Thermodynamics of Mixtures Containing Oxaalkanes. 7. Random

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Thermodynamics of Mixtures Containing Oxaalkanes. 7. Random Mixing in Ether + CCl4 Systems Juan Antonio González,*,† Isaías García de la Fuente,† José Carlos Cobos,† and Nicolás Riesco‡ †

GETEF, Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain Department of Earth Science and Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, U.K.

‡

S Supporting Information *

ABSTRACT: Mixtures of a linear or cyclic ether + CCl4 have been studied using the Flory model and the Kirkwood−Buff integrals formalism. The relative variation of the molar excess enthalpy, HmE , along the homologous series of the investigated systems was investigated in terms of the contributions to HmE from the breaking of the ether−ether and CCl4−CCl4 interactions upon mixing and the formation of ether−CCl4 interactions. For CH3(CH2)u−1O(CH2CH2O)v(CH2)u−1CH3 + CCl4 mixtures, an increase in u (v = 0) leads to a weakening of interactions between unlike molecules. In contrast, an increase in v (u fixed) or cyclization leads to stronger interactions between unlike molecules. For acetal mixtures, proximity effects weaken this type of interaction. From the application of the two models, it is shown that the structure of the mixtures is close to that of random mixing. Erroneously, strong orientational effects are predicted by the Flory model for 1,3-dioxolane or 1,3-dioxane + CCl4 systems, but this is because the theory cannot describe asymmetric HmE curves when the mixture compounds have similar values for Vi (molar volume) and for Vi* (reduction parameter for volume). The Flory results on the excess molar volumes are discussed in terms of the interactional, curvature, and P* contributions to this excess function.

1. INTRODUCTION Typical applications of the Flory model1 involve the simultaneous description of excess molar enthalpies, HmE , and excess molar volumes, VmE , of mixtures formed by an alkane and a nonpolar or slightly polar compound (benzene,2 N,N,Ntrialkylamine,3 monoether4) or by two polar compounds of the same chemical nature (1-alkanol +1-alkanol,5 2-methoxyethanol + hydroxyether6). The good agreement between experimental results and theoretical calculations indicates that the randommixing hypothesis, a basic assumption of the model, is largely valid for these solutions. The theory has been also applied to investigate order creation and destruction processes in mixtures of the type alkane + nonpolar or slightly polar compound of a spherical or platelike shape.7−10 Differences between experimental values and Flory results for the molar excess enthalpy, volume, or isobaric heat capacity and the derivatives of VmE with temperature or pressure are ascribed to order effects, as such effects are ignored by the model (random-mixing hypothesis). These studies allow for the conclusion that short orientational order exists in long-chain alkanes that does not appear in highly branched isomeric alkanes or short-chain alkanes. The theory has been also applied to predict isobaric expansion coefficients, αP; isentropic, κS, and isothermal, κT, compressibilities; and speeds of sound, u, of systems involving two alkanes, systems of the type cyclohexane or benzene + nalkane, 11−13 or more complex mixtures of the type alkoxyethanol + dibutyl ether or +1-butanol.14 On the other hand, the Flory model has been used to correctly predict the pressure dependence of the upper critical solution temperatures (UCSTs) and lower critical solution temperatures (LCSTs) of polymer solutions.15,16 In previous works, we showed that the model is a useful tool for investigating the existence of orientational effects in © 2012 American Chemical Society

complex mixtures by studying the variation of the interaction parameter, X12, with composition.17−20 Using this method, we have investigated the following systems: alkoxyethanol +1butanol or + dibutyl ether;17 1-alkanol + monoether;18 and ether + n-alkane,19 + benzene,20 or + toluene.20 Most oxaalkane + CCl4 solutions are characterized by negative HmE values, which are indicative of the existence of specific interactions between unlike molecules.21−23 Such interactions are also supported by solid−liquid equilibria and dielectric constant measurements.24−26 Thus, the formation of molecular addition compounds for 2,5-dioxahexane or 1,4dioxane + CCl4 mixtures has been ascribed to a charge-transfer interaction with the ether oxygen acting as the electron donor and the Cl atoms of CCl4 acting as electron acceptors.24,25 This makes the study of the validity of the random-mixing hypothesis in ether + CCl4 mixtures particularly interesting. The Kirkwood−Buff formalism27−29 has also been applied for a deeper understanding of the orientational and structural effects present in the solutions under study. In a previous article,30 we examined such systems in terms of the DISQUAC31 model [involving dispersive (DIS) and quasichemical (QUAC) interchange coefficients] and analyzed the influence of proximity and cyclization effects on the interaction parameters. From a practical point of view, mixtures containing ethers have a large variety of applications. In chemical systems, molecular recognition has been widely studied using a variety of model compounds such 1,3-dioxane and crown ethers.32,33 Ethers are used as additives to gasoline.34,35 Cyclic polyethers Received: Revised: Accepted: Published: 5108

January 11, 2012 March 11, 2012 March 12, 2012 March 12, 2012 dx.doi.org/10.1021/ie300094e | Ind. Eng. Chem. Res. 2012, 51, 5108−5116

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molecules of each component and of cross-fluctuations. The theory27−29 describes thermodynamic properties of solutions over the entire concentration range in an exact manner by means of the so-called Kirkwood−Buff integrals

have attracted interest as model substances for separation techniques and chemical analyses and in relation to their use in synthetic methods in organic chemistry.36,37 In the case of crown ethers, this is because they can selectively form strong electrostatic complexes with a large variety of ligands in different solvents.38−40

Gij =

2. MODELS 2.1. Flory Model. In this section, a brief summary of the Flory model is provided. More details are given in the original works.1,41−44 The main hypotheses of the theory are as follows: (i) Molecules are divided into segments, which are arbitrarily chosen isomeric portions of the molecule. (ii) The mean intermolecular energy per contact is proportional to −η/vs, where η is a positive constant that characterizes the energy of interaction for a pair of neighboring sites and vs is the segment volume. (iii) When stating the configurational partition function, the number of external degrees of freedom of the segments is assumed to be lower than 3. This is necessary to take into account restrictions on the precise location of a given segment by its neighbors in the same chain. (iv) Random mixing is assumed. The probability of having species i next to any given site is equal to θi, the site fraction. In the case of a very large total number of contact sites, the probability of formation of an interaction between contacts sites belonging to different liquids is θ1θ2. Under these hypotheses, the Flory equation of state is given by

(gij − 1)4πr 2 dr

Gii = RT κT +

xjVj̅ 2 xiVD

Gij = Gji = RT κT −

(5)

−

V xi

(6)

VV i̅ j̅ (7)

VD

where R is the gas constant; xi and V̅ i are the mole fraction and the partial molar volume of component i, respectively (i = 1, 2); V is the molar volume of the solution; and κT is the isothermal compressibility of the mixture. D is defined as:

PV 1 ̅ ̅ ̅ − = 1/3 T̅ VT (1) V̅ −1 where V̅ = V/V*, P̅ = P/P*, and T̅ = T/T* are the reduced volume, reduced pressure, and reduced temperature, respectively. Equation 1 is valid for pure liquids and liquid mixtures. For pure liquids, the reduction parameters, Vi*, Pi*, and Ti* are obtained from data on isobaric expansion coefficients, αPi, and isothermal compressibilities, κTi. The corresponding expressions for the reduction parameters for mixtures are given elsewhere.19 HmE is determined from

E⎞ x x ⎛ ∂ 2Gm ⎟ D = 1 + 1 2 ⎜⎜ RT ⎝ ∂x12 ⎟⎠ P ,T

(8)

where GmE stands for the excess molar Gibbs energy. Using the Gij quantities, it is possible to estimate the so-called linear coefficients of preferential solvation46,47

(2)

δii = xixj(Gii − Gij)

(9)

δij = xixj(Gij − Gjj)

(10)

These quantities satisfy the obvious relation ∑δij = 0 and are useful to determine the local mole fractions of species i around a central j molecule46−48

which can be also written as E Hm = x1V1*θ2X12 /V̅ + x1V1*φ2[(V1̅ − V2̅ )/V0̅ ] E (P2*/V2̅ − P1*/V1̅ ) + Vm /(V0̅ )2 (φ1P1* + φ2P1*)

xij = xi + (3)

δij Vc

(11) 46

where Vc is the volume of the solvation sphere, which can be estimated by simple methods.46

where V̅ 0 = φ1V̅ 1 + φ2V̅ 2. All the symbols have their usual meanings.19 The term that depends directly on X12 in eq 3 is called the interaction contribution41 to HmE . The remaining terms are the so-called equation-of-state contribution41 to HmE . The reduced volume of the mixture, V̅ , in eqs 2 and 3 is obtained from the equation of state. Therefore, the molar excess volume can be calculated as E Vm = (x1V1* + x2V 2*)(V̅ − φ1V1̅ − φ2V2̅ )

∞

The radial distribution function, gij, denotes the probability of finding a molecule of species i in a volume element at a distance r from the center of a molecule of species j. Therefore, the gij function provides information about the solution structure on the microscopic level. The Gij values are interpreted as follows: Gij > 0 represents an excess of molecules of type i in the space around a given molecule of species j. This means that the interactions between molecules of i and j are attractive. Gij < 0 means that i−i and j−j interactions are preferred to i−j interactions.28,45 The Gij integrals can be derived from experimental thermodynamic properties: chemical potential, partial molar volumes, and isothermal compressibility factor. The resulting equations are29,46

V 1/3

⎛1 x V *θ X 1⎞ E Hm = 1 1 2 12 + x1V1*P1*⎜ − ⎟ + x2V 2* V̅ V̅ ⎠ ⎝ V1̅ ⎛1 1⎞ P2*⎜ − ⎟ V̅ ⎠ ⎝ V2̅

∫0

3. ESTIMATION OF THE FLORY INTERACTION PARAMETER X12 is determined from a measurement of HmE at a given composition using the equation17,18 ⎛ ⎛ T̅ ⎞ T̅ ⎞ x1P1*V1*⎜1 − 1 ⎟ + x2P2*V 2*⎜1 − 2 ⎟ ⎝ ⎝ T̅ ⎠ T̅ ⎠ X12 = * x1V1 θ2

(4)

2.2. Kirkwood−Buff Integrals. This formalism is concerned with the study of fluctuations in the number of 5109

(12)

dx.doi.org/10.1021/ie300094e | Ind. Eng. Chem. Res. 2012, 51, 5108−5116


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For the application of this expression, it must be noted that VT is a function of HmE x P *V * x P *V * 1 E (x1P1*V1*T1̅ Hm = 11 1 + 2 2 2 + V1̅ V2̅ VT + x2P2*V 2*T2̅ )

(13)

and that, from the equation of state, V̅ = V̅ (T̅ ). More details have been provided elsewhere.17,18 Equation 12 generalizes the equation previously given to calculate X12 from HmE at x1 = 0.5.49 Properties of the pure compounds at 298.15 K needed for calculations, including molar volumes, αPi, κTi, and the corresponding reduction parameters Pi* and Vi* (i = 1, 2), are listed in Table S1 (Supporting Information). Values of these properties at T ≠ 298.15 K were estimated according to the method used previously.50 X12 values determined from experimental HmE data at x1= 0.5 are collected in Table S2 (Supporting Information).

4. RESULTS 4.1. Flory Results. HmE and VmE values obtained from the Flory model using X12 values at x1 = 0.5 are listed in Tables S2 and S3, respectively (Supporting Information). Experimental and theoretical values for HmE and VmE are compared graphically in Figures 1−4. For the sake of clarity, Table S2 (Supporting

Figure 2. HmE at 298.15 K for linear polyether (1) or acetal (1) + CCl4 (2) mixtures. Points represent experimental results:23 (●), 2,5dioxahexane, (▲) 2,4-dioxapentane, (▼) 3,6-dioxaoctane, (■) 2,5,8,11-tetraoxadodecane. Solid lines represent Flory calculations with interaction parameters from Table S2 (Supporting Information).

Figure 3. HmE at temperature T for cyclic ether (1) + CCl4 (2) mixtures. Points represent experimental results: (●) tetrahydrofuran85 (T = 303.15 K), (▲) 1,3-dioxolane,21 (▼) 1,3-dioxane,21 (■) 1,4dioxane86 (T = 298.15 K). Solid lines represent Flory calculations with interaction parameters from Table S2 (Supporting Information).

HmE

Figure 1. at 298.15 K for CH3(CH2)u−1O(CH2)u−1CH3 (1) + CCl4 (2) mixtures. Points represent experimental results: (●) u = 2,23 (■) u = 3,23 (▲) u = 5,23 (▼) u = 6.59 Solid lines represent Flory calculations with interaction parameters from Table S2 (Supporting Information).

given in the original works. To obtain detailed information on the concentration dependence of X12, this magnitude was E values at Δx1 determined using eq 12 and the mentioned Hm,exp = 0.05. The X12(x1) variation was estimated from the equation

Information) also includes the relative standard deviations for HmE , defined as ⎡ ⎢1 E σr(Hm) = ⎢ ⎢⎣ N

∑

1/2

E ⎛ HE ⎞2 ⎤ − Hm,calc ⎜ m,exp ⎟ ⎥ E ⎜ ⎟ ⎥ Hm,exp ⎝ ⎠ ⎥⎦

Δi = (14)

|ΔX12|imax |X12(x1 = 0.5)|

(15)

where |ΔX12|imax is the maximum absolute value of the X12(x1) − X12(x1 = 0.5) difference in the ranges [0.05,0.45] (i = 1) and [0.55,0.95] (i = 2). The corresponding values are listed in Table S4 (Supporting Information); see also Figure 5.

E Hm,exp

where N (= 19) is the number of data points and stands for the smoothed HmE values calculated at Δx1 = 0.05 in the composition range [0.05, 0.95] from polynomial expansions 5110



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Figure 6. δij at 298.15 K for ether (1) + CCl4 (2) mixtures. Solid lines, diethyl ether;88,89 dashed lines, 2,5-dioxahexane.88,89

Figure 4. VmE at 298.15 K for cyclic ether (1) + CCl4 (2) mixtures. Points represent experimental results:87 (●) tetrahydrofuran, (■) 1,4dioxane. Solid lines represent Flory calculations with interaction parameters from Table S2 (Supporting Information).

Figure 7. δij at 298.15 K for 1,4-dioxane (1) + organic solvent (2) mixtures. Solid lines, CCl4;87,90 dashed lines, heptane.73,90 Figure 5. X12 at 298.15 K for cyclic ether (1) + CCl4 (2) mixtures. Points represent results obtained from eq 12: (●) tetrahydrofuran,21 (■) tetrahydropyran,21 (▼) 1,3-dioxolane,21 (▲) 1,4-dioxane.86 Solid lines represent X12 values at x1 = 0.5 (Table S2, Supporting Information).

VmE = 0 was assumed. This introduces a small error in the calculation of the partial molar volumes of the components, magnitudes that are of secondary importance when Gij values are determined.45 The sources of the GmE and VmE data used are given in Table S5 (Supporting Information).

4.2. Results from the Kirkwood−Buff Formalism. Magnitudes needed for calculations, including molar volumes of pure compounds, Vi, and their isothermal compressibilities, κTi, are collected in Table S1 (Supporting Information). Experimental values for Gij and related quantities (Table S5, Supporting Information; Figures 6 and 7) were obtained as follows: For mixtures, the isothermal compressibilities were calculated assuming ideal solution behavior, that is, κT = Φ1κT1 + Φ2κT2, where Φi is the volume fraction of component i in the system. This assumption does not influence the final calculations of the Kirkwood−Buff integrals.51 D values were calculated using Redlich−Kister-type expansions for GmE determined from VLE data. In the absence of any VmE data,

5. DISCUSSION If effects related to so-called equation-of-state term are neglected,52,53 the HmE value of an A + S mixture is the result of three contributions: a negative term that arises from the creation of the new A−S interactions, ΔHA−S, and two positive contributions that come from the disruption, upon mixing, of the A−A (ΔHA−A) and S−S (ΔHS−S) interactions. Therefore, one can write54−56 E Hm = ΔHA−A + ΔHS−S + ΔHA−S

(16)

In our case, A represents ether, and S represents CCl4. Equation 16 can be extended57,58 to x1 → 0 to evaluate 5111



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comparison to those of monoethers. For example, μ̅(2,5dioxahexane) = 0.653.30 The stronger ether−ether interactions in polyether systems are also supported by the fact that, at 298.15 K, the systems 2,5,8,11-tetraoxadodecane + dodecane and 2,5,8,11,14-pentaoxapentadecane + decane are close to their UCSTs (280.81 and 291.98 K, respectively60). In addition, the larger etheric surface of polyethers makes the creation of the new ether−Cl interactions upon mixing easier. We note that HmE (3,6-dioxaoctane) < HmE (2,5-dioxahexane) (Table S2, Supporting Information). This can be explained by the lower ΔHO−O contribution to HmE and not a stronger ether−CCl4 interactions for the 3,6-dioxaoctane solution (Table S6, Supporting Information). In fact, μ̅(3,6-dioxaoctane) = 0.525,30 and in heptane solutions, HmE /J·mol−1 = 889 (3,6-dioxaoctane)61 < 1285 (2,5-dioxahexane).62 It is known that proximity effects lead to a weakening of the interactions between ether molecules in mixtures with alkanes,63 as μ̅(acetal) < μ̅(diether) [e.g., μ̅(3,5-dioxaheptane) = 0.42130] and then HmE (3,6-dioxaoctane) > HmE (3,5dioxaheptane)22 = 605 J·mol−1. In solutions containing CCl4, interactions between unlike molecules also become weaker when a diether is replaced by an acetal of similar size (Table S6, Supporting Information). In this case, the lower ΔHO−O contribution is overcompensated by a lower |ΔHO−CCl4| term, and this results in higher HmE values for acetal solutions (Table S2, Supporting Information). For linear polyether or acetal + heptane systems, using Flory theory, we previously obtained19 σr(HmE ) = 0.055 (2,5dioxahexane), 0.065 (2,5,8-trioxanonane), 0.065 (3,6-dioxaoctane), 0.058 (2,4-dioxapentane), 0.039 (3,5-dioxaheptane), and 0.055 (2,5,8,11-tetraoxadodecane). These values are similar to those determined here for CCl4 solutions (Table S2, Supporting Information). Therefore, it can be concluded that the mixture structure is initially close to random mixing. Note that the Δi values are lower than for the systems with linear monoethers (Table S4, Supporting Information). 5.3. Cyclic Ether + CCl4. For monoethers, cyclization (that is, replacement of a linear ether by a homomorphic cyclic one) also implies decreased HmE values, which can be explained as in the preceding section. Ether−CCl4 interactions are stronger in solutions with cyclic ethers, and the more negative ΔHO−CCl4 contribution (Table S6, Supporting Information) is prevalent over the more positive ΔHO−O term. This is because the μ̅ values of tetrahydrofuran, 0.723, and of tetrahydropyran, 0.619, are larger than those of the homomorphic linear ethers30 and the oxygen atom is less sterically hindered in cyclic molecules. In contrast, for mixtures with ethers containing two oxygen atoms, HmE (linear ether) < HmE (cyclic ether) (Table S2, Supporting Information). This behavior might be because the ΔHO−O contribution becomes more relevant in this case (Table S6, Supporting Information). Results from the Flory model for heptane mixtures are as follows: σr(HmE ) = 0.064 (tetrahydrofuran), 0.062 (tetrahydropyran), 0.094 (1,3-dioxolane), 0.159 (1,3-dioxane), and 0.071 (1,4-dioxane).19 For the systems with CCl4, σr(HmE ) differs substantially for systems containing cyclic monoethers, 1,4-dioxane, or cyclic acetals. For the former, orientational effects are weak, as indicated by low σr(HmE ) and Δi values (Tables S2 and S4, Supporting Information), so the randommixing hypothesis can be considered to be valid to a large extent. In contrast, the model predicts rather strong orientational effects in systems with 1,3-dioxane and 1,3-dioxolane.

ΔHO−CCl4, the enthalpy of the interactions between ether and CCl4 in the studied solutions. In such a case, ΔHO−O and ΔHCCl4−CCl4 can be replaced by H1E,∞ (partial excess molar enthalpy at infinite dilution of the first component) of ether or CCl4 + alkane systems. Thus ΔHO−CCl 4 = H1E, ∞(ether + CCl 4) − H1E, ∞ (ether + alkane) − H1E, ∞(CCl 4 + alkane) (17)

For cyclic ether + alkane systems in this work, the alkane was cyclohexane. For linear ether or CCl4 + alkane mixtures, the alkane considered was heptane. Table S6 (Supporting Information) lists ΔHO−CCl4 values for some selected mixtures. In the following sections, we are referring to values of the excess functions at 298.15 K and equimolar composition. 5.1. CH3(CH2)u−1O(CH2)u−1CH3 + CCl4. Here, HmE increases with u (Table S2, Supporting Information). This can be explained on the basis of the following effects: (i) The ether− CCl4 interactions become weaker, as indicated by the decrease of the |ΔHO−CCl4| term for increased u values, which predominates over the lower positive ΔHO−O contribution (Table S6, Supporting Information). This is due to the decrease of the effective dipole moment, μ̅,30,52 of the ether: 0.599 (u = 1) > 0.488 (u = 2) > 0.393 (u = 3) > 0.353 (u = 4) > 0.323 (u = 5).30 (ii) Steric effects also play a role, as interactions between unlike molecules are less probable for mixtures with ethers of larger u values because their etheric surface is smaller and is more sterically hindered by the longer adjacent alkyl groups. Orientational effects in di-n-alkylether + CCl4 mixtures and in di-n-alkylether or CCl4 + n-alkane systems are very similar. In fact, the mean relative standard deviation for HmE [σ̅r(HmE ), calculated as ∑σr(HmE )/NS, where NS is the number of systems] are 0.078, 0.046,19 and 0.073, respectively (see Table S7, Supporting Information). In view of these results, it is possible to conclude that the random-mixing hypothesis is a good approximation for these systems. Inspection of the variation of X12 with x1 shows that, as a general trend, the model underestimates interactions between like molecules for mixtures with lower concentrations of the ether and higher concentrations of CCl4. The same behavior is observed for di-nalkylether + n-alkane19 and CCl4 + decane or + dodecane systems. At x1 > 0.5, the model overestimates interactions between like molecules. A comment regarding some large Δi values listed in Table S4 (Supporting Information) is necessary. Such values might be related to experimental inaccuracies or to uncertain HmE values at low concentrations used for the determination of X12. Note that, usually, the HmE values are obtained from Redlich−Kister coefficients fitted to HmE data at concentrations more or less far from dilute regions. This is the case for the solutions diethyl ether + CCl4 at x1= 0.05 and 0.95 and dipropyl ether + CCl4 at x1= 0.95.23,59 5.2. Linear Polyether or Acetal + CCl4. The replacement of a linear monoether by a linear polyether of similar size leads to a decrease in HmE that can be ascribed to interactions between unlike molecules becoming stronger in the latter mixtures (higher |ΔHO−CCl4| values; Table S6, Supporting Information), in such way that the more negative ΔHO−CCl4 contribution is prevalent over the more positive ΔHO−O term. This is consistent with the higher μ̅ values of polyethers in 5112



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However, such effects are weak, as revealed by low |HmE | values (Table S2, Supporting Information). It should be noted here E values of the 1,4-dioxane + CH2Cl2 and 1,3that the Cpm dioxane + CH2Cl2 mixtures are positive and small, 2.45 and 3.03 J·mol−1·K−1, respectively,64 which points to the existence of dipolar interactions in these mixtures. Moreover, the E corresponding molar excess isochoric heat capacities, CVm , are −1 −1 65 −0.65 (1,4-dioxane) and 1.81 (1,3-dioxane) J·mol ·K . This allows for the conclusion that the random-mixing hypothesis is also a reasonable approximation for such solutions as, in terms E = 0.66 The same trend is expected for of Flory theory, CVm solutions with CCl4. The large σr(HmE ) value of the 1,3-dioxane + CCl4 system results from the fact that the model cannot represent very asymmetric curves, such as s-shaped curves, when the mixture compounds are characterized by similar Vi and Vi* values. The same behavior is encountered in diethyl ether or 1,4-dioxane + benzene mixtures.20 This is a shortcoming of the model. 5.4. Excess Molar Volumes. For most of the systems listed in Table S3 (Supporting Information), VmE is negative, which indicates that the negative contributions to this excess property from interactions between unlike molecules and/or from structural effects are predominant over the positive contribution from the breaking of interactions between like molecules. In addition, HmE and VmE usually have the same sign (negative) and change in the same sequence for the studied solutions. This suggests that, as a general trend, the main contribution to VmE is the interactional one. The observed deviations of the calculated VmE values from the experimental results can be rather easily analyzed in terms of the Prigogine−Flory−Patterson (PFP) version of the theory.67 In this version of the model, the interactional contribution is proportional to X12, the curvature term of VmE is proportional to −(V̅ 1−V̅ 2)2, and the so-called P* term is proportional to (P1* − P2*)(V̅ 1 − V̅ 2). Note the following important points: (i) In CH3(CH2)u−1O(CH2)u−1CH3 + CCl4 mixtures, VmE increases with u and is slightly positive for the di-n-hexylether solution. This might be the result of a weakening of the ether− CCl4 interactions and of a larger positive contribution to VmE from the disruption, upon mixing, of the CCl 4 −CCl 4 interactions. The VmE values of CCl4 + n-alkane systems are negative for the pentane mixture (−0.203 cm3·mol−1)68 and increase with alkane size (0.51 cm3·mol−1 for the solution with dodecane69). For u = 6, this positive contribution predominates, and VmE becomes slightly positive. In terms of the PFP theory, the observed variation in VmE is related to increases of the interactional and P* terms with u. The positive predicted VmE values for the systems with u = 5 and 6 are related to a large positive P* term. (ii) Similar behaviors are encountered for the HmE and VmE values of linear diether or acetal + CCl4 systems. The size increase of the oxaalkane leads to a VmE decrease, which should be interpreted as a consequence of a lower contribution to VmE from the disruption of the interactions between like molecules during the mixing process. For heptane solutions, VmE (2,5-dioxahexane)70 = 1.092 > VmE (3,6-dioxaoctane)71 = 0.7426 (values in cm3·mol−1). Proximity effects lead to an increase of VmE probably related to a weakening of the ether− CCl4 interactions in acetals compared to those in diethers, which predominates over the lower contribution from the breaking of the ether−ether interactions. For these mixtures, the contributions to VmE from the P* and curvature terms are negligible. Thus, differences between experimental and calculated VmE values can be ascribed to model overestimation

of the interactional contribution. (iii) For solutions containing cyclic monoethers, the model describes VmE rather accurately (Table S3, Supporting Information; Figure 4). This indicates that a close link exists between HmE and VmE . Accordingly, the P* and curvature contributions are also negligible in this case. On the other hand, VmE is more negative for solutions containing 1,3-dioxolane or 1,4-dioxane (Table S3, Supporting Information). Note that, in heptane solutions, VmE values of mixtures containing 1,3-dioxolane72 (0.7475 cm3·mol−1) or 1,4-dioxane73 (0.728 cm3·mol−1) are much higher than those of mixtures with tetrahydrofuran (THF) (0.3202 cm3·mol−1)74 or theophylline (THP) (0.2491 cm3·mol−1).74 It is remarkable that VmE (diethyl ether) < VmE (THF) (Table S3, Supporting Information), even though interactions between unlike molecules are slightly stronger in the THF solution (Table S6, Supporting Information). This might suggest the existence of structural effects in the diethyl ether mixture. Note that VmE /cm3·mol−1 = −0.203 (CCl4 + pentane68) < −0.036 (CCl4 + cyclopentane75). 5.5. Results from the Kirkwood−Buff Formalism. It is known that, for 1-alkanol + alkane systems, the Gij integrals and δij coefficients are large and positive quantities as a consequence of the self-association effects of 1-alkanols. Thus, for the 1butanol + heptane mixture at 313.15 K, the G11 and δ11 curves show maxima around 8000 and 900 cm3·mol−1, respectively, at x1 ≈ 0.15.76 In contrast, for the 1,4-dioxane or THF + heptane mixtures, G11 and δ11 have much lower values, as interactions between like molecules are much weaker. Thus, at 298.15 K and equimolar composition, G11/cm3·mol−1 = 405 (1,4dioxane) and 32.4 (THF)19 (see Figure 7). G11 and δ11 initially decrease when heptane is replaced by CCl4 (Table S5, Supporting Information; Figures 6 and 7). This behavior can be ascribed to the new ether−CCl4 interactions created upon mixing. Small |Gij| and |δij| values (Table S5, Supporting Information) are usually encountered in solutions with a random-mixing structure. In fact, calculations show that the local mole fractions, x11 and x12, are practically identical to the bulk values. This means that the studied solutions hardly show any preferential solvation, as was previously pointed out for the THF mixture. 77 Many other mixtures behave similarly.19,46,47,78−81 5.6. Comparison with Oxaalkane + Benzene Mixtures. For mixtures containing a given ether, HmE (CCl4) (Table S2, Supporting Information) < HmE (C6H6)20 (Figure 8). An exception was found for 1,3-dioxolane solutions: 164 J·mol−1 (CCl4)82 versus 79 J·mol−1 (C6H6).82 It is remarkable that, for systems with di-n-alkylethers, |ΔHO−S| is higher for S = CCl4 (Table S6, Supporting Information) than for S = C6H620 (Figure 8). The opposite behavior is encountered for solutions containing the remainder of the oxaalkanes. Thus, the higher positive contribution to HmE from the disruption of the S−S interactions when S = C6H6 can explain the higher HmE values for ether + C6H6 systems. Note the large difference in HmE values for mixtures with hexane: 316 J·mol−1 (CCl4)83 versus 897 J·mol−1 (C6H6).84 The magnitudes Gij and δij are similar for ether + CCl4 (Table S5, Supporting Information) and ether + C6H681 systems. For the tetrahydrofuran + C6H6 mixture,81 δ11= 5.6 cm3·mol−1 and δ12 = 5.8 cm3·mol−1. Thus, it is possible to conclude that the mixture structures are also similar for the two types of solutions and close to that of random mixing. 5113



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6. CONCLUSIONS The relative variation of HmE , along a homologous series, for ether + CCl4 mixtures has been discussed taking into consideration contributions to HmE from the breaking of the ether−ether and CCl4−CCl4 interactions upon mixing, as well as that related to the formation of new interactions between unlike molecules. An increase of u (v fixed) in CH3(CH2)u−1O(CH2CH2O)v(CH2)u−1CH3 + CCl4 mixtures leads to a weakening of the interactions between unlike molecules, which are also weakened by proximity effects in acetal systems. Effects related to an increase of v (u fixed) or to cyclization lead to stronger interactions between unlike molecules. Application of the Flory model showed that orientational effects are weak in the investigated systems, in such way that the mixture structure is close to random mixing. These findings were confirmed by Kirkwood−Buff integrals calculations. ASSOCIATED CONTENT

S Supporting Information *

Additional information as mentioned in the text, together with the necessary references. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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Figure 8. HmE at 298.15 K and equimolar composition (dashed lines) or (ΔHO−S/10) at 298.15 K (solid lines) for the mixtures ether + CCl4 (solid symbols, S = CCl4) or ether + benzene (open symbols, S = C6H6) versus n, the number of C + O atoms in the ether. Symbols: circles, di-n-alkylethers; squares, 2,5-dioxahexane or 3,6-dioxaoctane. For the sources of data, see Tables S2 and S6 (Supporting Information) (CCl4) or reference 20 (benzene).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +34-983-423136. Tel.: +34983-423757. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support received from the Ministerio de Educación y Ciencia, under Project FIS2010-16957. 5114



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Thermodynamics of Mixtures Containing Oxaalkanes. 7. Random

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