Prediction of Thermodynamic Properties of Various Fluids in Wide Ranges of Temperature and Pressure: Normal Fluids, Ionic Liquids, Molten Metals and Liquid Polymers

Table of Contents

 

Contents                                                                                                                      Page

 

Chapter One                                                                                                                      1

I.1. Outline                                                                                                                         2

I.2. Introduction                                                                                                                 2

I.3. Literature survay of the predictive methods……………………………………………………… 9

I.4. Objectives                                                                                                                   21

 

Chapter Two                                                                                                                   22

1. 1. Ionic liquids (ILs) 23

          II.1.1. Perturbed hard-spheremodels…………………………………………………………… 24

          II.1.2. Electrolyteperturbed hard-sphere model…………………………………………….. 41

          II.1.3. Density correlation method from a simple equation…………………………….. 49

II.2. Liquid Polymers                                                                                   52

        II.2.1.Pertubed Yukawa hard-corechain (PYHCC) EOS……………………………….. 52

          II.2.2. Perturbed hard-dimer-chain (PHDC) EOS…………………………………………. 57

          II.2. 3. New PHC EOS for polymeric liquids……………………………………………….. 62

II.3. Density prediction of molten metals using EOS…………………………………………….. 72

II.4. Prediction of Vapor-Liquid Equilibrium properties of atomic and polyatomic fluids using modified vdW family EOSs                          75

II.5. Estimation of critical points of hydrocarbonsusing similarity coefficient method……   80

II.6. Conclusions                                                                                                              86

 

Chapter Three                                                                                                              `86

III.1. Introduction                                                                                                            87

III.2.Estimation of the solubility parameters using statistical thermodynamic-based molecular model                                                      88

 

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          III.2.1. Application to molecular liquids………………………………………………………. 89

          III.2.2. Application to ionic liquids…………………………………………………………… 101

III.3.Estimation of surface thermodynamic properties usingstatistical thermodynamic-baesd molecular model          116

          III.3. 1. Application to normal fluids…………………………………………………………. 116

          III.3. 2. Application to ionic liquids………………………………………………………….. 123

III.4.Conclusions                                                                                                            128

 

Literature cited                                                                                                             133

Appendix                                                                                                      145

List of Tables

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Table II.1.                The %AAD ^b of predicted densities of studied ILs, using the PHS EOS based on the first (A) CSC method, compared with the measurements [107-133]………………………   31

Table II.2                              The %AAD ^b of predicted densities of studied ILs, using the PHS EOS based on the second (B) CSC method, compared with the measurements [107-133]………………   32

Table II.3                              The %AAD b of predicted densities of studied ILs, using the PHS EOS based on the third (C) CSC method, compared with the measurements [107-133]…………………   33

Table II.4                              The comparison of predicted densities of some selected ILs using Eq. (II.1) together with three parametrizing methods for which, their details have been mentioned in this section, all of which compared with the measurements [107-133]…………………………………………   34

Table II.5                              %AAD of estimated κ_T, α_P and B_T of some selected ILs using the proposed PHS, previous PHSC [30] and PHDC [31] EOSs, compared with those obtained from the Tait equation [40]    35

Table II.6                              The %AAD ^a of the predicted density of studied ILs using PMV EOS together with third CSC method (C), from the literature data [107-133]……………………………   39

Table II.7                              Th comparisons between AADs ^a of predicted densities of ILs using CS-vdW and MV-vdW EOSs based on the third CSC method (C), both compared with the literature data [107-133].  40

Table II.8                              The %AAD ^a of the correlated (at 0.1 MPa) and predicted (at the elevated pressures) densities of studied ILs using the proposed EPHS (Eq. (II.28)) and the preceding PHS EOS [139], compared with the measurements [107-133]……………………………………………………………..   46

Table II.9                              The %AAD of the correlated densities of studied ILs using Eq. (II.46) from the measured values [107-133].  54

 

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Table II.10                            The %AAD of the correlated (at 0.1 MPa) and predicted (at elevated pressures) specific volume of 14 studied polymeric liquids, using the proposed PHC EOS, compared with the literature data [155].                             60

Table II.11                            The %AAD ^a of the correlated (at 0.1 MPa) and predicted (at elevated pressures) specific volumes of studied polymeric liquids using the proposed PHDC model (Eq. (II.71)), compared with our preceding work (PYHC EOS) [156], Papari et al. (TM EOS) [46], and Sabzi-Boushehri (S & B) [55], all were compared with the literature data [155]……………………………………………………….. 63

Table II.12                            The %AAD^a of the correlated (at 0.1 MPA) and predicted (for elevated pressures) specific volumes of studied polymeric liquids using the new PHC EOS (Eq. (II.71)) and those obtained from our preceding works [156,159], all compared with the literature data [155]……………… 68

Table II.13                            The%AAD of estimated isothermal compressibility coefficients (κ_T) and reduced bulk modulus (B_T) of some selected polymeric liquids using the proposed PHC (Eq. (II.71)), compared with those obtained from the Tait equation………………………………………………………………….. 70

Table II.14                            The %AAD^a of the predicted densities of studied molten metals using the PMV EOS (Eq. (II.81)) and those estimated from the PHS EOSs which was previously proposed by Eslami [49,50] and Maftoon et al. [53], all compared with the experiment [160-163]……………………… 73

Table II.15                            The %AAD^aof the predicted VLE properties using the revised Scott-vdW and CS-vdW EOSs, compared with literature data [1]………………………………………………………. 78

Table II.16                            The %AAD of estimated critical parameters of C-H organic compounds using SC-EOS and those obtained by the Ambrose’s method [6], both compared with the literature data [2,69,162-165].          83

Table III.1                            Tthe relative deviations (RD ^a in %) of predicted solubility parameters of some non-polar and polar fluids together with the values of LJ parameters to be used in the proposed inversion methods. Our predictions were compared with the literature data [166]…………………… 95

 

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Table III.2                            The relative deviations (RD ^a in %) of calculated Hildebrand solubility parameters, δ^b of studied ILs at 298 K using new molecular model (Eqs. (III.3), (III.17)-(III.30)) from those obtained using some experimental and estimation methods reported in literature [181-192]…………… 107

Table III.3                            The estimation of miscibility of n-Decane and n-Octane in several studied imidazolium-based ILs at 298 K using their solubility parameter differences, |δ₁ – δ₂| and FH interaction parameters, χ₁₂. The values of δ₁ were obtained using the proposed model (i.e., Eqs. (III.3), (III.17)-(III.30)) and of δ₂ were available in literature [166]. The miscibility has been shown by bold faces.  111

Table III.4                            The miscibility estimation of 1-chloro, 2-fluoro Ethane and some studied imidazolium-based ILs using their solubility parameter differences, |δ₁ – δ₂| and FH interaction parameters, χ₁₂. The free-volume effects on the FH interaction parameters were also included here. The values of δ₁ were obtained using the proposed model (i.e., Eqs. (III.3),(III.17)-(III.30)) and of δ₂ were available in literature [166]. The miscibility has been shown by bold faces……………………………………………………… 112

Table III.5                            The%AAD of predicted surface tensions of entire normal fluids studied in this section, using the fowler’s approximation and statistical mechanical method, compared with those reported in literature [18].                        120

Table III.6                            The relative deviation (%Dev.)^a of predicted surface thermodynamic functions of entire normal fluids studied in this section, using the proposed method, compared with those obtained via the literature surface tension data [18] and Eqs. ((III.39) and (III.40))………………………… 121

Table III.7                            The %AAD of predicted surface tension of studied ILs using the new molecular model and those obtained by QSPR [204], both were compared with the measurements which were available in literature [193,202,203].                                                                                                 128

Table III.8                            The relative deviation (%Dev.)^a of the predicted surface thermodynamic functions of studied ILs in this section, using the proposed model, compared with those obtained via the quasi-linear dependence of literature surface tension data with respect to the temperature [18]….. 129

List of Figures

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Figure I.1.                An equation of state tree…………………………………………. 6

Figure II.2                    The Zeno-line regularity for [C₄mim][NTf₂]. To show the linearity of the Zeno-lines, the straight lines were passed though the points and their corresponding R-squared were reported.    38

Figure II.2                    Schematic representation of the physical basis of the Electrolyte perturbed hard-sphere model. The reference fluid consists of hard-sphere mixtures of molecular components (A-step). The next step is to account for the weak dispersion forces between components of mixture (B-step). The last step is to taken electrostatic forces between charged hard-spheres in the mixture (C-step)……………….            42

Figure II.3                    Deviation plot for the density of [C₄mim][BF₄] at several isotherms: 293 K (diamond), 313 K (square), 333 K (triangle) and 353 K (circle) . The filled markers represent the estimated densities of [C₄mim][BF₄] using our electrostatic model (Eq. (II.28)) and the corresponding open are those predicted from non-electrostatic one [139], both compared with the experimental values [123]………….            48

Figure II.4                    The effect of electrostatic contribution on the predcited density using proposed EPHS model (solid lines) and those obtained by PHS model (dashed) at low and moderate pressure limit.Markers representexperimentaldensity data for [C₄mim][BF₄] at 353.15 K [123] (♦) and [C₈mim][PF₆] at 333.15 K (○) [120].                       48

Figure II.5                    Schematic representation of the physical basis of the PHC model for polymer melts. The reference fluid consists of hard-spheres (A step) that form chains (e.g., tetramers) through covalent bonds (B step). The last step is to account for the weak dispersion forces between hard-chains (C-step).     53

Figure II.6                    Schematic representation of PHDC model for polymeric liquids.            59

 

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Figure II.7                    Specific volume vs. pressure for poly(1-octene) and poly(1-butene). The markers represent the literature isotherms [155] and solid lines are those correlated (at 0.1 MPa) and predicted (for elevated pressures) from the proposed model (Eq. (II.71)). a-plot: poly(1-octene) at 455.9 K (◊), 476.1 K (▲), 496.1 K (○), and 516 K (□). b-plot: poly(1-butene) at 464.4 K (◊), 484.5 K (▲), 504 K (○), and 534 K (open triangle).                   69

Figure II.8                    The agreement of estimated values of critical temperatures (a-plot) and critical pressures (b-plot) using the proposed SC-EOS with their literature data [2,65,165-168]……….. 84

Figure III.1                  Ttwo deviation plots for the predicted Hildebrand solubility parameters for n-butane (a-plot) and n-heptane (b-plot). The markers represent the relative deviations (RD in %) of predicted Hildebrand solubility parameters using the selected method (i.e., C-method) from those reported in literature [165].                                        98

Figure III.2                  Two deviation plots for the predicted heats of vaporization for n-butane (a-plot) and n-heptane (b-plot). The markers represent the relative deviations (RD in %) of predicted heats of vaporization using the selected method (i.e., C-method) from those reported in literature [165]……. 99

Figure III.3                  Two deviation plots for the predicted saturated vapour-pressures for n-butane (a-plot) and n-heptane (b-plot). The markers represent the relative deviations (RD in %) of predicted saturated vapour-pressures using the selected method (i.e., D-method) from those reported in literature [1,165].     100

Figure III.4                  The solubility parameter versus the number of carbon atoms, N in the alkyl chain for some studied imidazolium-based ILs with the common anions [NTf₂] (as shown in a-plot) and [BF₄](as shown in b-plot). The solid lines show the estimated values of Hildebrand solubility parameters by the proposed model (Eqs. (III.3), (III.17) – (22)) and the filled markers are those previously obtained from IGC method [194,195] and the measurements of heat of vaporization [183]……………………………………….            113

 

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Figure III.5                  The trend of Hildebrand solubility parameters with respect to the temperature for some selected ILs including [C₆mim][NTf₂] (a-plot), [C₄mim][Triflate] (b-plot) and both of [C₂mim][SCN] and [C₄mim][OcSO₄] (which were shown in c-plot). The markers represent Hildebrand solubility parameters taken from the IGC measurements [194,195] and the solid lines are those estimated using the new molecular model (i.e, Eqs. (III.3),(III.17)-(III.30))………………………………………………………………………. 114

Figure III.6                  The linear dependency of surface tension some selected hydrocarbons on the temperature along the saturation curve. The markers represent the literature data [18] and solid lines are those predicted by the revisited Fowler’s approximation; a-plot: n-butane (○), heptane (unfilled triangle), hexane (□), pentane (◊), and propane (_*). b-plot: n-octane (_*), ethane (Δ), R143a (○), R134a (□), and iso-pentane (◊). 122