J. Phys. Chem. B 2010, 114, 8449–8452
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Electric Conductivity in Electrolyte Solution under External Electromagnetic Field by Nonequilibrium Molecular Dynamics Simulation LiJun Yang and KaMa Huang* College of Electronics and Information Engineering, Sichuan UniVersity, Chengdu, 610064, People’s Republic of China ReceiVed: March 23, 2010
Nonequilibrium molecular dynamics (NMD) simulations are performed to investigate the effects of an external electromagnetic (E/M) field on NaCl electrolyte solutions at different temperatures using the SPC/E model. The electromagnetic wave propagates in the z-axis direction with a frequency of 2.45 GHz, and the intensity of the E/M field is 3 × 104 V/m. The results indicate that as the concentration of the electrolyte solution increased, the diffusion coefficient and the ionic mobility gradually decreased, but the electric conductivity gradually increased. In addition, all three of them will be increased when the temperature is increased. But their value will be reduced when the electromagnetic field is applied. 1. Introduction Electrolyte solutions have been studied experimentally1-3 and theoretically4-8 for many years, and they play an important role in solution chemistry and some aspects of cell and membrane biology.9 These studies have provided important information about the subject, and now there is increasing interest in the electric conductivity (EC)10,11 apart from the expected dielectric constant, viscosity, size, and charge of the ions. Although some studies have reported the DC conductivity under the external electric field,12,13 for the external E/M field, to our knowledge, there have been only a very few studies4,14 that analyzed the properties of electrolyte solutions. The distribution of the E/M field in the waveguide will be destroyed because the electrode can couple part of the E/M energy, when it inserts into the waveguide, leading to the measure of the EC being inaccurate. In recent years, molecular dynamics (MD) simulations have become an important tool in understanding the dynamics of electrolyte solutions at the molecular level.15,16 However, the MD technique is very costly for electrolyte solutions because the multiplicity of components needs a very long run to acquire the correct ionic properties. Recently, dielectric relaxation, radial distribution functions, and hydrogen bond statistics17,18 have also been investigated for electrolyte solutions. But more detailed dynamical aspects such as EC dependence on external E/M field in electrolyte solutions have not been investigated before. This issue is of fundamental interest because of the significant role that electrolyte solutions play as reaction media in diverse chemical and biological processes. Therefore, in this paper the nonequilibrium molecular dynamics (NMD) study of the effect of changing the concentration and temperature of electrolyte solution on EC, diffusion coefficient, and the ionic mobility in both the absence and the presence of external E/M field was carried out. 2. Experimental and Simulation Details 2.1. Experimental Details. The precisely designed experiments included some special techniques: (1) A specially * To whom correspondence should be addressed. E-mail: ljyang320@ 163.com (L.J.Y.) and
[email protected] (K.M.H.).
Figure 1. The structure of the ridged waveguide.
designed ridged waveguide with a hole in the side wall was used to produce a uniform distribution electric field in the solution, and the solution was pumped to flow through the ridge gap in a quartz glass pipeline with a diameter of 5 mm (Figure 1). (2) The temperature of the solution being tested was precisely controlled with use of a KXS-A trough ((0.5 °C) and pump (5 m/s). The temperature at the output port of the pipeline was precisely measured with a UMI-8 optical fiber thermometer with a 1 mm diameter optical fiber. (3) A Wheatstone bridge circuit was used to accurately measure the voltage variation resultes from the slight EC changes of the solution. To prepare suitable solutions, 11.69 and 58.44 g of sodium chloride were added to 2 L of deionized water, respectively. The power of the generator was 400 W and the frequency was 2.45 GHz. A continuous microwave source was used in our experiments. The output power could be sampled and recorded with a Tektronix DPO7254 oscillograph through a directional coupler. A pair of Pt electrodes connected to the Wheatstone bridge circuit was inserted into the glass pipeline to measure EC variations. Then EC variations could be obtained and recorded with a Tektronix DPO7254 oscillograph from the Wheatstone bridge circuit (Figure 2). 2.2. Simulation Details. In all the simulations, the water molecules were characterized by the SPC/E model. All ions were represented by a point charge having a Lennard-Jones (LJ)
10.1021/jp102593m 2010 American Chemical Society Published on Web 06/10/2010
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Figure 2. Diagram of the experimental system.
center on it. The potential parameters for ion-water and water-water interactions in this model were collected from the work of Lee.19 The simulations involved a total of 4000 water molecules contained within an isotropic simulation box and two different NaCl solution concentrations were considered: i.e., 0.1 and 0.5 M (molality), corresponding to 7 Na+, 7 Cl- and 35 Na+, 35 Cl-, respectively. The Nose´-Hoover thermostat was used to maintain the equilibrium temperature at 283, 289, and 295 K and periodic boundary conditions were imposed in all three dimensions. The trajectories of the atoms during the equilibration process were calculated by using the Verlet velocity algorithm. To make sure the pressure of the two systems is the same at 1 bar, the NPT ensemble was carried out in the pre-equilibrium process. The E/M field was applied in the NVT ensemble to isolate the field effects from the thermal effects, and hence the simulations were effectively nonequilibrium NVT (NNVT) simulations. External E/M fields were applied to those models,20 all of the fields were of frequency V ) 2.45 GHz, and the root-mean-square (rms) electric field intensities were Erms ) 3.0× 104 V/m,14 respectively. During the MD simulation, a time step of 1 fs was used in all simulations; a period of 50 ps was allowed for equilibration (NPT ensemble). Following the equilibration process, an E/M field of the specified frequency and intensity was applied for 100 ps. The generated trajectories were stored every 50 fs. 3. Results and Discussion 3.1. Diffusion Coefficient. The diffusion coefficient is a factor of proportionality representing the amount of substance diffusing across a unit area through a unit concentration gradient in unit time. In this paper, we use the Einstein relation:21
D)
d 1 lim 〈|r(t) - r(0)| 2〉 6 tf∞ dt
TABLE 1: Diffusion Coefficient D (×10-9 m2/s) for Na+ and Cl- Ions at Different Temperature with or without the External E/M Fielda 0.1 M
0.5 M
+
Cl
Na temp, K 283 289 295 a
E1
E2
E1
where r(t) is the position of the geometric center of a molecule at time t, to determine the diffusion coefficient D of the ions from the mean-squared displacement (MSD) with or without the external E/M field. The diffusion coefficient (D) calculated from the MSD of the ions is listed in Table 1. It is found that the diffusion coefficient increases with the temperature increase but decreases with the electrolyte solution under the external E/M
Na E2
E1
+
ClE2
E1
E2
0.6767 1.015 1.179 1.056 0.870 0.746 1.284 0.999 1.074 1.156 1.482 1.320 0.961 0.984 1.231 1.267 0.8312 1.339 1.611 2.037 1.024 1.122 1.300 1.603
E1 ) 3 × 104 V/m, E2 ) 0.
field due to the presence of ion atmosphere friction. It is also found that the friction of ion pairs increases with increasing ion concentration, and this will lead to a decrease in the value of D. 3.2. Absolute Mobility. The migration velocity,ui, of an ion, i, is directly proportional to the applied electric field strength, E (eq 2); the factor of proportionality, µi (eq 3), is named the mobility:
ui ) µiE
(2)
µi ) ui /E
(3)
The mobility has the dimension m2/(V · s). It is a single ion property, which depends on external variables like the temperature and the solvent, and on ion-specific properties like the particle size and shape, and its charge; it is dependent on the ionic strength of the solution as well. The mobility can be obtained by the Nernst-Einstein relation:22
µ)
(1)
-
∑ i
|zi |DiF RT
(4)
The ionic mobilities (µi) determined from eq 4 are listed in Table 2. Table 2 shows that the ionic mobilities decrease with increasing ion concentration and the external E/M field present. In addition, the ionic mobilities increase as the temperature increases, because the high temperature leads to the ions moving faster. 3.3. Electric Conductivity. The most popular model for describing the transport of anions under the influence of concentration and electric potential gradients is derived by using
Electric Conductivity in Electrolyte Solution
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TABLE 2: Ion Mobilities µ (×10-8 m2/(V · s)) for Na+ and Cl- Ions at Different Temperatures with or without the External E/M Fielda 0.1 M Na+ temp, K 283 289 295 a
E1
i ) |Z+ |FJ+ - |Z- |FJ-
(9)
0.5 M Cl-
E2
Let us write the relation that gives the current density:
E1
Na+ E2
E1
ClE2
E1
E2
Under the conditions of electroneutrality and no current I ) 0, by rearranging terms we obtain:
2.775 4.162 4.835 4.330 3.567 3.057 5.265 4.094 4.313 4.642 5.951 5.300 3.858 3.951 4.943 5.083 3.270 5.267 6.337 8.013 4.028 4.414 5.114 6.306
∇C |Z|FC )∇φ RT
(10)
E1 ) 3 × 104 V/m, E2 ) 0.
the following chain of arguments. First, in the absence of electric potential gradients, the mass flux of ions is given by Fick’s law as:
J ) -D(∇C)
(
|Z|F + C∇φ RT Migration (uC)Convection
)
(6)
where Z is the valence, F is Faraday’s constant, R is the ideal gas constant, T is the absolute temperature, and φ is the electric potential. The equations for the mass flux of the sample are associated with the names of Nernst-Planck and take the following form for the sample (Figure 2):
J+ )
D+ |Z+ |FC+ (∇φ) - D+(∇C+) - u+C+ RT
J- ) -
σ)
F2(|Z+ | 2C+D+ + |Z- | 2C-D-) i ) ∇φ RT
(11)
(5)
where C is the concentration. Now, assuming that the sample is placed in an electric circuit, Fick’s law should be modified to account for the effect of the resulting electric field. This is done via the Nernst-Planck law so that the flux is given by:23
J ) (-D∇C)Diffusion + -D
The electric conductivity σ can be obtained by combining eqs 7, 8, 9, and 10.
D- |Z- |FC(∇φ) + D-(∇C-) + u-CRT
where X+ (X ) D, Z, C) is the cation and X- is the anion.
(7)
(8)
for two given monovalent ions (Cl- and Na+ with |Z| ) 1), and C+ ) C-. Then the electric conductivity σ can be rewritten:
σ)
F2 |Z| 2C(D+ + D-) RT
(12)
Figure 3 shows the experimental results and our simulations for the ions using the SPC/E model with or without external E/M field. Those figures show that the EC values of the high concentration electrolyte solution are overestimated by about 12% in our simulations, while those of the low concentration electrolyte solution are in better agreement with experiments. Figure 4 illustrates the effects of the E/M field on the EC in the electrolyte solution with different concentrations, when the E/M field has a high intensity of Erms ) 3 × 104 V/m. Although the results are broadly similar to those presented for the case without E/M, slight differences can be identified between the two sets of results. For example, with the external E/M field, a more obvious reduction in the value of the EC is observed in the electrolyte solution with a higher concentration. This is partly due to the interaction between the ions and the solvent molecules. According to the Debye-Hu¨ckel theory, the ion-ion interaction can be described as a formation of an oppositely charged ionic atmosphere surrounding the central ions (Figure 5). This ionic atmosphere lowers the electric potential of the ions and thus retards the drift velocity. Under the action of an external E/M field, the ionic interaction will result in two different effects:
Figure 3. The calculation and the experiment value of EC: (a) with the external E/M field; (b) without the external E/M field.
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Yang and Huang 4. Conclusions In this paper, nonequilibrium molecular dynamics simulations of the electrolyte solution were performed at different temperatures (283, 289, and 295 K) in both the absence and the presence of external E/M field, to investigate the influence of an external E/M field on the diffusion coefficient, ionic mobilities, and EC of an electrolyte solution. The results have shown that the diffusion coefficient and ionic mobilities decrease, but the EC of the electrolyte solution increases, when the concentration of the electrolyte solution increases. And in the electrolyte solution with concentrations of both 0.1 and 0.5 M, the EC, diffusion coefficient, and ionic mobilities of the solutions increase as the temperature increases. When the external E/M field is applied, all three decrease due to the relaxation effect and the electrophoretic effect.
Figure 4. The calculation value of EC with the external E/M field vs without the E/M field.
Figure 5. The electrophoretic effect: FE ) the electric driving force; Fd ) the electrophoretic drag force caused by an ionic atmosphere.
(1) The relaxation effect is the distortion of the ionic clouds when the central ions move toward the electrode. This distortion produces a relaxation field, which produces a relaxation force acting on the central ions. (2) The electrophoretic effect arises because the motion of a central ion does not occur in an immobile medium but in a medium moving in the opposite direction to this ion. The ions will rub past each other, when the external E/M field is present, thus enhancing the viscous drag and lowering the kinetic energy. From Figure 5 it can be seen that the electrophoretic effect depends on several parameters. The two forces (FE and Fd) both relate to the concentration of the electrolyte and to the intensity of the external E/M field. Further, the electrophoretic effect is temperature dependent. The two different effects will both induce a decrease in the EC.
Acknowledgment. This project was supported by the National Science Foundation of China under Grant No. 60871064. References and Notes (1) Amang, D. N.; Alexandrova, S.; Schaetzel, P. Electrochim. Acta 2003, 48, 2563. (2) Akira, I.; Tetsuya, H.; Naokazu, K. Jpn. J. Appl. Phys. 1981, 20, 79. (3) Aupiais, J.; Delorme, A.; Baglan, N. J. Chromatogr., A 2003, 994, 199. (4) Huang, K. M.; Jia, Z. G.; Yang, X. Q. Acta. Phys.-Chim. Sin. 2008, 24, 20. (5) Kato, M. J. Theor. Biol. 1995, 177, 299. (6) Krabbenhøft, K.; Krabbenhøft, J. Cem. Concr. Res. 2008, 38, 77. (7) Pabsta, M.; Wrobel, G.; Ingebrandt, S.; Sommerhage, F.; Offenhausser, A. Eur. Phys. J. E.: Soft Matter Biol. Phys. 2007, 24, 1. (8) Jouyban, A.; Kenndler, E. Electrophoresis 2006, 27, 992. (9) Rioux, B.; Karplus, M. Annu. ReV. Biophys. Biomol. Struct. 1994, 23, 731. (10) Hu, Y. F.; Zhang, X. M.; Li, J. G.; Liang, Q. Q. J. Phys. Chem. B 2008, 112, 15376. (11) Roger, G. M.; Serge, D. V.; Bernard, O.; Turq, P. J. Phys. Chem. B 2009, 113, 8670. (12) Park, J. K.; Ryu, J. C.; Kim, W. K.; Kang, K. H. J. Phys. Chem. B 2009, 113, 12271. (13) Chowdhuri, S.; Chandra, A. J. Chem. Phys. 2001, 115, 3732. (14) Huang, K. M.; Yang, X. Q.; Hua, W.; Jia, G. Z.; Yang, L. J. New J. Chem. 2009, 33, 1486. (15) Jung, D. H.; Yang, J. H.; Jhon, M. S. Chem. Phys. 1999, 244, 331. (16) Purdue, M. J.; MacElroy, J. M. D.; O’Shea, D. F. J. Chem. Phys. 2006, 125, 114902. (17) Kiseleva, M.; Heinzinger, K. J. Chem. Phys. 1996, 105, 650. (18) Chang, K. T.; Weng, C. I. Mol. Phys. 2008, 106, 2515. (19) Lee, S. H. J. Phys. Chem. 1996, 100, 1420. (20) Yang, L. J.; Huang, K. M.; Yang, X. Q. J. Phys. Chem. A 2010, 114, 1185. (21) Chen, H. N.; Gregory, A. V. J. Phys. Chem. B 2010, 114, 333. (22) Guidi, V.; Martinelli, G.; Schiffrer, G. Phys. ReV. B 2005, 72, 155401. (23) Lawrence, D. J. Phys. Chem. 1972, 76, 2257.
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