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Surface tensions of non-polar liquids in high magnetic fields
Journal of Molecular Liquids 181 (2013) 51–54
Contents lists available at SciVerse ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Surface tensions of non-polar liquids in high magnetic fields Chuanjun Li ⁎, Long Chen, Zhongming Ren School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China Shanghai Key Laboratory of Modern Metallurgy and Materials Processing, Shanghai 200072, China
a r t i c l e
i n f o
Article history: Received 20 December 2012 Received in revised form 16 February 2013 Accepted 18 February 2013 Available online 7 March 2013 Keywords: Surface tension Nonpolar liquid Magnetic field Hydrogen bond
a b s t r a c t Thermophysical parameters of materials like the surface tension generally were modified in the high magnetic field. In the study, the surface tension of the non-polar liquid such as tetrachloromethane in high magnetic fields was examined using the ring method. It was found that the surface tension of the liquid linearly increased with the external magnetic field intensities and its change reached 1.65% in the magnetic field of 10 T. By comparing surface tensions of several liquids with different polarities in the magnetic field, the difference between variation trends for different liquids was probably because of the weaker effect of the magnetic field on dispersion forces than on hydrogen bonds by Lorentz force. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In recent decades, materials processing in a high static magnetic field have attracted wide attention with development of magnet technologies [1]. Not only have many novel phenomena in the high magnetic field like levitation, orientation, phase transformation and thermoelectromagnetic convection been found successively, but also some technologies have even successfully been applied to the production sphere. Meanwhile, it was found that various thermophysical parameters of substances would change by the action of the high magnetic field such as transition point [2], electrical resistivity [3], viscosity [4] and diffusion coefficient [5]. Therefore, in order to effectively take advantage of the magnetic field in various fields, it is necessary for scientific researches or industrial production relating to the magnetic field to accurately re-determine the thermophysical parameters of materials in the high magnetic field. The surface tension as an important parameter would determine interfacial behaviors in many technological processes. In view of the facts, some attempt has been performed to measure surface tensions of liquids in the magnetic field. Fujimura et al. experimentally demonstrated that the external magnetic field increased the surface tension of water–air interface [6,7]. It was proposed that the magnetic field stabilized the hydrogen bonds in water and thus increased the surface tension. Nevertheless, suppose there is no hydrogen bond in certain liquids, how does the surface tension change with magnetic
⁎ Corresponding author at: Shanghai Key Laboratory of Modern Metallurgy and Materials Processing, Shanghai 200072, China. Tel.: +86 21 56331346. E-mail addresses: [email protected] (C. Li), [email protected] (L. Chen), [email protected] (Z. Ren). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.02.010
field? Therefore, the work aims to investigate the effect of the magnetic field on surface tensions of liquids without hydrogen bonds. 2. Experimental procedure 2.1. Materials The tetrachloromethane as a typical nonpolar molecule with a purity of ≥99.5% (CHCl3 ≤ 0.05%, H2O ≤ 0.02%, Cl ≤ 0.0001%, CS2 ≤ 0.0005%, others ≤ 0.001%, Sinopharm Chemical Reagent Co., Ltd) was used to examine the effect of the magnetic field on the surface tension of the liquid without hydrogen bonds. In general, the pure liquid should be chosen to investigate its real surface tension. Nevertheless, the pure liquid is not required for comparison as long as the same liquid was used throughout. Therefore, the tetrachloromethane liquid was not further purified in this work. 2.2. Measuring surface tension by the ring method In order to measure the surface tensions of liquids in the high magnetic field, we developed a tensiometer adaptable to a superconducting magnet on the base of the ring method [8]. The tensiometer could continuously record the pull of the ring when the ring immersing in liquid slowly rose or the liquid level fell until it detached from the liquid level, from which the maximum pull of the ring can be obtained. The surface tension γ of the liquid can thus be calculated according to the following relation: γ ¼ f ⋅F max =4πR
ð1Þ
52
C. Li et al. / Journal of Molecular Liquids 181 (2013) 51–54
where Fmax is the maximum equilibrium force of detachment, R is the radius of the ring, g is the gravity acceleration and f is the Harkins– Jordan factor. The Harkins–Jordan factor could be calibrated by a commercial tensiometer (K100MK2, KRUSS, Germany), of which measurement precision could reach 0.01 mN/m. In the absence of the magnetic field, the surface tension of the same liquid was measured using the two sets of equipment, respectively. Then the Harkins–Jordan factor could be determined by the following equation: f ¼ 4πR⋅γ0 =F max
ð2Þ
where γ0 is the surface tension of the liquid at a given temperature obtained by the commercial tensiometer. In consequence, the surface tension can be attained using the above two equations. Before the experiments, all components of the tensiometer which was in contact with the liquid were cleaned sequentially with acetone and a given liquid. In the experiments, the proper amount of the liquid was infused into the beaker until the ring was wholly immersed. When the liquid level and the ring were at rest, the pull measured by the precision balance began to be collected by a computer. Subsequently, the double-plunger micro-pump commenced to pump the liquid. The lowering rate of the liquid level was set to 7.5 × 10 −5 m/s. The liquid level was slowly lowered until the ring detached from the liquid film. The remaining liquid in the beaker was thoroughly pumped and then the new liquid was infused for next measurement. The experiment in the same conditions was repeatedly carried out for more than ten times. The temperature of the liquid during the measurements was monitored by the T-type thermocouple and its fluctuation was in the range of ±0.5 K. 3. Result and discussion Fig. 1 shows that the surface tension of tetrachloromethane varies with the external magnetic field and the fitting curve of experimental data indicates that the surface tension of the liquid linearly varies with the magnetic field. The surface tensions and their change in various magnetic fields are listed in Table 1. It is seen that the change in surface tension of tetrachloromethane reaches 0.48 mN/m and increases by 1.65% in the magnetic field of 10 T. Firstly let’s estimate several errors during the measurement of the surface tension before further searching for the nature of change in surface tension in the magnetic field. The liquid film would be subjected to the magnetic force due to the inhomogeneity of the magnetic field. During measurements the ring was always in the center of the magnet, namely, the region of the maximum intensity of the magnetic field. When the liquid level was lowered to the position below the center of the magnet, the
Fig. 1. Surface tension of tetrachloromethane is plotted against the magnetic field.
Table 1 Surface tensions of tetrachloromethane obtained using the ring method in different magnetic fields at 284 K. Magnetic field (T)
Surface tension (mN/m)
Change in surface tension (mN/m)
0 2 4 6 8 10
29.03 29.06 29.24 29.32 29.42 29.51
0 0.03 0.21 0.29 0.39 0.48
± ± ± ± ± ±
0.08 0.08 0.02 0.04 0.02 0.05
liquid film would be subjected to a downward magnetic force Fm. One may calculate the force using the following expression, F m ¼ ∫ðmχ m =μ 0 Þ⋅ðBdB=dzÞdv
ð3Þ
where m, χm,, μ0 and v are mass, mass susceptibility, vacuum permeability and volume, respectively. BdB/dz is the product of magnetic field and its gradient along the vertical direction. In the case of 10 T, BdB/dz = − 6770z (−10 −2m b z b 10 −2m) near the center of the magnet. The molar susceptibility of tetrachloromethane is χmol = − 66.6 × 10 −12 m 3/mol at room temperature [9]. The height of liquid film is about 3.5 × 10 −3 m and its mass was estimated to be (0.4678 ± 0.0014) × 10 −3 kg. Then the magnetic force of liquid film is evaluated to be Fm ≈ 1.9 × 10 −9 N, corresponding to the surface tension of 1.6 × 10 −5 mN/m based on Eq. (1). It follows that the measurement error induced by the magnetic force is four orders of magnitude less than the change in surface tension in the magnetic field of 10 T. Additionally, the temperature fluctuation also induced the measurement error. The temperature of the liquid fluctuated in 1 K in all measurements, which was monitored by a thermometer. Since the temperature coefficient of the surface tension of tetrachloromethane is − 0.12 mN/m at 284 K [10], the temperature fluctuation of 1 K led to the error of 0.12 mN/m. It is worthwhile noting that the surface tension of the tetrachloromethane liquid in this work is measured to be 29.03 ± 0.08 mN/m at 284 K. The surface tension of pure tetrachloromethane as a function of temperature is written as γ = 62.91 − 0.1224T (mN/m), where T is the absolute temperature [10]. One easily obtains γ = 28.15 mN/m for the pure liquid at 284 K. Thus, the real surface tension of the liquid used in this work is higher than the value of the pure liquid reported in the reference. Obviously, a small amount of other components led to the increase of the surface tension in this work. However, the existence of impurities in the liquid cannot influence the relative variation of surface tension in the magnetic field as long as the same liquid was used throughout. Oxygen molecules were believed to reduce the surface tension due to the difference between concentrations of oxygen in air and liquid. Nevertheless, the change in surface tension induced by oxygen molecules is far less than the increase of surface tension in 10 T [6]. Moreover, the experimental results showed that the standard error gradually decreased as the magnetic field increased. This demonstrated that the higher magnetic field made the measurement more stable and thus the error was further reduced with increasing the magnetic field. It was noted whether the magnetic field affects the interaction between the liquid and the ring and thus measurement of the surface tension. Without doubt, the magnetic field influences the interaction between solid and liquid phases. However, as we know, the ring method is based on completely wetting between liquid and solid with exceedingly high surface free energy and the pull force depends on size and shape of the ring, the wetting angle and the surface tension of the liquid. At the point of the maximum pull, the wetting angle equals to zero and the liquid film is hung by the surface tension. Therefore, the maximum pull is only related to the surface tension of
C. Li et al. / Journal of Molecular Liquids 181 (2013) 51–54
53
the liquid, not to the interaction between liquid and the ring, that is, the measurement of the surface tension is not affected by the interaction between the liquid and ring in the magnetic field. From the preceding analysis, obviously, the change in surface tension in the magnetic field of 10 T is beyond the above-mentioned errors. This demonstrates that the magnetic field increases the surface tension of the non-polar liquid. In the constant pressure and temperature, the surface tension is the Gibbs free energy per unit area. The magnetic energy contributes to the Gibbs free energy and thus to the surface tension. For tetrachloromethane, the molar magnetic energy Gm can be calculated by using the expression, 2
Gm ¼ −χ m ⋅B =2μ 0 :
ð4Þ
One may obtain Gm = 2.65 × 10 −3 J/mol at the magnetic field of 10 T. This value is far less than the interaction energy between molecules (0.1 × 10 3 ~ 10 × 10 3 J/mol). Therefore, the contribution of the magnetic energy to the surface tension is extremely small. The energy states of molecules in the bulk and at the surface of a liquid are different because of the difference in local environment of molecules [11]. Some evidences showed that the molecules at surface have different properties from ones in bulk liquid in the magnetic field. Hosoda et al. measured the refractive indices of water at interface and bulk water in the magnetic field using the surface plasmon resonance and the position-sensitive detector, respectively, and found that the refractive indices obtained by the former were larger than those by the latter [12]. This meant that the nature of water at surface was different from that in bulk water in the magnetic field. Therefore, it is reasonable to believe that the surface entropy of liquids increases due to the change in surface structures in the magnetic field and further leads to increase in the surface tension, which needs further study. On the other hand, the surface tension could be expressed as a function of density, radial distribution function and potential function using statistical mechanical approach [13]. The radial distribution function and potential function reflect the liquid structure and molecular interaction, respectively. Since the surface tension of tetrachloromethane increased in the magnetic field, the magnetic field probably changed the liquid structure and even molecular interaction. It is well-known that tetrachloromethane molecules are non-polar and only dispersion forces induced by instantaneous dipoles universally exist, the magnetic field exerts the effect on instantaneous dipoles by Lorentz force and necessarily changes the motion of non-polar molecules in a way. This enhanced the connectivity of tetrachloromethane molecules and further changed the liquid structure. In fact, a lot of studies showed that the external magnetic field modified the structure of water molecules and thus changed its pertinent properties such as refractive index [12], and hydrogen bond [14]. Chang and Weng applied molecular dynamic simulation to find that the magnetic field changed the radial distribution function of liquid water and hence slightly increased the number of hydrogen bonds [14]. This demonstrated that the magnetic field induced the tighter bonds between water molecules and improved the stabilization of water. Hosoda et al. speculated that the stabilization of hydrogen bonds increased in the magnetic field by increasing the electron delocalization of water molecules [12]. Although the structure of tetrachloromethane is completely different from water, they belong to diamagnetic substances. From the viewpoint of electromagnetism, the diamagnetism is induced by anti-parallel magnetization of molecules to the magnetic field and depends on electron distribution. Provided that the electron delocalization of molecules occurs in the magnetic field, the intermolecular energy consequentially changes. Especially, the electrons abutting gas phase at the surface have no steric hindrance caused by neighbor molecules in liquid phase and electron delocalization would be more significant. As a result, the intermolecular energy at surface would increase by the action of the
Fig. 2. Surface tensions of tetrachloromethane and acetone vary with the external magnetic field. (The surface tensions of acetone in magnetic fields are referred to Ref. [8]).
magnetic field. Without doubt, these factors would increase the surface tension of the non-polar liquid. Nevertheless, the linear variation of the surface tension of tetrachloromethane with the magnetic field markedly is different from square relation of change in surface tension of water in the magnetic field [6,7]. At present, the reason why the surface tension of the liquid linearly varied with the external magnetic field is not clear. The distinct difference between two liquids is that the former has hydrogen bonds. Provided that this is the resource of different trends, the effect of the magnetic field on hydrogen-bonding molecules is more obvious than others. It can be explained below. The water molecules are polar and partially charged while the tetrachloromethane molecules are not almost charged although instantaneous dipoles exist. Therefore, the effect of Lorentz force on motion of water molecules is stronger than that of tetrachloromethane molecules due to the different polarities. Polar molecules would be confined more tightly than nonpolar ones. We compared variation trends of surface tensions of acetone and tetrachloromethane in the magnetic field and found that both of them linearly increased with increasing the magnetic field as showed in Fig. 2. The surface tensions of two liquids as a function of the magnetic field were determined to be γte = 0.048B + 29.04 and γac = 0.062B + 24.08 (γte and γac represent surface tensions of tetrachloromethane and acetone in mN/m, respectively, B is the magnetic field in Tesla). This showed that the effect of magnetic field on surface tensions of two liquids without hydrogen bonds was weaker than that of water with hydrogen bonds. Moreover, the almost constant refractive indices of n-hexane in the magnetic field also corroborated the operation of hydrogen bonds in comparison with water [12]. This seems to further testify the above inference. However, the linear relation needs further investigation. 4. Conclusion In conclusion, we applied the ring method to measure the surface tension of the tetrachloromethane liquid in various magnetic fields. It was found that the surface tension of the liquid linearly increased with increasing the magnetic field, which was markedly different from that of water. It was inferred that the effect of the external magnetic field on hydrogen bonds was more obvious than on dispersion forces by Lorentz force and thus the surface tension of the liquid without hydrogen bonds showed the different variations in comparison with water. Acknowledgments The authors are grateful for the financial support of China Postdoctoral Science Foundation (grant no. 2012T50411), Major State
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Basic Research Development Program (grant no. 2011CB610404), Projects of International Cooperation and Exchanges NSFC (grant no. 50911130365) and Natural Science Foundation of China (grant no. 51001068). References [1] M. Yamaguchi, Y. Tanimoto, Magneto Science, Springer, Tokyo, 2006. [2] T. Omori, K. Watanabe, R.Y. Umetsu, R. Kainuma, K. Ishida, Applied Physics Letters 95 (2009) 082508-3. [3] L. Schubnikow, W.J.D. Haas, Nature 126 (1930) 500-500. [4] S.A. Ghauri, M.S. Ansari, Journal of Applied Physics 100 (2006) 066101–066102.
[5] T. Miyake, Y. Inatomi, K. Kuribayashi, Japanese Journal of Applied Physics 41 (2002) L811–L813. [6] Y. Fujimura, M. Iino, Journal of Applied Physics 103 (2008) 124903–124904. [7] M. Iino, Y. Fujimura, Applied Physics Letters 94 (2009) 261902–261903. [8] C. Li, L. Chen, Z. Ren, The Review of Scientific Instruments 83 (2012) 043906-5. [9] D.R. Lide, CRC Handbook of Chemistry and Physics, 90th ed. CRC/Taylor and Francis, Boca Raton, 2010. (CD-ROM version). [10] J.J. Jasper, Journal of Physical and Chemical Reference Data 1 (1972) 841–1009. [11] E. Bormashenko, American Journal of Physics 78 (2010) 1309–1311. [12] H. Hosoda, H. Mori, N. Sogoshi, A. Nagasawa, S. Nakabayashi, Journal of Physical Chemistry A 108 (2004) 1461–1464. [13] J.G. Kirkwood, F.P. Buff, Journal of Chemical Physics 17 (1949) 338–343. [14] K. Chang, C. Weng, Journal of Applied Physics 100 (2006) 043917-6.
Contents lists available at SciVerse ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Surface tensions of non-polar liquids in high magnetic fields Chuanjun Li ⁎, Long Chen, Zhongming Ren School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China Shanghai Key Laboratory of Modern Metallurgy and Materials Processing, Shanghai 200072, China
a r t i c l e
i n f o
Article history: Received 20 December 2012 Received in revised form 16 February 2013 Accepted 18 February 2013 Available online 7 March 2013 Keywords: Surface tension Nonpolar liquid Magnetic field Hydrogen bond
a b s t r a c t Thermophysical parameters of materials like the surface tension generally were modified in the high magnetic field. In the study, the surface tension of the non-polar liquid such as tetrachloromethane in high magnetic fields was examined using the ring method. It was found that the surface tension of the liquid linearly increased with the external magnetic field intensities and its change reached 1.65% in the magnetic field of 10 T. By comparing surface tensions of several liquids with different polarities in the magnetic field, the difference between variation trends for different liquids was probably because of the weaker effect of the magnetic field on dispersion forces than on hydrogen bonds by Lorentz force. © 2013 Elsevier B.V. All rights reserved.
1. Introduction In recent decades, materials processing in a high static magnetic field have attracted wide attention with development of magnet technologies [1]. Not only have many novel phenomena in the high magnetic field like levitation, orientation, phase transformation and thermoelectromagnetic convection been found successively, but also some technologies have even successfully been applied to the production sphere. Meanwhile, it was found that various thermophysical parameters of substances would change by the action of the high magnetic field such as transition point [2], electrical resistivity [3], viscosity [4] and diffusion coefficient [5]. Therefore, in order to effectively take advantage of the magnetic field in various fields, it is necessary for scientific researches or industrial production relating to the magnetic field to accurately re-determine the thermophysical parameters of materials in the high magnetic field. The surface tension as an important parameter would determine interfacial behaviors in many technological processes. In view of the facts, some attempt has been performed to measure surface tensions of liquids in the magnetic field. Fujimura et al. experimentally demonstrated that the external magnetic field increased the surface tension of water–air interface [6,7]. It was proposed that the magnetic field stabilized the hydrogen bonds in water and thus increased the surface tension. Nevertheless, suppose there is no hydrogen bond in certain liquids, how does the surface tension change with magnetic
⁎ Corresponding author at: Shanghai Key Laboratory of Modern Metallurgy and Materials Processing, Shanghai 200072, China. Tel.: +86 21 56331346. E-mail addresses: [email protected] (C. Li), [email protected] (L. Chen), [email protected] (Z. Ren). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.02.010
field? Therefore, the work aims to investigate the effect of the magnetic field on surface tensions of liquids without hydrogen bonds. 2. Experimental procedure 2.1. Materials The tetrachloromethane as a typical nonpolar molecule with a purity of ≥99.5% (CHCl3 ≤ 0.05%, H2O ≤ 0.02%, Cl ≤ 0.0001%, CS2 ≤ 0.0005%, others ≤ 0.001%, Sinopharm Chemical Reagent Co., Ltd) was used to examine the effect of the magnetic field on the surface tension of the liquid without hydrogen bonds. In general, the pure liquid should be chosen to investigate its real surface tension. Nevertheless, the pure liquid is not required for comparison as long as the same liquid was used throughout. Therefore, the tetrachloromethane liquid was not further purified in this work. 2.2. Measuring surface tension by the ring method In order to measure the surface tensions of liquids in the high magnetic field, we developed a tensiometer adaptable to a superconducting magnet on the base of the ring method [8]. The tensiometer could continuously record the pull of the ring when the ring immersing in liquid slowly rose or the liquid level fell until it detached from the liquid level, from which the maximum pull of the ring can be obtained. The surface tension γ of the liquid can thus be calculated according to the following relation: γ ¼ f ⋅F max =4πR
ð1Þ
52
C. Li et al. / Journal of Molecular Liquids 181 (2013) 51–54
where Fmax is the maximum equilibrium force of detachment, R is the radius of the ring, g is the gravity acceleration and f is the Harkins– Jordan factor. The Harkins–Jordan factor could be calibrated by a commercial tensiometer (K100MK2, KRUSS, Germany), of which measurement precision could reach 0.01 mN/m. In the absence of the magnetic field, the surface tension of the same liquid was measured using the two sets of equipment, respectively. Then the Harkins–Jordan factor could be determined by the following equation: f ¼ 4πR⋅γ0 =F max
ð2Þ
where γ0 is the surface tension of the liquid at a given temperature obtained by the commercial tensiometer. In consequence, the surface tension can be attained using the above two equations. Before the experiments, all components of the tensiometer which was in contact with the liquid were cleaned sequentially with acetone and a given liquid. In the experiments, the proper amount of the liquid was infused into the beaker until the ring was wholly immersed. When the liquid level and the ring were at rest, the pull measured by the precision balance began to be collected by a computer. Subsequently, the double-plunger micro-pump commenced to pump the liquid. The lowering rate of the liquid level was set to 7.5 × 10 −5 m/s. The liquid level was slowly lowered until the ring detached from the liquid film. The remaining liquid in the beaker was thoroughly pumped and then the new liquid was infused for next measurement. The experiment in the same conditions was repeatedly carried out for more than ten times. The temperature of the liquid during the measurements was monitored by the T-type thermocouple and its fluctuation was in the range of ±0.5 K. 3. Result and discussion Fig. 1 shows that the surface tension of tetrachloromethane varies with the external magnetic field and the fitting curve of experimental data indicates that the surface tension of the liquid linearly varies with the magnetic field. The surface tensions and their change in various magnetic fields are listed in Table 1. It is seen that the change in surface tension of tetrachloromethane reaches 0.48 mN/m and increases by 1.65% in the magnetic field of 10 T. Firstly let’s estimate several errors during the measurement of the surface tension before further searching for the nature of change in surface tension in the magnetic field. The liquid film would be subjected to the magnetic force due to the inhomogeneity of the magnetic field. During measurements the ring was always in the center of the magnet, namely, the region of the maximum intensity of the magnetic field. When the liquid level was lowered to the position below the center of the magnet, the
Fig. 1. Surface tension of tetrachloromethane is plotted against the magnetic field.
Table 1 Surface tensions of tetrachloromethane obtained using the ring method in different magnetic fields at 284 K. Magnetic field (T)
Surface tension (mN/m)
Change in surface tension (mN/m)
0 2 4 6 8 10
29.03 29.06 29.24 29.32 29.42 29.51
0 0.03 0.21 0.29 0.39 0.48
± ± ± ± ± ±
0.08 0.08 0.02 0.04 0.02 0.05
liquid film would be subjected to a downward magnetic force Fm. One may calculate the force using the following expression, F m ¼ ∫ðmχ m =μ 0 Þ⋅ðBdB=dzÞdv
ð3Þ
where m, χm,, μ0 and v are mass, mass susceptibility, vacuum permeability and volume, respectively. BdB/dz is the product of magnetic field and its gradient along the vertical direction. In the case of 10 T, BdB/dz = − 6770z (−10 −2m b z b 10 −2m) near the center of the magnet. The molar susceptibility of tetrachloromethane is χmol = − 66.6 × 10 −12 m 3/mol at room temperature [9]. The height of liquid film is about 3.5 × 10 −3 m and its mass was estimated to be (0.4678 ± 0.0014) × 10 −3 kg. Then the magnetic force of liquid film is evaluated to be Fm ≈ 1.9 × 10 −9 N, corresponding to the surface tension of 1.6 × 10 −5 mN/m based on Eq. (1). It follows that the measurement error induced by the magnetic force is four orders of magnitude less than the change in surface tension in the magnetic field of 10 T. Additionally, the temperature fluctuation also induced the measurement error. The temperature of the liquid fluctuated in 1 K in all measurements, which was monitored by a thermometer. Since the temperature coefficient of the surface tension of tetrachloromethane is − 0.12 mN/m at 284 K [10], the temperature fluctuation of 1 K led to the error of 0.12 mN/m. It is worthwhile noting that the surface tension of the tetrachloromethane liquid in this work is measured to be 29.03 ± 0.08 mN/m at 284 K. The surface tension of pure tetrachloromethane as a function of temperature is written as γ = 62.91 − 0.1224T (mN/m), where T is the absolute temperature [10]. One easily obtains γ = 28.15 mN/m for the pure liquid at 284 K. Thus, the real surface tension of the liquid used in this work is higher than the value of the pure liquid reported in the reference. Obviously, a small amount of other components led to the increase of the surface tension in this work. However, the existence of impurities in the liquid cannot influence the relative variation of surface tension in the magnetic field as long as the same liquid was used throughout. Oxygen molecules were believed to reduce the surface tension due to the difference between concentrations of oxygen in air and liquid. Nevertheless, the change in surface tension induced by oxygen molecules is far less than the increase of surface tension in 10 T [6]. Moreover, the experimental results showed that the standard error gradually decreased as the magnetic field increased. This demonstrated that the higher magnetic field made the measurement more stable and thus the error was further reduced with increasing the magnetic field. It was noted whether the magnetic field affects the interaction between the liquid and the ring and thus measurement of the surface tension. Without doubt, the magnetic field influences the interaction between solid and liquid phases. However, as we know, the ring method is based on completely wetting between liquid and solid with exceedingly high surface free energy and the pull force depends on size and shape of the ring, the wetting angle and the surface tension of the liquid. At the point of the maximum pull, the wetting angle equals to zero and the liquid film is hung by the surface tension. Therefore, the maximum pull is only related to the surface tension of
C. Li et al. / Journal of Molecular Liquids 181 (2013) 51–54
53
the liquid, not to the interaction between liquid and the ring, that is, the measurement of the surface tension is not affected by the interaction between the liquid and ring in the magnetic field. From the preceding analysis, obviously, the change in surface tension in the magnetic field of 10 T is beyond the above-mentioned errors. This demonstrates that the magnetic field increases the surface tension of the non-polar liquid. In the constant pressure and temperature, the surface tension is the Gibbs free energy per unit area. The magnetic energy contributes to the Gibbs free energy and thus to the surface tension. For tetrachloromethane, the molar magnetic energy Gm can be calculated by using the expression, 2
Gm ¼ −χ m ⋅B =2μ 0 :
ð4Þ
One may obtain Gm = 2.65 × 10 −3 J/mol at the magnetic field of 10 T. This value is far less than the interaction energy between molecules (0.1 × 10 3 ~ 10 × 10 3 J/mol). Therefore, the contribution of the magnetic energy to the surface tension is extremely small. The energy states of molecules in the bulk and at the surface of a liquid are different because of the difference in local environment of molecules [11]. Some evidences showed that the molecules at surface have different properties from ones in bulk liquid in the magnetic field. Hosoda et al. measured the refractive indices of water at interface and bulk water in the magnetic field using the surface plasmon resonance and the position-sensitive detector, respectively, and found that the refractive indices obtained by the former were larger than those by the latter [12]. This meant that the nature of water at surface was different from that in bulk water in the magnetic field. Therefore, it is reasonable to believe that the surface entropy of liquids increases due to the change in surface structures in the magnetic field and further leads to increase in the surface tension, which needs further study. On the other hand, the surface tension could be expressed as a function of density, radial distribution function and potential function using statistical mechanical approach [13]. The radial distribution function and potential function reflect the liquid structure and molecular interaction, respectively. Since the surface tension of tetrachloromethane increased in the magnetic field, the magnetic field probably changed the liquid structure and even molecular interaction. It is well-known that tetrachloromethane molecules are non-polar and only dispersion forces induced by instantaneous dipoles universally exist, the magnetic field exerts the effect on instantaneous dipoles by Lorentz force and necessarily changes the motion of non-polar molecules in a way. This enhanced the connectivity of tetrachloromethane molecules and further changed the liquid structure. In fact, a lot of studies showed that the external magnetic field modified the structure of water molecules and thus changed its pertinent properties such as refractive index [12], and hydrogen bond [14]. Chang and Weng applied molecular dynamic simulation to find that the magnetic field changed the radial distribution function of liquid water and hence slightly increased the number of hydrogen bonds [14]. This demonstrated that the magnetic field induced the tighter bonds between water molecules and improved the stabilization of water. Hosoda et al. speculated that the stabilization of hydrogen bonds increased in the magnetic field by increasing the electron delocalization of water molecules [12]. Although the structure of tetrachloromethane is completely different from water, they belong to diamagnetic substances. From the viewpoint of electromagnetism, the diamagnetism is induced by anti-parallel magnetization of molecules to the magnetic field and depends on electron distribution. Provided that the electron delocalization of molecules occurs in the magnetic field, the intermolecular energy consequentially changes. Especially, the electrons abutting gas phase at the surface have no steric hindrance caused by neighbor molecules in liquid phase and electron delocalization would be more significant. As a result, the intermolecular energy at surface would increase by the action of the
Fig. 2. Surface tensions of tetrachloromethane and acetone vary with the external magnetic field. (The surface tensions of acetone in magnetic fields are referred to Ref. [8]).
magnetic field. Without doubt, these factors would increase the surface tension of the non-polar liquid. Nevertheless, the linear variation of the surface tension of tetrachloromethane with the magnetic field markedly is different from square relation of change in surface tension of water in the magnetic field [6,7]. At present, the reason why the surface tension of the liquid linearly varied with the external magnetic field is not clear. The distinct difference between two liquids is that the former has hydrogen bonds. Provided that this is the resource of different trends, the effect of the magnetic field on hydrogen-bonding molecules is more obvious than others. It can be explained below. The water molecules are polar and partially charged while the tetrachloromethane molecules are not almost charged although instantaneous dipoles exist. Therefore, the effect of Lorentz force on motion of water molecules is stronger than that of tetrachloromethane molecules due to the different polarities. Polar molecules would be confined more tightly than nonpolar ones. We compared variation trends of surface tensions of acetone and tetrachloromethane in the magnetic field and found that both of them linearly increased with increasing the magnetic field as showed in Fig. 2. The surface tensions of two liquids as a function of the magnetic field were determined to be γte = 0.048B + 29.04 and γac = 0.062B + 24.08 (γte and γac represent surface tensions of tetrachloromethane and acetone in mN/m, respectively, B is the magnetic field in Tesla). This showed that the effect of magnetic field on surface tensions of two liquids without hydrogen bonds was weaker than that of water with hydrogen bonds. Moreover, the almost constant refractive indices of n-hexane in the magnetic field also corroborated the operation of hydrogen bonds in comparison with water [12]. This seems to further testify the above inference. However, the linear relation needs further investigation. 4. Conclusion In conclusion, we applied the ring method to measure the surface tension of the tetrachloromethane liquid in various magnetic fields. It was found that the surface tension of the liquid linearly increased with increasing the magnetic field, which was markedly different from that of water. It was inferred that the effect of the external magnetic field on hydrogen bonds was more obvious than on dispersion forces by Lorentz force and thus the surface tension of the liquid without hydrogen bonds showed the different variations in comparison with water. Acknowledgments The authors are grateful for the financial support of China Postdoctoral Science Foundation (grant no. 2012T50411), Major State
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