Static Dielectric Permittivity of Homologous Series of Liquid Cyclic

Article pubs.acs.org/jced

Static Dielectric Permittivity of Homologous Series of Liquid Cyclic Ethers, 3n-Crown-n, n = 4 to 6 ́ Jolanta Swiergiel* and Jan Jadzẏ n

Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznań, Poland ABSTRACT: The static dielectric properties of the homologous series of liquid cyclic ethers, 12-crown-4, 15-crown-5, and 18-crown-6, were analyzed with the use of the electric modulus spectra. In isothermal conditions, the polarity of the ethers composed of the molecules with an even number of the oxygen atoms in the ring, 12-crown-4 and 18-crown-6, are quite similar to each other, whereas the odd number of the oxygen atoms in the ring of 15-crown-5 reflects itself in a considerable higher relative permittivity of the compound. It was shown that the observed permittivity behavior results chiefly from a different dipole moment of individual molecules of the ethers.

1. INTRODUCTION The cyclic ethers (macrocyclic polyethers) are the subject of interest in many fields of chemistry, materials science, and molecular biology.1−4 Much of the interest results from the remarkable ability of the ethers to selective bind of cations and, next, a possibility to transport the ions into lipophilic medium.5−8 Crown ethers are also of important interest to theoretical chemists because of the catalytic abilities of the compounds and their enzyme-like specificity.3 Exceptional properties of these ethers are certainly related to the flexibility of the crown rings, and this is why the conformational behavior of the rings in different environments and temperatures is actually one of the important topics of both theoretical and experimental supramolecular chemistry.9−18 An exceptional flexibility is the most important feature of the cyclic ethers backbone which can adopt quite different limiting structures, from open (ring-like) to folded (cage-like), depending on type of the actual environment. As in the both types of structure, the lone-pair orbitals of the ether oxygens are essentially different in their mutual arrangement, so the resultant polarity of the cyclic ethers is not easy to predict, and this is why theoretical conformational modeling is the subject of constant interest. The compounds studied in this paper are the best known representatives of the great family of crown ethers. We present the results of the static dielectric studies performed for 12crown-4, 15-crown-5, and 18-crown-6 in a wide temperature range. The aim of the present study is to show an influence of different number of −CH2CH2O− groups in the crown ring on the polarity of the liquid cyclic ethers.

Sigma-Aldrich. As the main impurity, which could strongly influence the permittivity value of the ethers, is water, the compounds were stored (in the liquid state) over 4 Å molecular sieves (Sigma-Aldrich) during about one week before the measurements. The impedance spectra were recorded with the use of an HP 4194A impedance/gain phase analyzer in the frequency range from 500 Hz to 5 MHz. A measuring capacitor consisted of three plane electrodes (the surface of about 1 cm2): one central and two grounded on each side, with a distance between them equal to 0.2 mm. The shape of the capacitor electrodes is rectangular, and they are made with a gold-plated copper. The construction details concerning the measuring cell are presented in the papers by Legrand et al.19,20 A standard calibration of the measuring cell, at 298.15 K, with the use of air (p = 1 atm, ε = 1.0005), cyclohexane (spectroscopic grade), carbon tetrachloride (spectroscopic grade), and chloroform and acetone (both liquids purified by distillation), was performed. The liquids were stored over 4 Å molecular sieves. The standard deviation from the linear dependence of the capacitance versus permittivity (including the permittivity of air) was equal 0.2. The capacitance of the cell (C0) was equal to 9.68 ± 0.05 pF. The probing electric field intensity E was equal to about 1 V·mm−1. The electrical heating of high performance with the use of a “Scientific Instruments” temperature controller, model 9700, assured very good temperature stabilization (± 2·10−3 K). As a cooling medium the vapor of liquid nitrogen was used. Such equipment allows one to determine the static permittivity with an uncertainty less than 0.5 %.

2. EXPERIMENTAL SECTION The studied compounds, 12-crown-4 (1,4,7,10-tetraoxacyclododecane), 15-crown-5 (1,4,7,10,13-pentaoxacyclopentadecane), and 18-crown-6 (1,4,7,10,13,16-hexaoxacyclooctadecane) (the sample purities of w = 0.99), were supplied from © 2012 American Chemical Society

Received: February 27, 2012 Accepted: July 9, 2012 Published: July 17, 2012 2271

dx.doi.org/10.1021/je300234g | J. Chem. Eng. Data 2012, 57, 2271−2274

Journal of Chemical & Engineering Data

Article

The static relative permittivity (εs) of cyclic ethers was determined from the analysis of the electric modulus spectra21−25 M *(ω) ≡ 1/ε* = M′(ω) + jM″(ω)

(1)

resulting from the transformation of the impedance spectra, Z*(ω) = Z′(ω) + jZ″(ω), according to relation: M *(ω) = jωC0Z*(ω)

(2)

Hence, the real (M′) and imaginary (M″) parts of the electric modulus are equal to: M′(ω) = −ωC0Z″(ω)

M″(ω) = ωC0Z′(ω)

(3)

ε*(ω) = ε′(ω) − jε″(ω), appearing in eq 1, is the complex dielectric permittivity, ω = 2πf is the angular frequency of the electric stimulus, f is the linear frequency, and j = (−1)1/2. C0 = kε0 is the electric capacitance of empty measuring cell, k = S/l, S and l are the electrode surface and the distance between the electrodes, respectively, and ε0 = 8.85 pF·m−1 is the permittivity of free space. The measurements were performed with decreasing temperature. The frequencies of the measuring electric field used in our experiment are relatively low in comparison to the frequency range where the orientational dipolar relaxation occurs in crown ethers studied,15 so the results obtained in this paper concern the static dielectric properties of the compounds.

3. RESULTS AND DISCUSSION Figure 1 presents the electric modulus spectra recorded for 15crown-5, as an example. The spectra are similar for other crown ethers under investigation as illustrated in Figure 2, where the electric modulus spectra of all studied cyclic ethers are presented in the complex plane at 323 K. The spectra have the form of semicircles with the centers placed in the real axes of the electric modulus; that is, the shape of the modulus spectra of the ethers is of Debye's type.25 As the frequency range of the electric stimulus used in our experiments corresponds to the static dielectric regime of the compounds, the real and imaginary parts of the permittivity are given by: ε′ = εs

ε″(ω) = σDC/ωε0

and

Figure 1. Electric modulus spectra, M*(ω) = 1/ε*(ω), of 15-crown-5 resulting from transformation of the impedance spectra according to eq 2. The solid lines represent the best fit of eq 5 to the experimental data (points).

(4) Figure 2. Electric modulus spectra of cyclic ethers, 3n-crown-n, n = 4, 5, 6, in the complex plane, at 323 K. The crosses on the abscissa are the centers of the semicircles.

where σDC denotes the dc ionic conductivity in liquid. As it was shown recently,25 in the static dielectric cases, the electric modulus spectra are described with following Debye type equations: M′(ω) =

εs−1

−

εs−1 1 + ω 2τσ2

and

M″(ω) =

modulus formalism has that advantage of the dielectric spectra that it markedly reduces the electrode polarization effects which can strongly influence the static permittivity. However, that remark concerns only the situation where the frequency of the electric stimulus used is significantly lower in comparison to the frequency region where the dipolar relaxation in the compound studied occurs. Then, in the static dielectric region the electric modulus spectra are of the simplest possible (the Debye type), and from the fitting of eq 5 to the experimental data the static permittivity is determined with a very high accuracy. Figure 3 contains also the permittivity data of 18-crown-6 measured by Perrin et al.11 in the temperature range from (50 to 90) °C. In the paper the experimental results are presented in a form of an empirical equation: ε−1 = 0.1072 + 0.000192t, t is the temperature in the Celsius scale, and the correlation coefficient is given by the authors as 0.996. According to those presented

εs−1ωτσ 1 + ω 2τσ2 (5)

or in the complex notation: M *(ω) = εs−1 −

εs−1 1 + jωτσ

(6)

where τσ = ε0εs/σDC is the conductivity relaxation time. As can be seen in Figure 2, eq 5 perfectly reproduces (the solid lines) the electric modulus spectra of 15-crown-5 and also other crown ethers studied (Figure 3). Figure 3 presents temperature dependences of the static permittivity of crown ethers obtained from the best fit of eq 5 to the electric modulus spectra. The using of the electric 2272



Article

Table 2. Values of the Parameters of Equation 7 Corresponding to Cyclic Ethers 3n-Crown-n of Different n and Standard Deviations Calculated with Equation 8 n

A

4 5 6

−0.311 1.037 −10.406

σ*

C/K2

B/K 3

2.225·10 1.253·103 10.540·103

5

3.258·10 9.098·105 −14.031·105

0.0075 0.0038 0.0020

The numerical data of the dielectric permittivities of the crown ethers are presented in Table 1. The solid lines in Figure 3 represent the best fit of the empirical equation: B C + 2 (7) T T to the experimental permittivity data. T is the absolute temperature. The values of the fitting parameters A, B, and C are presented in Table 2. Table 2 contains also the standard deviations, σ*, calculated with the formula:

Figure 3. Temperature dependences of the static dielectric permittivity of 3n-crown-n of different number n of oxygen atoms in the ring. The solid lines represent the best fit of eq 7 to the experimental data (points). The literature permittivity data11 for 18-crown-6 are represented by full symbols.

εs(T ) = A +

Table 1. Static Dielectric Permittivity (εs) of Liquid Cyclic Ethers 3n-Crown-n of Different Number n of Oxygen Atoms in the Ring

⎛ ∑ (ε − ε )2 ⎞1/2 icalc i iexp ⎟ σ * = ⎜⎜ ⎟ n − n d p ⎝ ⎠

εs n T/K 273.15 275.65 278.15 280.65 283.15 285.65 288.15 290.65 293.15 295.65 298.15 300.65 303.15 305.65 308.15 310.65 313.15 315.65 318.15 320.65 323.15 325.65 328.15 330.65 333.15 335.65 338.15 340.65 343.15 345.65 348.15 350.65 353.15

4

10.95 10.82 10.70 10.58 10.45 10.34 10.22 10.11 10.00 9.90 9.79 9.69 9.59 9.49 9.41 9.31 9.22 9.13 9.04 8.94 8.86 8.76 8.68 8.59

5 17.82 17.56 17.30 17.05 16.81 16.57 16.34 16.11 15.89 15.68 15.48 15.28 15.08 14.88 14.69 14.50 14.31 14.14 13.96 13.79 13.63 13.46 13.30 13.15 13.00

(8)

where nd and np denote the number of the experimental points and the number of the parameters, respectively. The data presented in Figure 3 show that the studied crown ethers are the liquid of a medium polarity, but in that score, the compound with the odd number of the ether’s oxygen distinctly predominates over the “even” cyclic ethers. The odd−even effect in the static permittivity is expected as due to the “unpaired” oxygen, the crown ring of 15-crown-5 molecule, independently on the variety of its possible conformation,13 should exhibit the polarity higher than the rings with an even number of oxygen atoms. The effect manifests itself in the dipole moment values of the single molecules of cyclic ethers measured by Caswell and Savannunt26 in diluted solutions of the ethers in nonpolar media. The dipole moment of 15-crown5 molecule is significantly higher than that of remaining ether molecules.

6

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +48 61 86 95 162. E-mail: [email protected].

8.90 8.86 8.82 8.77 8.73 8.69 8.64 8.59 8.54 8.49 8.44 8.39 8.34 8.29 8.24 8.19

Notes

The authors declare no competing financial interest.

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REFERENCES

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just below our calculations, this empirical equation is too simplified, and it is necessary to add the quadratic term. 2273



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Static Dielectric Permittivity of Homologous Series of Liquid Cyclic

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