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The dielectric relaxation of binary mixtures of propanediamine and propanediol
Journal of Non-Crystalline Solids 353 (2007) 1916–1919 www.elsevier.com/locate/jnoncrysol
The dielectric relaxation of binary mixtures of propanediamine and propanediol Y. Amo a
a,*
, S. Oshima b, Y. Tominaga
c
Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata 990-8560, Japan b Physics Institute, Faculty of Science, Ochanomizu University, Ostuka, Bunkyo-ku, Tokyo 112-8610, Japan c GSHS Ochanomizu University, Ostuka, Bunkyo-ku, Tokyo 112-8610, Japan Available online 24 April 2007
Abstract Dielectric spectra of binary mixtures of propanediamine (PDA) and propanediol (PDO) are measured by TDR (time domain reflectometry). The KWW (Kohlrausch–Williams–Watts) function is used to obtain relaxation parameters. The observed relaxation time has a maximum at around 0.7 mole fraction of PDO. The concentration dependence of the relaxation time suggests that the intermolecular interaction between PDA and PDO is stronger than that of pure amines and of pure alcohols. Ó 2007 Elsevier B.V. All rights reserved. PACS: 33.20.Bx; 61.20.Lc; 64.75.+g Keywords: Dielectric properties, relaxation, electric modulus; Ferroelectric; Time resolved measurements
1. Introduction It has been already reported that the binary mixture of polyamine and polyalcohol shows a glass transition [1,2]. The grass transition temperature of alcohol–amine mixture depends on the concentration and shows a clear maximum. This result indicated that the hydrogen bond structure among molecules is changed. The hydrogen bond N–H N is formed among amine molecules, while O–H O bonds are formed on the alcohol molecules. The hydrogen bond O–H N is formed when polyamine and polyalcohol are mixed each other. The O–H N bond is stronger than N–H N and O– H O [1]. The glass transition temperature becomes higher with increasing the O–H N bond. The amount of the O–H N bond should be related to the dielectric properties of the mixture in the liquid state. In the present work, we investigate the dielectric relaxation of amine–
*
Corresponding author. Tel.: +81 23 628 4730; fax: +81 23 628 4591. E-mail address: [email protected] (Y. Amo).
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.01.054
alcohol mixtures using TDR at room temperature to support the Takeda’s speculation [1]. 2. Experiment 1,2-Propanediol(12PDO), 1,3-propanediol(13PDO) and 1,2-propanediamine(12PDA) are purchased from Aldrich Co. Ltd. 1,3-propanediamine(13PDA) is purchased from Wako Pure Chemical Industry. Four kind of mixtures, 12PDA–12PDO, 12PDA–13PDO, 13PDA–12PDO and 13PDA–13PDO are prepared. The concentration range of PDA–PDO mixture is from 0 (pure PDA) to 100 (pure PDO) mol%. The mixture was homogenized by stirring over a water bath keeping the temperature around 50 °C for more than 5 h. This is because some of the present materials are so viscous at room temperature. The complex dielectric spectrum are measured by a TDR system consists of a digitizing oscilloscope (HP54120T, Hewlett-Packard) and a step pulse generator (HP54121A, Hewlett-Packard). Pulse height is 200 mV and its rising time is 35 ps. A personal computer (Power
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
Macintosh 8100, Apple Computer) is connected via SCSI– GPIB interface to the oscilloscope for obtaining the time domain signal and data processing. An open-ended co-axial line of 2.19 mm / is used for a sample cell. All the reflected signals are recorded at room temperature (295 K). The dielectric spectra are obtained from 107.5 Hz to 10 10 Hz using the algorithm of the precision difference method [3,4]. The reflected signal of the air is used for the standard. 3. Results and analysis Fig. 1(a) and (b) shows the concentration dependence of complex permittivity of 12PDA–12PDO mixtures using the precision difference method. Permittivity of the mixtures are obtained in the same manner. Permittivity decreases with decreasing PDO concentration. The loss peak shifts to the low frequency with decreas-
a 30 (12PDA)(12PDO) 25
ε'
20 15
12PDO mol% 100 90 80 70 50 30 10 0
10 5 0 7.5
8.0
8.5
9.0
9.5
10.0
1917
ing PDO concentration to 80 mol%, and shifts to higher frequency with decreasing PDO concentration from 80 mol% to 0 mol%. The Kohlrausch–Williams–Watts (KWW) function was used for fitting analysis [5]. This equation , t bKWW Uor ; P ðtÞ ¼ exp s
ð1Þ
0 < bKWW 6 1;
where Uor P ðtÞ is a step response function of orientational polarization, s is a relaxation time, and bKWW is a parameter to stretch the exponential decay function. The Laplace transform of the Eq. (1) represents the bandshape of the complex dielectric constant. We have calculated the frequency domain form of Eq. (1) numerically for non-linear least square method. The absolute value of e* cannot obtain from the Laplace transform of the Uor P ðtÞ because the result of the Laplace transform is normalized and gives the frequency dependent part of the dielectric constant. So we use two additional fitting parameters, De which represents the peak height of the dielectric spectrum and the dielectric constant of induced polarization e1 which represents the constant offset of the real part of the dielectric relaxation. Bandshape for the KWW function becomes asymmetrically broader as b become smaller. This equation is often applied to the dielectric spectra of glass transition materials. Although our results are recorded at the room temperature, that is, far from the glass transition temperature, the KWW function is well reproduced the measured spectra. Another candidate of model function to fit an asymmetrically broadened spectrum is superposition of the Debye type relaxation. In the Backer’s work, superposition of the four Debye relaxation was used to fit the complex dielectric spectra of propanediol, and alcohol mixtures from 1 MHz to 72 GHz [6]. Number of the fitting parameters in the four Debye model is 9. On the other hand, one
log(f) 35
12PDO mol% 100 90 80 70 50 30 10 0
14
(12PDA)(12PDO) 12 10
ε'
8
30 25 20
Δε
b
15
6 4
10
2
5
0
(13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
0
7.5
8.0
8.5
9.0
9.5
10.0
log(f) Fig. 1. Complex permittivity of 12PDA and 12PDO mixtures. (a) Real part and (b) imaginary part. Concentrations are shown in mol% of PDAs.
0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 2. Relaxation strength of PDA–PDO mixtures plotted against the mole fraction of PDO.
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
KWW function has 4 fitting parameters. So we use KWW function to obtain relaxation parameters because this is the simplest model to reproduce our spectra. Fig. 2 shows the concentration dependence of relaxation strength De of PDA–PDO mixtures. Concentration is shown in mole fraction of PDO. De increases linearly with increasing PDO concentration. Values of De depend on the molecular structure of PDO and do not depend on the molecular structure of PDA. Fig. 3 shows the concentration dependence of the e1. The e1 slightly increases with increasing PDO concentration. Values of e1 for less than 0.3 mole fraction of PDO contain certain ambiguity, because the whole bandshape of dielectric relaxation cannot be obtained.
1.0
0.8
0.6
βKWW
1918
0.4 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) 5
Fig. 5. b in KWW function increases with increasing PDA concentration.
4
The PDO concentration dependence of the dielectric relaxation time shown in Fig. 4 has a maximum value. The peak position of the relaxation time of 13PDO– 12PDA and 13PDO–13PDA are at around 0.7 mole fraction of PDO. The relaxation time of 12PDO–13PDA and 12PDO–12PDA has maximum value around 0.8 mole fraction of PDO. Fig. 5 shows the PDO concentration dependence of bKWW. Relaxation peak becomes broader with decreasing PDO concentration. Below 0.3 mole fraction of PDO, the bKWW does not converge to appropriate values, because the relaxation time is too fast to obtain the whole bandshape of the relaxation spectra. The behavior of e00 (x) of the PDA is the same of Debye type relaxation: e00 (x) / x. Therefore the bKWW of PDA nearly equals 1.
ε∞
3
2 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
1
0 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 3. e1 of PDA–PDO mixtures plotted against the mole fraction of PDO.
4. Discussion -9.0
-9.5
logτ
-10.0
-10.5 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
-11.0
-11.5 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 4. Concentration dependence of the relaxation time of PDA–PDO mixtures plotted against the mole fraction of PDO.
The PDA–PDO mixtures are quite different from alcohol–water mixtures: the relaxation time has a maximum at 0.7 or 0.8 mole fraction of PDO. Sudo et al. determined the dielectric relaxation time for various alcohols and water mixtures [7]. The relaxation time of alcohol–water system increases monotonically with increasing alcohol concentration [7,8]. In the PDA–PDO system, hydrogen bond is formed between different kinds of groups, –NH2 and –OH. Takeda has pointed out that the hydrogen bond O–H N is stronger than O–H O and/or N–H N that formed in pure components, and the hydrogen bond structure would be more developed by introducing stronger types of hydrogen bond a finite temperature [1]. The relaxation time of pure PDO is longer than that of the pure PDA. When PDA added to PDO, number of stronger hydrogen bonds O– H N increase and the relaxation time becomes longer than that of pure PDO. Distribution of hydrogen bonds,
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
to obtain the free energy DG from the relaxation time. For the ideal mixing state, the free energy should be DGmix ¼ xDG1 þ ð1 xÞDG2
5
4
τratio
O–H N, O–H O and N–H N, would affect the concentration dependence of the relaxation time. The relaxation time of the mixtures become longest at 0.7 or 0.8 mole fraction of PDO at room temperature. On the other hand, the glass transition temperature of PDA–PDO mixtures shows a maximum at 0.5 mole fraction of PDO. These two concentrations are apparently different. Since the value of s depends on the distribution of the hydrogen bonds, and the distribution would depends on the temperature. Sudo et al. have analyzed the relaxation time of alcohol– water mixture using the difference between the free energy of the mixtures and that of the ideal mixing state of two component liquids [7]. They use the Eyling formula h DG s¼ exp ð2Þ kT RT
1919
3
2
(13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
1 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 6. Concentration dependence of sratio plotted against the mole fraction of PDO.
ð3Þ
where DG1 and DG2 are the free energy of liquid 1 and liquid 2, respectively, and x is the mole fraction of liquid 1. For an ideal behavior of the relaxation time, sideal, for the mixture is written using Eqs. (2) and (3) h DGmix ð1xÞ exp sideal ¼ ð4Þ ¼ sx1 s2 kT RT
Our results of the measurement at room temperature support the Takeda’s speculation. The distribution of the hydrogen bonds may be different from that at near the glass transition temperature. Determination of the relaxation parameter near the glass transition temperature is future problem.
where s1 and s2 are the dielectric relaxation time of pure liquid 1 and pure liquid 2, respectively. Both s1 and s2 are determined from experimental data and sideal corresponding to the arbitrary concentration x is calculated from Eq. (4). The indicator of the deviation from ideal behavior is sratio which is defined by s/sideal at the same concentration, where s is the observed relaxation time of the liquid mixture. We apply the same method to our results and obtained sratio are plotted against the mole fraction of PDO (Fig. 6). The concentration dependence of sratio has a maximum value around at 0.4 or 0.5 mole fraction of PDO. This result is similar to the Fig. 4 in Ref. [7] and seems to be consistent with the concentration dependence of the glass transition temperature Tg. Suppose that the liquid 1 and liquid 2 have a relaxation time s1 and s2, respectively. The low concentration liquid1 (liquid2) region, the relaxation time of binary mixture is almost same as the s2 (s1), i.e. sratio nearly equals 1. When the mixing is not ideal, deviation from ideal state should become large around 1:1 mixture. sratio analysis enhances the difference between pure and mixed state. Strong hydrogen bonds formation should be occurred at the concentration corresponding to the longest relaxation time. The absolute value of s indicate the average strength of the hydrogen bonds between species.
5. Conclusion We obtain the dielectric spectra of binary mixtures of 1,2- and 1,3-propanediamine(PDA) and 1,2- and 1,3-propanediol(PDO) measured by TDR (time domain reflectometry). The KWW function is used to determine the relaxation parameters: relaxation strength De, e1, relaxation time s and stretching parameter bKWW. The relaxation time has a maximum at around 0.7 mole fraction of PDO. The concentration dependence of the relaxation time suggests that the intermolecular interaction between PDA and PDO is stronger than that of pure amines and of pure alcohols. References [1] K. Takeda, K. Murata, S. Yamashita, J. Phys. Chem. B 103 (1999) 3457. [2] K. Takeda, K. Murata, S. Yamashita, O. Yamamuro, T. Matsuo, H. Suga, Prog. Theor. Phys. Suppl. (1997) 83. [3] R.H. Cole, S. Mashimo, P. Winsor, J. Phys. Chem. 84 (1980) 786. [4] S. Mashimo, S. Kuwabara, S. Yagihara, K. Higasi, J. Chem. Phys. 90 (1989) 3292. [5] G. Williams, D.C. Watts, Trans. Faraday Soc. 67 (1971) 1323. [6] U. Becker, M. Stockhausen, J. Mol. Liq. 81 (1999) 89. [7] S. Sudo, N. Shinyashiki, Y. Kitsuki, S. Yagihara, J. Phys. Chem A 106 (2002) 458. [8] F. Wang, R. Pottel, U. Kaatze, J. Phys. Chem. B 101 (1997) 922.
The dielectric relaxation of binary mixtures of propanediamine and propanediol Y. Amo a
a,*
, S. Oshima b, Y. Tominaga
c
Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata 990-8560, Japan b Physics Institute, Faculty of Science, Ochanomizu University, Ostuka, Bunkyo-ku, Tokyo 112-8610, Japan c GSHS Ochanomizu University, Ostuka, Bunkyo-ku, Tokyo 112-8610, Japan Available online 24 April 2007
Abstract Dielectric spectra of binary mixtures of propanediamine (PDA) and propanediol (PDO) are measured by TDR (time domain reflectometry). The KWW (Kohlrausch–Williams–Watts) function is used to obtain relaxation parameters. The observed relaxation time has a maximum at around 0.7 mole fraction of PDO. The concentration dependence of the relaxation time suggests that the intermolecular interaction between PDA and PDO is stronger than that of pure amines and of pure alcohols. Ó 2007 Elsevier B.V. All rights reserved. PACS: 33.20.Bx; 61.20.Lc; 64.75.+g Keywords: Dielectric properties, relaxation, electric modulus; Ferroelectric; Time resolved measurements
1. Introduction It has been already reported that the binary mixture of polyamine and polyalcohol shows a glass transition [1,2]. The grass transition temperature of alcohol–amine mixture depends on the concentration and shows a clear maximum. This result indicated that the hydrogen bond structure among molecules is changed. The hydrogen bond N–H N is formed among amine molecules, while O–H O bonds are formed on the alcohol molecules. The hydrogen bond O–H N is formed when polyamine and polyalcohol are mixed each other. The O–H N bond is stronger than N–H N and O– H O [1]. The glass transition temperature becomes higher with increasing the O–H N bond. The amount of the O–H N bond should be related to the dielectric properties of the mixture in the liquid state. In the present work, we investigate the dielectric relaxation of amine–
*
Corresponding author. Tel.: +81 23 628 4730; fax: +81 23 628 4591. E-mail address: [email protected] (Y. Amo).
0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.01.054
alcohol mixtures using TDR at room temperature to support the Takeda’s speculation [1]. 2. Experiment 1,2-Propanediol(12PDO), 1,3-propanediol(13PDO) and 1,2-propanediamine(12PDA) are purchased from Aldrich Co. Ltd. 1,3-propanediamine(13PDA) is purchased from Wako Pure Chemical Industry. Four kind of mixtures, 12PDA–12PDO, 12PDA–13PDO, 13PDA–12PDO and 13PDA–13PDO are prepared. The concentration range of PDA–PDO mixture is from 0 (pure PDA) to 100 (pure PDO) mol%. The mixture was homogenized by stirring over a water bath keeping the temperature around 50 °C for more than 5 h. This is because some of the present materials are so viscous at room temperature. The complex dielectric spectrum are measured by a TDR system consists of a digitizing oscilloscope (HP54120T, Hewlett-Packard) and a step pulse generator (HP54121A, Hewlett-Packard). Pulse height is 200 mV and its rising time is 35 ps. A personal computer (Power
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
Macintosh 8100, Apple Computer) is connected via SCSI– GPIB interface to the oscilloscope for obtaining the time domain signal and data processing. An open-ended co-axial line of 2.19 mm / is used for a sample cell. All the reflected signals are recorded at room temperature (295 K). The dielectric spectra are obtained from 107.5 Hz to 10 10 Hz using the algorithm of the precision difference method [3,4]. The reflected signal of the air is used for the standard. 3. Results and analysis Fig. 1(a) and (b) shows the concentration dependence of complex permittivity of 12PDA–12PDO mixtures using the precision difference method. Permittivity of the mixtures are obtained in the same manner. Permittivity decreases with decreasing PDO concentration. The loss peak shifts to the low frequency with decreas-
a 30 (12PDA)(12PDO) 25
ε'
20 15
12PDO mol% 100 90 80 70 50 30 10 0
10 5 0 7.5
8.0
8.5
9.0
9.5
10.0
1917
ing PDO concentration to 80 mol%, and shifts to higher frequency with decreasing PDO concentration from 80 mol% to 0 mol%. The Kohlrausch–Williams–Watts (KWW) function was used for fitting analysis [5]. This equation , t bKWW Uor ; P ðtÞ ¼ exp s
ð1Þ
0 < bKWW 6 1;
where Uor P ðtÞ is a step response function of orientational polarization, s is a relaxation time, and bKWW is a parameter to stretch the exponential decay function. The Laplace transform of the Eq. (1) represents the bandshape of the complex dielectric constant. We have calculated the frequency domain form of Eq. (1) numerically for non-linear least square method. The absolute value of e* cannot obtain from the Laplace transform of the Uor P ðtÞ because the result of the Laplace transform is normalized and gives the frequency dependent part of the dielectric constant. So we use two additional fitting parameters, De which represents the peak height of the dielectric spectrum and the dielectric constant of induced polarization e1 which represents the constant offset of the real part of the dielectric relaxation. Bandshape for the KWW function becomes asymmetrically broader as b become smaller. This equation is often applied to the dielectric spectra of glass transition materials. Although our results are recorded at the room temperature, that is, far from the glass transition temperature, the KWW function is well reproduced the measured spectra. Another candidate of model function to fit an asymmetrically broadened spectrum is superposition of the Debye type relaxation. In the Backer’s work, superposition of the four Debye relaxation was used to fit the complex dielectric spectra of propanediol, and alcohol mixtures from 1 MHz to 72 GHz [6]. Number of the fitting parameters in the four Debye model is 9. On the other hand, one
log(f) 35
12PDO mol% 100 90 80 70 50 30 10 0
14
(12PDA)(12PDO) 12 10
ε'
8
30 25 20
Δε
b
15
6 4
10
2
5
0
(13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
0
7.5
8.0
8.5
9.0
9.5
10.0
log(f) Fig. 1. Complex permittivity of 12PDA and 12PDO mixtures. (a) Real part and (b) imaginary part. Concentrations are shown in mol% of PDAs.
0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 2. Relaxation strength of PDA–PDO mixtures plotted against the mole fraction of PDO.
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
KWW function has 4 fitting parameters. So we use KWW function to obtain relaxation parameters because this is the simplest model to reproduce our spectra. Fig. 2 shows the concentration dependence of relaxation strength De of PDA–PDO mixtures. Concentration is shown in mole fraction of PDO. De increases linearly with increasing PDO concentration. Values of De depend on the molecular structure of PDO and do not depend on the molecular structure of PDA. Fig. 3 shows the concentration dependence of the e1. The e1 slightly increases with increasing PDO concentration. Values of e1 for less than 0.3 mole fraction of PDO contain certain ambiguity, because the whole bandshape of dielectric relaxation cannot be obtained.
1.0
0.8
0.6
βKWW
1918
0.4 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) 5
Fig. 5. b in KWW function increases with increasing PDA concentration.
4
The PDO concentration dependence of the dielectric relaxation time shown in Fig. 4 has a maximum value. The peak position of the relaxation time of 13PDO– 12PDA and 13PDO–13PDA are at around 0.7 mole fraction of PDO. The relaxation time of 12PDO–13PDA and 12PDO–12PDA has maximum value around 0.8 mole fraction of PDO. Fig. 5 shows the PDO concentration dependence of bKWW. Relaxation peak becomes broader with decreasing PDO concentration. Below 0.3 mole fraction of PDO, the bKWW does not converge to appropriate values, because the relaxation time is too fast to obtain the whole bandshape of the relaxation spectra. The behavior of e00 (x) of the PDA is the same of Debye type relaxation: e00 (x) / x. Therefore the bKWW of PDA nearly equals 1.
ε∞
3
2 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
1
0 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 3. e1 of PDA–PDO mixtures plotted against the mole fraction of PDO.
4. Discussion -9.0
-9.5
logτ
-10.0
-10.5 (13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
-11.0
-11.5 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 4. Concentration dependence of the relaxation time of PDA–PDO mixtures plotted against the mole fraction of PDO.
The PDA–PDO mixtures are quite different from alcohol–water mixtures: the relaxation time has a maximum at 0.7 or 0.8 mole fraction of PDO. Sudo et al. determined the dielectric relaxation time for various alcohols and water mixtures [7]. The relaxation time of alcohol–water system increases monotonically with increasing alcohol concentration [7,8]. In the PDA–PDO system, hydrogen bond is formed between different kinds of groups, –NH2 and –OH. Takeda has pointed out that the hydrogen bond O–H N is stronger than O–H O and/or N–H N that formed in pure components, and the hydrogen bond structure would be more developed by introducing stronger types of hydrogen bond a finite temperature [1]. The relaxation time of pure PDO is longer than that of the pure PDA. When PDA added to PDO, number of stronger hydrogen bonds O– H N increase and the relaxation time becomes longer than that of pure PDO. Distribution of hydrogen bonds,
Y. Amo et al. / Journal of Non-Crystalline Solids 353 (2007) 1916–1919
to obtain the free energy DG from the relaxation time. For the ideal mixing state, the free energy should be DGmix ¼ xDG1 þ ð1 xÞDG2
5
4
τratio
O–H N, O–H O and N–H N, would affect the concentration dependence of the relaxation time. The relaxation time of the mixtures become longest at 0.7 or 0.8 mole fraction of PDO at room temperature. On the other hand, the glass transition temperature of PDA–PDO mixtures shows a maximum at 0.5 mole fraction of PDO. These two concentrations are apparently different. Since the value of s depends on the distribution of the hydrogen bonds, and the distribution would depends on the temperature. Sudo et al. have analyzed the relaxation time of alcohol– water mixture using the difference between the free energy of the mixtures and that of the ideal mixing state of two component liquids [7]. They use the Eyling formula h DG s¼ exp ð2Þ kT RT
1919
3
2
(13PDA)(13PDO) (12PDA)(13PDO) (12PDA)(12PDO) (13PDA)(12PDO)
1 0.0
0.2
0.4
0.6
0.8
1.0
Concentration (PDO mole fraction) Fig. 6. Concentration dependence of sratio plotted against the mole fraction of PDO.
ð3Þ
where DG1 and DG2 are the free energy of liquid 1 and liquid 2, respectively, and x is the mole fraction of liquid 1. For an ideal behavior of the relaxation time, sideal, for the mixture is written using Eqs. (2) and (3) h DGmix ð1xÞ exp sideal ¼ ð4Þ ¼ sx1 s2 kT RT
Our results of the measurement at room temperature support the Takeda’s speculation. The distribution of the hydrogen bonds may be different from that at near the glass transition temperature. Determination of the relaxation parameter near the glass transition temperature is future problem.
where s1 and s2 are the dielectric relaxation time of pure liquid 1 and pure liquid 2, respectively. Both s1 and s2 are determined from experimental data and sideal corresponding to the arbitrary concentration x is calculated from Eq. (4). The indicator of the deviation from ideal behavior is sratio which is defined by s/sideal at the same concentration, where s is the observed relaxation time of the liquid mixture. We apply the same method to our results and obtained sratio are plotted against the mole fraction of PDO (Fig. 6). The concentration dependence of sratio has a maximum value around at 0.4 or 0.5 mole fraction of PDO. This result is similar to the Fig. 4 in Ref. [7] and seems to be consistent with the concentration dependence of the glass transition temperature Tg. Suppose that the liquid 1 and liquid 2 have a relaxation time s1 and s2, respectively. The low concentration liquid1 (liquid2) region, the relaxation time of binary mixture is almost same as the s2 (s1), i.e. sratio nearly equals 1. When the mixing is not ideal, deviation from ideal state should become large around 1:1 mixture. sratio analysis enhances the difference between pure and mixed state. Strong hydrogen bonds formation should be occurred at the concentration corresponding to the longest relaxation time. The absolute value of s indicate the average strength of the hydrogen bonds between species.
5. Conclusion We obtain the dielectric spectra of binary mixtures of 1,2- and 1,3-propanediamine(PDA) and 1,2- and 1,3-propanediol(PDO) measured by TDR (time domain reflectometry). The KWW function is used to determine the relaxation parameters: relaxation strength De, e1, relaxation time s and stretching parameter bKWW. The relaxation time has a maximum at around 0.7 mole fraction of PDO. The concentration dependence of the relaxation time suggests that the intermolecular interaction between PDA and PDO is stronger than that of pure amines and of pure alcohols. References [1] K. Takeda, K. Murata, S. Yamashita, J. Phys. Chem. B 103 (1999) 3457. [2] K. Takeda, K. Murata, S. Yamashita, O. Yamamuro, T. Matsuo, H. Suga, Prog. Theor. Phys. Suppl. (1997) 83. [3] R.H. Cole, S. Mashimo, P. Winsor, J. Phys. Chem. 84 (1980) 786. [4] S. Mashimo, S. Kuwabara, S. Yagihara, K. Higasi, J. Chem. Phys. 90 (1989) 3292. [5] G. Williams, D.C. Watts, Trans. Faraday Soc. 67 (1971) 1323. [6] U. Becker, M. Stockhausen, J. Mol. Liq. 81 (1999) 89. [7] S. Sudo, N. Shinyashiki, Y. Kitsuki, S. Yagihara, J. Phys. Chem A 106 (2002) 458. [8] F. Wang, R. Pottel, U. Kaatze, J. Phys. Chem. B 101 (1997) 922.