideal for the case of a multicomponent system is n ideal = RT∑ i= 1 () i 3 ( x ln Λ −1 A ρ ) (III.4) i m i The sum is over all species i of the mixture, xi = Nm (i)/ Nm is the molar fraction, ρm (i) = Nm (i) /V the molecular density, Nm (i) the number of molecules, Λ i the thermal de Broglie wavelength, and V the volume of the system. ρm, the total number of chains divided by the volume, can be related to the total monomeric density by n n ⎛ ⎞ ( i) ρ = ⎜∑ mi xi ⎟ρ m = ∑ mi ρ (III.5) ⎝ i= 1 ⎠ i= 1 being ρ (i) = xiρm the monomeric density of species i and mi its chain length. Lennard-Jones Reference Term The reference term accounts for the repulsive and attractive interactions of the segments forming the chains giving the Helmholtz free energy of a mixture of spherical Lennard-Jones. In this work the Lennard-Jones EOS proposed by Johnson et al. (1993), which is a modified Benedict-Webb-Rubin EOS was used to describe the reference fluid. ( ) ⎟ ⎛ 8 6 ⎞ ref a p 3 p A = ε ⎜ ∑ ρN Aσ + ∑bpGp (III.6) ⎝ p= 1 p p= 1 ⎠ where NA is the Advogadro number and parameters ap, bp and Gp were fitted to molecular simulation data of the LJ fluid over a broad range of temperatures and densities (Johnson et al., 1993). - 99 -
Chain Term Modeling Originally Wertheim derived in an analytical way the energetic contribution (and thus the form of the corresponding EoS) that came about from the association of spherical particles. One of the successes of the theory came from the fact that, in the limit of infinitely strong bonding on an infinitely small association site placed at the edge of a given molecule, one can, in fact, account for polymerization of the monomers. The resulting equations are both reasonably simple and accurate. Multisegmented chain molecules are formed by imposing strong, covalent-like bonds on the equisized segments, each of which has one or two bonding sites. To form a chain of m segment diameters in length, a fluid is created made up of m species of LJ spheres. Numbering the species 1, 2, 3,…,m it is specified that spheres of type 1 bond only to spheres of type 2, and spheres of type 2 bond only to spheres of type 1 and 3, …, and spheres of type m bond only to spheres of type m-1. Also it is required that a stoichiometric ratio of spheres is present. As a result, all the spheres will be forced to bond as specified and thus to create a chain. The Helmholtz free energy due to the formation of chains from mi spherical monomers is A chain = RT n ∑ i= 1 x i ( − m ) i ( ii) LJ 1 ln g ( σ ) (III.7) ii where R is the ideal gas constant. The pair radial distribution function gLJ (ii) (σii) of the reference fluid for the interaction of two segments in a mixture of segments, evaluated at the segment contact σ, provides structural information to the theory at the first-order level. As explained before, this means that the model assumes conformality between branched and linear isomers of the same number of segments and also any information is considered about the attractive chain self-interaction beyond the formation of bonds. Association Term Associating fluids are able to form clusters of associated molecules. The fraction of clusters of a given size can be estimated by using general statistical arguments (Flory, 1953). - 100 -
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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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Page 67 and 68: ΔH vap = TΔS vap 2⎛ d ln P ⎞
Page 69 and 70: I.4. Solubility at atmospheric pres
Page 71 and 72: Experimental Methods, Results and D
Page 79 and 80: x2 (T,P2) 7.0E-03 6.0E-03 5.0E-03 4
Page 81 and 82: L 2,1 0.70 0.60 0.50 0.40 0.30 285
Page 93 and 94: P / MPa 6 5 4 3 2 1 0 P / MPa 14 12
Page 95 and 96: II.6. Liquid - Liquid Equilibrium I
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: Modeling The equation of state is w
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
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Modeling Finally, Figure III.24 pre
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III.4.4. VLE and LLE of Alkane and
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Modeling number of perfluro-n-alkan
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y C6F14 1.0 0.8 0.6 0.4 0.2 0.0 0.0
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P / MPa 0.08 0.07 0.06 0.05 0.04 0.
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P / MPa 0.12 0.10 0.08 0.06 0.04 0.
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Modeling approach based on the meth
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Modeling Blas, F. J.; Vega, L. F.,
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DIPPR, Thermophysical Properties Da
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Modeling Hildebrand, J. H.; Fisher,
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Modeling McCabe, C.; Jackson, SAFT-
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Modeling Poling, B.; Prauznitz, J.;
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Modeling Wertheim, M. S., Fluids wi
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