Investigation of dielectric relaxation in tributyl phosphate from susceptibility and conductivity measurement under microwave field

(1)

Investigation of dielectric relaxation in tributyl phosphate from susceptibility and conductivity measurement under microwave field

T BACHHAR¹, S K SIT², S H LASKAR¹and S SAHOO^3,*

1Department of Electronics and Instrumentation Engineering, National Institute of Technology Silchar, Silchar 788010, India

2Department of Physics, Dr. Meghnad Saha Institute of Technology, Haldia 721657, India

3Department of Electronics and Communication Engineering, National Institute of Technology Jamshedpur, Jamshedpur 831014, India

*Author for correspondence (swagatdebmsit@yahoo.co.in) MS received 12 May 2020; accepted 28 October 2020

Abstract. Susceptibility (v_ij’s) and conductivity (r_ij’s) measurement techniques are proposed to determine dielectric behaviour in terms of relaxation timesand dipole momentlof tributyl phosphate (TBP,j) dissolved in various non-polar solvent (i) (p-xylene, cyclohexane and n-heptane) under S-band, C-band, X-band and Ku-band microwave field at different temperatures (25, 30 and 35C) within Debye’s dielectric model. The possibility of double relaxation times (s2 and s1) for inter- and intra-molecular rotation of the polar molecule TBP is predicted from measured data of v⁰_ij(=e⁰_ij-e?ij),v⁰⁰_ij(=e⁰⁰_ij) andv_0ij(=e_0ij–e?ij) at different weight fractionsw_j’s of solute, applying slope and intercept of

v_0ijv⁰_ij

v⁰_ij against ^v

00 ij

v⁰_ij linear equation to confirm mono relaxation behaviour s2 only. s’s are measured from individual variation of real and imaginary parts of v_ijand r_ijwith wj’s as well as linear relation of imaginary against real. The dipole momentslj’s are measured from both the measurement techniques under S-band (3.2 GHz), C-band (6.8 GHz), X-band (11.2 GHz) and Ku-band (16.5 GHz) microwave field at 25, 30 and 35C temperatures. Various molecular associations are determined in terms of relaxation time s and dipole moment l in polar–non-polar liquid mixture.

Thermodynamic energy parameters are also calculated from Eyring rate theory to predict molecular dynamics or nature of molecular environment surrounding the polar molecule TBP. Debye relaxation mechanism in all the systems under observation is validated by the estimated Debye factor from both the measurement methods. A new simple microwave sensor is proposed to design for determination of TBP concentration from measured penetration depth at different temperatures under microwave field.

Keywords. Dielectric relaxation; relaxation time; susceptibility; conductivity; dipole moment; penetration depth.

1. Introduction

Debye dielectric model of polar–non-polar liquid mixture gives a clear concept about various solute–solute, solute–

solvent and self-molecular associations in a simple and straightforward way [1–4]. Solute–solute and solute–solvent associations [5–8] are easily identified in microwave region because microwave has the inherent ability to detect weaker molecular association [9,10]. The purpose of this investigation is to provide adequate information of dielectric behaviour in terms of permittivity, susceptibility, conductivity, relaxation time, dipole moment, etc., which can be treated as an analytical tool to correlate other physico- chemical properties of industrially important material TBP.

Solvent power of material under test can be determined by electrostatic factor [11], which is a product of dipole

moment and dielectric constant. Dipole moment clearly indicates solute–solvent molecular orientation, whereas dielectric constant of material signifies the dissolution ability of ions of test material. Polar solute dissolved in non- polar solvent forming dilute solution helps to investigate solute molecule in quasi-isolated state and at the same time dielectric relaxation characteristics is mildly affected by dipolar field [8,9]. The purpose of this study is to study the dielectric relaxation characteristics of TBP (j) dissolved in various non-polar solvents (i), such as p-xylene, cyclohexane andn-heptane at 25, 30 and 35C temperatures, under effective dispersive region [9,10] of S-band (3.2 GHz), C- band (6.8 GHz), X-band (11.2 GHz) and Ku-band (16.5 GHz) microwave field from susceptibility and conductivity measurement technique, using Debye dielectric model [12] of liquid mixture. No such type of investigation https://doi.org/10.1007/s12034-021-02366-wSadhana(0123456789().,-volV)FT3](0123456789().,-volV)

(2)

using vector network analyser set up, as shown in figure 1, has been performed on TBP so far to the best of our knowledge. Debye [10,12] model compared to other established dielectric model is simple, straightforward and more topical to understand dielectric relaxation phenomena.

The present work is concentrated on experimental determination of dielectric characteristics in the form of real v⁰_ij (=e⁰_ij-e?ij) and imaginaryv⁰⁰_ij(=e⁰⁰_ij) parts of high frequency orientational susceptibility v_ij and static v_0ij (= e_0ij-e?ij) [13], to investigate the probability of double relaxation timess2ands1due to inter- and intra-molecular rotation of the polar molecules at 25, 30 and 35C temperatures, under S-band, C-band, X-band and Ku-band microwave field.

Further, the dielectric characteristics is also investigated in terms of real r⁰_ij (= x[₀2⁰⁰_ij) and imaginary r⁰⁰_ij (= x[₀[⁰_ij) parts of high frequency complex conductivity [14] r_ijk of solution under similar molecular environment. The conductivity r_ij of the solution related to bound molecular charge, whereas susceptibility v_ij measurement deals with orientational polarization and permittivity measurement [15] associated with all types of polarization of the polar molecule. A comparative analysis of dielectric characteri- zation of TBP under different frequency range of microwave field at different temperatures is also performed to understand the effect of orientational polarization over the bound molecular charge, as illustrated in table 1. s’s calculated by both the measurement techniques are placed in table 2. The variations of^v^0ij^v

0 ij

v⁰_ij against ^v

00 ij

v⁰_ij are plotted in figure2to study the existence of double relaxation timess2

and s1 for inter- and intra-molecular rotation of polar molecules. The variations ofv⁰_ij–w_j;v⁰⁰_ij–w_jandv⁰⁰_ij–v⁰_ijcurves are presented in figures 3,4 and5, respectively. Similarly, the plot of r⁰_ij–w_j; r⁰⁰_ij–w_j and r⁰⁰_ij–r⁰_ij curves is shown in figures6,7and8, respectively. Dipole momentlj’s can be estimated either from susceptibility method using slope of

v⁰_ij–w_jcurve or from conductivity method using slope ofr_ij– wjcurve, as presented in figure9and placed in table3. The variations ofsandlof TBP dissolved in p-xylene, cyclohexane and n-heptane with respect to temperature are also illustrated in figure 10. The estimated thermodynamic energy parameters [9] such as enthalpy of activation (DHs), free energy of activation (DFs), entropy of activation (DSs) from both the methods are placed in table4from the linear plot of ln(sjT) against 1/T curves of figure 11. Different types of molecular association formed in polar–non-polar mixture under observation are predicted in figure 12. The penetration depths are calculated from variation of measured dielectric properties of TBP for different concentrations under microwave frequency range at 25C, as shown in figure13and placed in table5.

2. Experimental

The sample TBP is good quality E-Merck grade. Solventsp- xylene, cyclohexane andn-heptane of AR grade were pro- cured from BDH, India and distilled before use. The high temperature probe measurement method [16] consists of Rohde & Schwarz made ZNB-20 Vector Network Ana- lyzer, dielectric assessment kit (DAK) and DAK evaluation software is used to measuree⁰_ijande⁰⁰_ij, as shown in figure1.

The probe is immersed into the polar–non-polar mixture sample, i.e., TBP ?p-xylene (System-I) or TBP ?cyclohexane (System-II) or TBP?n-heptane (System-III). The electromagnetic fields at the probe end penetrate into the material and changes as they come into contact with the material. The resulting measured reflections (reflection coefficient, S₁₁) are then converted into dielectric properties values (permittivity e) via DAK evaluation software. The system is capable of determining permittivity up to 20 GHz.

The high temperature dielectric probe kit is calibrated using

Figure 1. (a) Network analyser setup and (b) coaxial probe with flange.

(3)

Table1.Measuredvaluesofrelativepermittivitiese0 ij,e00 ij,e0ijande?ij;orientationalsusceptibilitiesv0 ij,v00 ij,v0ijandhighfrequencycomplexconductivityrij,r0 ijandr00 ijofTBP dissolvedinp-xylene,cyclohexaneandn-heptaneat25,30and35Ctemperaturesunder3.2,6.8,11.2and16.5GHzelectricfield. SystemFreq.(GHz)Temp.(C)Weightfractione0 ije00 ije0ije?ijv0 ijv00 ijv0ijr0 ijr00 ijrij (I)TBP?p-xylene3.2250.00482.27040.06412.41512.21650.05390.06410.19860.01140.40420.4044 0.00702.31280.15792.46022.25770.07410.15790.20250.02810.41170.4127 0.00882.35490.28332.48232.26950.08540.28330.21280.05040.41920.4222 0.01242.40550.31912.51492.29230.09320.31910.22260.05680.42820.4320 300.00482.26710.06212.40712.21680.05030.06210.19030.01110.40360.4038 0.00702.29170.14972.43072.22940.06230.14970.20130.02660.40800.4089 0.00882.33380.26382.46942.25690.07690.26380.21250.04700.41550.4181 0.01242.37780.30672.51382.28890.08890.30670.22490.05460.42330.4268 350.00482.25340.06042.38912.20530.04810.06040.18380.01080.40120.4013 0.00702.28020.12222.41882.22820.05200.12220.19060.02180.40590.4065 0.00882.30490.24722.44672.24260.06230.24720.20410.04400.41030.4127 0.01242.34120.27892.47942.26870.07250.27890.21070.04960.41680.4197 6.8250.00482.26150.09142.41512.21650.04500.09140.19860.03460.85550.8562 0.00702.30910.16732.46022.25770.05140.16730.20250.06330.87350.8758 0.00882.34710.29912.48232.26950.07760.29910.21280.11310.88790.8951 0.01242.38120.32312.51492.29230.08890.32310.22260.12220.90010.9084 11.2250.00482.25100.10112.41512.21650.03490.10110.19860.06301.40251.4039 0.00702.30510.17212.46022.25770.04740.17210.20250.10721.43621.4402 0.00882.32360.30602.48232.26950.05410.30600.21280.19071.44781.4603 0.01242.35690.33622.51492.29230.06460.33620.22260.20941.46851.4834 16.5250.00482.24470.11422.41512.21650.02820.11420.19860.10482.06042.0631 0.00702.29360.18432.46022.25770.03590.18430.20250.16922.10532.1121 0.00882.31120.32392.48232.26950.04170.32390.21280.29732.12152.1422 0.01242.34550.35802.51492.29230.05320.35800.22260.32862.15302.1779 (II)TBP?cyclohexane3.2250.00482.19540.05272.23952.14650.04890.05270.09300.00940.39080.3909 0.00702.21210.12812.25432.15190.06020.12810.10240.02280.39380.3945 0.00882.23870.22342.27842.16600.07270.22340.11240.03980.39850.4005 0.01242.25470.30142.29852.17170.08300.30140.12680.05370.40140.4050 300.00482.18040.04762.22022.13810.04230.04760.08210.00850.38820.3883 0.00702.20110.11152.24062.14330.05780.11150.09730.01980.39180.3923 0.00882.21940.23332.26102.15620.06320.23330.10430.04150.39510.3973 0.01242.23730.30012.28222.16350.07380.39610.11870.05340.39830.4019 350.00482.15720.03902.19752.12030.03690.03900.07720.00690.38400.3841 0.00702.17260.10032.21202.13000.04260.10030.08200.01790.38680.3872 0.00882.20070.21322.24752.14310.05760.21320.09470.03800.39180.3936 0.01242.21710.29762.25422.15150.06560.35760.10270.05300.39470.3982 6.8250.00482.18510.06742.23952.14650.03860.06740.09300.02550.82660.8270 0.00702.20310.13672.25432.15190.05120.13670.10240.05170.83340.8350 0.00882.22930.23812.27842.16600.06330.23810.11240.09010.84330.8481 0.01242.24680.31192.29852.17170.07510.31190.12680.11800.84990.8581

(4)

Table1.Continued SystemFreq.(GHz)Temp.(C)Weightfractione0 ije00 ije0ije?ijv0 ijv00 ijv0ijr0 ijr00 ijrij 11.2250.00482.17520.07322.23952.14650.02870.07320.09300.04561.35531.3561 0.00702.19730.14122.25432.15190.04540.14120.10240.08801.36911.3719 0.00882.22250.24352.27842.16600.05650.24350.11240.15171.38481.3931 0.01242.23690.32402.29852.17170.06520.32400.12680.20191.39371.4082 16.5250.00482.16720.08892.23952.14650.02070.08890.09300.08161.98931.9910 0.00702.18800.15322.25432.15190.03610.15320.10240.14062.00842.0133 0.00882.20930.25412.27842.16600.04330.25410.11240.23322.02802.0414 0.01242.22480.33302.29852.17170.05310.33300.12680.30572.04222.0650 (III)TBP?n-heptane3.2250.00482.02320.03872.07451.98740.03580.03870.08710.00690.36020.3603 0.00702.05040.11612.09131.99040.06000.18610.10090.02060.36500.3656 0.00882.09050.21492.13012.01850.07200.24490.11160.03830.37220.3742 0.01242.20230.30032.25142.12850.07380.30230.12290.05350.39210.3957 300.00481.98390.02832.02651.95010.03380.02830.07640.00500.35320.3532 0.00702.03540.10552.07011.98030.05510.10550.08980.01880.36230.3628 0.00882.06340.18782.10222.00210.06130.18780.10010.03340.36730.3688 0.01242.10650.28712.15042.03550.07100.28710.11490.05110.37500.3785 350.00481.94110.02211.98941.91010.03100.02210.07530.00390.34560.3456 0.00701.99800.06672.03121.94800.05000.06670.08320.01190.35570.3559 0.00882.04020.15332.07221.98120.05900.15330.09100.02730.36320.3642 0.01242.08090.20592.12002.01620.06470.20590.10380.03670.37040.3722 6.8250.00482.01160.04232.07451.98740.02420.04230.08710.01600.76100.7612 0.00702.04210.12292.09131.99040.05170.12290.10090.04650.77250.7739 0.00882.08660.22592.13012.01850.06810.22590.11160.08550.78930.7939 0.01242.19970.31372.25142.12850.07120.31370.12290.11870.83210.8405 11.2250.00482.00590.05152.07451.98740.01850.05150.08710.03211.24981.2502 0.00702.03600.13302.09131.99040.04560.13300.10090.08291.26861.2713 0.00882.07520.23782.13012.01850.05670.23780.11160.14821.29301.3015 0.01242.19270.32382.25142.12850.06420.32380.12290.20181.36621.3810 16.5250.00481.99820.06872.07451.98740.01080.06870.08710.06311.83421.8353 0.00702.02550.14492.09131.99040.03510.14490.10090.13311.85921.8640 0.00882.06090.24242.13012.01850.04240.24240.11160.22251.89171.9047 0.01242.18550.31542.25142.12850.05700.31540.12290.30792.00612.0296

(5)

three elements and the software. The three elements are air, a metallic shorting block and water. The measurede⁰_ijande⁰⁰_ij are accurate within±0.5 and±1.67%, respectively.e0ijand e1ij were measured by Dipolemeter DM 01 and Abbe’s refractometer, respectively. The real v⁰_ijð¼e⁰_ije1ijÞ and imaginary v⁰⁰_ijð¼e⁰⁰_ijÞparts of complex orientational susceptibility v_ij and static orientational susceptibility

v_0ij¼e0ije1ij

as well as imaginary r⁰⁰_ij (= x[02⁰_ij) and real r⁰_ij (= x[₀2⁰⁰_ij) parts of complex conductivity r_ij at different w_j’s of solute (TBP) were estimated by simple normalization of permittivity data. The temperature of the measurements was maintained at 25, 30and 35C within the accuracy limit of ±0.1C by a water-circulating thermostat.

Table 2. Measured values ofsfrom slope and intercept of^v^0ij^v

0 ij

v⁰_ij against ^v

00 ij

v⁰_ij of equation (1); ratio of slopes ofv⁰⁰_ij-wjandv⁰_ij-wjcurve;

linear slope ofv⁰⁰_ij-v⁰_ijcurve; ratio of slopes ofr⁰⁰_ij-w_jandr⁰⁰_ij-w_jcurve of equation (4), linear slope ofr⁰⁰_ij-r⁰_ij curve of equation (5) of TBP dissolved inp-xylene, cyclohexane andn-heptane at 25, 30 and 35C temperatures under 3.2, 6.8, 11.2 and 16.5 GHz electric field.

System Freq. (GHz) Temp.

(C)

Measureds(ps) fromvijmeasurement Measureds(ps) fromrijmeasurement Straight

line equation

(1)

Ratio of slopes of v⁰⁰_ij–wjandv⁰_ij–wj

curve

Linear slope ofv⁰⁰_ij–v⁰_ij

curve

Ratio of slopes ofr⁰⁰_ij–w_j andr⁰_ij–wjcurve

equation (4)

Linear slope of r⁰⁰_ij–r⁰_ij curve equation (5) (I) TBP?

p-xylene

3.2 25 27.32 28.22 29.79 30.35 30.78

30 26.17 27.03 28.96 29.97 30.30

35 25.03 25.84 27.72 28.93 29.11

6.8 25 27.16 27.85 28.22 29.33 29.81

30 26.12 26.76 27.12 28.02 29.11

35 25.01 25.72 26.55 27.03 28.44

11.2 25 26.02 26.80 27.14 27.23 28.18

30 25.33 25.89 26.30 27.77 28.02

35 24.31 24.77 25.16 26.32 27.39

16.5 25 25.87 26.79 27.06 27.19 28.05

30 25.20 25.41 26.00 26.25 27.58

35 24.22 24.61 25.03 26.13 26.72

(II) TBP? cyclohexane

3.2 25 26.88 26.91 27.33 29.11 29.73

30 25.72 25.88 26.24 27.22 28.32

35 24.87 24.90 25.11 26.04 27.17

6.8 25 25.71 25.19 26.16 27.27 27.88

30 24.12 24.21 25.66 26.11 26.76

35 22.83 22.88 24.21 25.39 25.12

11.2 25 24.66 24.86 25.31 26.34 27.01

30 22.10 22.51 24.61 25.51 26.30

35 20.21 20.77 23.39 24.72 25.02

16.5 25 23.09 23.06 24.15 25.55 26.41

30 20.88 21.33 23.33 24.43 25.61

35 19.71 20.55 21.31 21.83 24.30

(III) TBP? n-heptane

3.2 25 24.17 25.02 25.61 26.59 26.87

30 22.30 23.12 24.66 25.60 25.92

35 21.29 21.55 21.87 23.74 24.34

6.8 25 22.89 23.83 23.92 25.02 26.11

30 20.78 21.11 21.33 24.87 24.90

35 19.90 20.33 20.76 23.11 24.20

11.2 25 21.04 21.08 21.51 22.81 24.22

30 20.32 20.15 20.44 21.44 23.81

35 19.30 19.62 19.76 20.32 21.79

16.5 25 19.71 20.38 20.40 22.60 21.69

30 18.64 19.52 18.81 20.88 20.39

35 18.22 18.88 19.02 19.76 19.93

(6)

Figure 2. Variations of^v^0ij^v

0 ij

v⁰_ij against ^v

00 ij

v⁰_ij at differentwj’s of TBP dissolved in p-xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP ? p-xylene; (II) __d__ for TBP ? cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

Figure 3. Variations of v⁰_ij against w_j’s of TBP dissolved in p-xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP?p-xylene; (II) __d__ for TBP?cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

(7)

Figure 4. Variations of v⁰⁰_ij againstwj’s of TBP dissolved inp-xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP? p-xylene; (II) __d__ for TBP ? cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

Figure 5. Variations of v⁰⁰_ij against v⁰_ij of TBP dissolved inp-xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP? p-xylene; (II) __d__ for TBP? cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

(8)

3. Theoretical formulation

3.1 Relaxation timesjand dipole momentlj

from susceptibility (vij) measurement

Bergman’s equations [17] for two Debye-type dispersions are solved to get straight line equation in terms of

established symbols ofv⁰⁰_ij,v⁰_ijandv0ij[10] as v_0ijv⁰_ij

v⁰_ij ¼x sð 1þs2Þ v⁰⁰_ij v⁰_ij !

x²s1s2 ð1Þ such thatc₁?c₂= 1.

Figure 6. Variations of r⁰_ij against w_j’s of TBP dissolved in p- xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP ?p-xylene; (II) __d__ for TBP?cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

Figure 7. Variations of r⁰⁰_ij against wj’s of TBP dissolved in p- xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP ?p-xylene; (II) __d__ for TBP?cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

Figure 8. Variations of r⁰⁰_ij against r⁰_ij of TBP dissolved inp- xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP?p-xylene; (II) __d__ for TBP?cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

Figure 9. Variations ofrijagainstwj’s of TBP dissolved inp- xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.2 and 16.5 GHz electric field at 25C. (I) __j__ for TBP?p-xylene; (II) __d__ for TBP?cyclohexane; (III) __m__ for TBP?n-heptane, respectively.

(9)

The equation (1) is a straight line of variables ^v^0ij^v

0 ij

v⁰_ij

against ^v

00 ij

v⁰_ij having slopes x(s1 ? s2) and intercept of x²s1s2 for different w_j’s of solute under a given angular frequency x(= 2pf) of electric field, as shown in figure2.

Thes’s were also estimated from the ratio of slopes ofv⁰⁰_ij– w_jandv⁰_ij–w_jcurves atw_j?0 in figures4and3to eliminate polar–polar interactions. The slope ofv⁰⁰_ij–v⁰_ijlinear equation

of figure 5 can also be used to estimate s from Murthy et al[18].

The hfljdue to orientation polarization alone is given by:

l_j¼ 27e0KBTMjb Nq_ieijþ22

b

!1=2

ð2Þ

where all the symbols carry usual significance [10].

Table 3. Measured dipole momentsl’s due tosfrom graphical method equation (1); estimatedl’s due tosfrom ratio of slopes ofv⁰⁰_ij–wj

andv⁰_ij–wjcurve and linear slope ofv⁰⁰_ij–v⁰_ijcurve; measuredl’s due tosfrom ratio of slopes ofr⁰⁰_ij–wjandr⁰_ij–wjcurve of equation (4) and linear slope ofr⁰⁰_ij–r⁰_ijcurve of equation (5) of TBP dissolved inp-xylene, cyclohexane andn-heptane at 25, 30 and 35C temperatures under 3.2, 6.8, 11.2 and 16.5 GHz electric field.

System Freq. (GHz)

Temp.

(C)

Measuredl910³⁰(C m) fromv_ijmethod

Measuredl910³⁰(C m) fromrij

method From graphical

method

From ratio of slope method

From linear slope method

From ratio of slope method

From linear slope method (I) TBP?

p-xylene

3.2 25 11.13 11.33 11.49 11.61 11.75

30 11.67 11.77 11.81 11.90 11.97

35 11.81 11.91 12.03 12.31 12.43

6.8 25 11.55 11.62 11.66 11.77 11.87

30 11.70 11.80 12.12 12.33 12.51

35 11.87 11.98 12.54 12.60 12.62

11.2 25 11.70 11.88 12.23 12.30 12.70

30 11.88 11.97 12.34 12.65 12.72

35 11.94 12.34 12.56 12.78 12.88

16.5 25 11.73 11.90 11.94 12.28 12.33

30 12.28 12.54 12.78 12.80 12.91

35 12.42 12.75 12.86 12.91 12.96

(II) TBP? cyclohexane

3.2 25 10.57 10.68 10.82 10.98 11.11

30 11.17 11.75 11.81 11.90 11.94

35 11.33 11.55 11.69 11.96 12.05

6.8 25 11.29 11.51 11.45 11.64 11.78

30 11.45 11.63 11.76 11.80 11.83

35 11.56 11.74 11.85 11.93 11.97

11.2 25 11.62 11.81 11.90 11.96 12.13

30 11.77 11.89 11.97 12.08 12.36

35 11.83 11.96 12.11 12.33 12.47

16.5 25 11.78 11.88 11.90 11.98 12.33

30 11.81 11.94 12.06 12.23 12.48

35 11.97 12.33 12.54 12.78 12.83

(III) TBP? n-heptane

3.2 25 10.31 10.46 10.57 10.62 10.73

30 10.45 10.51 10.62 10.71 10.87

35 10.61 10.72 11.13 10.84 10.90

6.8 25 10.44 10.56 10.70 10.81 11.11

30 10.51 10.67 11.17 11.31 11.43

35 10.72 10.81 11.25 11.44 11.57

11.2 25 10.57 10.67 11.32 11.50 11.62

30 10.76 11.11 11.53 11.62 11.80

35 10.90 11.55 11.66 11.76 11.91

16.5 25 10.63 11.05 11.48 11.80 11.84

30 10.85 11.29 11.74 11.85 12.05

35 10.96 11.43 11.87 12.22 12.44

(10)

Figure 10. Variations of relaxation times_j’s and dipole momentl_j’s with temperature t(inC) of TBP dissolved inp-xylene, cyclohexane andn-heptane under 3.2, 6.8, 11.4 and 16.5 GHz electric field. (I) __j__;…A…for TBP?p-xylene; (II) __d__;…/…

for TBP?cyclohexane; (III) __m__;…:…for TBP?n-heptane fors(__) andl(……), respectively.

Figure 11. Linear plot of ln(sjT) against 1/T curve of TBP dissolved in p-xylene, cyclohexane andn-heptane at 25, 30, 35 and 40C temperatures under 3.2, 6.8, 11.2 and 16.5 GHz electric field. (I) —j—;.…A…for TBP?p-xylene; (II) —d— ;…/…for TBP?cyclohexane; (III) —m—;…:…for TBP?n-heptane from susceptibility ( ___ ) and conductivity (……) measurement, respectively.

(11)

Table4.MeasuredvaluesofthermodynamicenergyparameterslikeenthalpyofactivationDHs,freeenergyofactivationDFs,entropyofactivationDSsfromln(sjT)against 1/Tcurves,usingsfromsusceptibilityandconductivitymeasurementtechniques.DebyefactorsjT/g,DFg=(DFs/c),DHg=(DHs/c)forviscousflowprocessofTBPdissolvedin p-xylene,cyclohexaneandn-heptaneat25,30and35Ctemperaturesunder3.2GHzelectricfield. SystemTemp. (C)

DHs(kJmol–1 )DFs(kJmol–1 )DSs(kJmol–1 K–1 )Debyefactor(910–5 )DFg=(DFs/c)DHg=(DHs/c) Fromvij methodFromrij methodFromvij methodFromrij methodFromvij methodFromrij methodFromvij methodFromrij methodFromvij methodFromrij methodFromvij methodFromrij method (I)TBP? p-xylene252.260.9512.7113.07-0.0351-0.04072.542.5727.7133.739.449.52 3012.8613.23-0.0350-0.04052.672.7478.65268.95 3513.0013.39-0.0349-0.04042.792.8979.23272.43 (II)TBP? cyclohexane251.862.3712.6712.92-0.0363-0.03542.452.51150.40342.6623.0822.48 3012.8213.06-0.0362-0.03532.672.66152.40348.16 3512.9113.27-0.0359-0.03502.792.79154.09353.42 (III)TBP? n-heptane253.902.7412.4112.67-0.0286-0.03332.332.4133.0562.4811.647.90 3012.4612.84-0.0283-0.03322.382.5833.4063.62 3512.5912.93-0.0282-0.03312.502.6933.8764.50

(12)

3.2 Relaxation times_jand dipole momentl_j from conductivity (r_ij) measurement

The imaginary r⁰⁰_ij is related to real r⁰_ij part of total con- ductivityr_ij [14] by the following relation:

r⁰⁰_ij¼r1ijþ 1 xsj

r⁰_ij ð3Þ

Bothr⁰⁰_ijandr⁰_ijare the functions ofw_j’s at different temperatures. To eliminate the polar–polar interactions in estimation of sj, we can safely convert equation (3) in the following form:

sj¼1 x

b₁

b₂ ð4Þ

whereb₁andb₂are the slopes ofr⁰⁰_ij–w_jandr⁰_ij–w_jcurves at w_j ?0, see figures7and6, respectively.

On differentiation of equation (3) w.r.t r⁰_ij one gets:

sj¼ 1

xb⁰ ð5Þ

whereb⁰ is the slope ofr⁰⁰_ij-r⁰_ijlinear relation, as shown in figure8. All thes’s (±10%) are placed in table2.

The dipole moment l_jis given by

l_j¼ 27MjKBTb Nq_iðeiþ2Þ²xb

" #1=2

ð6Þ

The symbols used in equation (6) carry usual meanings [14] in SI unit. All the l’s (±5%) are placed in table2.

3.3 Penetration depth

The penetration depth,dpof radiofrequency and microwave power is defined as the depth, where the power is reduced to 1/e(e= 2.7183), about 37%, of its value at the surface of the material. The d_pvalue in metre of a lossy material can be calculated [16,19] as follows:

d_p¼ c

2pf

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2e⁰

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ ê_e⁰⁰0

q 2

1

s ð11Þ

4. Results and discussion

Measured susceptibility vij’s and conductivity rij’s at different weight fraction w_j’s of TBP (j) dissolved in various non-polar solvents (i)p-xylene, cyclohexane andn-heptane at 25, 30 and 35C temperatures under 3.2 GHz (S-band), 6.8 GHz (C-band), 11.2 GHz (X-band) and 16.5 GHz (Ku- band) electric field are placed in table 1. The probe technique with network analyser assembly consists of Rohde &

Schwarz made ZNB-20 Vector Network Analyzer and Dielectric Assessment Kit (DAK), it covers wide range

of frequencies of 100 KHz to 20 GHz and 200 MHz to 20 GHz, respectively. The dielectric property of material under investigation is concerned with the above frequency range only where effective dispersion occurs [8–10], that is, permittivity falls off with rising frequency and dielectric losse⁰⁰_ijreaches its maximum at an angular frequencyx¼¹_s, thereafter falls to half of its maximum value. The slope of x(s₁ ? s₂) and intercept of x²s₁s₂ of ^v^0ij^v

0 ij

v⁰_ij against ^v

00 ij

v⁰_ij

straight line equation at differentwj’s, figure2, is used to identify the possible existence of double relaxation times [13]s2ands1for inter- and intra-molecular rotation of the polar molecule. The ratio of slopes [10] ofv⁰_ij–w_jandv⁰⁰_ij–w_j curves, in figures3and4, respectively, and slopes of linear relation [14] of v⁰⁰_ij–v⁰_ij equation, as shown in figure 5, are also used to estimate another set of s and are listed in table 2. It is observed from figure 5 that the least squares fitted straight lines are not exactly linear passing through the experimental points, except system (I) under 3.2 and 6.8 GHz, system (II) under 16.5 GHz and system (III) under 6.8 GHz. This observation signifies that ratio of slopes method is a better choice to avoid polar–polar interaction [14,16] compared to linear slope method. Conductivity measurement method [14], on the other hand, is used to derive s’s from the ratio of slopes of r⁰_ij–w_j and r⁰⁰_ij–w_j curves in figures 6 and 7, respectively, and from r⁰⁰_ij–r⁰_ij linear relation in figure 8. All the estimated s’s (±10%) from both type of conductivity methods are placed in table2. It is evident from table2that the singles₂for inter- molecular rotation of TBP of greater magnitude is observed from double relaxation measurement technique. This indicates the molecular rigidity of the polar molecule under different state of molecular environment, temperature and microwave field. All the calculated s’s of TBP mixed in different non-polar solvents have a tendency to decrease with increase in temperature, establishing the fact that polar–non-polar mixture samples under observation surely follow the Debye relaxation mechanism [20]. The variation of ^v^0ij^v

0 ij

v⁰_ij against ^v

00 ij

v⁰_ij at differentwj’s and temperatures is linear in nature, except some data points that are slightly scattered under 11.2 GHz at 25C for TBP ?cyclohexane and under 6.8 GHz at 25C for TBP?n-heptane polar–non- polar liquid mixture. The correlation coefficients (r) for the fitted straight-line equations are very close to unity (–1Br B 1), indicating the almost perfect correlation between variables. The deviation from linearity may be due to inherent presence of solute–solute (dimer) and solute–

solvent (monomer) molecular association in polar–non- polar liquid mixture [16]. Similar nonlinear nature is shown for all the graphs ofv⁰⁰_ij andv⁰_ij against wj’s showing maximum value at certain w_j’s of solute, indicating maximum absorption of high frequency electric energy, resulting in maximum polarization of polar molecule. It is also con- cluded that because of solvent effect [21], same polar

(13)

Figure 12. Various solute–solvent and solute–solute molecular association. (a) TBP ? p-xylene, (b) TBP ? cyclohexane, (c) TBP?n-heptane and (d) TBP?TBP.

(14)

molecules dissolved in various non-polar solvents generate different polarization at infinite dilution, i.e., w_j ? 0. All the graphs are best fitted through the data points minimizing the sum of squares of the points from the plotted curves.

The gradual increase of v⁰⁰_ij against v⁰_ij under different frequency range of microwave electric field exhibits linear behaviour, as illustrated in figure 5. The nonlinear variations ofr⁰_ij–w_jandr⁰⁰_ij–w_jgraphs, shown in figures6and7, Figure 13. Concentration variation effect on penetration depth of TBP dissolved in p-xylene,

cyclohexane andn-heptane over the frequency range from 3.2 to 16.5 GHz at 25C. (I) —j— for 0.0048; (II) —d— for 0.0070; (III) —m— for 0.0088 and (IV) —w— for 0.0124 weight fraction of TBP, respectively.

Table 5. Penetration depth (in mm) of TBP dissolved inp-xylene, cyclohexane andn-heptane with different concentrations under 3.2, 6.8, 11.20 and 16.5 GHz electric field at 25C.

System Frequency (GHz)

TBP concentration (weight fraction)

0.0048 0.0070 0.0088 0.0124

(I) TBP?p-xylene 3.2 496.1 203.4 114.5 102.8

6.8 163.4 90.3 51.0 47.5

11.2 89.5 53.2 30.1 27.6

16.5 53.7 33.7 19.3 17.6

(II) TBP?cyclohexane 3.2 419.5 173.3 141.5 105.4

6.8 217.8 107.9 62.4 47.8

11.2 121.5 63.3 37.0 27.9

16.5 67.8 39.5 24.0 18.4

(III) TBP?n-heptane 3.2 775.6 260.4 142.2 104.5

6.8 333.0 115.5 63.6 47.1

11.2 165.8 64.7 36.6 27.8

16.5 84.2 40.2 24.3 19.2

(15)

are similar in nature like the graphs plotted in figures3and 4. It is observed in the investigation that the magnitude of v⁰_ijð¼e⁰_ije1ijÞ is less than r⁰⁰_ij (= x[₀2⁰⁰_ij), whereas v⁰⁰_ijð¼e⁰⁰_ijÞis greater thanr⁰_ij(=x[02⁰⁰_ij) at differentw_j’s and temperatures of polar–non-polar mixture. No curves, in figure 7, meet at a point probably due to solute–solvent (monomer) association [21]. The dipole moments l_j’s can be calculated with the help of slope bof v⁰_ij-w_j curve, as shown in figure 3. They are placed in table 3 along with other estimated l’s from linear slope and ratio of slopes method. lj’s are also measured in terms of dimensionless parameters b’s and slopesb’s ofrij-w_jcurves in figure9 along with measured l’s from linear slope and ratio of slopes method and listed in table3. The nonlinear variation of l’s with respect to change in temperature at constantw_j of TBP is observed in figure 10. The elongation of bond angles and bond moments of the polar molecule with the rise in temperature causes this type of non-linear variation under microwave field, as observed earlier [19,22]. The convex or concave shape of lj-t and sj–t curves are probably due to solute–solute molecular association for larger rotating unit [10], as demanded by Debye model.

TBP dissolved in various non-polar solvents generate different values ofsandl at specific frequency and temperature, as shown in figure 10, probably for solvent effect [16]. Eyring et al [23] treated dipole rotation from one equilibrium position to another over a potential barrier after gaining sufficient energy from the activated process similar to rate process equation. The thermodynamic energy parameters [10], such asDHs,DFs,DSs,are estimated from slopes and intercepts of ln(s_jT) against 1/T curves, of fig- ure11, applying Eyringet al[23] rate theory. It is observed that the variation of ln(sjT) against 1/Tis a straight line that proves that dielectric relaxation process is a rate process.

The entropy of a system is a measure of orderly nature of a system under observation. If DSs’s are –ve then it is con- cluded that the environment of a particular system is cooperative in nature.DSs’s are –ve for all the systems from both the measurement method as shown in table 4 signi- fying cooperative nature for activated state. Enthalpy of activation related to bonding nature of the molecules and excitations to the activated states involve breaking of bonds.

All the systems possess?ve value ofDHsandDHg, and the difference between them clearly signifies that relaxation process involves different types of molecular association through hydrogen bonding (figure12). It is also found that DFs’s are less than DFg for all the systems, indicating dielectric relaxation process involves with rotational motion of molecular entity only, whereas viscous flow related to translational as well as rotational motion. All the systems surely follow the Debye relaxation mechanism [12,21]

because derived Debye factors (sjT/g) are almost same order in nature from all the methods. Figure12a, b and c repre- sents various solute–solvent (monomer) association occur- red due to interaction of fractional –ve charged^–at the side

of O-atom of TBP with fractional?ve charged^?at the side of H atom of p-xylene, cyclohexane and n-heptane, respectively. Similarly solute–solute (dimer) association is formed in between fractional –ve charge d^–at the side of O-atom of TBP and fractional?ve charged^?at the side of P atom of TBP, as shown in figure 12d. Effective dipole moments are increased due to dipole–dipole interaction occurring in between polar–non-polar molecules. There also exists inductive and mesomeric effects between two atoms of polar groups due to their difference in electron affinity to cause monomer and dimer molecular association to happen.

Dielectric spectral-based sensor for detecting TBP may be developed from derived strong linear correlation between dielectric property and TBP concentration. Penetration depth of the electromagnetic energy in the test materials can be used as an analytical tool for designing the proposed sensor in practice [16,19]. It is observed that the penetration depth decreases linearly with increase in frequency for all the systems, as shown in figure13. For a specific frequency, the penetration depth decreases with increase in concentration of TBP [16], as observed in table5. The penetration depth is higher than 20 mm for all the systems under 3.2 to 11.2 GHz, microwave field enables one to conduct dielectric property measurements for the development of a prac- tical microwave-based sensor [16,19].

5. Conclusion

Dielectric relaxation parameter s and l within accuracy limit of (±10%) and (±5%), respectively, are determined using measured data of conductivityr_ij’s and susceptibility vij’s at different temperatures under S-band, C-band, X-band and Ku-band microwave field, applying Debye dielectric model to empirically relating other physico- chemical properties of TBP. The existence of mono relaxation behaviour of all the systems under observation establishes molecular rigidity of TBP under microwave electric field at different temperatures. Various molecular environment are also predicted from different thermodynamic parameters. Different molecular associations are proposed for difference in electron affinity of atoms in a polar group of molecule. Future sensor development is also ascertained from sufficient penetration depth related to dielectric constant of TBP.

References

[1] Gill D S, Sharma A N and Schneider H 1982J. Chem. Soc.

Faraday Trans. I.78465

[2] Gill D S and Cheema J S 1983Z. Phys. Chem.134205 [3] Kalidas C and Schneider H 1980J. Phys. Chem.120145 [4] Anderson L S, Gujda G B and Stuchly S S 1986IEEE Trans.

Instr. Meas.3513

(16)

[5] Chetterjee A K, Saha U, Nande N, Basak R C and Acharyya S 1992Indian J. Phys.66291

[6] Boruah B K and Baishya B 2005Indian J. Phys.791041 [7] Nourand A E and Messieh A E 1999J. Mol. Liq.79235 [8] Sahoo S, Middya T R and Sit S K 2014Pramana J. Phys.

83579

[9] Sahoo S and Sit S K 2016Can. J. Phys.941 [10] Sahoo S and Sit S K 2009Mater. Sci. Eng. B16331 [11] Dack M R J 1976 The influence of solvents on chemical

reactivity. In solutions and solubilities, Part II(New York:

John Wiley & Sons-Interscience)

[12] Debye P 1929Polar molecules(New York: Chemical Cat- alogue Co., Inc.) p 172

[13] Sahoo S and Sit S K 2017Ind. J. Pure Appl. Phys.55207 [14] Sahoo S and Sit S K 2017Pramana J. Phys.881

[15] Malathi M, Sabasan R and Krishnan S 2004J. Mol. Liq.109 11

[16] Sahoo S 2020Indian J. Phys.94639

[17] Bergmann K, Roberti D M and Smyth C P 1960 J. Phys.

Chem.64665

[18] Murthy M B R, Patil R L and Deshpande D K 1989Indian J.

Phys.63491

[19] Guo W, Zhu X, Liu Y and Zhuang H 2010J. Food Eng.97 275

[20] Sahoo S and Sit S K 2007Ind. J. Pure Appl. Phys.45529 [21] Sahoo S and Sit S K 2010Indian J. Phys.841549 [22] Jorat L J, Noyel G A and Huck J R 1991IEEE Trans. Electr.

Insul.26763

[23] Eyring H, Glasstone S and Laider K J 1941Theory of rate process(New York: McGraw-Hill)