Dielectric Properties of Ethanol and Gasoline Mixtures by Terahertz

Article pubs.acs.org/JPCA

Dielectric Properties of Ethanol and Gasoline Mixtures by Terahertz Spectroscopy and an Effective Method for Determination of Ethanol Content of Gasoline Enis Arik,† Hakan Altan,‡ and Okan Esenturk*,† †

Department of Chemistry, Middle East Technical University, Ankara 06800, Turkey Department of Physics, Middle East Technical University, Ankara 06800, Turkey

‡

ABSTRACT: Investigation of frequency dependent permittivity of mixture solutions provides information on the role of intermolecular interactions on relaxation processes of solvent and solute molecules. In this study the dielectric properties of ethanol/gasoline mixtures in the terahertz spectral region are investigated. Frequency dependent absorption coefficients, refractive indices, and complex permittivities of pure ethanol and gasoline, and their mixtures at varying ethanol volume percentages (v/v %) are reported. As the mixing ratio changes, meaningful shifts are observed in the frequency dependent refractive index and absorption coefficients associated with the dominant component, ethanol. The relaxation dynamics of the pure gasoline and ethanol are successfully modeled with the Debye model using the ultrafast nature of the terahertz transients, and those of mixture solutions are investigated by an additive model with an assumption of minimum interaction due to the significant differences in their molecular natures; polar and nonpolar. Successful modeling of the mixtures confirms the weak interaction assumption and enables us to accurately determine the ethanol content. Among five ethanol/gasoline blends, except for one mixture, the estimated percent ethanol in gasoline is predicted with an accuracy of ca. 1% with respect to the actual ethanol percentage. In addition, the results show that free OH contribution to the macroscopic polarization is significantly higher at low concentrations (5−20%) and lower at 50% compared to the case of pure ethanol. The measurements and analysis presented here show that time domain terahertz studies can offer invaluable insight into development of new models for polar/nonpolar complex mixture solutions.

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hexafluorobenzene,16 chloroform/carbon tetrachloride,17 acetonitrile/water,18 acetonitrile/carbon tetrachloride,19 water in cyclohexane/n-heptane/carbon tetrachloride/benzene,20 and acetonitrile/1-ethyl-3-methylimidazolium.21 The main advantage of THz permittivity measurements on such mixtures comes from THz light absorption differences of polar and nonpolar molecules. The polar molecules align themselves along with the electric field, resulting in stronger absorption whereas induced dipole interaction with the field only results in a weaker absorption of the THz light by the nonpolar molecules. Here the study takes advantage of their polar and nonpolar molecular interaction with THz light to determine the ethanol content in gasoline through permittivity measurements and investigation of relaxation processes. The interest in the ethanol content determination comes from a recent increase in the usage of oxygenated fuel additives such as ethanol in gasoline either for enhancing fuel performance and/or for lowering exhaust emissions or for lowering the cost of gasoline per liter. The allowed usage amount of ethanol in gasoline varies from a few percent to 25% from country to country. However, an increase in ethanol content beyond a critical level not only decreases the performance of the car but may also damage the

INTRODUCTION Investigation of dielectric properties of pure and mixture liquids in microwave and terahertz (THz) frequency range has been a central focus of recent studies. Such investigations provide valuable information on thermal relaxation processes of molecules and their intermolecular interactions, which then may be used for better characterization of solvent dynamics,1 charge transfer kinetics,2 water/ion/biologically relevant molecule interactions,3,4 electrolytic solutions,5 and testing of models.6−11 The broader the bandwidth of the ultrafast THz pulses, the higher the number of relaxation process that can be monitored, resulting in more reliable data. Besides fundamental understanding of the complex interplay of intermolecular forces in the dynamics of solute and solvent molecules in a solution, a further analysis of the dielectric data also opens up new application areas such as fractional content determination as presented in this study for the determination of ethanol content in a commercially available petroleum product, gasoline. Aside from specific interactions such as H-bonding, molecular interactions in mixture solutions are predominantly determined by dipole orientations of the molecules. Some of the recent examples of THz and microwave investigations into the various combinations of dipolar interactions (polar/polar, polar/nonpolar, etc.) in mixture solutions were done for 1hexanol/n-heptane,12 ethanol/cyclohexane,13 NMF/carbon tetrachloride,14 methanol/carbon tetrachloride,5,15 benzene/ © 2014 American Chemical Society

Received: January 22, 2014 Revised: April 1, 2014 Published: April 4, 2014 3081

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engines due to the lower burning temperature of ethanol added fuels compared to that of the pure gasoline.22 Therefore, determination of the gasoline quality and ethanol content in gasoline with a fast, reliable, and relatively cheap technique is a welcomed opportunity both by the companies and by government agencies. The dielectric relaxation of pure ethanol1,23,24 and its mixture with various polar24,25 and nonpolar13,26 liquids have already been investigated at microwave and THz frequencies. The static properties such as the refractive index and absorption coefficient of gasoline by THz frequencies have also been investigated toward THz spectroscopy application for identification of gasoline octane rating,27 for discrimination of legal and illegal gasoline,28 and also for comparison of gasoline with other organic solvents.29 In addition, investigation of ethanol/ gasoline mixtures for ethanol content determination was reported using FT-NearIR,30 FT-MidIR,31 and Raman spectroscopy32 techniques, which are capable of detecting ethanol content in gasoline with high accuracy. However, there are two important advantages of application of THz-TDS on such systems. (1) The very low energy of the THz light compared to IR/NIR or visible energy brings the measurements into a safer region of the spectrum. (2) This is a new region for exploration, and THz waves appears to be very suitable to investigate dynamics associated with mixing of polar/nonpolar molecules. It is also important to note that techniques such as optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) has been successful in analyzing intermolecular dynamics in liquids. This technique provides the Raman spectrum over a wide spectral range, from 1 to 400 cm−1 by measuring the decay of the anisotropic relaxation of birefringence induced by “intense” ultrashort laser pulses.33,34 N-alcohols, including ethanol, were also studied by optical Kerr effect spectroscopy to explain the relation between intermolecular interactions and carbon chain length.35 For a specific information about the liquid dynamics, linear spectroscopy techniques (i.e., THz spectroscopy) may be more suitable. To the best of our knowledge, there are no reported THz studies in the literature on characterization of dielectric properties of ethanol/gasoline mixtures and its use for ethanol concentration determination. In the following sections we present characterization of dielectric properties of pure ethanol, gasoline, and their mixtures by THz time domain spectroscopy. The results were then modeled by the Debye relaxation model to determine the solvent and solute dynamics in weakly interacting systems through dielectric properties of a polar/nonpolar mixture at various polar component concentrations. We have further used the data and successfully applied a simple additive method for determination of polar component amount in mixture solutions using the dielectric properties of pure components.

Figure 1. Schematic diagram of the THz-TDS system.

mm (OAPM1) and 50 mm (OAPM2) focal length and polymethylpentene (TPX) lenses with 100 mm focal length were used for beam guide through the sample and to focus onto the ZnTe crystal. The spectrometer has a bandwidth of 1.6 THz (through a quartz sample cell, ca. 3 THz otherwise), as illustrated in Figure 2. Figure 2 also presents power and absorption spectrum of water vapor collected by the spectrometer.36

Figure 2. Power absorption spectrum of wet air and absorption spectrum of water vapor, presenting the effective bandwidth of the spectrometer. Observed water bands match very well with the reported ones (dashed lines) by Withayachumnankul et al.36 The inset shows a representative time-domain THz transient.

The gasoline (95-octane) was purchased from MOV Petrol Ofisi, and ethanol, spectroscopic grade (+99%), was purchased from Merck. Both samples were used as is. The ethanol/ gasoline mixture samples were prepared with 5%, 10%, 20%, 30%, and 50% v/v ethanol content. The liquid samples were introduced at the focal point of the THz light in a 2 mm path length quartz cuvette holder. An empty quartz cuvette is used as a reference. Background. The THz region (0.05−10 THz) exists between microwave and infrared regions, where 1 THz is equivalent to 300 μm, 33.3 cm−1, or 0.004 eV. THz spectroscopy has been successfully applied in molecular spectroscopy of gases,37 liquids,38,39 solids,40,41 biological samples (such as DNA and proteins),42,43 and explosives44−48 or in many more areas such as astronomy49 and communica-

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EXPERIMENTAL SECTION Setup and Chemicals. A home-built THz-time domain spectrometer (THz-TDS) is used during the data collection (Figure 1). The spectrometer consists of a 800 nm, 20 fs, 330 mW, 75 MHz Ti:sapphire oscillator (Femtosource, Femtolaser), a Si-lens fitted photoconductive antenna (PCA, BATOP) for generation, and a 2 mm thick ⟨110⟩ ZnTe crystal (Cradley crystals) for THz detection. A total of 85% of the laser power is used at PCA for THz light generation, and the rest is used for detection of the THz signal at the ZnTe crystal via electro-optic sampling. Combination of off-axis parabolic mirrors with 120 3082

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tion.50 Some of the common advantages of the use of timedomain techniques with ultrafast pulses in terahertz spectroscopy can be listed as coherent and fast measurement with high signal-to-noise (S/N) ratio, large spectral bandwidth enabling ultrafast dynamic studies of materials, room temperature measurement capability, determination of complex permittivity through direct measurement of electric field, convenient absorption measurement of both weakly and strongly absorbing materials, no knowledge requirement of optical constants of supportive materials, and also the possibility to obtain experimental data of solvent response to solute at nonideal conditions (high concentrations), which is critically important for correct modeling of mixture solutions. The measurement of the transient electric field of THz pulse enables direct determination of amplitude and phase through fast Fourier transform (FFT) of the recorded electric field. The frequency dependent refractive index, n(ω), and the absorption coefficient, α(ω), are calculated from the phases and amplitudes of reference and sample by eqs 1 and 2. c n(ω) = nref + (Øsample − Øref ) (1) ωd 2 ⎛ A sample ⎞ α(ω) = − ln⎜ ⎟ d ⎝ A ref ⎠

molecular interactions from van der Waals to ionic including Hbonding. The gained knowledge will be useful in understanding the complex processes that govern associations, dissociations, transport, and charge transfer mechanisms. The Debye model has already been shown to accurately determine the relaxation dynamics of both pure ethanol and nonpolar liquids.17,23 In this study we have also applied the Debye relaxation model to characterize the dynamics of the pure liquids and mixtures of ethanol and gasoline. A general expression describing complex dielectric function, ε̂(ω), according to the Debye model is given in eq 5.23 n

ε(̂ ω) = ε∞ +

j=1

where c is the speed of light, d is the thickness of the sample, ω is the angular frequency, and nref ref is the refractive index of the reference. The complex dielectric function, ε̂(ω) is equal to n̂2 where n̂(ω) = n + ik(ω) and k(ω) = cα/2ω. Thus, frequency dependent real and imaginary dielectric functions are calculated using eqs 3 and 4, respectively. (3)

ε″(ω) = 2nk

(4)

εj − εj + 1 (1 + iωτj)

(5)

Here, ε∞ is dielectric constant at high frequency limit, ε1 is the static dielectric constant, εj are intermediate values of the dielectric constant, and τj is the Debye relaxation time that corresponds to the jth relaxation process. The dielectric relaxation dynamics of ethanol and various other alcohols have been shown to have three distinct relaxation steps due to their chain forming hydrogen bonding nature. The accepted interpretation of the fast relaxation is a signature of the orientation of the OH groups1,23,59 and/or breaking and forming of H-bonding,1,60,61 and the slow relaxation steps are the signatures of thermal reorganizations of the molecules toward the thermodynamic equilibrium state.1,21 During the fitting process of pure ethanol, we have fixed the static dielectric constant, ε1, and the slowest relaxation time, τ1, to the reported values by Kindt et al.23 The gasoline is expected to have a single Debye relaxation process because liquids with no hydrogen bonding capabilities have been shown to have only one relaxation processes in general.1,62 However, our data could not be modeled well by single relaxation process probably because gasoline is a mixture of many nonpolar compounds. Thus, we considered double-Debye model, where the slow step is considered to be the cooperative relaxation process and the faster one is considered as large angle rotations of “free or single molecules” with small translations. Besides the characterization of dielectric properties of the mixtures, an equally important aim of our study is to develop a reliable and effective way to determine the percentage of ethanol in gasoline with simplest possible approach. Here, a basic contribution approach is considered for the mixture solutions. In this approach the complex dielectric function of a mixture, ε̂(ω)m, is defined as an additive combination of gasoline and ethanol.18,58

(2)

ε′(ω) = n2(ω) − k 2(ω)

∑

The measurement technique of this study is based on the interaction of the electromagnetic field (ultrafast THz pulses) with molecules in solution and follow up of its effects at the molecular level. Such interaction results in orientational polarization of the molecules with permanent dipole moments and/or induced polarization of the molecules with polarizabilities. These interactions are generally assumed to be linearly independent.51 After the interaction with the field the molecules thermally relax, which may take from femtoseconds to nanoseconds, depending on the interaction between the molecules.1,23,51−53 Thus, follow up of the relaxation dynamics determined from the dielectric properties of the solutions gives information on the intermolecular interactions at molecular level. For further details, the reader may refer to refs 52, 54, 55, and 56. THz spectroscopy based on ultrafast pulses becomes a valuable tool to investigate such dynamics in liquids. Our spectrometer has a bandwidth from 0.05 THz (∼3 ps) to 1.6 THz (∼100 fs), which is sufficient to analyze the relaxation times in these mixtures (wcτ = 1, wc is the critical angular frequency and τ is the relaxation time). Modeling. Several models have been suggested and applied for the characterization of the dielectric response of polar and nonpolar molecules. Often, the Debye model is used in the gigahertz and terahertz regions,1,18,23,52,54,57,58 where the polarization relaxation of the molecule to its equilibrium state has an exponential behavior given that no strong absorption features exist within the measurement frequency range. Such investigations of dielectric relaxations give insight on all types of

⎛ ε −ε ε −ε ⎞ ε −ε ε(̂ ω)m = A⎜ε∞ 1 + 11 2 12 2 + 12 2 13 2 + 13 2 ∞ 12 ⎟ 1 1 1 ω τ ω τ + + + ω τ13 ⎠ ⎝ 11 12 ⎛ ε −ε ε −ε ⎞ + B⎜ε∞ 2 + 21 2 222 + 22 2 ∞ 22 ⎟ 1 + ω τ21 1 + ω τ22 ⎠ ⎝ ⎛ ⎛ (ε − ε )ωτ (ε − ε13)ωτ12 (ε − ε∞ 1)ωτ13 ⎞ 12 11 ⎟ + i⎜⎜A⎜ 11 + 12 + 13 2 2 2 2 1 + ω τ12 1 + ω2τ132 ⎠ ⎝ ⎝ 1 + ω τ11 ⎛ (ε − ε )ωτ (ε − ε∞ 2)ωτ22 ⎞⎞ 22 21 ⎟⎟⎟ + B⎜ 21 + 22 2 2 1 + ω2τ22 2 ⎠⎠ ⎝ 1 + ω τ21

(6)

A and B correspond to the fractional contribution of the ethanol and gasoline, respectively. The sum of A and B are constrained to be less than or equal to 1. The parameters (ε∞1, ε11, ε12, ε13, τ11, τ12, τ13) of the multiplier A are the ones 3083

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determined from pure ethanol and the parameters (ε∞2, ε21, ε22, τ21, τ22) of the multiplier B are the ones determined from pure gasoline modeling. The first approach was to fix all the parameters (relaxation times, size of coupling between relaxation modes and the dielectric field, (εj − ε ∞ )) with an assumption that intermolecular interaction would be minimal and would not significantly affect the relaxation times because ethanol is a polar molecule and gasoline consists of nonpolar molecules. However, the first approach could not model the mixtures well. When they are mixed, an interruption of those networking Hbonds between ethanol molecules is expected to occur; thus the most significant effect is expected to be observed in the fastest relaxation step of ethanol and gasoline. Therefore, in the second approach, the fastest relaxation components of the equation were allowed to vary during the fitting. The fitting of experimental data is significantly improved. Previous studies have already shown that ethanol and gasoline do not have an absorption band within the frequency range of the measurements; thus the addition of an oscillator mode to the fitting process was not considered.1,23,52 In addition, previous studies have also shown that such inclusion did not improve the fitting.

Figure 4. Power transmission spectra of ethanol/gasoline mixtures.

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RESULTS AND DISCUSSION Figure 3 presents measured time dependent THz pulse profiles of the pure liquids and the mixtures. Pure ethanol only

Figure 3. THz pulse profiles of pure gasoline, ethanol, and their mixtures in volume percent of ethanol.

transmits ca. 6% of THz signal amplitude compared to the reference, whereas pure gasoline transmits ca. 70%. Both the decrease in amplitude and shift in peak position in time domain are proportional with the ethanol concentration in the mixture as the amount changes from 5% to 50% (v/v). Power spectra of the mixtures show that absorption increases and bandwidth of the system decreases with the increase in ethanol concentration due to ethanol’s stronger absorption (Figure 4). Parts a−c of Figure 5 present the frequency dependent refractive index, absorption coefficient, and real part of permittivity, respectively, of pure liquids and their mixtures derived from the THz transmission measurements. The pure gasoline has the lowest and pure ethanol has the highest refractive index at all frequencies. The mixtures lie in between as expected. A similar trend is observed for the absorption coefficients of the pure and mixture liquids. Both the index and the absorption coefficient of the mixtures increase with the increase in ethanol content, and there is no observed anomaly.

Figure 5. Frequency dependent (a) refractive index, (b) absorption coefficient, and (c) real part of permittivity of pure ethanol, gasoline, and their mixtures (v/v).

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Table 1. Dielectric Relaxation Parameters of Ethanol and Gasoline, As Determined by Least-Squares Fit of the Dataa liquid

ref

ε∞

ε1

ε2

ε3

τ1 (ps)

τ2 (ps)

τ3 (ps)

ethanol ethanol ethanol gasoline

this work 1 23 this work

2.12 (0.04) 2.69 1.93 1.94 (0.03)

24.35b 24.32 24.35 2.36 (0.03)

4.44 (0.09) 4.49 4.15 2.06 (0.002)

2.96 (0.03) 3.82 2.72

161b 163 161 3.18(0.34)

2.35 (0.20) 8.97 3.3 0.05 (0.01)

0.24 (0.02) 1.81 0.22

Standard errors are shown in parentheses as 2σ uncertainties in the fitted parameters. bDielectric constant at zero frequency, ε1, and relaxation time of the slowest step, τ1, kept fixed at the values given in ref 23 during fittings. a

The observed relatively weak absorption of gasoline compared to that of ethanol is expected because gasoline is mainly composed of nonpolar molecules.27 Our results for refractive index and absorption coefficient for both ethanol and gasoline are in good agreement with the previously reported values in the literature.23,28 Slight differences may be due to the variation of the sample sources. The real part of permittivity vs frequency of pure ethanol, gasoline, and their mixtures are given in Figure 5c. The trend in the real part of permittivity values of mixtures is similar to the refractive index values. Table 1 lists fitting results obtained by modeling of the experimental data according to three for ethanol and two for gasoline Debye relaxation processes and their comparison with the reported literature values. The fitting process includes concurrent fitting of real and imaginary parts of the dielectric data. The behavior of the pure ethanol has already been discussed,23 and our results correlate well with those studies. We have also observed three distinct relaxation dynamics in ethanol. Following the previous studies, the fastest process is attributed to the H-bonding and the slower ones are attributed to the free rotation and collective orientation, respectively. In the first relaxation time (the slowest step), τ1 and ε1 of ethanol were taken from ref 23 and held constant during the fitting. The main relaxation mode (slowest step, τ1 = 161 ps) is considered to be the cooperative relaxation of bulk solvent; flexing and/or reorientation of chains in molecules. The intermediate step τ2 = 2.35 ps is believed to correspond to the rotation of a chain end or free ethanol molecule. The fastest relaxation step (τ3 = 0.24 ps) is characteristic of hydrogen bonding. Gasoline includes mostly nonpolar ingredients and is considered to be a non-hydrogen bonded liquid system. Complex dielectric data of pure gasoline was successfully modeled with double Debye that resulted relaxation times of 3.18 ps (τ1, slow relaxation) and 0.05 ps (τ2, fast relaxation). Because gasoline is a mixture composed of many different compounds, it is a challenge to define the relaxation states clearly. A fast step is believed to be molecular and the slow step is expected to be a collective motion. Figures 6 and 7 compare the Debye model and the experimental data of pure ethanol and gasoline, respectively. The THz frequencies used for the measurements of all the mixtures cover enough bandwidth to accurately determine the relaxation dynamics in the solutions. The fastest relaxation process (0.24 ps) of ethanol corresponds to ca. 0.7 THz and is within the bandwidth of the measurement. The dielectric constant at infinite frequency is determined to be 2.12, which is within the previously reported range of values.1,23 The observed absorption of THz waves are considered to be from the permanent dipole moments of ethanol, which can be referred to as permanent dipolar absorption,17 and from transient dipole moments induced by collisions of nonpolar molecules such as the ones in gasoline, which can be described as collisionally induced absorption. Thus, the frequency

Figure 6. Real (e′) and imaginary (e″) permittivity of ethanol together with the fit of the triple Debye relaxation model (solid lines).

Figure 7. Real (e′) and imaginary (e″) permittivity of gasoline together with the fit of the double Debye relaxation model (solid lines).

dependent absorption coefficients observed from the mixtures at various ethanol concentrations can be considered as an addition of absorption coefficients of gasoline and ethanol according to their amounts in the mixture solution as stated in the Modeling section. However, they may deviate from such linear contribution at high ethanol concentrations because the collisionally induced absorption could be dominated by gasoline and ethanol molecules. To determine the volume fraction of ethanol content in gasoline, we first assumed that interaction of molecules in the mixtures are weak and can be ignored considering the fact that the dielectric properties of pure gasoline (mainly nonpolar molecules) and pure ethanol (very polar molecule) are very different. Thus, the mixtures were modeled initially without any interaction (eq 6). A and B in the equation represent the fractions of ethanol and gasoline in the mixture, respectively. Therefore, the dielectric parameters determined from pure 3085

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Figure 8. Experimental real (a) and imaginary (b) part of permittivity data (symbols) for mixtures of ethanol/gasoline together with the Debye relaxation model (black solid line).

Table 2. Parameters A, B (A + B ≤ 1), ε13, τ13, ε22, and τ22 (with Standard Errors in Parentheses) of Mixtures Derived from the Fitting of the Experimental Data

a

parameters

50%

30%

20%

10%

5%

A (fraction) B (fraction) ε∞1 ε11a ε12a ε13 a τ11 τ12a τ13 ε∞2a ε21a ε22 τ21a τ22

0.50 (0.04) 0.47 (0.09) 2.12 24.35 4.44 2.62 (0.08) 161 2.35 0.47 (0.10) 1.94 2.36 2.72 (0.21) 3.18 0.1 (0.05)

0.31 (0.01) 0.69 (0.04) 2.12 24.35 4.44 3.13 (0.08) 161 2.35 0.31 (0.02) 1.94 2.36 2.15 (0.8) 3.18 0.03 (0.000)

0.20 (0.02) 0.80 (0.05) 2.12 24.35 4.44 3.21 (0.08) 161 2.35 0.43 (0.06) 1.94 2.36 2.18 (0.05) 3.18 0.07 (0.03)

0.13 (0.01) 0.87 (0.03) 2.12 24.35 4.44 3.10 (0.06) 161 2.35 0.38 (0.06) 1.94 2.36 2.11 (0.02) 3.18 0.07 (0.03)

0.06 (0.001) 0.92 (0.005) 2.12 24.35 4.44 4.95 (0.000) 161 2.35 0.35 (0.000) 1.94 2.36 2.10 (0.01) 3.18 0.0008 (0.002)

Parameters were derived from the fit of pure ethanol and gasoline and held constant.

ethanol and gasoline (given in Table 1) were directly used during the fitting process. A concurrent fitting process of real and imaginary components of dielectric permittivity was applied; therefore, the model should simultaneously satisfy the real and imaginary dielectric data. For all the mixtures, the estimated ethanol contents (A) were found to be higher than the amounts used for mixing, thus the gasoline contents (B) were found to be lower. The variations between the estimated and actual values suggest that the effect of molecular interactions even between nonpolar and polar molecules on the relaxation dynamics of ethanol and gasoline should not be completely ignored during the fitting process. The possible weak interactions between the ethanol and the molecules in gasoline are expected to have a stronger impact more on the fastest relaxation steps rather than the slower ones, as stated in the modeling part. Therefore, the parameters ε13, τ13, ε22, and τ22 in eq 6 that correspond to the fastest steps of the pure components were relaxed while others were held fixed during the fitting process. The results are shown in Figure 8. As expected, the fits are much better than the previous case when both the residual and regression values of the fits are compared. The resultant fit parameters are given in Table 2. The derived values of the composition, A and B are very close to their expected values. Figure 9 presents the estimated fraction of ethanol, A, vs percent ethanol, which could be used as a calibration curve to

Figure 9. Estimated ethanol fractions, A (circles), in mixtures vs the added amount (percent ethanol).

determine the ethanol content of a given mixture with an unknown amount of ethanol. The accuracy of the proposed model is calculated through the subtraction of estimated ethanol concentrations from actual one. Although the absolute error is found to be 2.83% for 10% ethanol/gasoline blend, the estimated ethanol fractions in gasoline are predicted with an accuracy of ca. 1% with respect to the actual ethanol concentrations for the rest. With the further improvements of 3086

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Table 3. Summary of Relaxation Times and Corresponding Dielectric Constants of the Fastest Step in Pure Liquids and Mixturesa 50% ethanol gasoline

20%

τ

ε

τ

0.47 0.1

2.62 2.72

0.43 0.07

ethanol gasoline a

5% ε

τ

pure ε

3.21 0.35 4.95 2.18 0.008 2.10 Amplitudes (Ai = εi − ε∞) of the Mixtures

τ

ε

ε∞

0.24 0.005

2.96* 2.06

2.12* 1.94

50%

20%

5%

pure

0.5 0.78

1.09 0.24

2.83 0.16

0.84 0.12

The full data are available in Table 2.

relaxation time of the fastest relaxation step, the free rotations of the molecules. The amplitude of the relaxations are a measure of their contribution to the macroscopic polarization;52 thus changes in the amplitude provide information on the intermolecular interactions and organizational changes in the mixtures, as well. The relative contribution of the fast relaxation process (A3 = ε3 − ε∞) of the ethanol to the macroscopic polarization is decreasing as the ethanol content in the mixture is increasing from 5% to 50% (Table 3). In fact, the relative contribution at 50% is lower than the pure ethanol. Compared to the case of pure ethanol, this might be a signature of a more organized ethanol in gasoline, resulting in fever number of ethanol molecules with free OH. At 5% ethanol where the amplitude jumps to 2.83 compared to 0.84 for pure ethanol, the free OH contribution to the macroscopic polarization becomes much more pronounced. At this concentration it is expected to have much more free OH relative to the total number of OH in the solution when compared to the case of pure ethanol or a concentrated one thus it is consistent with the observed result. This leads to a conclusion that free OH contribution to the macroscopic polarization at this low concentration is significantly higher compared to the rest of the relaxation processes of ethanol. When only relaxations of the gasoline molecules are considered, the contribution of the fastest relaxation step (rotational motions of individual molecules) is increasing relative to the Debye relaxation (collective thermal relaxation) of gasoline molecules due to the increase in its lifetime. When the relative contributions of ethanol and gasoline to the macroscopic polarization are considered, we have noticed that ethanol has significantly higher contribution to the macroscopic polarization and its contribution is increasing as the ethanol content increases and dominates at 50% mixture. This is mainly due to the strong dipole, hence high dielectric constant, of ethanol compared to that of gasoline. With a small amount of ethanol addition to a low dielectric gasoline, the effect becomes significant. During the modeling of the experimental data we have also considered Bruggeman effective medium theory64 to determine the effective dielectric properties of the mixtures through the interaction between ethanol and the molecules in gasoline; however, it was not successful. That is most probably due to the complexity of gasoline components and differences in molecular nature (polar−nonpolar) of the molecules that makes it difficult to observe and explain interactions with the Bruggeman model.

the system it may be possible to conduct measurements with minimized systematic and measurement errors and also with increased S/N ratio. However, the aim of the study is to show that such measurements can also be used for accurate determination of ethanol concentration in gasoline using a fast and reliable technique, THz-TDS. Besides the determination of ethanol content in gasoline, the fitting results can also be used to better understand the relaxation dynamics in a polar/nonpolar mixture. The relaxation time of the fastest step of ethanol significantly increases from 0.24 to 0.35 ps when 5% ethanol is mixed with gasoline. This must be due to the changes in intermolecular forces acting on the ethanol molecules mainly in hydrogen bonding because the nonpolar solvent has no hydrogen bonding capability. In addition, the partial molar volume of ethanol is also expected to increase when ethanol is mixed with a nonpolar solvent. The partial molar volume of