Dielectric Constant of Polyhydric AlcoholâDMSO Mixture Solution at

Article pubs.acs.org/JPCA

Dielectric Constant of Polyhydric Alcohol−DMSO Mixture Solution at the Microwave Frequency Qian Jie and Jia Guo-Zhu* College of Physics and Electronics Engineering, Sichuan Normal University, Chengdu 610066, China ABSTRACT: Dielectric spectrum of polyhydric alcohol (1,2,3)-DMSO (dimethyl sulfoxide) mixtures, at full concentration, have been determined by the dielectric relaxation spectroscopy (DRS) method at frequencies from 20 MHz to 20 GHz at room temperature. The mixture behavior is described according to four Davidson−Cole terms whose evolution with composition is analyzed. The binding energies and hydrogen bond (HB) numbers between solute−solute and solvent−solute pairs are obtained from the permittivity using the Luzar model. The average HBs number associated with DMSO decreases with increasing mole fraction of DMSO. The binding energy of solute−solute (E11) and solvent−solute (E12) interaction decreases with the increased numbers of carbon atoms in the alcohols.

in mixture13−17 would affects the melting point, boiling point, solubility, and density of the solution. Aqueous DMSO or alcohol solution have been extensively investigated experimentally and theoretically by ab initio calculations and molecular dynamics simulations,18 as well as NMR,19 X-ray,20 dielectric spectroscopy,21 fluorescence,22 UVRaman,23 and infrared.24 Because of DRS monitors, the collective motion of a molecular ensemble through the response of the total dipole moment of the sample to an alternating electric field presents a significant contribution for a cooperative nature of hydrogen-bonding liquids research.25 Under and Khirade26 have reported the dielectric relaxation in DMSO−ethylene glycol mixture. Many investigations have reported dielectric relaxation of DMSO or alcohol and its mixture.27−30 Especially Kaatze et al.31−41 have measured DMSO or alcohol mixed with other solvents for many years, and using the wait-and-switch model, those elegant works concentrate on hydrogen network fluctuations in which individual HBs weaken and reform with correlation times. However, their lack of an analysis about HB interaction strength and dipolar ordering type is up to the extent of substitution of the DMSO or alcohol. Therefore, in this article, we study the result of a dielectric relaxation of polyhydric alcohol−DMSO mixtures by DRS and consider the three pairs of HB, the interaction for solute−solute (pair 1), solvent−solute (pair 2), and solvent−solvent (pair 3), respectively. We choose ethylene glycol (EG) and glycerol (Gly) as the representatives of polyhydric alcohol and used ethanol (EtOH) and 1,2-propanol (1PrOH, 2PrOH) as the control groups. At the same time, HB energies between alcohol

1. INTRODUCTION Microwave dielectric heating is rapidly becoming an established procedure in synthetic chemistry.1 The interaction between microwave and substance mainly embodies in microwave absorption and reflection. The ability of medium to absorb microwave mainly depends on its dielectric property, which may be related to the loss tangents of the solvent.2,3 Selecting appropriate polar solvent in chemical industry can accelerate or restrain the chemical reaction, and change the dynamics mechanism of them. Therefore, studying dielectric properties of polar organic solvents under microwave radiation becomes a basic and important work for microwave energy applications. DMSO is a aprotic polar solvent widely used in biological and medical applications4,5 because many authors concentrate on its dielectric properties. DMSO consists of one highly polar SO group, which interacts easily with water forming strong HBs,6,7 and two hydrophobic groups, CH3. This nonpolar− polar combination characteristics makes DMSO and its mixtures very important in organic chemistry.8 Lu et al.6 has studied DMSO−water mixture by dielectric relaxation spectroscopy, and by comparing pure water, the average HBs number per molecule is reduced. According to the mean field approximation for a hydrogen-bonded mixture, Luzar et al.9 have proposed a new theoretical model that is satisfactorily in agreement with the experimental data for DMSO−water system.10 Another multipurpose organic is polyhydric alcohols, which apply to oils, resins, and antifreeze for explosive as a kind of organic solvent.11 Ethylene glycol as antifreeze to engine and glycerol used in cosmetic industry has two or three hydroxyl groups, respectively. Because the hydroxyl (−OH) is easy to attract partially positive hydrogen atoms of other molecules to form clusters and network by intermolecular HBs.12 Furthermore, the structure breaking and structure making existed © 2013 American Chemical Society

Received: August 17, 2013 Revised: November 18, 2013 Published: November 19, 2013 12983

dx.doi.org/10.1021/jp4082245 | J. Phys. Chem. A 2013, 117, 12983−12989

The Journal of Physical Chemistry A

Article

Figure 1. Complex permittivity spectrum (ε′ and ε″) of polyhydric alcohol (ethanol and ethylene glycol)−DMSO mixtures at 298 K at DMSO mole fraction x2 = 0, 0.2, 0.5, 0.8, and 1.0.

Figure 2. Complex permittivity spectrum (ε′ and ε″) of polyhydric alcohol (1,2-propanol, and glycerol)−DMSO mixtures at 298 K at DMSO mole fraction x2 = 0, 0.2, 0.5, 0.8, and 1.0.

molecules (E11) and between DMSO and alcohol molecules (E12) are reported.

range at 0.1 intervals were prepared. The complex dielectric constant spectrum of alcohol−DMSO mixtures were measured by Microwave Network Analyzer (PNA-N5227A) and an Agilent slim-form probe (85070E) under the frequency 20 MHz to 20 GHz. The calibration of the system was performed with the aid of three standards: air, an Agilent standard short circuit, and pure water at 298 K. The whole measuring system

2. EXPERIMENTAL SECTION All of the DMSO (≥99.5%) and polyhydric alcohols used in these experiments have been purchased from Chengdu Kelong Chemical Reagent Factory. The mixtures with full mole fraction 12984



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was placed in an air-conditioned room maintained at 298 ± 0.5 K. Each sample was measured at least four times on different occasions. The real and imaginary parts ε′(ω) and ε″(ω) were evaluated using the Agilent Materials Measurement Software 85070 with accuracy Δε′/ε′ = 0.05, Δε″/ε″ = 0.05. Fitting the experimental dielectric spectrum in a complex nonlinear least-squares routine by the Havriliak−Negami function:6,42 ε(ω) = ε∞ +

ε 0−ε∞ [1 + (jωτ )1 − α ]β

(1)

where τ is the relaxation time, ε∞ is the high-frequency dielectric parameter, and ε0 is the static dielectric constant. The shape parameters α(0 ≤ α ≤ 1) and β (0 ≤ β ≤ 1) describe symmetric and asymmetric distribution of relaxation times, respectively.

Figure 3. Complex permittivity spectrum (ε′ and ε″) of pure solvent at 298 K. The symbols present the experimental result. The solid lines are the fitted curve that accord well with Davidson−Cole function.

3. RESULTS The dielectric spectrum of the polyhydric alcohol−DMSO mixtures at the frequency range from 20 GHz to 20 MHz at room temperature is shown in Figures 1 and 2. All of the real part ε′ decreases with the increase of frequency. The imaginary part ε″ increases with x2 at small DMSO content, and then decreases with DMSO poured in, and with increasing DMSO, the peak of ε″ shifts toward higher frequency, which indicates the decrease of relaxation time. Particularly, because of the multiple hydroxyl group of EG and Gly, ε″ sharply decreases compared to monohydric alcohols. This phenomenon shows that the different interaction of HB led to the different complex dielectric properties of polyhydric alcohol−DMSO mixtures in whole mole fraction range. To obtain the dielectric relaxation parameters, a curve-fitting procedure is performed for the dielectric spectrum using Genetic Algorithm. From Figures 1 and 2, the shape of permittivity spectrum for polyhydric alcohol−DMSO is asymmetric. The permittivity spectrum ε(ω) of the system were then fitted by ε′(ω) and ε″(ω) to eq 1 with adjustable α and β.6 To check more complex spectral functions that might be related to more specific solution models, although Debye, Cole−Cole, Davidson−Cole, or Havriliak−Negami function is selected, we find the most appropriate way for displaying the frequency dispersion of the data is the Davidson−Cole function, while α = 0 and 0 < β ≤ 1. Figure 3 shows that the dielectric parameters of pure sample in this work accord well with literature data.6 Table 1 list the literature results of ε0 and τ for pure solvent and their evaluated data. During the fitting procedure of other literatures, we first considered ε∞ as adjustable parameter and found its value to vary from 2.5 to 5.5 with solute concentration. The four parameters fitted by Davidson−Cole function are shown in Figure 4. From Figure 4, the static permittivity ε0 of alcohols mixed with DMSO gradually increases with the increasing of DMSO. The high-frequency limiting permittivity ε∞ of the mixture is weakly influenced by x2. The relaxation time τ of these alcohols execpt for EG sharply decrease in 0 < x2 < 0.2, and above 0.2, τ decreases slowly. However, EG is opposite in this case. The spread of relaxation time β decreased indicates that the dielectric relaxation obviously deviates compared to pure DMSO.

Table 1. Experimental Static Permittivity ε0 and Dielectric Relaxation Time τ at 298 K ε0 pure solvent ethanola ethylene glycolb 1-propanolc 2-propanold glycerole DMSOf a e

literature 24.32 43.67 (at 293 K) 20.69 17.51 (at 308 K) 43.00 (±2%) 47.29 b

τ (ps) experimental (±3%) 22.81 43.01 21.27 12.35 43.57 49.04

Reference 43. Reference 26. Reference 35. fReference 6.

c

experimental (±10%)

literature 163 127 (at 293 K) 366 224 (at 308 K) 1400 (±10%) 20.92

Reference 44.

d

166 134 279 298 1300 23.25

Reference 45.

4. DISCUSSION 4.1. Excess Inverse Relaxation Time (1/τ)E. An excess inverse relaxation time (1/τ)E represents the average broadening of dielectric spectra that can be expressed as42,46,47 (1/τ )E = (1/τ )m − [(1/τ )1x1 + (1/τ )2 x 2]

(2)

and the excess permittivity is given by ε E = (ε0 − ε∞)m − [(ε0 − ε∞)1x1 + (ε0 − ε∞)2 x 2]

(3)

ε related to ε0 and τ provides significant information regarding interaction between the polar−polar liquid system due to HB interaction, and where x1and x2 represent the mole fraction of polyhydric alcohol and DMSO, respectively, in the mixture. The excess dielectric constant and excess inverse relaxation time at room temperature 298 K are shown in Figure 5. From Figure 5a, (1/τ)E < 0 proves solute−solvent interaction produces a field such that the effective dipoles rotate slowly as the strength of the heterogeneous HB increases. From Figure 4b, εE > 0 in EtOH−DMSO and EG−DMSO indicates there is formation of monomers and dimers. 1,2-PrOH and Gly-DMSO εE < 0 suggest the solute−solvent mixture may form multimers leading to the less effective dipoles. 4.2. Bruggeman Mixture Formula. The Bruggeman mixture formula is express as43,47 E

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Figure 4. Plot of static permittivity (ε0 ± 3%), high-frequency limiting permittivity (ε∞ ± 3%), relaxation time (τ ± 10%), and shape parameter (β ± 0.7%) at full mole fraction range for polyhydric alcohol−DMSO mixtures at 298 K.

Figure 5. (a) Excess inverse relaxation time (1/τ)E and (b) excess dielectric constant (ε0)E for polyhydric alcohol−DMSO mixtures at 298 K.

⎡ (ε − ε02) ⎤⎛ ε01 ⎞1/3 f B = ⎢ 0m ⎥⎜ ⎟ ⎣ (ε01 − ε02) ⎦⎝ ε0m ⎠

f B in Figure 6 is the nonideal behavior of a mole fraction of alcohol as the Bruggeman equation expected. Because the permittivity is highly sensitive to the hydrogen-bond structures, the static permittivity for the binary mixtures cannot be assumed to be those given by a simple mole-fraction mixture law.43 4.3. Luzar Model. On the basis of the statistical behavior of the solute−solvent interaction, the luzar model assumes that only solute−solute and solute−solvent pairs are formed in the

(4)

where f B is the Bruggeman dielectric factor, and it presents the static permittivity of a mixture with the volume fraction of solute. ε0m, ε01, and ε02 are the static permittivity for the mixture, polyhydric alcohol, and DMSO, respectively. From the above equation, a linear relationship is expected from a plot of f B vs x2. 12986



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alcohol−DMSO mixture. The static dielectric constant and Kirkwood correlation factor gi in mixture are given by12 2

[(ε0 − ε∞)(2ε0i + ε∞ i)/9ε0] = 4π /9kT ∑ giρi μi 2 i=1

(5)

where μi is the corresponding dipole moment, i = 1 and 2 represent alcohol and DMSO, respectively; k the Boltzmann constant, ρi the density, T the temperature. g1 and g2, respectively, indicate the Kirkwood correlation factor for alcohol and DMSO liquid system, which give us clues about the orientation of electric dipoles in polar liquids. Considering only the HBs contribution to the dipole−dipole correlation, the Luzar model gives the theoretical treatment of g1 and g2 as9,12

Figure 6. Bruggeman factor at full DMSO mole fraction range.

g1 = 1 + Z11 cos φ11 + Z12 cos φ12(μ2 /μ1)

(6)

g2 = 1 + Z 21 cos φ21(μ1 /μ2 )

(7)

where φ11 and φ12 are the angles between neighboring dipoles, both of them are taken to be 1/3, and the subscript in φij means alcohol−alcohol and alcohol−DMSO pairs, respectively. Z11 = 11 12 21 2⟨nHB ⟩, Z12 = 2⟨nHB ⟩, and Z21 = 2⟨nHB ⟩(1 − x2)/x2, respectively, represent the average number of particles forming HB with alcohol−alcohol and alcohol−DMSO pairs. x2 is the mole fraction of DMSO. Corresponding to different fraction in alcohol−DMSO system, the value of g1 and g2 is computed by those parameters given in Table 2 and are shown in Figure 8. 12 21 The average HBs number ⟨n11 HB⟩, ⟨nHB⟩, and ⟨nHB⟩ per alcohol molecule for 1i (i = 1,2) pairs has been given as follows: 1i ⟨nHB ⟩ = n1iω1i /n1

(8)

In function 8, the probability of bond formation between alcohol and DMSO is ω1i = 1/(1 + α1i e−βE1i). α1i and β = 1/kT, regarding hydrogen-bonded and non-hydrogen-bonded pairs, is the ratio of the two sub-volumes of the phase space. n1 is the number density of DMSO molecules. Only two energy levels existed, E11 for alcohol−alcohol and E12 for alcohol-DMSO pair 12 formed bonds. The values of ⟨n11 HB⟩ and ⟨nHB⟩ depend on the densities of the HB pairs between alcohol−alcohol molecule n11 and alcohol−DMSO n12. For ethanol, 1,2-propanol, n11 = 2n1 − n12; for ethylene glycol, n11 = 3n1 − n12; and for glycerol, n11 = 4n1 − n12. Figure 7 shows a curve of the average HBs number between alcohol−alcohol molecules (11 pairs) and alcohol− DMSO (12 pairs) against x2. Obviously, the values of ⟨n11 HB⟩ and ⟨n12 ⟩ depend on x in alcohol−DMSO mixtures. HB 2 Seen from Figure 7, for monohydric alcohol (EtOH and 1,2PrOH), with increasing mole fraction of DMSO n11 decreases while n12increases, and the value of n11, as well as that of n12 is 1 at x2 = 0.4. Comparing with monohydric, the intersection of n11and n12 of polyhydric alcohols (EG and Gly) shift toward low x2. This result suggests that the effect of one DMSO molecule interacting with surrounding polyhydric alcohol molecule by HB is different from monohydric alcohol. The dynamical structure of a cooperative domain (CD) is defined as a domain in which the reorientation of molecules cooperatively occurs with dipole correlations. The population of two kinds of CDs against x2 for EG−DMSO and Gly− DMSO mixtures is discussed. On the basis of the cooperative domain model, since no DMSO molecules are added, the pure EG must include only CDEG. At 0 < x2 < 0.4, DMSO molecule and its surrounding EG molecules interact with each other by HB, and these molecules for CDDMSO−EG. With x2 increased, the fraction of CDDMSO−EGincreases, and that of CDEG decreases. At

Figure 7. Mole fraction dependency for average molar HBs number of DMSO and alcohol molecules per unit volume for polyhydric alcohol−DMSO mixture.

Figure 8. Kirkwood correlation factor (g1,g2) against x2 for the polyhydric alcohol−DMSO mixtures at 298 K.

mixture such as water−DMSO system;12 here, we use the same model to explain the dielectric property of the polyhydric 12987



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Table 2. Molecular Parameters of the Static Dielectric Constants and the Binding Energy molecular parameter

EtOH

EG

1PrOH

2PrOH

Gly

dipole moment of alcohol in debyes, u1 dipole moment of DMSO in debyes, u2 polarizability for alcohol in α11 polarizability for alcohol in α12 binding energy for alcohol−alcohol (E11 ± 0.50 kJ/mol) binding energy for alcohol-DMSO (E12 ± 0.50 kJ/mol)

1.73 D 3.96 D 41 30 −14.00 −17.07

1.69 D 3.96 D 42 30 −13.66 −17.57

1.68 D 3.96 D 41 29 −13.86 −16.82

1.66 D 3.96 D 38 28 −13.83 −16.17

2.56 D 3.96 D 42 28 −11.52 −15.61

(4) de la Torre, J. C. Biological Action and Medical Applications of DMSO. Ann. N.Y. Acad. Sci. 1983, 411, 1−404. (5) Wiewiór, P. P.; Shirota, H.; Castner, E. W., Jr. Aqueous Dimethyl Sulfoxide Solutions: Inter- and Intra-Molecular Dynamics. J. Chem. Phys. 2001, 116, 4643. (6) Lu, Z. J.; Manias, E.; Macdonald, D. D.; Lanagan, M. Dielectric Relaxation in Dimethyl Sulfoxide/Water Mixtures Studied by Microwave Dielectric Relaxation Spectroscopy. J. Phys. Chem. A 2009, 113, 12207−12214. (7) Moyá, M. L.; Rodríguez, A.; Muñoz, M.; Graciani, M. M.; Fernández, G. Study of the Bromide Ion Reaction with Methyl Naphthalene-2-sulfonate in Water−DMSO TTAB Micellar Solutions. J. Phys. Org. Chem. 2006, 19, 676−682. (8) Bordallo, H. N.; Herwig, K. W.; Luther, B. M.; Levinger, N. E. Quasi-Elastic Neutron Scattering Study of Dimethyl-sulfoxide−water Mixtures: Probing Molecular Mobility in a Nonideal Solution. J. Chem. Phys. 2004, 121, 12457. (9) Luzar, A.; Stefan, J. Dielectric Behaviour of DMSO−Water Mixtures. A Hydrogen-Bonding Model. J. Mol. Liq. 1990, 46, 221− 238. (10) Sudo, S.; Oshiki, N.; Shinyashiki, N.; Yagihara, S.; Kumbharkhane, A. C.; Mehrotra, S. C. Dielectric Properties of Thyleneglycol-1,4-dioxane Mixtures Using TDR Method. J. Phys. Chem. A 2007, 111, 2993−2998. (11) Ramachandran, K.; Sivagurunathan, P.; Dharmalingam, K.; Mehrotra, S. C. Dielectric Relaxation Study of Amide−Alcohol Mixtures by Using Time Domain Reflectometry. Acta. Phys-Chim. Sin. 2007, 23, 1508−1515. (12) Kumbharkhane, A. C.; Shinde, M. N.; Mehrotra, S. C.; Oshiki, N.; Shinyashiki, N.; Yagihara, S.; Sudo, S. Structural Behavior of Alcohol-1,4-Dioxane Mixtures through Dielectric Properties Using TDR. J. Phys. Chem. A 2009, 113, 10196−10201. (13) Glasser, L.; Crossley, J.; Smyth, C. P. Microwave Absorption and Molecular Structure in Liquids. LXXIX. Dielectric Behavior and Association of Some Normal Alcohols in n-Heptane Solution. J. Chem. Phys. 1972, 57, 3977. (14) Helambe, S. N.; Chaudhari, A.; Mehrotra, S. C. Temperature Dependent Dielectric Study of n-Nitriles in Methanol Using Time Domain Reflectometry. J. Mol. Liq. 2000, 84, 235−244. (15) Vyas, A. D.; Rana, V. A. Dielectric Relaxation of Some Rigid Polar Molecules and Their Binary Mixture in Benzene Solution. Indian J. Pure Appl. Phys. 2002, 40, 69−71. (16) Chaudhari, A.; Khirade, P.; Singh, R.; Helambe, S. N.; Narain, N. K.; Mehrotra, S. C . Temperature Dependent Dielectric Relaxation Study of Tetrahydrofuran in Methanol and Ethanol at Microwave Frequency Using Time Domain Technique. J. Mol. Liq. 1999, 82, 245−253. (17) Kumbharkhane, A. C.; Puranik, S. M.; Mehrotra, S. C. Dielectric Relaxation Study and Structural Properties of 2-Nitroacetophenoneethanol Solutions from 10 MHz to 10 GHz. J. Mol. Liq. 1992, 51, 307−319. (18) Noto, R.; Martorana, V.; Emanuele, A.; Fornili, S. L. Comparison of the Water Perturbations Induced by Two Small Organic Solutes: ab Initio Calculations and Molecular Dynamics Simulation. J. Chem. Soc., Faraday Trans. 1995, 91, 3803−3808. (19) Dale, J. A.; Dull, D. L. Determined by 19 F NMR Analysis on the Derived Mosher Esters of the Parent Epoxy-Alcohol. J. Org. Chem. 1969, 34, 2543.

around x2 = 0.4, the average HBs number between EG and DMSO molecules and the average size of CDDMSO−EG are maximum. For x2 > 0.4, the number of alcohol molecules decreases with increasing x2, and it leads to a decrease in the average HBs number between EG and DMSO molecules, which is reflected in the decrease in CDDMSO−EG. Similarly, we can obtain a result for Gly-DMSO. Figure 8 indicates that g1 and g2 decrease with increasing x2. In 0 < x2 < 0.5, g2 decreases sharply, and above 0.5, g2 nearly keeps steady. The binding energy for solute−solute (E11) and solvent− solute (E12) are shown in Table 2. As shown in Table 2, the binding energies E11 and E12 decrease with the number of carbon atoms increased. According to the maximum measurement error of the static permittivity ε0 and permittivity at high frequency ε∞ of ±3%, we estimate E11 and E12 to be 0.50.

5. CONCLUSIONS The behavior of dielectric relaxation at microwave frequencies of polyhydric alcohol−DMSO mixtures was reported over full concentration range. Analyzed from the relaxation time, the polyhydric alcohols−DMSO appear as diverse relaxation dynamics in different mole fraction range. The position of a peak for the imaginary part of the permittivity shifts toward higher frequency with increased DMSO. Two types of HBs (alcohol−alcohol pair and alcohol−DMSO pair) are revealed by Luzar model, and it indicates that the average HBs number depends on not only solution composition but also the number of carbons.

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AUTHOR INFORMATION

Corresponding Author

*(J.G.-Z.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project was supported by the National Science Foundation of China under Grant No. 61102044. We would like to thank the Agilent technology Cheng Du Ltd. for the loan of Vector Network Analyzer Agilent N5227A PNA-X.

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REFERENCES

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Dielectric Constant of Polyhydric AlcoholâDMSO Mixture Solution at