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aTaras Shevchenko National University of Kyiv, Kyiv, Ukraine. bNational University of Food Technologies, Kyiv, Ukraine. *e-mail: [email protected].
ISSN 0020-1685, Inorganic Materials, 2017, Vol. 53, No. 15, pp. 1473–1477. © Pleiades Publishing, Ltd., 2017. Original Russian Text © A.N. Alekseev, M.M. Lazarenko, M.V. Lazarenko, K.N. Kovalev, S.Yu. Tkachev, 2016, published in Zavodskaya Laboratoriya, Diagnostika Materialov, 2016, Vol. 82, No. 9, pp. 43–47.

INVESTIGATION OF STRUCTURE AND PROPERTIES PHYSICAL METHODS OF RESEARCH AND CONTROL

Characterization of Dielectric Properties in Liquid–Solid Phase Transition A. N. Alekseeva, *, M. M. Lazarenkoa, **, M. V. Lazarenkob, K. N. Kovaleva, and S. Yu. Tkacheva, *** a

Taras Shevchenko National University of Kyiv, Kyiv, Ukraine bNational University of Food Technologies, Kyiv, Ukraine *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] Received July 3, 2015

Abstract⎯A method for determining the complex dielectric permeability of liquids based on the temperature changes in geometrical parameters (thickness) of samples and over the phase transition range is proposed. Allowing the measurements to be made in a wide temperature range (–190 to 60°C) at different frequencies (0.1–100 kHz), this technique is used for establishing the complex dielectric permeability of ethanol as a function of temperature. The accuracy of coincidence of the obtained values with the data reported in the literature is 3%. Keywords: complex dielectric permeability, liquids, phase transitions DOI: 10.1134/S002016851715002X

The complex dielectric permeability ε* = ε' – iε" at frequencies of f ≤ 1000 kHz is usually measured on capacitor cells with plane-parallel or coaxial cylindrical electrodes which are in direct contact with a sample [1]. The experiment is aimed at measuring the cell parameters (complex resistance Z * or conductivity G*) as a function of temperature T or frequency f by means of AC bridges and RLC and Q meters or via time-domain methods, applying the Fourier transformation of time dependences of the charge and discharge currents i(t) of the measuring cell with a sample [2]. To find the ε' and ε" parameters from the obtained Z* or G* values, it is necessary to know the geometric parameters of samples or electrodes of the cell, which can be established either via direct measurement or by calibrating a cell with reference liquids with known dielectric characteristics. Their determination at room temperature is a quite trivial task, but investigating ε*(T) needs to consider the thermal expansion of samples, cells, and other factors. The liquid–solid phase transitions in a wide temperature range, accompanied by changes in sample dimensions, can even cause strains in the lattice, sometimes leading to its failure. Since the chemical composition of samples may vary upon their contact with the measuring cell material owing to solvent evaporation, oxidation, and contamination, it is thus desirable to keep the samples sealed upon their preparation for measurements.

This work is aimed at elaborating a method which allows the dielectric properties of liquids to be examined in the temperature range including the phase transitions, as well as at its testing during the study of the complex dielectric permeability ε*(T, f) of ethylene. The liquid sample was sealed at room temperature in an elastic polymer thin film capsule (PC) with a regular geometric shape. The PC was placed in the measuring system with four electrodes [3] that enabled us to control the sample thickness during the measurements (Fig. 1). * The system parameters, i.e., the capacitances C12 * (measured at contacts 1 and 2, 1 and 4, and C14 respectively, Fig. 1) and the dielectric loss tangent * , were determined on a setup composed of a tan δ12 P5083 automatic AC bridge connected to a computer. Two measuring cells used in the experiment consisted of two equal four-electrode systems (Fig. 1) positioned in the air thermostat. This allowed the ε*(T, f) function to be studied at temperatures T = –190 to 60°C and at frequencies f = 0.1–100 kHz. The temperatures of the electrodes and sample were evaluated by means of differential thermocouples (copper– constantan) at a fixed temperature (T = 0°C) of the external junction. Establishing parameters ε 'L and ε "L in the liquid requires consideration of the temperature depen-

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4

2

tems were implemented either in the thermostabilization mode or at monotonic heating at a rate of about 1°C/min. The capacitance C * and tan12δ* of the capacitor

3 2hf

(a) PC

2

3

1

PC

H

hL

4

5 C AB

(b)

12

B d2 C

d1 (c)

1

Fig. 1. Diagram of the experimental setup: (a, b) PC without and with sample; (c) PC (1–4—electrodes; 5—liquid sample; (A, B, C) areas in the capacitor filled with air, polymer and air, and sample with air, respectively.

* , was containing the PC and the air capacitance C14 evaluated on a P5083 AC automatic bridge, connected to a computer via a SETU-10 controller (ΔC/C = 0.1%; ΔC = 10–3 pF; Δ tan δ = 10–5). The therm-EMF of the thermocouple was measured on a R3003 voltage comparator and recorded with a controller (ΔT = 0.5°C). The acquired data were used to calculate the ε*L (T,f) and hL(T) dependences. If the electrode system contains an empty PC with a total thickness of 2hf, then the capacitances C * (hf) 12

and C * (hf) being measured can be written as 14

dences of film thickness hf and sample thickness hL. Since the direct measurement error hf with a micrometer at room temperature is Δhf/Δhf ≈ 10% (no film strain taken into account), the double calibration of a measuring cell is thus expedient. To align the empty cell, dielectric columns with thickness h (the measurement error was Δh = 10–5 m) were installed between electrodes 1 and 3 (Fig. 1); this * (h–1) and C * (h–1) allowed us to establish the C14 14 dependences, which within the error of capacitance, measured using a bridge P5083, are as follows:

A12 ', + C12 h * = A14 + C ' , C14 14 h * = C12

(1) (2)

' and C14 ' are where A12 and A14 are coefficients, and C12 the mounting capacitances and capacitances of the ' , and connecting conductors. As is found, A12, A14, C12 ' are constant (the error of about 1%) over the whole C14 ranges of studied temperatures and frequencies (at h ≤ 2.5 mm). The PC was made of a double thin (2hf = 0.14 mm) polymer film (polyethylene) circularly welded with a heated punch (d1 = 35 mm, d2 = 30 mm, Fig. 1). The sample was injected into a channel made in a cavity inside the capsule with a seringe. After removing the residuals of air and welding the channel, the PC was *,C*, placed in the electrode cell system to measure C12 14 * (first, for the empty PC and, then, for the and tan δ12 PC filled with a liquid). The air thermostat with the electrode system in a Dewar vessel was cooled with liquid nitrogen and exposed for some time. The subsequent measurements of capacitance C* and dielectric loss tangent tanδ* in both electrode sys-

* (h ) = C 0 (h ) + C (h ) − C 0(h ) + C ' , C12 j 12 f f f f f 12 * (h ) = C14 f

(3)

A14 ', + C14 2hf

(4)

A12 * ' ), C f0(hf ) = ε 0S1 , (C14 (hf ) − C14 A14 2hf 0 C f (hf ) = ε f C f (hf ) are the capacitances of a capacitor C12 with the air dielectric 2hf thick, of a capacitor with the air dielectric of the same geometry as the PC, and of a capacitor with PC, respectively (ε0 = 8.85 pF/m is the dielectric permeability of vacuum). Then the following conditions are implemented:

where C120 (hf ) =

C f (hf ) = C12(hf ) + 2hf =

ε 0S1 − A12 C14 (hf ), A14

(5)

A14 , C14 (hf )

(6)

* (h ) − C ' , C14(hf) = C * (h ) − C ' , where C12(hf) = C12 f 12 14 f 14

and S1 = π d12 4 is the total area of PC. If one places a liquid-filled PC with a total thickness H = hL + 2hf in a four-electrode system, then * (H ) = C 0 (H ) + C (H ) − C 0 (H ) + C ' , C12 12 fL fL 12

(7)

A14 ', (8) + C14 H where CfL(H) is the capacitance of a zone between the electrodes, where the PC is positioned (see Fig. 1b); * (H ) = C14

A12 C14 (H ); A14 εS C (H ) 0 C fL (H ) = 0 1 = ε 0S1 14 . H A14 CfL(H) was calculated using the electric equivalent scheme of the sample position in a cell (Fig. 2). C12(H ) = 0

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1 1 = 1 + , C fL (H ) C f (hf ) C L (hL ) + C E (hL )

being the area of the sample;

C E (hL ) =

(9)

(a)

ε 0ε L S 2 2 , S2 = π d2 4 H − 2hf

ε 0(S1 − S 2 ) . H − 2hf

(10)

−1 The C fL (H ) parameter can also be evaluated from the measured C12(H) and C14(H) magnitudes in much the same way as Eqs. (3)–(6):

1

2 hL 2h f

where hL = H – 2hf; CL(hL) =

H

Then we obtain

(b) Fig. 2. (a) Position of sample in the measuring cell; (b) the electric equivalent scheme for calculations: (1) sample; (2) PC.

−1

⎡ ⎤ ε S − A12 1 = ⎢C12(H ) + 0 1 C14 (H )⎥ . C fL (H ) ⎣ A14 ⎦ Using the expressions (9) and (10), we have ε0 [S 2(ε L − 1) + S1] . hL It follows simultaneously from Eq. (9) that C L (hL ) + C E (hL ) =

(11)

(12)

1 1 = 1 − 1 ≡ . (13) C L (hL ) + C E (hL ) C fL (H ) C f (hf ) Δ C (H , hf ) Combining expressions (12) and (13) and making the transformations needed, we obtain the following formulas for the calculation of dielectric permeability εL and the layer thickness hL: ε 'L = 1 −

S1 Δ C + , S 2 C L0

(14)

⎡ ⎤ (15) hL = H − 2hf = A14 ⎢ 1 − 1 ⎥ , ⎣C14 (H ) C14 (hf )⎦ where CL0 = ε0S2/hL. Formulas (14) and (15) contain the magnitudes established experimentally upon the measurements of capacitance for the electrode system with a PC filled with a sample [C12(H), C14(H)] and without it [C12(hf)), C14(hf)], as well as the PC areas (the total S1 and that of sample S2) (ΔS/S = 0.5%). The dielectric loss tangent in liquid tanδL was found using the formulas for the total C* and tanδ* values for capacitors connected in series (--) and parallel (||) with parameters C1, tanδ1 and C2, tanδ2 (at tan2 δ ! 1): (a) series connection: 1 = 1 + 1, C --* C1 C 2

(16)

(C1 + C 2 ) tan δ*-- = C 2 tan δ1 + C1 tan δ 2, (b) parallel connection: C * = C1 + C 2, INORGANIC MATERIALS

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C * tan δ* = C1 tan δ1 + C 2 tan δ 2.

(19)

For polyethylene (in our case, the PC material) and air, tan δf ≈ 10–4 ≈ 0. On the basis of this condition along with Eqs. (16)–(19), tanδL and the imaginary dielectric permeability component ε "L can thus be expressed in the form

* * C12(H ) ⎡1 + 1 Δ S ⎤ , tan δ L = tan δ12 C f (hf ) ⎢⎣ ε L S 2 ⎥⎦

(20)

* * C12(H ) ⎡ε + Δ S ⎤ , (21) ε "L = tan δ12 ⎢ L S ⎥ 2⎦ C f*(hf ) ⎣ where ΔS = S1 – S2. The thicknesses measured directly on a micrometer for the empty PC and the liquid-filled PC were not taken into account because of the large error even at room temperature. To find the hL value, the C14 capacitance data of the air capacitor (ΔC/C = 0.1%) were used instead. This allowed the hL(T) dependence to be plotted during the experiment, as well as its correct use in the calculation of parameters ε 'L and ε "L . This is essential when investigating phase transitions and vitrification of liquid systems, where the variations in hL are particularly pronounced. The technique was tested in the study of complex dielectric permeability of ethylene (CHIMIE-PLUS Laboratoires Corp.), characterized by the presence of phase transitions in the probed temperature range. The results are shown in Fig. 3. The nature of physical processes occurring upon heating the sample was analyzed by means of the dependences (see Fig. 3) using the technique described in [8]. In the vicinity of –140°C, the shift in the inflection ε'(T) and the maximum ε"(T) toward higher temperatures with increasing frequency is due to the dielectric relaxation [4] which is manifested as inflection in the temperature dependences of specific heat capacity Cp(T) and relative thickness Δh/h0(T).

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ε'

(a) [5] [6] [4],[7]

5 kHz 10 kHz 20 kHz 50 kHz

100

60

40

100 –60

0

60

0

0.4

120

50

0.2

60

Δh/h0

0

0 0

Cp –200 –150 –100 –50 T, °C 5 kHz 10 kHz 20 kHz 50 kHz

ε'' 15

0

50

100

(b)

10 5 0 –200

–150

–100 –50 T, °C

0

50

Fig. 3. The temperature dependences of (a) real ε' and (b) imaginary ε" parts of dielectric permeability.

The maxima observed at –130°C in ε'(T) and ε"(T), as well as the endothermic peak in Cp(T), are probably due to a first-order phase transition. At a further increase in temperature, the exothermic peak on the Cp(T) curve at –122°C is accompanied by a decrease in ε'(T) and ε"(T) and by an increase in relative thickness Δh/h0(T), which can be due to recrystallization in the sample. Contemporaneously with the endothermic peak on the Cp(T) curve near –114°C, one observes an increase

[4,7]

[6]

20

Cp, kJ/(kg °C)

ε'

50

Δh/h0

50

100 f, kHz

Fig. 4. The frequency dependence of dielectric permeability of ethylene (T = 30°C).

in ε'(T), which can be explained by the solid–liquid phase transition. At higher temperatures the relaxation process is characterized by a decrease in ε' at increasing frequency. Here, the maximum on the ε"(T) curve is shifted toward increased temperatures. The results were compared with the data reported in the literature over the range of –90 to –70°C, where the dielectric permeability is independent of the frequency (Fig. 3). This coincidence was 5% [6] and 3% [5]. In turn, the results in [5, 6] are different by 8%. The frequency dependence of the dielectric permeability of ethylene at 30°C is displayed in Fig. 4. It is evident that ε' decreases with increasing frequency and tends to the static dielectric permeability values found in [4, 6, 7]. At 100 kHz, the error is 4% [4, 7] and 10% [6]. The data reported in [4, 6, 7] diverge by 10%. Thus, the technique proposed allows one to establish the characteristics of food products which can be used in industrial technological processes [9, 10]. The data acquired confirm the needs to control the sample thickness and provide additional information on phase and relaxation processes. REFERENCES 1. Usikov, S.V., Elektrometriya zhidkostei (Electrometry of Liquids), Leningrad: Khimiya, 1974. 2. Gusev, Yu.A., Osnovy dielektricheskoi spektroskopii (Fundamentals of Dielectric Spectroscopy), Kazan: Kazan. Gos. Univ., 2008. 3. Golik, A.Z., Alekseev, A.N., and Zabashta, Yu.F., Low-temperature relaxation of dielectric properties of polyoxymethylene. I. Objectives and experiment planning, Ukr. Fiz. Zh., 1977, vol. 22, no. 6, pp. 944–949. 4. Gregory, A.P. and Clarke, R.N., Traceable measurements of the static permittivity of dielectric reference liquids over the temperature range 5–50°C, Meas. Sci. Technol., 2005, vol. 16, pp. 1506–1516. 5. Brand, R., Lunkenheimer, P., Schneider, U., and Loidl, A., The excess wing in the dielectric loss of glassINORGANIC MATERIALS

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CHARACTERIZATION OF DIELECTRIC PROPERTIES forming ethanol: a relaxation process, Phys. Rev. B, 2000, vol. 62, no. 3, pp. 8878–8883. 6. Dielektricheskie svoistva chistykh zhidkostei (The Dielectric Properties of Pure Liquids), Es’kova, N., Ed., Moscow: Khimiya, 1972. 7. Mohsen-Nia, M., Amiri, H., and Jazi, B., Dielectric constants of water, methanol, ethanol, butanol and acetone: measurement and computational study, J. Solution Chem., 2010, vol. 39, pp. 701–708. 8. Alekseev, O.M., Lazarenko, M.M., Puchkovs’ka, G.O., Bezrodnaya, T.V., and Sendzyuk, A.A., Peculiarities of the thermal motion in crystals formed by cetyltrimethylammonium bromide molecules, Ukr. J. Phys., 2010, vol. 55, no. 9, pp. 973–979.

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9. Pop, G.S., Ratsibors’ka, A.A., Bilen’ka, V.I., Bodachivs’ka, L.Yu., Alekseev, O.M., and Lazarenko, M.M., Features of thermal molecular motion amineamides of rapeseed oil acids, Vopr. Khim. Khim. Tekhnol., 2012, vol. 3, pp. 64–69. 10. Lazarenko, M.M., Lazarenko, M.V., Baglyuk, S.V., Kopil’tsev, D.V., and Pleshakova, O.V., Effect of molecular mobility in the system of triacylglycerols on their dielectric and thermal properties, Nauk. Prats. Nats. Univ. Kharchov. Tekhnol., 2013, no. 50, pp. 119– 123.

Translated by O. Maslova