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Solid-liquid equilibria of eicosane, tetracosane or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures
Accepted Manuscript Solid-liquid equilibria of eicosane, tetracosane or biphenyl + 1-octadecanol, or + 1eicosanol mixtures Issam Boudouh, Juan Antonio González, Ismahane Djemai, Djamel Barkat PII:
S0378-3812(17)30104-8
DOI:
10.1016/j.fluid.2017.03.012
Reference:
FLUID 11429
To appear in:
Fluid Phase Equilibria
Received Date: 30 January 2017 Revised Date:
14 March 2017
Accepted Date: 14 March 2017
Please cite this article as: I. Boudouh, J.A. González, I. Djemai, D. Barkat, Solid-liquid equilibria of eicosane, tetracosane or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures, Fluid Phase Equilibria (2017), doi: 10.1016/j.fluid.2017.03.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT SOLID-LIQUID EQUILIBRIA OF EICOSANE, TETRACOSANE OR BIPHENYL + 1OCTADECANOL, OR + 1-EICOSANOL MIXTURES
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Issam Boudouh1,2, Juan Antonio González3,*, Ismahane Djemai4, Djamel Barkat1
Département de Chimie Industrielle, Université Mohamed Khider, BP 145 RP, Biskra 07000-
Algeria 2
Département de Génie des Procédés et Pétrochimie, Université Echahid Hamma Lakhdar, BP
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789, El Oued 39000-Algeria
G.E.T.E.F., Grupo Especializado en Termodinámica de Equilibrio entre Fases, Departamento
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de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, E-47071, Valladolid, Spain 4
Département d’Hydraulique, Université de Batna 2, Fesdis 05510-Algeria
*corresponding author, e-mail: [email protected]; Fax:+34-983-423136; Tel: +34-983423757
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*corresponding author, e-mail: [email protected]; Fax : + 213-32120702, Tel : 213-
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( ) n-C20(1) + 1-octadecanol(2), and ( ) biphenyl(1) + 1-eicosanol(2) (-----) Ideal Solubility model (____) DISQUAC calculations
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SOLID-LIQUID EQUILIBRIA OF EICOSANE, TETRACOSANE OR BIPHENYL + 1OCTADECANOL, OR + 1-EICOSANOL MIXTURES
1
Département de Chimie Industrielle, Université Mohamed Khider, BP 145 RP, Biskra 07000-
Algeria 2
Département de Génie des Procédés et Pétrochimie, Université Echahid Hamma Lakhdar, BP
789, El Oued 39000-Algeria
G.E.T.E.F., Grupo Especializado en Termodinámica de Equilibrio entre Fases, Departamento
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3
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Issam Boudouh1,2, Juan Antonio González3,*, Ismahane Djemai4, Djamel Barkat1
de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, E-47071, Valladolid, Spain
Département d’Hydraulique, Université de Batna 2, Fesdis 05510-Algeria
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*corresponding author, e-mail: [email protected]; Fax:+34-983-423136; Tel: +34-983-
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423757
*corresponding author, e-mail: [email protected]; Fax : + 213-32120702, Tel : 21332-120701
ACCEPTED MANUSCRIPT Abstract A differential scanning calorimetric (DSC) technique has been used to obtain solidliquid equilibrium temperatures for n-C20, or n-C24, or biphenyl + 1-octadecanol, or + 1eicosanol mixtures. All the systems show a simple eutectic point. The final composition of these points is determined on the basis of the Tamman plots using values of the eutectic heat and of the heat of melting, which are also reported. Deviations of activity coefficients ( γ ) from unity for
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the mentioned mixtures and for the systems n-C24 or n-C28 + cyclododecane, or + cyclododecanol and for dodecane + cyclohexanol are discussed in terms of the alcohol selfassociation and size effects. Mixtures with alkanols show positive ( γ − 1) values. Such differences are larger for the cyclohexanol system, as this is the most self-associated alcohol
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considered. Size effects lead to slightly negative ( γ − 1) values for cyclododecane solutions. Using the regressed parameters, DISQUAC provides a good description of the phase diagrams for the mixtures under consideration and improves results from the UNIFAC (Dortmund)
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model. The influence of size effects on the DISQUAC interaction parameters is discussed.
Keywords
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SLE/ DSC/ alkanols/alkane/biphenyl/DISQUAC
ACCEPTED MANUSCRIPT 1. Introduction There are a number of effects which must be taken into account when determining interaction parameters in the framework of any theoretical model. The different positions of a polar group within a linear chain (steric effects), or in a cyclic ring (cyclization), or regarding an aromatic ring (aromaticity), or the relative separation of two equal or different polar groups within the same molecule (proximity effects), or large differences in size between the mixture
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compounds are all of them effects which can drastically change the interaction parameters. For example, in the Dortmund UNIFAC model [1], specific main groups are defined for aniline or pyridine, and a main group is also defined in order to improve predictions on thermodynamic properties of mixtures including cyclic molecules. It has been shown that proximity effects
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between the − OH and − O − groups in alkoxyethanols [2] lead to DISQUAC [3] interaction parameters for the (OH/O) contacts which are very different to those corresponding to 1-alkanol + linear ether systems [2,4]. In this work, we examine the dependence of the DISQUAC
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interaction parameters with the molecular structure for the contacts (aliphatic/hydroxyl) and (aromatic/hydroxyl) in the following binary systems: n-C20, n-C24, or biphenyl + 1-octadecanol, or + 1-eicosanol. With this idea, we report here solid-liquid equilibrium (SLE) temperatures, obtained by means of a differential scanning calorimetric (DSC) technique, for the mentioned systems. In addition, cyclization is also investigated in similar terms using SLE data available in the literature for the cyclohexanol + dodecane [5] and cyclododecanol + n-C24, or + n-C28 [6]
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mixtures. Systems of the type 1-alkanol + n-alkane [7,8], or + cyclohexane [9], or + benzene, or + toluene [10] and cycloalkanol + alkane [11] have been extensively studied by one of us using DISQUAC. In the case of long chain 1-alkanol ( ≥ 1-octadecanol)) + n-alkane mixtures, values of the first dispersive interaction parameter for the (CH2/OH) contacts were determined using
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SLE data for solutions including shorter n-alkanes. Calculations show that these parameters are not useful for systems with long n-alkanes (e.g, n-C20, or n-C24), and that new parameters are required. Results obtained from DISQUAC are compared to those determined using UNIFAC,
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with interaction parameters from the literature (see below). From a practical point of view, solubility of a solid in pure or mixed solvents are of great importance in chemical process design, particularly when process conditions have to be specified to prevent the precipitation of a solid. SLE data for systems containing alkanols with a large number of C atoms are relevant in fat, cosmetic and oil technology. Biphenyl is a polycyclic aromatic hydrocarbon which can be considered built by blocks of benzene. The study of biphenyl systems is needed for a better understanding of aromatic-aromatic interactions which are commonly encountered in very complex systems [12]. Due to its stability and inertness, biphenyl is employed as heat-storage material [13], and the eutectic mixture diphenyl ether + biphenyl is used as heat transfer agent [14].
ACCEPTED MANUSCRIPT 2.
Experimental
2.1
Materials
All the chemicals were used as delivered without any further purification. Information about the source and purity of the pure compounds is collected in Table 1. Table 2 lists physical properties determined in this work (see below), together with values from the literature, of the pure compounds used along the experimental research: Tm , melting temperature, ∆H m molar
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enthalpy of fusion, ∆C pm , change of the molar heat capacity during the melting process of the compound, Ttr , transition temperature and ∆H tr , the molar enthalpy of transition. These properties are in fair agreement with values reported in the literature. We have not observed a
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solid-solid phase transition for n-C20 or for 1-eicosanol. Nevertheless, transitions temperatures, very close to the corresponding melting points have been reported for these chemicals. Thus, for n-C20, Ttr /K = 309.2 and Tm /K = 310.05 [15,16] and for 1-icosanol, Ttr /K = 337.65; Tm /K =
2.2
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338.05 [17].
Procedure and experimental results
1-Octadecanol or 1-eicosanol and n-alkanes or biphenyl are completely miscible in the liquid state. Details on the experimental methodology applied to determine the solid-liquid phase diagrams have been given previously [18-20]. Mixtures were heated under constant agitation until complete melting of the least volatile compound and the sample was heated very
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slowly inside a glass cell. After melting, the cell was immersed rapidly in a liquid nitrogen bath to obtain a homogeneous solid mixture. Then, a small amount of solid (5-10 mg) was sealed in the aluminium pan of the DSC (204F1 Phoenix ASC). The solubility measurements were conducted under an inert atmosphere (20 ml min-1). The heating rate was 0.8 K min-1. The
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equipment was calibrated using 99.99% pure Indium ( Tm = 429.70 K; ∆H m = 28.45 J g-1). Mole fractions were calculated on the basis of the relative atomic mass table of 2015 issued by the
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Commission on Isotopic Abundances and Atomic Weights (IUPAC) [21]. The standard uncertainty in the final mole fraction is estimated to be 0.0005. For the investigated systems, the DSC curves show several peaks (see Figure S1 of
supplementary material for the tetracosane(1) + 1-eicosanol(2) mixture). One of them occurs at the same temperature and is found at any composition (except for the pure compounds) and corresponds to a simple eutectic point. For the mentioned mixture, the solid-solid transition of pure alkane is also observed (Figure S1, supplementary material). The determination of the liquidus temperature is more difficult as one can have several effects superimposed on the DSC curves. For simplicity, as in other previous applications [22,23], we have selected the maximum peak temperature of the broadest peak as the liquidus temperature. Regarding to data acquisition of
∆H m of pure compounds and onsets of the SLE temperatures and processing were done with
ACCEPTED MANUSCRIPT Perkin Elmer’s Pyris software [24]. The standard uncertainty of the equilibrium temperatures is 0.1 K and the relative standard uncertainty for the heats of fusion and solid-solid transitions (Table 2) is estimated to be 0.03. Results for the solid-liquid equilibrium temperatures vs. composition are given in Tables 3-4 (see Figures 1-3). Our results for the biphenyl + 1-octadecanol mixture compare well with those available in the literature [25] (Figure 2). Values of the eutectic heat and of the heat of melting needed to determine the final composition of the eutectic points on the
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basis of the Tamman plots [24,26,27] are listed in Tables 5-6 (see Figure 4).
MODELS
3.1 DISQUAC
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Some important features of the model are briefly summarized. (i) The group contribution model DISQUAC is based on the rigid lattice theory developed by Guggenheim [28]. (ii) The total molecular volumes, ri, surfaces, qi, and the molecular surface fractions, αi, of
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the system compounds are calculated additively on the basis of the group volumes RG and surfaces QG recommended by Bondi [29]. As volume and surface units, the volume RCH4 and surface QCH4 of methane are taken arbitrarily [30]. The geometrical parameters for the groups considered along the work are listed in Table 7. (iii) The molar excess functions, as Gibbs energy, GmE , or enthalpy, H mE , are the result of two contributions: a dispersive (DIS) term due to the contribution from the dispersive interactions; and a quasichemical (QUAC) term arising
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from the anisotropy of the field forces created by the solution molecules.
For GmE a
combinatorial term, GmE,COMB , given by the Flory-Huggins equation [30,31] must be considered.
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Thus,
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GmE = GmE,COMB + GmE,DIS + GmE,QUAC H mE = H mE,DIS + H mE,QUAC
(1) (2)
(iv) The interaction parameters are dependent on the molecular structure; (v) the value z = 4 for the coordination number is used for all the polar contacts. This is one of the more important shortcomings of the model, partially removed via the hypothesis of considering structure dependent interaction parameters. The equations used to calculate the DIS and QUAC contributions to GmE and H mE are given elsewhere [32]. The temperature dependence of the interaction parameters is expressed in DIS QUAC ; Cst,l where s≠t and l = 1 terms of the DIS and QUAC interchange coefficients [32], Cst,l
ACCEPTED MANUSCRIPT (Gibbs
energy;
DIS/QUAC Cst,1 = gstDIS/QUAC (T0 ) / RT0 );
l
=
2
(excess
enthalpy;
DIS/QUAC DIS/QUAC DIS/QUAC Cst,2 = hstDIS/QUAC (T0 ) / RT0 )), l = 3 (heat capacity; Cst,3 = cpst (T0 ) / R )). To =
298.15 K is the scaling temperature. The corresponding equations are:
(3)
hstDIS/QUAC DIS/QUAC To DIS/QUAC To = Cst,2 − Cst,3 − 1 RT T T
(4)
R
DIS/QUAC = Cst,3
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DIS/QUAC cpst
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gstDIS/QUAC T T DIS/QUAC DIS/QUAC T0 DIS/QUAC = Cst,1 + Cst,2 − 1 + Cst,3 ln( 0 ) − 0 + 1 RT T T T
(5)
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The equation of the solid-equilibrium curve of a pure solid component 1 including one first order transition is, for temperatures below that of the phase transition [33,34]: − ln x1 = (∆H m1 / R ) [1/ T − 1/ Tm1 ] − (∆CPm1 / R ) [ ln(T / Tm1 ) + (Tm1 / T ) − 1] +
(∆H tr1 / R) [1/ T − 1/ Ttr1 ] + ln γ 1
(6)
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Conditions at which eqn. (6) is valid have been specified elsewhere [35]. In eqn. (6), x1 is the mole fraction and γ1 the activity coefficient of component 1 in the solvent mixture, at temperature T. In this work, DISQUAC and Dortmund UNIFAC models are used to calculate γ1. All the physical constants needed for calculations are listed in Table 2 and in Table S1
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(supplementary material).
Modified UNIFAC (Dortmund version)
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This version of UNIFAC [1,36] differs from the original UNIFAC [37] by the combinatorial term and the temperature dependence of the interaction parameters. The equations used to calculate GmE and H mE are obtained from the well-known fundamental equation for the activity coefficient γi of component i:
ln γ i = ln γ iCOMB + ln γ iRES
(7)
where ln γ iCOMB and ln γ iRES represent the combinatorial and residual term, respectively. Equations can be found elsewhere [32]. In UNIFAC (Dortmund), two main groups, OH and CH3OH, are defined for predicting thermodynamic properties of mixtures with alkanols. The
ACCEPTED MANUSCRIPT main group OH is subdivided in three subgroups: OH(p), OH(s) and OH(t) for the representation of primary, secondary and tertiary alkanols, respectively. The CH3OH group is a specific group for methanol solutions. No specific groups have been introduced for cyclic alkanols, and we have used the interaction parameters for OH(p) when conducting calculations for the systems with the considered cycloalkanols. On the other hand, parameters for biphenyl and cyclic molecules can be determined from those listed for the main groups 3 (ACH) and 42
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(c-CH2), respectively. The subgroups within the same main group have different geometrical parameters, and identical group energy-interaction parameters. It must be mentioned that the geometrical parameters, the relative van der Waals volumes and the relative van der Waals surfaces are not calculated form molecular parameters like in the original UNIFAC, but fitted
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together with the interaction parameters to the experimental values of the thermodynamic properties considered. The geometrical and interaction parameters were taken from literature
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and used without modifications [1,38].
Estimation of the DISQUAC interaction parameters
In terms of DISQUAC, the mixtures under study are regarded as possessing three surfaces: (i) type a, aliphatic, (CH3, CH2, in n-alkanes, or 1-alkanols); (ii) type s; s = b, aromatic in biphenyl; s = c, c-CH2 or c-CH in cyclic alkanes or alkanols; type h, OH in linear or cyclic alkanols). The general procedure applied in the estimation of the interaction parameters has
remarks are now given. 4.2.1
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been explained in detail elsewhere [32]. Final parameters are listed in Table 8. Some important
n-Alkane + 1-octadecanol or + 1-eicosanol
There is only one contact (a,h) in these mixtures. The corresponding interaction
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parameters are available in the literature for systems containing 1-alkanols from methanol to 1DIS eicosanol [9,10,39,40] (see Discussion Section). Here, new Cah,1 coefficients have been
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determined (Table 8) for mixtures with 1-octadecanol or 1-eicosanol on the basis of the present SLE data, assuming that the other interchange coefficients remain unchanged. 4.2.2
Biphenyl + 1-octadecanol, or + 1-eicosanol
These mixtures are characterized by three contacts: (a,b), (a,h) and (b,h). The interaction
parameters for the (a,b) contacts are purely dispersive and have been determined from DIS QUAC thermodynamic data for biphenyl + n-alkane systems [22]. The Cah,l and Cah,l (l =1,2,3)
coefficients are already known (Table 8). Our previous study on 1-alkanol + naphthalene systems [41] shows that the QUAC interaction parameters for the (b,h) contacts are the same as those given for 1-alkanol + benzene, or + toluene systems [10]. Here, we have applied the same DIS rule and, under the assumption that the Cbh,l (l =2,3) parameters are the same as in systems with DIS value (Table 8). benzene, we have determined the corresponding Cbh,l
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n-Alkane + cyclododecane
These systems are characterized by the single contact (a,c). One of the more difficult problems when treating cyclic molecules is the assessment of geometrical parameters [42,43], as it is known that cycloalkanes do not form a homologous series [42]. In the case of cyclic molecules, the following values of relative group increments for molecular volumes and areas have been reported: rc-CH2 = 0.58645; qc-CH2 = 0.66377-0.0385 m (4 ≤ m ≤ 8); and rc-CH = 0.38493;
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qc-CH = 0.39480-0.0385 m (4 ≤ m ≤ 8) [42,43].
For the present systems, we have assumed: (i)
the geometrical parameters of the c-CH2 and c-CH groups are the same as in cyclooctane (m = 8); (ii) As cyclohexane + n-alkane systems have been extensively studied, considering a whole set of thermodynamic properties ( GmE ; H mE ; vapour-liquid and solid-liquid equilibria) and
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DIS alkanes from pentane to hexacosane [31], the Cac,l (l = 2,3) values used are the same as in the
SLE available in the literature [6]. 4.2.4
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DIS corresponding systems with cyclohexane. The Cac,l coefficient (Table 8) has been fitted against
n-Alkane + cycloalkanol
These mixtures are built by three contacts: (a,c), (a,h) and (c,h). The interaction parameters for the (a,c) contacts are merely dispersive, and as in other applications, have been neglected along calculations. Mixtures with cyclopentanol, cyclohexanol or cycloheptanol and alkanes have been investigated previously using DISQUAC [11]. An important result is that the
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QUAC interchange coefficients Csh,l (s = a,c; l =1,2,3) do not depend on the considered alkanol [11]. DIS coefficient have been fitted to the SLE data Thus, for the cyclohexanol system, only the Cah,1 DIS [5], while for the cyclododecanol mixtures, both Csh,1 (s = a,c) coefficients have been
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determined using SLE measurements [6] (Table 8).
Theoretical results
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A comparison between SLE calculations using DISQUAC, UNIFAC and the ideal
solubility model (IDSM) with experimental results is shown in Tables 9 and 10 (see Figures 13, 5-7, S2 and S3). For the sake of clarity, relative deviations for the equilibrium temperature (TSLE), defined as:
2
1 σ r (TSLE ) = { N
T − TSLE,calc 1/ 2 } ∑ SLE,exp TSLE,e xp
are given in Table 9, which also lists the mean absolute deviation for TSLE :
(8)
ACCEPTED MANUSCRIPT ∆(TSLE ) / K =
1 N
∑T
SLE,exp
− TSLE,calc
(9)
In eqns. (8) and (9), N stands for the number of data points for each system, DISQUAC provides good SLE results and improves UNIFAC calculations (Table 9). DISQUAC also describes the coordinates of the eutectic points in the correct range of temperature and
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composition (Table 10).
Discussion
Mixtures formed by alkane and alkanols show values of activity coefficients ( γ ) larger
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than 1 (Figure 1,3,6,7,S3). In fact, such trend is more marked for the cyclohexanol solution (Table 9, Figure 5), as this alkanol is more self-associated. Interestingly, cyclododecane mixtures are characterized by γ values slightly lower than 1 (Figure 4 and S2), which may be
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ascribed to the difference in size between the system compounds, an effect which produces heterocoordination [44,45]. Values of γ larger than 1 are also encountered for biphenyl systems (Figures 2,3), particularly at x1 values slightly larger than x1eu , a region where biphenylbiphenyl interactions are predominant. The phase diagrams at x1 < x1eu are correctly described by the IDSM, and it is possible to conclude that enthalpic and entropic effects are
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counterbalanced in that region. The phase diagrams of the mixtures n-C20(1) + 1-octadecanol(2), or + 1-eicosanol(2) and n-C24(1) + 1-eicosanol(2) show a simple eutectic point at high x1 values (Table 10, Figures 1,3), and the ( γ − 1) differences become more positive at compositions close to x1eu but lower than this value (see below).
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The comparison of ( γ − 1) values for different n-alkane(1) + 1-alkanol(2) systems is here pertinent in order to get a better understanding of effects related to alcohol self-association
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and to the difference in size between compounds on the mentioned deviations. For example, positive ( γ 2 − 1) values are observed for the heptane(1) + 1-tetradecanol(2) mixture over the entire concentration range [46] (Figure S4) what clearly reveals that the interactional contribution to ln γ 2 is predominant over that due to size effects. The systems n-C16(1) + 1tetradecanol(2), or + 1-hexadecanol(2), or + 1-octadecanol(2), where size effects are of minor importance, also show positive ( γ 2 − 1) values [46,47]. For all these systems, larger positive ( γ 2 − 1) values are encountered at high dilution of the alcohol. Interestingly, the heptane(1) + 1-eicosanol(2) mixture show ( γ 2 − 1) negative values at x1 values ≈ [0.19,0.80] (Figure S3), which can be explained assuming that in that region, ln γ 2 is mainly determined by size effects. Comparison of ( γ − 1) differences for systems containing isomeric linear or cyclic alcohols and
ACCEPTED MANUSCRIPT n-alkane shows that larger values are obtained for linear 1-alkanol mixtures. Thus, IDSM
provides for the n-C24(1) + 1-dodecanol(2) system [48], σ r = 0.019, a much higher value than that obtained for the n-C24(1) + cyclododecanol(2) mixture (Table 9), and indicates that effects related to alcohol self-association are much more relevant in the case of linear 1-alkanol mixtures. This is consistent with the relative H mE values of linear or cyclic alkanol + n-alkane
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systems, which are larger for cycloalkanol solutions. For example, at 298.15 K and equimolar composition, H mE (heptane)/J mol-1 = 745 (cyclohexanol) [49]; 527 (1-hexanol) [50]. These values reveal that self-association of cycloalkanols is weaker and that, therefore, is more easily broken by alkanes. DISQUAC
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6.1
Regarding the DISQUAC interaction parameters some remarks are needed. (i) We note DIS that for n-C20(1) or n-C24(1) + 1-octadecanol(2) or + 1-eicosanol(2) mixtures, the Cah,1 value (=
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−5 ) is meaningfully lower than that reported previously for systems formed by one of these alcohols and n-alkane (= 32) [9,10]. In fact, the latter value was then determined using SLE data for solutions including shorter alkanes, and was assumed to be constant from 1-hexadecanol. Figure S4 shows that DISQUAC and IDSM provide similar results for the heptane(1) + 1eicosanol(2) at x1 ≈ [0.19,0.80]. Thus, in the framework of DISQUAC, the GmE,COMB contribution is nearly counterbalanced by the interactional contribution in that region. For the n-
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C20(1) + 1-eicosanol(2) system, the GmE,COMB term is much lower in absolute value (Table 11) DIS and the Cah,1 value must be decreased in order to provide not very large positive ( γ − 1) values. DIS That is, regarding heptane(1) + 1-octadecanol(2) or + 1-eicosanol(2) mixtures, the Cah,1
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coefficient of systems with n-C20, or n-C24 must be decreased in order to compensate the increasing of the GmE,COMB term (Table 11). (ii) We also note that this contribution in aromatic
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hydrocarbon(1) + 1-octadecanol(1), or + 1-eicosanol(2) mixtures changes in the sequence: DIS benzene < biphenyl (Table 11). Therefore, the observed decrease of Cbh,1 when replacing
benzene by biphenyl can be explained similarly as above. (iii) DISQUAC provides rather good results for cyclododecane systems (Table 9, Figure 5), similar to those provided by IDSM or UNIFAC, using similar interaction parameters than for cyclohexane, and this means that the assessment of geometrical parameters has been correctly conducted. (iv) This is also supported by DISQUAC results for cyclododecanol mixtures. (v) Finally, it must be remarked that the QUAC present calculations show two important results: (a) Csh,1 (s = a,c; l = 1,2,3) coefficients for
(a/h) and (c/h) contacts in systems involving cycloalkanols remain constant from cyclopentanol
ACCEPTED MANUSCRIPT QUAC to cyclododecanol [11]; (b) The Cbh,1 (l = 1,2,3) coefficients are the same for mixtures with
benzene, toluene, naphthalene or biphenyl. 6.2
UNIFAC
We note that, as average, deviations between experimental data and model calculations increase in the order: IDSM > UNIFAC > DISQUAC (Table 9). This demonstrates the predictive ability of UNIFAC regarding SLE calculations. A relevant result is that the model
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fails when describing the SLE phase diagram of the cyclohexanol system, characterized by strong effects related to alcohol self-association. This suggests that a new main UNIFAC group for cyclic alkanols should be introduced. On the other hand, Table 11 compares GmE,COMB values obtained using the Flory-Huggins term (DISQUAC) [31,32] and a modified Stavermann-
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Guggenheim term (UNIFAC) [36] for the systems under study. It is remarkable that, particularly for 1-alkanol + n-alkane systems, DISQUAC is much more sensitive to the
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difference in size between mixture compounds than UNIFAC. This also points out to the DIS necessity of providing a new Cah,1 coefficient for such mixtures.
7.
Conclusions
Phase diagrams for the n-C20, or n-C24 or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures have been reported. These systems and several alkane + cycloalkanol systems
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examined show positive ( γ − 1) values. Larger differences are observed for the n-C12 + cyclohexanol mixture as the involved alcohol is more self-associated. Slightly negative ( γ − 1) values are encountered for the n-C24, or n-C28 + cyclododecane mixtures due to the difference size between the system compounds. DISQUAC describes well the phase diagrams of the
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List of symbols
interchange coefficient
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8.
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studied systems.
∆ C pm
change of the molar heat capacity during the melting process of the compound
G
Gibbs energy
H
enthalpy
∆H m
molar enthalpy of fusion,
∆H tr
molar enthalpy of transition
TSLE
solid-liquid equilibrium temperature
Tm
melting temperature
Ttr
transition temperature
ACCEPTED MANUSCRIPT x
mole fraction in liquid phase
Greek letters
∆
absolute mean deviation (equation 8)
γ
activity coefficient
σr
relative standard deviation (equation 7)
combinatorial term
DIS
dispersive term
E
excess property
QUAC
quasichemical term
Subscripts
SC
COMB
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Superscripts
eutectic
i,j
compound in the mixture, (i, j =1,2)
l
order of the interchange coefficient (l = 1, Gibbs energy; l = 2, enthalpy; l = 3, heat capacity).
M AN U
eu
m
molar property or fusion point
s,t
type of contact surface in DISQUAC (s ≠ t = a (CH3; CH2); b (biphenyl); c (cCH2; c-CH), h (OH) transition
TE D
tr
Acknowledgments
acknowledged.
9.
[2]
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AC C
[1]
EP
Funding from the Université Echahid Hamma Lakhdar El Oued is gratefully
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AC C
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SC
[69]
ACCEPTED MANUSCRIPT
TABLE 1 Sample description Ma /g mol-1
Purityb
Chemical
CAS number
Eicosane
112-95-8
282.547
Avocado
0.99
Tetracosane
646-31-1
338.653
Avocado
0.99
Biphenyl
92-52-4
154.208
Acros
0.99
1-octadecanol
112-92-5
270.494
Fluka
1-eicosanol
629-96-9
298.547
Fluka
> 0.98 > 98
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M AN U
SC
Molar mass; in mole fraction
RI PT
b
AC C
a
Source
ACCEPTED MANUSCRIPT
TABLE 2 Physical propertiesa of pure compounds at 0.1 MPa: melting temperature, Tm , enthalpy of
enthalpy of the transition, ∆H tr .
329.3 331.65
Biphenyl
J mol-1 K-1
∆H tr /
Ttr /K
kJ mol-1
51.80
329.10
27.35
b
b
18.83b
39.16
47.2c,d
331.2e
41.07e
331.82f
65.4f
325.6g
69.6g
336.9
71.24
338.05b
41.84b
338.0c
68.60c
338.1e
73.72e
337.0g
78.4g
308.2
72.49
309.75i
69.87i
309.65j
69.92j
310.0k
69.88k
311.6l
69.03l
308.95m
66.82m
308.7n
73.5n
321.2
60.98
323.75i
AC C
Tetracosane
kJ mol-1
331.65c,d
EP
Eicosane
∆Cp,m /
TE D
1-eicosanol
b
∆H m /
328.45
SC
1-octadecanol
Tm /K
330.6e
26.9c,d 25.6e
330.97f
M AN U
Compound
RI PT
fusion, ∆H m ; heat capacity change at the melting point, ∆C pm ; transition temperature, Ttr and
337.65b
13.93b 30.7c
85.86h
66.6o
319.35
33.82
54.89i
321.25i
31.3i
323.0n
57.2n
319.9n
29.9n
323.65o
57.31o
318.90o
27.68o
323.75o
54.9o
321.25o
31.30o
324.45m
55.51m
320.38m
31.18m
323.75p
54.9p
324.10q
59.3q
321.03q
33.18q
341.1
19.51
36.3r
ACCEPTED MANUSCRIPT 342.10s
18.53s
342.1t
18.57t
TABLE 2 (continued)
a
340.69v
18.6v
342.08w
18.6w
343.5x
19.3x
342.37y
19.7y
RI PT
341.62u
The standard uncertainty for pressure is u ( P ) = 1 kPa; the combined expanded uncertainty
(0.95 level of confidence) for temperatures is U c (Tm ) = U c (Ttr ) = 0.2 K and the relative expanded
uncertainty
(0.95
level
of
confidence)
for
SC
combined
enthalpies
is
U rc ( ∆H m ) = U rc ( ∆H tr ) = 0.06; b[17]; c[51]; d[52]; e[53]; f[54]; g[55]; h[56]; i[57]; j[58]; k[19]; [59]; m[60]; n[61]; o[62]; p[63]; q[20]; r[64]; s[13]; t[65]; u[66]; v[67]; w[68]; x[69]; y[70]
AC C
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l
ACCEPTED MANUSCRIPT
TABLE 3 Solid-liquid equilibrium temperatures for eicosane(1), or tetracosane(1) or biphenyl(1)
x1
TSLE /K
Solid phaseb
0.1021
328.4
Alkanol (cr,II)
0.1967
327.5
Alkanol (cr,II)
0.2990
325.9
Alkanol (cr,II)
0.4010
324.9
Alkanol (cr,II)
0.5016
322.8
Alkanol (cr,II)
0.6028
322.0
Alkanol (cr,II)
0.7036
320.5
Alkanol (cr,II)
0.8066
317.7
0.8978
314.2
0.9576
308.9
0.9784
307.8
0.0992
328.6
Alkanol(cr,II)
327.9
Alkanol(cr,II)
326.4
Alkanol(cr,II)
324.7
Alkanol(cr,II)
323.1
Alkanol(cr,II)
319.4
Eutecticc
319.6
Alkane(cr,I)
0.5995
320.0
Alkane(cr,I)
0.6833
320.5
Alkane(cr,I)
0.7902
320.7
Alkane(cr,I)
0.8902
320.7
Alkane(cr,I)
0.1054
328.6
Alkanol(cr,II)
0.3054
324.8
Alkanol(cr,II)
0.4049
322.5
Alkanol(cr,II)
0.4551
321.5
Eutecticc
0.5052
325.0
Biphenyl(cr)
0.3107 0.3952 0.4411 0.5070
AC C
0.5542
EP
0.2009
M AN U
TE D
n- C24
SC
n- C20
RI PT
+ 1-octadecanol(2) mixtures at 0.1 MPaa
Alkanol (cr,II) Alkanol (cr,II) Alkanol (cr,II) Eutecticc
Biphenyl
ACCEPTED MANUSCRIPT 0.5550
326.2
Biphenyl(cr)
0.6048
329.0
Biphenyl(cr)
0.7050
332.7
Biphenyl(cr)
0.8052
335.4
Biphenyl(cr)
0.9047
337.6
Biphenyl(cr)
TABLE 3 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005, and the combined expanded
RI PT
a
uncertainty (0.95 level of confidence) for temperature is U c (T ) = 0.2 K; b(cr) describes a
single solid phase; (cr,I) and (cr,II) represent the solid phases I and II of n-C24 or 1-octadecanol;
EP
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M AN U
SC
coordinates of the eutectic point determined from Tamman plot (see Table 5)
AC C
c
ACCEPTED MANUSCRIPT
TABLE 4 Solid-liquid equilibrium temperatures for eicosane(1), or tetracosane(1), or
x1
TSLE /K
Solid phaseb
0.1021
335.6
Alkanol(cr)
0.1981
333.2
Alkanol(cr)
0.2880
330.8
Alkanol(cr)
0.4010
329.3
Alkanol(cr)
0.4929
327.5
Alkanol(cr)
0.6027
325.2
Alkanol(cr)
0.7034
322.9
Alkanol(cr)
0.8056
320.4
0.8976
316.9
0.9341
313.2
0.9779
307.9
0.0975
336.3
Alkanol(cr)
334.5
Alkanol(cr)
333.2
Alkanol(cr)
331.5
Alkanol(cr)
330.1
Alkanol(cr)
328.2
Alkanol(cr)
326.2
Alkanol(cr)
0.8033
324.3
Alkanol(cr)
0.8439
322.7
Alkanol(cr)
0.9033
321.1
Eutecticc
0.1055
335.8
Alkanol(cr)
0.3050
333.0
Alkanol(cr)
0.4051
331.8
Alkanol(cr)
0.4553
331.3
Alkanol(cr)
0.5051
330.9
Alkanol(cr)
0.5552
329.9
Alkanol(cr)
0.2949 0.4046 0.5009 0.6009
AC C
0.7071
EP
0.1906
M AN U
TE D
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-eicosanol(2) mixtures at 0.1 MPaa
Alkanol(cr) Alkanol(cr) Alkanol(cr) Eutecticc
Biphenyl
ACCEPTED MANUSCRIPT 0.6052
328.7
eutecticc
0.6552
330.2
Biphenyl(cr)
0.7051
331.8
Biphenyl(cr)
0.8048
334.4
Biphenyl(cr)
0.9049
336.9
Biphenyl(cr)
TABLE 4 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005, and the combined expanded
RI PT
a
uncertainty (0.95 level of confidence) for temperature is U c (T ) = 0.2 K; b(cr) describes a
single solid phase; ccoordinates of the eutectic point determined from Tamman plot (see Table
AC C
EP
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M AN U
SC
6, Figure 4)
ACCEPTED MANUSCRIPT
TABLE 5 Heat of melting, ∆H m and eutectic heat , ∆H eu , for eicosane(1), or tetracosane(1) or
x1
∆H m /J g-1
∆H eu /J g-1
0.
191.52
0
0.1021
169.32
27.85
0.1967
155.61
53.05
0.2990
132.63
77.54
0.4010
112.73
104.33
0.5016
96.64
131.83
0.6028
76.04
0.7036
56.94
0.8066
36.25
0.8978
19.45
0.9576
8.75
0.9784
0
1.
256.56
0.
191.52
0
155.70
34.89
114.99
73.62
75.93
112.41
42.11
144.00
0.4411
27.78
165.93
0.5070
0
185.07
0.5542
18.57
162.86
0.5995
34.08
146.54
0.6833
67.90
117.48
0.7902
103.51
75.15
0.8902
145.36
38.43
1.
180.06
0
0.
191.52
0
0.0992 0.2009 0.3107
AC C
0.3952
M AN U
TE D
0
EP
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-octadecanol(2) mixtures at 0.1 MPaa
157.12 186.21 211.41 234.39
248.89
255.22
Biphenyl
ACCEPTED MANUSCRIPT 0.1054
151.13
39.96
0.3054
62.73
111.35
0.4049
23.14
150.66
0.4551
0
171.47
0.5052
13.39
156.79
0.5550
24.87
140.94
0.6048
36.94
124.14
0.7050
59.28
93.54
0.8052
85.68
62.42
0.9047
107.49
30.30
1.
129.37
0
SC
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005 and the
M AN U
a
RI PT
TABLE 5 (conitued)
combined expanded uncertainty (0.95 level of confidence) for enthalpies
AC C
EP
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is U rc ( ∆H m ) = U rc ( ∆H eu ) = 0.06
ACCEPTED MANUSCRIPT
TABLE 6 Heat of melting, ∆H m and eutectic heat , ∆H eu , for eicosane(1), or tetracosane(1) or
x1
∆H m /J g-1
∆H eu /J g-1
0.
238.63
0
0.1021
213.70
28.56
0.1981
193.10
52.34
0.2880
170.91
78.34
0.4010
144.92
103.54
0.4929
120.42
131.82
0.6027
93.63
0.7034
68.35
0.8056
46.15
0.8976
24.05
0.9341
13.26
0.9779
0
1.
256.56
0
238.63
0
216.97
21.10
188.20
40.49
163.64
59.89
134.95
84.35
0.5009
107.55
100.68
0.6009
79.51
21.60
0.7071
52.84
145.06
0.8033
29.74
163.39
0.8439
19.21
172.06
0.9033
0
185.11
1.
180.06
0
0.
238,63
0
0.1055
196.62
35.21
0.0975 0.1906 0.2949
AC C
0.4046
M AN U
TE D
0.
EP
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-eicosanol(2) mixtures at 0.1 MPaa
157.91 185.41 209.90
233.60
245.09
256.14
Biphenyl
ACCEPTED MANUSCRIPT 0.3050
21.57
94.89
0.4051
84.45
122.41
0.4553
63.38
140.78
0.5051
40.93
164.32
0.5552
28.29
176.93
0.6052
0
190.35
0.6552
22.69
176.39
0.7051
35.34
148.81
0.8048
64.11
97.74
0.9049
93.53
44.43
1.
129.37
0.
SC
a
RI PT
TABLE 6 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005 and the
is U rc ( ∆H m ) = U rc ( ∆H eu ) = 0.06
TABLE 7
M AN U
combined expanded uncertainty (0.95 level of confidence) for enthalpies
TE D
Relative group increments for molecular volumes rG = VG / VCH 4 and areas, qG = AG / ACH 4 calculated according to the Bondi’s method ( VCH 4 =17.12 10-6 m3 mol-1; ACH 4 = 2.90 10-5 m2 mol)
Group
− CH3 − CH2 −
AC C
c-CH2 a c-CHa
c-CH2
b
rG
qG
Ref.
0.79848
0.73103
[30]
0.59755
0.46552
[30]
0.58645
0.43277
[42]
0.38493
0.16380
[42]
EP
1
0.58645
0.3558
[42]
b
c-CH
0.38493
0.0868
[42]
C6H5-
2.67757
1.83793
[30]
− OH
0.46963
0.50345
[39]
a
in cyclic molecules with 6 C atoms; bin cyclic molecules with 8 or more C atoms.
ACCEPTED MANUSCRIPT
TABLE 8 DIS QUAC Dispersive and quasichemical interchange coefficients, Cst,l and Cst,l (l = 1, Gibbs energy; l
= 2, enthalpy; l = 3, heat capacity), for (s,t) contactsa in alkanol + organic solvent mixtures and
Contact
DIS Cst,2
DIS Cst,3
QUAC Cst,l
(a,h)b
−5
14.7
− 39.5
12.2
c
3.6
3.9
− 20.0
12.2
d
3.0
5.3
− 20.0
12.2
(c,h)e
4.0
3.8
− 20.0
(c,h)f
(a,h)
(a,h)
12
71.1
15.0
71.1
15.0
71.1
12.2
15.0
71.1
4.25
5.2
− 20.0
12.2
15.0
71.1
− 4.5
2.4
− 39
8.9
16.7
21.2
h
0.035
0.36
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a
QUAC Cst,3
g
(b,h) (a,c)
QUAC Cst,2
SC
DIS Cst,l
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in cyclododecane + n-alkane systems.
− 1.86
type a, aliphatic in n-alkanes or 1-alkanols; type b, aromatic in biphenyl; type c, c-CH2 or c-CH
in cyclododecane or cyloalkanols; type h, -OH is linear or cyclic alkanols; bin 1-octadecanol or 1-eicosanol + n-C20, or + n-C24; cin cyclohexanol + n-alkane; din cyclododecanol + n-alkane; ein cyclohexanol + cyclohexane; fin cyclododecanol + cyclic alkane; gin 1-octadecanol, or 1-
AC C
EP
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eicosanol + biphenyl; hin cyclododecane + n-alkane
ACCEPTED MANUSCRIPT
TABLE 9 SLE results from DISQUAC, UNIFAC and from the ideal solubility model for solute + alkanol or cyclododecane + n-alkane mixtures: ∆ (TSLE ) , absolute mean deviation (eq. 5), σ r (TSLE ) , standard relative deviation (eq. 4). IDEAL
∆ (TSLE ) / σ r (TSLE ) K
DISQUACb
∆ (TSLE ) / σ r (TSLE ) ∆ (TSLE ) / K
11
2.4
0.011
0.55
n-C24 + 1-octadecanol
11
1.4
0.005
1.3
biphenyl + 1-octadecanol
10
3.7
0.015
13
3.1
0.012
n-C20 + 1-eicosanol
11
2.1
n-C24 + 1-eicosanol
10
2.4
biphenyl + 1-eicosanol
11
3.1
n-C12 + cyclohexanol
22
7.9
n-C24 + cyclododecanol
24
2.3
n-C28 + cyclododecanol
22
1.4
n-C24 + cyclododecane
22
22
b
σ r (TSLE )
0.002
2.0
0.009
this work
0.005
2.0
0.008
this work
0.66
0.003
1.5
0.006
this work
0.60
0.002
1.2
0.004
[25]
M AN U 0.010
2.2
0.008
4.2
0.015
this work
0.009
0.28
0.001
1.4
0.005
this work
0.012
1.5
0.005
0.78
0.003
this work
0.038
0.98
0.006
0.012
0.69
0.003
2.1
0.008
[6]
0.007
0.48
0.002
1.4
0.005
[6]
0.62
0.003
0.47
0.002
0.71
0.003
[6]
0.059
0.003
0.27
0.001
0.83
0.003
[6]
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a
[5]
c
number of data points; calculations using interaction parameters from Table 8; calculation
EP
using interaction parameters from the literature [1,38]
AC C
Ref.
K
SC
n-C20 + 1-octadecanol
n-C28 + cyclododecane
UNIFc
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Na
System
ACCEPTED MANUSCRIPT
TABLE 10 Coordinates of the eutectic points ( x1eu , Teu ) for solute(1) + alkanol(2) or cyclododecane(1) + nalkane(2) mixtures calculated according to the DISQUACa (DQ), UNIFACb (UNIF) and ideal
Teu /K
n-C20 + 1-octadecanol
Exp. 0.978
DQ 0.976
UNIF. IDEAL Exp. 0.994 0.879 307.8
n-C24 + 1-octadecanol
0.507
0.765
0.858
0.672
319.4
biphenyl + 1-
0.455
0.482
0.434
0.621
321.5
octadecanol 0.464
0.444
0.978
0.985
n-C24 + 1-eicosanol
0.903
0.899
0.942
biphenyl + 1-eicosanol
0.605
0.618
0.586
n-C12 + cyclohexanol
n.a.
0.161
n-C24 + cyclododecanol
0.805
0.708
n-C28 + cyclododecanol
0.533
n-C24 + cyclododecane
0.318 0.227
this work
319.3
320.0
317.0
this work
322.9
324.5
318.55
this work
325.5
307.9
308.0
0.775
321.1
320.3
0.678
328.7
325.8
0.165
n.a.
259.5
0.814
0.554
320.5
321.4
0.485
0.622
0.443
330.0
0.316
0.354
0.316
0.219
0.229
0.224 b
[25] 307.2
this work
320.7
318.3
this work
329.9
322.5
this work
237.9
[5]
310.1
322.3
[6]
330.4
319.8
331.5
[6]
309.2
311.4
310.1
312.0
[6]
316.3
318.0
319.8
319.4
[6]
EP
calculations using parameters listed in Table 8; calculations using parameters from [1,38]
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a
UNIF. IDEAL 308.1 306.8
323.0
0.914
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n-C28 + cyclododecane
DQ 308.0
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n-C20 + 1-eicosanol
Ref.
SC
x1eu
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solubility models.
ACCEPTED MANUSCRIPT
TABLE 11 Combinatorial contribution in the framework of the DISQUAC model, GmE,COMB , to the molar excess Gibbs energy at equimolar composition and 298.15 K System
n-C7 + 1-octadecanol
− 250
n-C7 + 1-eicosanol
− 305 −2
n-C20 + 1-octadecanol
− 0.14
n-C24 + 1-dodecanol
− 121
n-C24 + 1-octadecanol
− 20
n-C24 + 1-eicosanol
Benzene + 1-octadecanol Benzene + 1-eicosanol Biphenyl + 1-octadecanol
n-C28 + cyclododecane n-C12 + cyclohexanol n-C24 + cyclododecanol
30
75
75 6 55
− 7.5
60
− 562
− 476
− 638
− 527
− 174
− 147
− 221
− 179
− 238
− 29
− 166
− 52
− 146
244
− 150
4
− 219
− 33
using the Flory-Huggins term [31,32]; busing the modified Stavermann-Guggenheim term [36]
AC C
a
EP
n-C28 + cyclododecanol
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Biphenyl + 1-eicosanol n-C24 + cyclododecane
62
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n-C20 + 1-eicosanol
UNIFACb
SC
DISQUACa
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GmE,COMB /J mol-1
Figure 1
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SC
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ACCEPTED MANUSCRIPT
AC C
SLE for the n-C24(1) + 1-eicosanol(2). mixture. Points, experimental results (this work). Solid lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model, or from UNIFAC.
Figure 2
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SC
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ACCEPTED MANUSCRIPT
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SLE for the biphenyl(1) + 1-octadecanol(2) mixture. Points, experimental results: ( ) (this work); (O) [25]. Solid lines, DISQUAC calculations with interaction parameters
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listed in Table 8. Dashed lines, results from the ideal solubility model, or from UNIFAC.
Figure 3
EP
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SC
RI PT
ACCEPTED MANUSCRIPT
AC C
SLE for the n-C20(1) + 1-octadecanol(2) ( ), and biphenyl(1) + 1-eicosanol(2) (
)
systems. Points, experimental results (this work). Solid lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed line, results from the ideal solubility model, or from UNIFAC.
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SC
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ACCEPTED MANUSCRIPT
Fig. 4. Tamman plot (eutectic heat, ∆H eu ( ), and heat of melting, ∆H m ( ), vs. composition
AC C
EP
( x1 ) for the n-C24(1) + 1-octadecanol(1) system.
AC C
Figure 5
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SC
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ACCEPTED MANUSCRIPT
SLE for the n-C28(1) + cyclododecane(2) mixture. Points, experimental results [6]. Solid
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
Figure 6
EP
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SC
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ACCEPTED MANUSCRIPT
AC C
SLE for the n-C12(1) + cyclohexanol(2) mixture. Points, experimental results [5]. Solid
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
Figure 7
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TE D
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SC
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ACCEPTED MANUSCRIPT
SLE for the n-C28(1) + cyclododecanol(2) mixture. Points, experimental results [6]. Solid
AC C
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
ACCEPTED MANUSCRIPT Phase diagrams for n-C20, or n-C24 or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures are reported Data from the literature for the systems alkane + cycloalkanol, or + cyclododecane are also examined. All the mixtures with alkanols show positive (activity coefficient − 1) differences. Larger differences are observed for the n-C12 + cyclohexanol mixture as the alcohol is more
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self-associated.
AC C
EP
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SC
DISQUAC describes well the phase diagrams of the studied systems.
S0378-3812(17)30104-8
DOI:
10.1016/j.fluid.2017.03.012
Reference:
FLUID 11429
To appear in:
Fluid Phase Equilibria
Received Date: 30 January 2017 Revised Date:
14 March 2017
Accepted Date: 14 March 2017
Please cite this article as: I. Boudouh, J.A. González, I. Djemai, D. Barkat, Solid-liquid equilibria of eicosane, tetracosane or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures, Fluid Phase Equilibria (2017), doi: 10.1016/j.fluid.2017.03.012. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT SOLID-LIQUID EQUILIBRIA OF EICOSANE, TETRACOSANE OR BIPHENYL + 1OCTADECANOL, OR + 1-EICOSANOL MIXTURES
1
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Issam Boudouh1,2, Juan Antonio González3,*, Ismahane Djemai4, Djamel Barkat1
Département de Chimie Industrielle, Université Mohamed Khider, BP 145 RP, Biskra 07000-
Algeria 2
Département de Génie des Procédés et Pétrochimie, Université Echahid Hamma Lakhdar, BP
3
SC
789, El Oued 39000-Algeria
G.E.T.E.F., Grupo Especializado en Termodinámica de Equilibrio entre Fases, Departamento
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de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, E-47071, Valladolid, Spain 4
Département d’Hydraulique, Université de Batna 2, Fesdis 05510-Algeria
*corresponding author, e-mail: [email protected]; Fax:+34-983-423136; Tel: +34-983423757
AC C
EP
32-120701
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*corresponding author, e-mail: [email protected]; Fax : + 213-32120702, Tel : 213-
AC C
EP
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M AN U
SC
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ACCEPTED MANUSCRIPT
( ) n-C20(1) + 1-octadecanol(2), and ( ) biphenyl(1) + 1-eicosanol(2) (-----) Ideal Solubility model (____) DISQUAC calculations
AC C
EP
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SC
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ACCEPTED MANUSCRIPT
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ACCEPTED MANUSCRIPT
SC
SOLID-LIQUID EQUILIBRIA OF EICOSANE, TETRACOSANE OR BIPHENYL + 1OCTADECANOL, OR + 1-EICOSANOL MIXTURES
1
Département de Chimie Industrielle, Université Mohamed Khider, BP 145 RP, Biskra 07000-
Algeria 2
Département de Génie des Procédés et Pétrochimie, Université Echahid Hamma Lakhdar, BP
789, El Oued 39000-Algeria
G.E.T.E.F., Grupo Especializado en Termodinámica de Equilibrio entre Fases, Departamento
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3
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Issam Boudouh1,2, Juan Antonio González3,*, Ismahane Djemai4, Djamel Barkat1
de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, E-47071, Valladolid, Spain
Département d’Hydraulique, Université de Batna 2, Fesdis 05510-Algeria
EP
4
*corresponding author, e-mail: [email protected]; Fax:+34-983-423136; Tel: +34-983-
AC C
423757
*corresponding author, e-mail: [email protected]; Fax : + 213-32120702, Tel : 21332-120701
ACCEPTED MANUSCRIPT Abstract A differential scanning calorimetric (DSC) technique has been used to obtain solidliquid equilibrium temperatures for n-C20, or n-C24, or biphenyl + 1-octadecanol, or + 1eicosanol mixtures. All the systems show a simple eutectic point. The final composition of these points is determined on the basis of the Tamman plots using values of the eutectic heat and of the heat of melting, which are also reported. Deviations of activity coefficients ( γ ) from unity for
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the mentioned mixtures and for the systems n-C24 or n-C28 + cyclododecane, or + cyclododecanol and for dodecane + cyclohexanol are discussed in terms of the alcohol selfassociation and size effects. Mixtures with alkanols show positive ( γ − 1) values. Such differences are larger for the cyclohexanol system, as this is the most self-associated alcohol
SC
considered. Size effects lead to slightly negative ( γ − 1) values for cyclododecane solutions. Using the regressed parameters, DISQUAC provides a good description of the phase diagrams for the mixtures under consideration and improves results from the UNIFAC (Dortmund)
M AN U
model. The influence of size effects on the DISQUAC interaction parameters is discussed.
Keywords
AC C
EP
TE D
SLE/ DSC/ alkanols/alkane/biphenyl/DISQUAC
ACCEPTED MANUSCRIPT 1. Introduction There are a number of effects which must be taken into account when determining interaction parameters in the framework of any theoretical model. The different positions of a polar group within a linear chain (steric effects), or in a cyclic ring (cyclization), or regarding an aromatic ring (aromaticity), or the relative separation of two equal or different polar groups within the same molecule (proximity effects), or large differences in size between the mixture
RI PT
compounds are all of them effects which can drastically change the interaction parameters. For example, in the Dortmund UNIFAC model [1], specific main groups are defined for aniline or pyridine, and a main group is also defined in order to improve predictions on thermodynamic properties of mixtures including cyclic molecules. It has been shown that proximity effects
SC
between the − OH and − O − groups in alkoxyethanols [2] lead to DISQUAC [3] interaction parameters for the (OH/O) contacts which are very different to those corresponding to 1-alkanol + linear ether systems [2,4]. In this work, we examine the dependence of the DISQUAC
M AN U
interaction parameters with the molecular structure for the contacts (aliphatic/hydroxyl) and (aromatic/hydroxyl) in the following binary systems: n-C20, n-C24, or biphenyl + 1-octadecanol, or + 1-eicosanol. With this idea, we report here solid-liquid equilibrium (SLE) temperatures, obtained by means of a differential scanning calorimetric (DSC) technique, for the mentioned systems. In addition, cyclization is also investigated in similar terms using SLE data available in the literature for the cyclohexanol + dodecane [5] and cyclododecanol + n-C24, or + n-C28 [6]
TE D
mixtures. Systems of the type 1-alkanol + n-alkane [7,8], or + cyclohexane [9], or + benzene, or + toluene [10] and cycloalkanol + alkane [11] have been extensively studied by one of us using DISQUAC. In the case of long chain 1-alkanol ( ≥ 1-octadecanol)) + n-alkane mixtures, values of the first dispersive interaction parameter for the (CH2/OH) contacts were determined using
EP
SLE data for solutions including shorter n-alkanes. Calculations show that these parameters are not useful for systems with long n-alkanes (e.g, n-C20, or n-C24), and that new parameters are required. Results obtained from DISQUAC are compared to those determined using UNIFAC,
AC C
with interaction parameters from the literature (see below). From a practical point of view, solubility of a solid in pure or mixed solvents are of great importance in chemical process design, particularly when process conditions have to be specified to prevent the precipitation of a solid. SLE data for systems containing alkanols with a large number of C atoms are relevant in fat, cosmetic and oil technology. Biphenyl is a polycyclic aromatic hydrocarbon which can be considered built by blocks of benzene. The study of biphenyl systems is needed for a better understanding of aromatic-aromatic interactions which are commonly encountered in very complex systems [12]. Due to its stability and inertness, biphenyl is employed as heat-storage material [13], and the eutectic mixture diphenyl ether + biphenyl is used as heat transfer agent [14].
ACCEPTED MANUSCRIPT 2.
Experimental
2.1
Materials
All the chemicals were used as delivered without any further purification. Information about the source and purity of the pure compounds is collected in Table 1. Table 2 lists physical properties determined in this work (see below), together with values from the literature, of the pure compounds used along the experimental research: Tm , melting temperature, ∆H m molar
RI PT
enthalpy of fusion, ∆C pm , change of the molar heat capacity during the melting process of the compound, Ttr , transition temperature and ∆H tr , the molar enthalpy of transition. These properties are in fair agreement with values reported in the literature. We have not observed a
SC
solid-solid phase transition for n-C20 or for 1-eicosanol. Nevertheless, transitions temperatures, very close to the corresponding melting points have been reported for these chemicals. Thus, for n-C20, Ttr /K = 309.2 and Tm /K = 310.05 [15,16] and for 1-icosanol, Ttr /K = 337.65; Tm /K =
2.2
M AN U
338.05 [17].
Procedure and experimental results
1-Octadecanol or 1-eicosanol and n-alkanes or biphenyl are completely miscible in the liquid state. Details on the experimental methodology applied to determine the solid-liquid phase diagrams have been given previously [18-20]. Mixtures were heated under constant agitation until complete melting of the least volatile compound and the sample was heated very
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slowly inside a glass cell. After melting, the cell was immersed rapidly in a liquid nitrogen bath to obtain a homogeneous solid mixture. Then, a small amount of solid (5-10 mg) was sealed in the aluminium pan of the DSC (204F1 Phoenix ASC). The solubility measurements were conducted under an inert atmosphere (20 ml min-1). The heating rate was 0.8 K min-1. The
EP
equipment was calibrated using 99.99% pure Indium ( Tm = 429.70 K; ∆H m = 28.45 J g-1). Mole fractions were calculated on the basis of the relative atomic mass table of 2015 issued by the
AC C
Commission on Isotopic Abundances and Atomic Weights (IUPAC) [21]. The standard uncertainty in the final mole fraction is estimated to be 0.0005. For the investigated systems, the DSC curves show several peaks (see Figure S1 of
supplementary material for the tetracosane(1) + 1-eicosanol(2) mixture). One of them occurs at the same temperature and is found at any composition (except for the pure compounds) and corresponds to a simple eutectic point. For the mentioned mixture, the solid-solid transition of pure alkane is also observed (Figure S1, supplementary material). The determination of the liquidus temperature is more difficult as one can have several effects superimposed on the DSC curves. For simplicity, as in other previous applications [22,23], we have selected the maximum peak temperature of the broadest peak as the liquidus temperature. Regarding to data acquisition of
∆H m of pure compounds and onsets of the SLE temperatures and processing were done with
ACCEPTED MANUSCRIPT Perkin Elmer’s Pyris software [24]. The standard uncertainty of the equilibrium temperatures is 0.1 K and the relative standard uncertainty for the heats of fusion and solid-solid transitions (Table 2) is estimated to be 0.03. Results for the solid-liquid equilibrium temperatures vs. composition are given in Tables 3-4 (see Figures 1-3). Our results for the biphenyl + 1-octadecanol mixture compare well with those available in the literature [25] (Figure 2). Values of the eutectic heat and of the heat of melting needed to determine the final composition of the eutectic points on the
3.
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basis of the Tamman plots [24,26,27] are listed in Tables 5-6 (see Figure 4).
MODELS
3.1 DISQUAC
SC
Some important features of the model are briefly summarized. (i) The group contribution model DISQUAC is based on the rigid lattice theory developed by Guggenheim [28]. (ii) The total molecular volumes, ri, surfaces, qi, and the molecular surface fractions, αi, of
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the system compounds are calculated additively on the basis of the group volumes RG and surfaces QG recommended by Bondi [29]. As volume and surface units, the volume RCH4 and surface QCH4 of methane are taken arbitrarily [30]. The geometrical parameters for the groups considered along the work are listed in Table 7. (iii) The molar excess functions, as Gibbs energy, GmE , or enthalpy, H mE , are the result of two contributions: a dispersive (DIS) term due to the contribution from the dispersive interactions; and a quasichemical (QUAC) term arising
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from the anisotropy of the field forces created by the solution molecules.
For GmE a
combinatorial term, GmE,COMB , given by the Flory-Huggins equation [30,31] must be considered.
EP
Thus,
AC C
GmE = GmE,COMB + GmE,DIS + GmE,QUAC H mE = H mE,DIS + H mE,QUAC
(1) (2)
(iv) The interaction parameters are dependent on the molecular structure; (v) the value z = 4 for the coordination number is used for all the polar contacts. This is one of the more important shortcomings of the model, partially removed via the hypothesis of considering structure dependent interaction parameters. The equations used to calculate the DIS and QUAC contributions to GmE and H mE are given elsewhere [32]. The temperature dependence of the interaction parameters is expressed in DIS QUAC ; Cst,l where s≠t and l = 1 terms of the DIS and QUAC interchange coefficients [32], Cst,l
ACCEPTED MANUSCRIPT (Gibbs
energy;
DIS/QUAC Cst,1 = gstDIS/QUAC (T0 ) / RT0 );
l
=
2
(excess
enthalpy;
DIS/QUAC DIS/QUAC DIS/QUAC Cst,2 = hstDIS/QUAC (T0 ) / RT0 )), l = 3 (heat capacity; Cst,3 = cpst (T0 ) / R )). To =
298.15 K is the scaling temperature. The corresponding equations are:
(3)
hstDIS/QUAC DIS/QUAC To DIS/QUAC To = Cst,2 − Cst,3 − 1 RT T T
(4)
R
DIS/QUAC = Cst,3
SC
DIS/QUAC cpst
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gstDIS/QUAC T T DIS/QUAC DIS/QUAC T0 DIS/QUAC = Cst,1 + Cst,2 − 1 + Cst,3 ln( 0 ) − 0 + 1 RT T T T
(5)
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The equation of the solid-equilibrium curve of a pure solid component 1 including one first order transition is, for temperatures below that of the phase transition [33,34]: − ln x1 = (∆H m1 / R ) [1/ T − 1/ Tm1 ] − (∆CPm1 / R ) [ ln(T / Tm1 ) + (Tm1 / T ) − 1] +
(∆H tr1 / R) [1/ T − 1/ Ttr1 ] + ln γ 1
(6)
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Conditions at which eqn. (6) is valid have been specified elsewhere [35]. In eqn. (6), x1 is the mole fraction and γ1 the activity coefficient of component 1 in the solvent mixture, at temperature T. In this work, DISQUAC and Dortmund UNIFAC models are used to calculate γ1. All the physical constants needed for calculations are listed in Table 2 and in Table S1
3.2
EP
(supplementary material).
Modified UNIFAC (Dortmund version)
AC C
This version of UNIFAC [1,36] differs from the original UNIFAC [37] by the combinatorial term and the temperature dependence of the interaction parameters. The equations used to calculate GmE and H mE are obtained from the well-known fundamental equation for the activity coefficient γi of component i:
ln γ i = ln γ iCOMB + ln γ iRES
(7)
where ln γ iCOMB and ln γ iRES represent the combinatorial and residual term, respectively. Equations can be found elsewhere [32]. In UNIFAC (Dortmund), two main groups, OH and CH3OH, are defined for predicting thermodynamic properties of mixtures with alkanols. The
ACCEPTED MANUSCRIPT main group OH is subdivided in three subgroups: OH(p), OH(s) and OH(t) for the representation of primary, secondary and tertiary alkanols, respectively. The CH3OH group is a specific group for methanol solutions. No specific groups have been introduced for cyclic alkanols, and we have used the interaction parameters for OH(p) when conducting calculations for the systems with the considered cycloalkanols. On the other hand, parameters for biphenyl and cyclic molecules can be determined from those listed for the main groups 3 (ACH) and 42
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(c-CH2), respectively. The subgroups within the same main group have different geometrical parameters, and identical group energy-interaction parameters. It must be mentioned that the geometrical parameters, the relative van der Waals volumes and the relative van der Waals surfaces are not calculated form molecular parameters like in the original UNIFAC, but fitted
SC
together with the interaction parameters to the experimental values of the thermodynamic properties considered. The geometrical and interaction parameters were taken from literature
4.
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and used without modifications [1,38].
Estimation of the DISQUAC interaction parameters
In terms of DISQUAC, the mixtures under study are regarded as possessing three surfaces: (i) type a, aliphatic, (CH3, CH2, in n-alkanes, or 1-alkanols); (ii) type s; s = b, aromatic in biphenyl; s = c, c-CH2 or c-CH in cyclic alkanes or alkanols; type h, OH in linear or cyclic alkanols). The general procedure applied in the estimation of the interaction parameters has
remarks are now given. 4.2.1
TE D
been explained in detail elsewhere [32]. Final parameters are listed in Table 8. Some important
n-Alkane + 1-octadecanol or + 1-eicosanol
There is only one contact (a,h) in these mixtures. The corresponding interaction
EP
parameters are available in the literature for systems containing 1-alkanols from methanol to 1DIS eicosanol [9,10,39,40] (see Discussion Section). Here, new Cah,1 coefficients have been
AC C
determined (Table 8) for mixtures with 1-octadecanol or 1-eicosanol on the basis of the present SLE data, assuming that the other interchange coefficients remain unchanged. 4.2.2
Biphenyl + 1-octadecanol, or + 1-eicosanol
These mixtures are characterized by three contacts: (a,b), (a,h) and (b,h). The interaction
parameters for the (a,b) contacts are purely dispersive and have been determined from DIS QUAC thermodynamic data for biphenyl + n-alkane systems [22]. The Cah,l and Cah,l (l =1,2,3)
coefficients are already known (Table 8). Our previous study on 1-alkanol + naphthalene systems [41] shows that the QUAC interaction parameters for the (b,h) contacts are the same as those given for 1-alkanol + benzene, or + toluene systems [10]. Here, we have applied the same DIS rule and, under the assumption that the Cbh,l (l =2,3) parameters are the same as in systems with DIS value (Table 8). benzene, we have determined the corresponding Cbh,l
ACCEPTED MANUSCRIPT 4.2.3
n-Alkane + cyclododecane
These systems are characterized by the single contact (a,c). One of the more difficult problems when treating cyclic molecules is the assessment of geometrical parameters [42,43], as it is known that cycloalkanes do not form a homologous series [42]. In the case of cyclic molecules, the following values of relative group increments for molecular volumes and areas have been reported: rc-CH2 = 0.58645; qc-CH2 = 0.66377-0.0385 m (4 ≤ m ≤ 8); and rc-CH = 0.38493;
RI PT
qc-CH = 0.39480-0.0385 m (4 ≤ m ≤ 8) [42,43].
For the present systems, we have assumed: (i)
the geometrical parameters of the c-CH2 and c-CH groups are the same as in cyclooctane (m = 8); (ii) As cyclohexane + n-alkane systems have been extensively studied, considering a whole set of thermodynamic properties ( GmE ; H mE ; vapour-liquid and solid-liquid equilibria) and
SC
DIS alkanes from pentane to hexacosane [31], the Cac,l (l = 2,3) values used are the same as in the
SLE available in the literature [6]. 4.2.4
M AN U
DIS corresponding systems with cyclohexane. The Cac,l coefficient (Table 8) has been fitted against
n-Alkane + cycloalkanol
These mixtures are built by three contacts: (a,c), (a,h) and (c,h). The interaction parameters for the (a,c) contacts are merely dispersive, and as in other applications, have been neglected along calculations. Mixtures with cyclopentanol, cyclohexanol or cycloheptanol and alkanes have been investigated previously using DISQUAC [11]. An important result is that the
TE D
QUAC interchange coefficients Csh,l (s = a,c; l =1,2,3) do not depend on the considered alkanol [11]. DIS coefficient have been fitted to the SLE data Thus, for the cyclohexanol system, only the Cah,1 DIS [5], while for the cyclododecanol mixtures, both Csh,1 (s = a,c) coefficients have been
5.
EP
determined using SLE measurements [6] (Table 8).
Theoretical results
AC C
A comparison between SLE calculations using DISQUAC, UNIFAC and the ideal
solubility model (IDSM) with experimental results is shown in Tables 9 and 10 (see Figures 13, 5-7, S2 and S3). For the sake of clarity, relative deviations for the equilibrium temperature (TSLE), defined as:
2
1 σ r (TSLE ) = { N
T − TSLE,calc 1/ 2 } ∑ SLE,exp TSLE,e xp
are given in Table 9, which also lists the mean absolute deviation for TSLE :
(8)
ACCEPTED MANUSCRIPT ∆(TSLE ) / K =
1 N
∑T
SLE,exp
− TSLE,calc
(9)
In eqns. (8) and (9), N stands for the number of data points for each system, DISQUAC provides good SLE results and improves UNIFAC calculations (Table 9). DISQUAC also describes the coordinates of the eutectic points in the correct range of temperature and
6.
RI PT
composition (Table 10).
Discussion
Mixtures formed by alkane and alkanols show values of activity coefficients ( γ ) larger
SC
than 1 (Figure 1,3,6,7,S3). In fact, such trend is more marked for the cyclohexanol solution (Table 9, Figure 5), as this alkanol is more self-associated. Interestingly, cyclododecane mixtures are characterized by γ values slightly lower than 1 (Figure 4 and S2), which may be
M AN U
ascribed to the difference in size between the system compounds, an effect which produces heterocoordination [44,45]. Values of γ larger than 1 are also encountered for biphenyl systems (Figures 2,3), particularly at x1 values slightly larger than x1eu , a region where biphenylbiphenyl interactions are predominant. The phase diagrams at x1 < x1eu are correctly described by the IDSM, and it is possible to conclude that enthalpic and entropic effects are
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counterbalanced in that region. The phase diagrams of the mixtures n-C20(1) + 1-octadecanol(2), or + 1-eicosanol(2) and n-C24(1) + 1-eicosanol(2) show a simple eutectic point at high x1 values (Table 10, Figures 1,3), and the ( γ − 1) differences become more positive at compositions close to x1eu but lower than this value (see below).
EP
The comparison of ( γ − 1) values for different n-alkane(1) + 1-alkanol(2) systems is here pertinent in order to get a better understanding of effects related to alcohol self-association
AC C
and to the difference in size between compounds on the mentioned deviations. For example, positive ( γ 2 − 1) values are observed for the heptane(1) + 1-tetradecanol(2) mixture over the entire concentration range [46] (Figure S4) what clearly reveals that the interactional contribution to ln γ 2 is predominant over that due to size effects. The systems n-C16(1) + 1tetradecanol(2), or + 1-hexadecanol(2), or + 1-octadecanol(2), where size effects are of minor importance, also show positive ( γ 2 − 1) values [46,47]. For all these systems, larger positive ( γ 2 − 1) values are encountered at high dilution of the alcohol. Interestingly, the heptane(1) + 1-eicosanol(2) mixture show ( γ 2 − 1) negative values at x1 values ≈ [0.19,0.80] (Figure S3), which can be explained assuming that in that region, ln γ 2 is mainly determined by size effects. Comparison of ( γ − 1) differences for systems containing isomeric linear or cyclic alcohols and
ACCEPTED MANUSCRIPT n-alkane shows that larger values are obtained for linear 1-alkanol mixtures. Thus, IDSM
provides for the n-C24(1) + 1-dodecanol(2) system [48], σ r = 0.019, a much higher value than that obtained for the n-C24(1) + cyclododecanol(2) mixture (Table 9), and indicates that effects related to alcohol self-association are much more relevant in the case of linear 1-alkanol mixtures. This is consistent with the relative H mE values of linear or cyclic alkanol + n-alkane
RI PT
systems, which are larger for cycloalkanol solutions. For example, at 298.15 K and equimolar composition, H mE (heptane)/J mol-1 = 745 (cyclohexanol) [49]; 527 (1-hexanol) [50]. These values reveal that self-association of cycloalkanols is weaker and that, therefore, is more easily broken by alkanes. DISQUAC
SC
6.1
Regarding the DISQUAC interaction parameters some remarks are needed. (i) We note DIS that for n-C20(1) or n-C24(1) + 1-octadecanol(2) or + 1-eicosanol(2) mixtures, the Cah,1 value (=
M AN U
−5 ) is meaningfully lower than that reported previously for systems formed by one of these alcohols and n-alkane (= 32) [9,10]. In fact, the latter value was then determined using SLE data for solutions including shorter alkanes, and was assumed to be constant from 1-hexadecanol. Figure S4 shows that DISQUAC and IDSM provide similar results for the heptane(1) + 1eicosanol(2) at x1 ≈ [0.19,0.80]. Thus, in the framework of DISQUAC, the GmE,COMB contribution is nearly counterbalanced by the interactional contribution in that region. For the n-
TE D
C20(1) + 1-eicosanol(2) system, the GmE,COMB term is much lower in absolute value (Table 11) DIS and the Cah,1 value must be decreased in order to provide not very large positive ( γ − 1) values. DIS That is, regarding heptane(1) + 1-octadecanol(2) or + 1-eicosanol(2) mixtures, the Cah,1
EP
coefficient of systems with n-C20, or n-C24 must be decreased in order to compensate the increasing of the GmE,COMB term (Table 11). (ii) We also note that this contribution in aromatic
AC C
hydrocarbon(1) + 1-octadecanol(1), or + 1-eicosanol(2) mixtures changes in the sequence: DIS benzene < biphenyl (Table 11). Therefore, the observed decrease of Cbh,1 when replacing
benzene by biphenyl can be explained similarly as above. (iii) DISQUAC provides rather good results for cyclododecane systems (Table 9, Figure 5), similar to those provided by IDSM or UNIFAC, using similar interaction parameters than for cyclohexane, and this means that the assessment of geometrical parameters has been correctly conducted. (iv) This is also supported by DISQUAC results for cyclododecanol mixtures. (v) Finally, it must be remarked that the QUAC present calculations show two important results: (a) Csh,1 (s = a,c; l = 1,2,3) coefficients for
(a/h) and (c/h) contacts in systems involving cycloalkanols remain constant from cyclopentanol
ACCEPTED MANUSCRIPT QUAC to cyclododecanol [11]; (b) The Cbh,1 (l = 1,2,3) coefficients are the same for mixtures with
benzene, toluene, naphthalene or biphenyl. 6.2
UNIFAC
We note that, as average, deviations between experimental data and model calculations increase in the order: IDSM > UNIFAC > DISQUAC (Table 9). This demonstrates the predictive ability of UNIFAC regarding SLE calculations. A relevant result is that the model
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fails when describing the SLE phase diagram of the cyclohexanol system, characterized by strong effects related to alcohol self-association. This suggests that a new main UNIFAC group for cyclic alkanols should be introduced. On the other hand, Table 11 compares GmE,COMB values obtained using the Flory-Huggins term (DISQUAC) [31,32] and a modified Stavermann-
SC
Guggenheim term (UNIFAC) [36] for the systems under study. It is remarkable that, particularly for 1-alkanol + n-alkane systems, DISQUAC is much more sensitive to the
M AN U
difference in size between mixture compounds than UNIFAC. This also points out to the DIS necessity of providing a new Cah,1 coefficient for such mixtures.
7.
Conclusions
Phase diagrams for the n-C20, or n-C24 or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures have been reported. These systems and several alkane + cycloalkanol systems
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examined show positive ( γ − 1) values. Larger differences are observed for the n-C12 + cyclohexanol mixture as the involved alcohol is more self-associated. Slightly negative ( γ − 1) values are encountered for the n-C24, or n-C28 + cyclododecane mixtures due to the difference size between the system compounds. DISQUAC describes well the phase diagrams of the
C
List of symbols
interchange coefficient
AC C
8.
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studied systems.
∆ C pm
change of the molar heat capacity during the melting process of the compound
G
Gibbs energy
H
enthalpy
∆H m
molar enthalpy of fusion,
∆H tr
molar enthalpy of transition
TSLE
solid-liquid equilibrium temperature
Tm
melting temperature
Ttr
transition temperature
ACCEPTED MANUSCRIPT x
mole fraction in liquid phase
Greek letters
∆
absolute mean deviation (equation 8)
γ
activity coefficient
σr
relative standard deviation (equation 7)
combinatorial term
DIS
dispersive term
E
excess property
QUAC
quasichemical term
Subscripts
SC
COMB
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Superscripts
eutectic
i,j
compound in the mixture, (i, j =1,2)
l
order of the interchange coefficient (l = 1, Gibbs energy; l = 2, enthalpy; l = 3, heat capacity).
M AN U
eu
m
molar property or fusion point
s,t
type of contact surface in DISQUAC (s ≠ t = a (CH3; CH2); b (biphenyl); c (cCH2; c-CH), h (OH) transition
TE D
tr
Acknowledgments
acknowledged.
9.
[2]
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[69]
ACCEPTED MANUSCRIPT
TABLE 1 Sample description Ma /g mol-1
Purityb
Chemical
CAS number
Eicosane
112-95-8
282.547
Avocado
0.99
Tetracosane
646-31-1
338.653
Avocado
0.99
Biphenyl
92-52-4
154.208
Acros
0.99
1-octadecanol
112-92-5
270.494
Fluka
1-eicosanol
629-96-9
298.547
Fluka
> 0.98 > 98
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Molar mass; in mole fraction
RI PT
b
AC C
a
Source
ACCEPTED MANUSCRIPT
TABLE 2 Physical propertiesa of pure compounds at 0.1 MPa: melting temperature, Tm , enthalpy of
enthalpy of the transition, ∆H tr .
329.3 331.65
Biphenyl
J mol-1 K-1
∆H tr /
Ttr /K
kJ mol-1
51.80
329.10
27.35
b
b
18.83b
39.16
47.2c,d
331.2e
41.07e
331.82f
65.4f
325.6g
69.6g
336.9
71.24
338.05b
41.84b
338.0c
68.60c
338.1e
73.72e
337.0g
78.4g
308.2
72.49
309.75i
69.87i
309.65j
69.92j
310.0k
69.88k
311.6l
69.03l
308.95m
66.82m
308.7n
73.5n
321.2
60.98
323.75i
AC C
Tetracosane
kJ mol-1
331.65c,d
EP
Eicosane
∆Cp,m /
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1-eicosanol
b
∆H m /
328.45
SC
1-octadecanol
Tm /K
330.6e
26.9c,d 25.6e
330.97f
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Compound
RI PT
fusion, ∆H m ; heat capacity change at the melting point, ∆C pm ; transition temperature, Ttr and
337.65b
13.93b 30.7c
85.86h
66.6o
319.35
33.82
54.89i
321.25i
31.3i
323.0n
57.2n
319.9n
29.9n
323.65o
57.31o
318.90o
27.68o
323.75o
54.9o
321.25o
31.30o
324.45m
55.51m
320.38m
31.18m
323.75p
54.9p
324.10q
59.3q
321.03q
33.18q
341.1
19.51
36.3r
ACCEPTED MANUSCRIPT 342.10s
18.53s
342.1t
18.57t
TABLE 2 (continued)
a
340.69v
18.6v
342.08w
18.6w
343.5x
19.3x
342.37y
19.7y
RI PT
341.62u
The standard uncertainty for pressure is u ( P ) = 1 kPa; the combined expanded uncertainty
(0.95 level of confidence) for temperatures is U c (Tm ) = U c (Ttr ) = 0.2 K and the relative expanded
uncertainty
(0.95
level
of
confidence)
for
SC
combined
enthalpies
is
U rc ( ∆H m ) = U rc ( ∆H tr ) = 0.06; b[17]; c[51]; d[52]; e[53]; f[54]; g[55]; h[56]; i[57]; j[58]; k[19]; [59]; m[60]; n[61]; o[62]; p[63]; q[20]; r[64]; s[13]; t[65]; u[66]; v[67]; w[68]; x[69]; y[70]
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l
ACCEPTED MANUSCRIPT
TABLE 3 Solid-liquid equilibrium temperatures for eicosane(1), or tetracosane(1) or biphenyl(1)
x1
TSLE /K
Solid phaseb
0.1021
328.4
Alkanol (cr,II)
0.1967
327.5
Alkanol (cr,II)
0.2990
325.9
Alkanol (cr,II)
0.4010
324.9
Alkanol (cr,II)
0.5016
322.8
Alkanol (cr,II)
0.6028
322.0
Alkanol (cr,II)
0.7036
320.5
Alkanol (cr,II)
0.8066
317.7
0.8978
314.2
0.9576
308.9
0.9784
307.8
0.0992
328.6
Alkanol(cr,II)
327.9
Alkanol(cr,II)
326.4
Alkanol(cr,II)
324.7
Alkanol(cr,II)
323.1
Alkanol(cr,II)
319.4
Eutecticc
319.6
Alkane(cr,I)
0.5995
320.0
Alkane(cr,I)
0.6833
320.5
Alkane(cr,I)
0.7902
320.7
Alkane(cr,I)
0.8902
320.7
Alkane(cr,I)
0.1054
328.6
Alkanol(cr,II)
0.3054
324.8
Alkanol(cr,II)
0.4049
322.5
Alkanol(cr,II)
0.4551
321.5
Eutecticc
0.5052
325.0
Biphenyl(cr)
0.3107 0.3952 0.4411 0.5070
AC C
0.5542
EP
0.2009
M AN U
TE D
n- C24
SC
n- C20
RI PT
+ 1-octadecanol(2) mixtures at 0.1 MPaa
Alkanol (cr,II) Alkanol (cr,II) Alkanol (cr,II) Eutecticc
Biphenyl
ACCEPTED MANUSCRIPT 0.5550
326.2
Biphenyl(cr)
0.6048
329.0
Biphenyl(cr)
0.7050
332.7
Biphenyl(cr)
0.8052
335.4
Biphenyl(cr)
0.9047
337.6
Biphenyl(cr)
TABLE 3 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005, and the combined expanded
RI PT
a
uncertainty (0.95 level of confidence) for temperature is U c (T ) = 0.2 K; b(cr) describes a
single solid phase; (cr,I) and (cr,II) represent the solid phases I and II of n-C24 or 1-octadecanol;
EP
TE D
M AN U
SC
coordinates of the eutectic point determined from Tamman plot (see Table 5)
AC C
c
ACCEPTED MANUSCRIPT
TABLE 4 Solid-liquid equilibrium temperatures for eicosane(1), or tetracosane(1), or
x1
TSLE /K
Solid phaseb
0.1021
335.6
Alkanol(cr)
0.1981
333.2
Alkanol(cr)
0.2880
330.8
Alkanol(cr)
0.4010
329.3
Alkanol(cr)
0.4929
327.5
Alkanol(cr)
0.6027
325.2
Alkanol(cr)
0.7034
322.9
Alkanol(cr)
0.8056
320.4
0.8976
316.9
0.9341
313.2
0.9779
307.9
0.0975
336.3
Alkanol(cr)
334.5
Alkanol(cr)
333.2
Alkanol(cr)
331.5
Alkanol(cr)
330.1
Alkanol(cr)
328.2
Alkanol(cr)
326.2
Alkanol(cr)
0.8033
324.3
Alkanol(cr)
0.8439
322.7
Alkanol(cr)
0.9033
321.1
Eutecticc
0.1055
335.8
Alkanol(cr)
0.3050
333.0
Alkanol(cr)
0.4051
331.8
Alkanol(cr)
0.4553
331.3
Alkanol(cr)
0.5051
330.9
Alkanol(cr)
0.5552
329.9
Alkanol(cr)
0.2949 0.4046 0.5009 0.6009
AC C
0.7071
EP
0.1906
M AN U
TE D
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-eicosanol(2) mixtures at 0.1 MPaa
Alkanol(cr) Alkanol(cr) Alkanol(cr) Eutecticc
Biphenyl
ACCEPTED MANUSCRIPT 0.6052
328.7
eutecticc
0.6552
330.2
Biphenyl(cr)
0.7051
331.8
Biphenyl(cr)
0.8048
334.4
Biphenyl(cr)
0.9049
336.9
Biphenyl(cr)
TABLE 4 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005, and the combined expanded
RI PT
a
uncertainty (0.95 level of confidence) for temperature is U c (T ) = 0.2 K; b(cr) describes a
single solid phase; ccoordinates of the eutectic point determined from Tamman plot (see Table
AC C
EP
TE D
M AN U
SC
6, Figure 4)
ACCEPTED MANUSCRIPT
TABLE 5 Heat of melting, ∆H m and eutectic heat , ∆H eu , for eicosane(1), or tetracosane(1) or
x1
∆H m /J g-1
∆H eu /J g-1
0.
191.52
0
0.1021
169.32
27.85
0.1967
155.61
53.05
0.2990
132.63
77.54
0.4010
112.73
104.33
0.5016
96.64
131.83
0.6028
76.04
0.7036
56.94
0.8066
36.25
0.8978
19.45
0.9576
8.75
0.9784
0
1.
256.56
0.
191.52
0
155.70
34.89
114.99
73.62
75.93
112.41
42.11
144.00
0.4411
27.78
165.93
0.5070
0
185.07
0.5542
18.57
162.86
0.5995
34.08
146.54
0.6833
67.90
117.48
0.7902
103.51
75.15
0.8902
145.36
38.43
1.
180.06
0
0.
191.52
0
0.0992 0.2009 0.3107
AC C
0.3952
M AN U
TE D
0
EP
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-octadecanol(2) mixtures at 0.1 MPaa
157.12 186.21 211.41 234.39
248.89
255.22
Biphenyl
ACCEPTED MANUSCRIPT 0.1054
151.13
39.96
0.3054
62.73
111.35
0.4049
23.14
150.66
0.4551
0
171.47
0.5052
13.39
156.79
0.5550
24.87
140.94
0.6048
36.94
124.14
0.7050
59.28
93.54
0.8052
85.68
62.42
0.9047
107.49
30.30
1.
129.37
0
SC
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005 and the
M AN U
a
RI PT
TABLE 5 (conitued)
combined expanded uncertainty (0.95 level of confidence) for enthalpies
AC C
EP
TE D
is U rc ( ∆H m ) = U rc ( ∆H eu ) = 0.06
ACCEPTED MANUSCRIPT
TABLE 6 Heat of melting, ∆H m and eutectic heat , ∆H eu , for eicosane(1), or tetracosane(1) or
x1
∆H m /J g-1
∆H eu /J g-1
0.
238.63
0
0.1021
213.70
28.56
0.1981
193.10
52.34
0.2880
170.91
78.34
0.4010
144.92
103.54
0.4929
120.42
131.82
0.6027
93.63
0.7034
68.35
0.8056
46.15
0.8976
24.05
0.9341
13.26
0.9779
0
1.
256.56
0
238.63
0
216.97
21.10
188.20
40.49
163.64
59.89
134.95
84.35
0.5009
107.55
100.68
0.6009
79.51
21.60
0.7071
52.84
145.06
0.8033
29.74
163.39
0.8439
19.21
172.06
0.9033
0
185.11
1.
180.06
0
0.
238,63
0
0.1055
196.62
35.21
0.0975 0.1906 0.2949
AC C
0.4046
M AN U
TE D
0.
EP
n- C24
SC
n- C20
RI PT
biphenyl(1) + 1-eicosanol(2) mixtures at 0.1 MPaa
157.91 185.41 209.90
233.60
245.09
256.14
Biphenyl
ACCEPTED MANUSCRIPT 0.3050
21.57
94.89
0.4051
84.45
122.41
0.4553
63.38
140.78
0.5051
40.93
164.32
0.5552
28.29
176.93
0.6052
0
190.35
0.6552
22.69
176.39
0.7051
35.34
148.81
0.8048
64.11
97.74
0.9049
93.53
44.43
1.
129.37
0.
SC
a
RI PT
TABLE 6 (continued)
standard uncertainties are: u ( P ) = 1 kPa; u ( x1 ) = 0.0005 and the
is U rc ( ∆H m ) = U rc ( ∆H eu ) = 0.06
TABLE 7
M AN U
combined expanded uncertainty (0.95 level of confidence) for enthalpies
TE D
Relative group increments for molecular volumes rG = VG / VCH 4 and areas, qG = AG / ACH 4 calculated according to the Bondi’s method ( VCH 4 =17.12 10-6 m3 mol-1; ACH 4 = 2.90 10-5 m2 mol)
Group
− CH3 − CH2 −
AC C
c-CH2 a c-CHa
c-CH2
b
rG
qG
Ref.
0.79848
0.73103
[30]
0.59755
0.46552
[30]
0.58645
0.43277
[42]
0.38493
0.16380
[42]
EP
1
0.58645
0.3558
[42]
b
c-CH
0.38493
0.0868
[42]
C6H5-
2.67757
1.83793
[30]
− OH
0.46963
0.50345
[39]
a
in cyclic molecules with 6 C atoms; bin cyclic molecules with 8 or more C atoms.
ACCEPTED MANUSCRIPT
TABLE 8 DIS QUAC Dispersive and quasichemical interchange coefficients, Cst,l and Cst,l (l = 1, Gibbs energy; l
= 2, enthalpy; l = 3, heat capacity), for (s,t) contactsa in alkanol + organic solvent mixtures and
Contact
DIS Cst,2
DIS Cst,3
QUAC Cst,l
(a,h)b
−5
14.7
− 39.5
12.2
c
3.6
3.9
− 20.0
12.2
d
3.0
5.3
− 20.0
12.2
(c,h)e
4.0
3.8
− 20.0
(c,h)f
(a,h)
(a,h)
12
71.1
15.0
71.1
15.0
71.1
12.2
15.0
71.1
4.25
5.2
− 20.0
12.2
15.0
71.1
− 4.5
2.4
− 39
8.9
16.7
21.2
h
0.035
0.36
M AN U
a
QUAC Cst,3
g
(b,h) (a,c)
QUAC Cst,2
SC
DIS Cst,l
RI PT
in cyclododecane + n-alkane systems.
− 1.86
type a, aliphatic in n-alkanes or 1-alkanols; type b, aromatic in biphenyl; type c, c-CH2 or c-CH
in cyclododecane or cyloalkanols; type h, -OH is linear or cyclic alkanols; bin 1-octadecanol or 1-eicosanol + n-C20, or + n-C24; cin cyclohexanol + n-alkane; din cyclododecanol + n-alkane; ein cyclohexanol + cyclohexane; fin cyclododecanol + cyclic alkane; gin 1-octadecanol, or 1-
AC C
EP
TE D
eicosanol + biphenyl; hin cyclododecane + n-alkane
ACCEPTED MANUSCRIPT
TABLE 9 SLE results from DISQUAC, UNIFAC and from the ideal solubility model for solute + alkanol or cyclododecane + n-alkane mixtures: ∆ (TSLE ) , absolute mean deviation (eq. 5), σ r (TSLE ) , standard relative deviation (eq. 4). IDEAL
∆ (TSLE ) / σ r (TSLE ) K
DISQUACb
∆ (TSLE ) / σ r (TSLE ) ∆ (TSLE ) / K
11
2.4
0.011
0.55
n-C24 + 1-octadecanol
11
1.4
0.005
1.3
biphenyl + 1-octadecanol
10
3.7
0.015
13
3.1
0.012
n-C20 + 1-eicosanol
11
2.1
n-C24 + 1-eicosanol
10
2.4
biphenyl + 1-eicosanol
11
3.1
n-C12 + cyclohexanol
22
7.9
n-C24 + cyclododecanol
24
2.3
n-C28 + cyclododecanol
22
1.4
n-C24 + cyclododecane
22
22
b
σ r (TSLE )
0.002
2.0
0.009
this work
0.005
2.0
0.008
this work
0.66
0.003
1.5
0.006
this work
0.60
0.002
1.2
0.004
[25]
M AN U 0.010
2.2
0.008
4.2
0.015
this work
0.009
0.28
0.001
1.4
0.005
this work
0.012
1.5
0.005
0.78
0.003
this work
0.038
0.98
0.006
0.012
0.69
0.003
2.1
0.008
[6]
0.007
0.48
0.002
1.4
0.005
[6]
0.62
0.003
0.47
0.002
0.71
0.003
[6]
0.059
0.003
0.27
0.001
0.83
0.003
[6]
TE D
a
[5]
c
number of data points; calculations using interaction parameters from Table 8; calculation
EP
using interaction parameters from the literature [1,38]
AC C
Ref.
K
SC
n-C20 + 1-octadecanol
n-C28 + cyclododecane
UNIFc
RI PT
Na
System
ACCEPTED MANUSCRIPT
TABLE 10 Coordinates of the eutectic points ( x1eu , Teu ) for solute(1) + alkanol(2) or cyclododecane(1) + nalkane(2) mixtures calculated according to the DISQUACa (DQ), UNIFACb (UNIF) and ideal
Teu /K
n-C20 + 1-octadecanol
Exp. 0.978
DQ 0.976
UNIF. IDEAL Exp. 0.994 0.879 307.8
n-C24 + 1-octadecanol
0.507
0.765
0.858
0.672
319.4
biphenyl + 1-
0.455
0.482
0.434
0.621
321.5
octadecanol 0.464
0.444
0.978
0.985
n-C24 + 1-eicosanol
0.903
0.899
0.942
biphenyl + 1-eicosanol
0.605
0.618
0.586
n-C12 + cyclohexanol
n.a.
0.161
n-C24 + cyclododecanol
0.805
0.708
n-C28 + cyclododecanol
0.533
n-C24 + cyclododecane
0.318 0.227
this work
319.3
320.0
317.0
this work
322.9
324.5
318.55
this work
325.5
307.9
308.0
0.775
321.1
320.3
0.678
328.7
325.8
0.165
n.a.
259.5
0.814
0.554
320.5
321.4
0.485
0.622
0.443
330.0
0.316
0.354
0.316
0.219
0.229
0.224 b
[25] 307.2
this work
320.7
318.3
this work
329.9
322.5
this work
237.9
[5]
310.1
322.3
[6]
330.4
319.8
331.5
[6]
309.2
311.4
310.1
312.0
[6]
316.3
318.0
319.8
319.4
[6]
EP
calculations using parameters listed in Table 8; calculations using parameters from [1,38]
AC C
a
UNIF. IDEAL 308.1 306.8
323.0
0.914
TE D
n-C28 + cyclododecane
DQ 308.0
M AN U
n-C20 + 1-eicosanol
Ref.
SC
x1eu
RI PT
solubility models.
ACCEPTED MANUSCRIPT
TABLE 11 Combinatorial contribution in the framework of the DISQUAC model, GmE,COMB , to the molar excess Gibbs energy at equimolar composition and 298.15 K System
n-C7 + 1-octadecanol
− 250
n-C7 + 1-eicosanol
− 305 −2
n-C20 + 1-octadecanol
− 0.14
n-C24 + 1-dodecanol
− 121
n-C24 + 1-octadecanol
− 20
n-C24 + 1-eicosanol
Benzene + 1-octadecanol Benzene + 1-eicosanol Biphenyl + 1-octadecanol
n-C28 + cyclododecane n-C12 + cyclohexanol n-C24 + cyclododecanol
30
75
75 6 55
− 7.5
60
− 562
− 476
− 638
− 527
− 174
− 147
− 221
− 179
− 238
− 29
− 166
− 52
− 146
244
− 150
4
− 219
− 33
using the Flory-Huggins term [31,32]; busing the modified Stavermann-Guggenheim term [36]
AC C
a
EP
n-C28 + cyclododecanol
TE D
Biphenyl + 1-eicosanol n-C24 + cyclododecane
62
M AN U
n-C20 + 1-eicosanol
UNIFACb
SC
DISQUACa
RI PT
GmE,COMB /J mol-1
Figure 1
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
SLE for the n-C24(1) + 1-eicosanol(2). mixture. Points, experimental results (this work). Solid lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model, or from UNIFAC.
Figure 2
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
EP
SLE for the biphenyl(1) + 1-octadecanol(2) mixture. Points, experimental results: ( ) (this work); (O) [25]. Solid lines, DISQUAC calculations with interaction parameters
AC C
listed in Table 8. Dashed lines, results from the ideal solubility model, or from UNIFAC.
Figure 3
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
SLE for the n-C20(1) + 1-octadecanol(2) ( ), and biphenyl(1) + 1-eicosanol(2) (
)
systems. Points, experimental results (this work). Solid lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed line, results from the ideal solubility model, or from UNIFAC.
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 4. Tamman plot (eutectic heat, ∆H eu ( ), and heat of melting, ∆H m ( ), vs. composition
AC C
EP
( x1 ) for the n-C24(1) + 1-octadecanol(1) system.
AC C
Figure 5
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
SLE for the n-C28(1) + cyclododecane(2) mixture. Points, experimental results [6]. Solid
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
Figure 6
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
SLE for the n-C12(1) + cyclohexanol(2) mixture. Points, experimental results [5]. Solid
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
Figure 7
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
SLE for the n-C28(1) + cyclododecanol(2) mixture. Points, experimental results [6]. Solid
AC C
lines, DISQUAC calculations with interaction parameters listed in Table 8. Dashed lines, results from the ideal solubility model.
ACCEPTED MANUSCRIPT Phase diagrams for n-C20, or n-C24 or biphenyl + 1-octadecanol, or + 1-eicosanol mixtures are reported Data from the literature for the systems alkane + cycloalkanol, or + cyclododecane are also examined. All the mixtures with alkanols show positive (activity coefficient − 1) differences. Larger differences are observed for the n-C12 + cyclohexanol mixture as the alcohol is more
RI PT
self-associated.
AC C
EP
TE D
M AN U
SC
DISQUAC describes well the phase diagrams of the studied systems.