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Dielectric Properties of N,N-Dimethylformamide Aqueous Solutions in External Electromagnetic Fields by Molecular Dynamics Simulation LiJun Yang, KaMa Huang,* and XiaoQing Yang College of Electronics and Information Engineering, Sichuan UniVersity, Chengdu, 610064, P.R. China ReceiVed: October 13, 2009; ReVised Manuscript ReceiVed: NoVember 18, 2009
Nonequilibrium molecular dynamics (NMD) simulations of the N, N-dimethylformamide (DMF) aqueous solution have been performed in the canonical ensemble (NVT) in both the absence and presence of external electromagnetic (E/M) field, using the SPC/E model for water and the optimized potentials for liquid simulations-all atom (OPLS-AA) model for DMF. The electromagnetic wave propagates in the z-axis direction with a frequency of 10 GHz, and the intensity of the electromagnetic field in the range 0 to 3 × 109 V/m is assumed in the simulation. The results indicate that as the intensity of the electromagnetic field increased, the dipole alignment of the DMF aqueous solution molecules became more pronounced and the molecular polarizability gradually increased. In addition, the hydration number and the static dielectric constant of DMF aqueous solutions decreased as the intensity of the electromagnetic field increased. I. Introduction N,N-Dimethylformamide (DMF) is a polar solvent that is widely used in the production of acrylic fibers, plastics, and so on due to the unique physical and chemical properties.1-3 DMF and water are miscible in all properties of their solution exhibiting strong deviations from ideality.4 Although there are many experimental observations describing such behavior, the underlying molecular mechanisms remain unclear. Many studies have been performed to investigate the physical and chemical properties of their binary mixtures through two major methods: the experimental method and molecular dynamics simulation method. DMF solutions have been studied with a wide range of experimental techniques, including neutron diffraction,5 NMR,6 electric diffraction,7 and dielectric spectroscopy.8-11 The overall picture arising from those studies is the existence of interactions between the components in the bulk and surface. In the second category, molecular dynamics (MD) simulation techniques have provided some detailed information about the thermodynamics, structure, and dynamics of DMF aqueous solution.12,13 The microwave-enhanced chemical reaction is based on the efficiency of the interaction of molecules in reaction mixture with electromagnetic waves generated “microwave dielectric effect”. This process mainly depends on the specific polarity of molecules. Although microwave-enhanced chemical reactions have achieved great success in the laboratory stage, some difficulties arose in the application of high-power microwaves in chemistry, which limited the transfer of the laboratory experimental system to industrial applications. One of the major problems is “dielectric breakdown” (when high-power microwaves are applied, the rapid increment of reflection and absorption may destroy the microwave generator and may burn the organic reactants). Usually, the molecular polarizability (MP) and dielectric constant (DC) describe a material’s ability to absorb, transmit, and reflect electromagnetic energy. Thus, the most important fundamental work is to know the dielectric properties of the mixture at the external E/M field. However, * Corresponding author. E-mail:
[email protected]. Tel: (86) 2885408779. Fax: (86) 28-85408779.
the molecular polarizability and the static dielectric constant were not mentioned in those researches under the varied intensities of the external E/M field. Therefore, in this paper the nonequilibrium molecular dynamics (NMD) study of the effect of changing the concentration of DMF on the hydration number, molecular polarizability, and the static dielectric constant under external E/M field was carried out. II. Computational Method A. Incorporation of E/M Filed. In the simulations, the E/M field was taken to be uniform and plane-polarized in the z-axis direction; i.e., the electric component is taken to act in the x-axis direction and the magnetic component in the y-axis direction, the plane of polarization is then the x-y plane. The intensities of the electric field and magnetic field are formulated as follows: 14
b) E(t) ) Emax cos(wt)(1bi + 0bj + 0k
(1)
b) B(t) ) Bmax cos(wt)(0bi + 1bj + 0k
(2)
The two expressions satisfy Maxwell’s equations and are related by E(t)/B(t) ) c, where c is the speed of light. The effects of the applied E/M field on the trajectories of the atoms were modeled using the modified Verlet velocity algorithm,15 in which the half-time step velocity and position are found in the conventional manner and the full-time step velocity is dependent TABLE 1: Potential Parameters for SPC/E and DMF ε (kJ · mol-1)
σ (nm)
q (e)
Water O H H
0.650 0 0
0.3166 0 0
-0.8476 0.4238 0.4238
O N CF(CdO) CM(N-CH3) HF(CdO) HM(N-CH3)
DMF 0.8778 0.7106 0.4389 0.2759 0.0627 0.1254
0.296 0.3250 0.375 0.35 0.242 0.25
-0.5 -0.140 0.5 -0.11 0.00 0.06
10.1021/jp909802c 2010 American Chemical Society Published on Web 12/11/2009
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{
1 δt -δt V (t+δt/2) + f (t+δt) P i,x 2mi i,x 2 δt Q Vi,z(t+δt/2) + (f (t+δt) + qi(t+δt) E(t+δt)) 2mi i,z δt f (t+δt) Vi,y(t+δt) ) Vi,y(t+δt/2) + 2mi i,y 1 δt Vi,z(t+δt) ) Vi,z(t+δt/2) + [f (t+δt) + P 2mi i,z δt qi(t+δt) E(t+δt)] + 2 δt f (t+δt) (3) Q Vi,x(t+δt/2) + 2mi i,x
Vi,x(t+δt) )
[(
)]}
{
[(
)]}
where Figure 1. Probability distribution of the dipole moment of the DMF aqueous solutions under external electric filed.
upon the respective intensities of the electric and magnetic fields. The full-time step velocity is given by16
P ) 1 + (δtqi(t+δt) B(t+δt))2 Q ) qi(t+δt) B(t+δt)
(4)
B. Interaction Potentials and Simulation Details. In all the simulations, the water molecules were characterized by the SPC/E model and the OPLS-AA (optimized potentials for liquid simulations-all atom) model of DMF molecules. In these models,
Figure 2. Radial distribution functions of 1 M DMF aqueous solution with and without applied E/M field: (a) O-O; (b) O-H; (c) H-H; (d) C-C.
Dielectric Properties of N,N-Dimethylformamide
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TABLE 2: Positions of the First Peak of goo(r) in Water-DMF Mixture as a Function of External E/M Fields Roo (Å) E (V/m) 3 3 3 3 3 0
× × × × ×
109 108 107 106 105
1M
3M
2.73 2.71 2.71 2.71 2.71 2.71
2.75 2.73 2.73 2.73 2.71 2.71
TABLE 3: Positions of the First and Second Peaks of goh(r) in Water-DMF Mixture as a Function of External E/M Fields Roh (Å) first peak E (V/m) 3 3 3 3 3 0
× × × × ×
109 108 107 106 105
second peak
1M
3M
1M
3M
0.97 0.97 0.97 0.97 0.97 0.97
0.97 0.97 0.97 0.97 0.97 0.97
1.79 1.77 1.77 1.77 1.77 1.77
1.83 1.81 1.81 1.79 1.77 1.75
the intermolecular interaction is given by the sum of site-site potentials of the form
u(ri,rj) ) 4εij
[( ) ( ) ] σij rij
12
-
σij rij
6
+
qiqj rij
(5)
The Lennard-Jones parameters σij and εij are obtained by using the combination rules σij ) 1/2(σi + σj), εij ) (εiεj)1/2. Where qi is the partial charge on site i, σi and εi are the Lennard-Jones interaction parameters between sites i and j of distinct molecules, and r is the separation between these sites. The values of the potential parameters qi, σi, and εi for water and DMF are summarized in Table 1. The simulations involved a total of 4000 water molecules contained within an isotropic simulation box and considered two different DMF solution concentrations; i.e., 1 M and 3 M (molality), corresponding to 72 DMF molecules and 216 DMF molecules, respectively. The Nose´-Hoover thermostat was used to maintain the equilibrium temperature at 298 K and periodic boundary conditions were imposed in all three dimensions. The trajectories of the atoms during the equilibration process were calculated using the Verlet velocity algorithm. To make sure the pressure of 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, all of the fields were of frequency V ) 10 GHz, and the root-mean-square (rms) electric field intensities were ERMS ) 3 × 109, 3 × 108, 3 × 107, 3 × 106, and 3 × 105 V/m (Emax ) 21/2ERMS), respectively.
Figure 3. Radial distribution functions of 3 M DMF aqueous solution with and without applied E/M field: (a) O-O; (b) O-H; (c) H-H; (d) C-C.
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Figure 4. Variation of the peak height of RDF for pairs of hydrogen and oxygen atoms in DMF aqueous solutions as a function of external E/M field: (a) O-O; (b) the first peak of O-H; (C) the second peak of O-H.
Note that the frequency and intensity of the E/M field are deliberately assigned high values such that the effects of the field on the DMF aqueous solution can be readily determined within a short simulation time. During the MD simulation, a time step of 1 fs was used in all simulation; 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 were applied for 100 ps. The trajectories generated were stored every 50 fs. III. Results and Discussion Figure 1 illustrates the probability distribution of the dipole moment of DMF and water under the various intensities of external electric field. The probability distribution is very close to zero with no E/M field applied, indicating a random-like orientation of the DMF and the water molecular. However, when the E/M field is applied, the probability distribution is not zero. And when the electric field increases, all of the molecular dipole moment is almost in the direction of the electric field. This result implies that the dipole alignment of the DMF and water molecules becomes more pronounced as the strength of the E/M field increases.
To detect the structural changes of the DMF aqueous solutions under the E/M field, this paper analyzed the radial distribution functions (RDF) in the DMF aqueous solution. There are 13 site-site RDFs for those mixtures. Here a smaller subset of RDFs will be focused on. Figure 2 presents the RDFs of the O-O, O-H, H-H, and C-C in the DMF aqueous solution with a concentration of 1 M both with and without an E/M field. Those figures show that the height of the first peak in each set of profiles decreases as the intensity of the E/M field increases. The first minimum increased with increasing field strength can be found from Figure 2a-d. Nevertheless Tables 2 and 3 show that the positions of the first peaks are not affected by the external field. This result indicates that the first neighbor structure of DMF is reducing significantly with applying an external field. Figure 3 presents the RDFs of O-O, O-H, H-H, and C-C in the DMF aqueous solution with a concentration of 3 M both with and without an E/M field. In those figures, the intensity of the external E/M field was applied with the same as Figure 2. Although the results are broadly similar to those presented for the low-concentration case, slight differences can be identified between the two sets of results. The variations in the heights of
Dielectric Properties of N,N-Dimethylformamide
Figure 5. Variation of the hydration number in DMF aqueous solutions as a function of external E/M field.
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Figure 7. Static dielectric constant of DMF aqueous solutions as a function of external E/M field.
εs - 1 ) 4π
p ε0E
(6)
where ε0 is the vacuum dielectric constant, p is the molecular polarizability, and E is the intensity of the external field. Using this formula, the static dielectric constant of DMF aqueous solution at 298 K and under various electric fields is obtained (Figure 7). As shown in the figure, the static dielectric constant decreases when the strength of the E/M field increases for both 1 and 3 M solutions. IV. Conclusions
Figure 6. Molecular polarizability of DMF aqueous solutions as a function of external E/M field.
the first peak for goo(r) and goh(r) in DMF aqueous solutions as a function of the external E/M field are shown in Figure 4. From Figure 4, a more obvious reduction in the height of the first and the second peak of the DMF solution is observed than at the lower concentration. It was also found that the positions of the first peak of goo(r) and second peaks of goh(r) shifted to distances bigger than 0.04 Å (seen Tables 2 and 3). From Figure 4, the application of the E/M field to the DMF aqueous solution making the first atomic coordination shells are apt to be less structured, leading to the height of the peak decrease, suggesting that the dimer DMF · H2O is rapidly destroyed. The dipole energy E0P0 ≈ 4.8 eV is more than the hydrogen-bond energy of 2.5 eV per bond when the intensity of the external E/M field is up to 3 × 109 V/m, leading to the height of the peak and the hydration number decreases abruptly (Figure 5). This reveals the randomization of the position and orientation of water molecules, and thus weakening of the water network. Figure 6 illustrates the variation of the molecular polarizability of DMF aqueous solutions with concentrations of 1 and 3 M, as a function of external E/M field. As can be seen from this figure, the molecular polarizability gradually increases with the electric field strength, which shows that the direction of molecular dipole moment is gradually with the same direction of the external field. The relationship between the static dielectric constant and the applied electric field is given by
In this paper, nonequilibrium molecular dynamics simulations of the DMF aqueous were performed at 298 K under different strengths of external E/M field, ranging from 0 to 3 × 109 V/m, to investigate the influence of an external field on structural and dielectric properties of DMF solution. The results show that the dipole alignment of DMF solution improved and the molecular polarizability gradually increased as the E/M field increased. Moreover, the height of the first peak in each set of profiles decreased with the intensity of the E/M field increase. Furthermore, the positions of the first peaks of goo (r) and second peaks of goh(r) shifted, when the external fields were applied. In the DMF solution with concentrations of 1 and 3 M, the hydration number and static dielectric constant of the solution decreased as the intensity of the external E/M field increase. Although the typical microwave field strength used in industrial and experimental settings is several orders of magnitude lower than those used in this study, the intense field employed here is to investigate the effects of the field on the DMF aqueous solution, which can be readily determined within a short simulation time with current computer technology. However, unfortunately, at the present time, there are no experimental measurement data on the molecular level under external electromagnetic field. Acknowledgment. This project was supported by National Science Foundation of China under Grant no. 60531010 and Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070610120. We also thank Dr. Prof. Hui Shang (China University of Petroleum) for providing the language revised. References and Notes (1) Gao, J.; Pavelites, J. J.; Habibollazadeh, D. J. Phys. Chem. 1996, 100, 2689.
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(2) Desfranc¸ois, C.; Pe´riquet, V.; Carles, S.; Schermann, J. P.; Adamowicz, L. Chem. Phys. 1998, 239, 475. (3) Vargas, R.; Garza, J.; Dixon, D. A.; Hay, B. P. J. Am. Chem. Soc. 2000, 122, 4750. (4) Jia, G. Z.; Huang, K. M.; Yang, X. Q.; Song, J. P.; Yang, L. J. Acta Phys. Chim. Sin. 2009, 25, 1906. (5) Yamagami, M.; Wakita, H.; Yamaguchi, T. J. Chem. Phys. 1995, 103, 8174. (6) Wallach, D.; Wesley, T.; Huntress, J. J. Chem. Phys. 1969, 50, 1219. (7) Schultzl, G.; Hargittai, I. J. Phys. Chem. 1993, 97, 4966. (8) Sharma, A. K.; Sharrna, D. R.; Sharrna, K. C.; Gill, D. S. Z. Phys. Chem. F. 1984, 141, 15. (9) Sharma, A. K.; Sharrna, D. R. Ind. J. Pure Appl. Phys. 1985, 23, 418.
Yang et al. (10) Bass, S. J.; Nathan, W. I.; Meighan, R. M.; Cole, R. H. J. Phys. Chem. 1964, 68, 509. (11) Barthel, J.; Bachhuber, K.; Buchner, R.; Gill, J. B.; Kleebaur, M. Chem. Phys. Let. 1990, 67, 62. (12) Lei, Y.; Li, H. R.; Pan, H. H.; Han, S. J. J. Phys. Chem. A 2003, 107, 1575. (13) Jia, G. Z.; Huang, K. M.; Yang, L. J.; Yang, X. Q. Int. J. Mol. Sci. 2009, 10, 1590. (14) English, N. J.; MacElroy, J. M. D. J. Chem. Phys. 2003, 118, 1589. (15) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon: Oxford, U.K., 1987). (16) Chang, K. T.; Weng, C. I. Mol. Phys. 2008, 106, 2515.
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