Study of the binary mixtures of {monoglyme + (hexane, cyclohexane, octane, dodecane)} by ECM-average and PFP models

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Highlights

  • Polarization of the real mixture is less than that of the ideal mixture.

  • Molar excess volume does not exert the dominant effect on the polarization of the mixture.

  • Similar influence of molecular interactions on the behaviour of excess permittivity.

  • Excess molar volume is more influenced by the interactions than excess permittivity.

Abstract

Excess molar volumes and excess permittivity of binary mixtures involving monoglyme and alkanes, such as n-hexane, cyclohexane, n-octane and n-dodecane, were calculated from density and relative permittivity measurements for the entire composition range at several temperatures (288.15, 298.15 and 308.15) K and atmospheric pressure. The excess permittivity was calculated on the basis of a recent definition considering the ideal volume fraction. Empirical equations for describing the experimental data in terms of temperature and concentration are given. The experimental values of permittivity have been compared with those estimated by well-known models from literature. The results have indicated that better predictions are obtained when the volume change on mixing is incorporated in these calculations. The contribution of interactions to the excess permittivity was analysed by means of the ECM-average model. The Prigogine–Flory–Patterson (PFP) theory of the thermodynamics of solutions was used to shed light on the contribution of interactions to the excess molar volume. The work concludes with an interpretation of the information given by the theoretical models and the behaviour of both excess magnitudes.

Introduction

On the one hand, relative permittivity is a macroscopic thermo-physical magnitude related to certain microscopic magnitudes of matter, which can provide useful information on intermolecular interactions and structure. On the other hand, relative permittivity data of pure chemicals and mixtures also make up a valuable resource for simulation in industrial processes. As this magnitude is not included in the thermodynamic formalism of mixtures, which is based on the interpretation of excess quantities, a substantial theoretical and experimental effort is being made to improve the methods, thus allowing meaningful conclusions at a molecular level from this quantity. In this regard, the recent definition of excess permittivity of a mixture allows reliable information to be gathered on the behaviour of a given mixture. This definition has been demonstrated from a molecular [1] and a thermodynamic standpoint [2], [3], with both demonstrations arriving at the same expression for ideal excess permittivity.

During the last few years, some studies have been performed on the thermodynamic properties of mixtures containing {polyoxyethylene glycol dimethyl ethers (also called glymes) + organic components}. The glymes or n(ethylene glycol) dimethyl ethers have attracted scientific and industrial interest due to their electrochemical stability, their solvation capacity in polar and apolar solvents, their excess molar heat capacities (some of them with W-shaped-concentration dependence at several temperatures) and their immiscibility windows with long-chain alkanes. Glymes have found application in lithium battery electrolytes, capacitors, anticancer drug production, pharmaceutical production of stabilizers, refrigeration, heat pumping systems and the paint and pesticide industries, among others.

Long-chain alkanes have been the subject of intense thermodynamic studies to understand the nature of molecular interactions when they are mixed with other types of components. Hence, the aim of the present study is to investigate the influence of temperature and hydrocarbon chain (linear and cyclic) on the excess molar volumes and excess relative permittivities. As a complement to previous research works [4], [5], experimental relative permittivity, ɛ, at frequency 1 MHz, and density on mixing, ρ, over the whole composition range at temperatures (288.15, 298.15 and 308.15) K for the binary mixtures {1,2-dimethoxy ethane, (CH3O)(CH2CH2O)CH3, also called monoglyme + (cyclohexane or n-hexane or n-octane or n-dodecane)} at atmospheric pressure were measured. From these experimental values the excess permittivity, ɛE, and excess molar volumes, VmE, on mixing over the entire mole fraction range were calculated. The permittivity values were fitted to a logarithmic equation as a function of the ideal volume fraction and temperature. A polynomial equation as a function of mole fraction and temperature was used to adjust the density values.

The experimental values of the relative permittivity have been compared with those estimated by the following theoretical models: Looyenga [6], Kraszewski [7], Böttcher [8], Iglesias-Peón [9] and ECM-average [10]. The main advantage of these models is that they only require the permittivity value of the pure components and their ideal volume fraction. In order to ascertain the influence of the excess molar volume on the permittivity behaviour the volume change on mixing (non-volume additivity) was incorporated in some of the models mentioned above. Finally, the Prigogine–Flory–Patterson (PFP) theory and the ECM-average model were selected to analyse the influence of interactions on the behaviour of excess molar volume and excess permittivity, respectively.

Section snippets

Materials

Information about the chemicals used is shown in table 1. Chemicals were degassed ultrasonically, dried over molecular sieves Type 3 · 10−8 cm and 4 · 10−8 cm with a pore size of 108 cm (supplied by Aldrich) and kept in an inert argon (with a maximum water content of (2.14 ± 10−6) by mass fraction) atmosphere.

Apparatus and procedure

The permittivity was obtained using a HP4284A precision LCR Meter together with the measuring cell HP16452A, which has parallel plate geometry. A HP16452-61601 test lead was used to connect the

Experimental results

The experimental physical properties of pure components are shown in table 2. They are in accordance with those published in the literature. The experimental relative permittivities on mixing, ɛ, and densities of mixing, ρ, are shown in TABLE 3, TABLE 4, TABLE 5, TABLE 6.

The relative permittivity for each mixture is described as a function of the ideal volume fraction of the alkane, ϕ, and temperature, T, by the following double-polynomial expression [40]:Lnε=ijγijTiϕj,the parameters γij are

Prediction of excess permittivity

The relative permittivity of each system has been estimated using well-known models in the literature:

Looyenga [6]ε=ε11/3+ϕ2(ε21/3-ε11/3)3.

Kraszewski et al. [7]ε1/2=δ1ε11/2+δ2ε21/2.

Böttcher [8]3ε12ε+ε1δ1+3ε22ε+ε2δ2=1.

Iglesias-Peón [9]4ε3+3εid22ln1+ϕ1(ε1/ε2-1(ε1/ε2)ϕ1-1ε-εid3=0.

ECM-average [10]ε=εid-εB(1-ϕA1/3)ϕA(rA/B-1)23ϕA1/31+(1-ϕA1/3)ϕA1/3(rA/B-1)+ϕA2/31+(1-ϕA1/3)ϕA2/3(rA/B-1)+1ϕA1/3+(1-ϕA1/3)rA/B,VA>VBIn this equation, the sub-index A refers to the component with the greatest molar volume, V

Volumetric analysis from the Prigogine–Flory–Patterson theory

The Prigogine–Flory–Patterson (PFP) theory [48], [49], [50], [51], [52], [53], [54], [55] has been widely used to analyse excess thermodynamic properties, such as excess molar volume, excess molar enthalpy and excess isentropic compressibility for different kinds of mixtures [56], [57], [58], [59], [60]. In this theory, excess thermodynamic properties of liquid mixtures are considered to be the sum of three contributions: the interactional contribution, which is proportional to the only

Discussion

The negative behaviour of ɛE for all mixtures reveals the existence of a lower degree of polarization in the real mixture than in the ideal one. A plausible reason behind this behaviour may be the existence of a break in the dipole–dipole interactions between glyme molecules due to the presence of alkanes. Furthermore, the orientation of linear hydrocarbons is broken when they are inserted in-between the glyme polar moieties.

Since an increased molar volume entails a lower number of dipoles per

Conclusions

The following more general conclusions can be drawn:

  • (a)

    The negative sign of ɛE means that polarization of the real mixture is less than that of the ideal mixture, and approaches ideal behaviour when temperature increases.

  • (b)

    The results of the Böttcher and Kraszewski models, considering volume change on mixture, suggest the influence of VmE on the ɛE behaviour.

  • (c)

    The increase in both ɛE (resting negative) and VmE (resting positive) with temperature seems to indicate that the molar excess volume does not

Acknowledgements

We gratefully appreciate the financial support provided by the Xunta de Galicia (Spain) through our research project (INCITE08PXIB312201PR).

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