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Dimensionality Effects in Dipolar Fluids: A Density Functional Theory Study

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DOI: 10.4236/jmp.2013.43A056    3,663 Downloads   5,948 Views   Citations

ABSTRACT

Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments and interact via a combination of hard-sphere, van-der-Waals, and dipolar interactions. The DFT predicts complex phase behavior involving first- and second-order isotropic-to-ferroelectric transitions, where the ferroelectric ordering is characterized by global polarization within the plane. We compare this phase behavior, particularly the onset of ferroelectric ordering and the related tri-critical points, with corresponding three-dimensional systems, slab-like systems (with finite extension into the third direction), and true two-dimensional systems with two-dimensional dipole moments.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

R. Geiger and S. Klapp, "Dimensionality Effects in Dipolar Fluids: A Density Functional Theory Study," Journal of Modern Physics, Vol. 4 No. 3A, 2013, pp. 401-408. doi: 10.4236/jmp.2013.43A056.

References

[1] K. Butter, P. H. Bomans, P. M. Frederik, G. J. Vroege and A. P. Philipse, “Direct Observation of Dipolar Chains in Ferrofluids in Zero Field Using Cryogenic Electron Microscopy,” Journal of Physics: Condensed Matter, Vol. 15, No. 15, 2003, Article ID: S1451. doi:10.1088/0953-8984/15/15/310
[2] M. Klokkenburg, R. P. A. Dullens, W. K. Kegel, B. H. Erne and A. P. Philipse, “Quantitative Real-Space Analysis of Self-Assembled Structures of Magnetic Dipolar Colloids,” Physical Review Letters, Vol. 96, No. 3, 2006, Article ID: 037203. doi:10.1103/PhysRevLett.96.037203
[3] N. Osterman, D. Babic, I. Poberaj, J. Dobnikar and P. Ziherl, “Observation of Condensed Phases of Quasiplanar Core-Softened Colloids,” Physical Review Letters, Vol. 99, No. 24, 2007, Article ID: 248301. doi:10.1103/PhysRevLett.99.248301
[4] J. Richardi, M. P. Pileni and J. J. Weis, “Self-Organization of Magnetic Nanoparticles: A Monte Carlo Study,” Physical Review E, Vol. 77, No. 6, 2008, Article ID: 061510. doi:10.1103/PhysRevE.77.061510
[5] S. O. Lumsdon, E. W. Kaler and O. D. Velev, “Two-Dimensional Crystallization of Microspheres by a Coplanar AC Electric Field,” Langmuir, Vol. 20, No. 6, 2004, pp. 2108-2116. doi:10.1021/la035812y
[6] J. J. Jurez and M. A. Bevana, “Interactions and Microstructures in Electric Field Mediated Colloidal Assembly,” Journal of Chemical Physics, Vol. 131, No. 13, 2009, Article ID: 134704. doi:10.1063/1.3241081
[7] S. C. Glotzer and M. J. Solomon, “Anisotropy of Building Blocks and Their Assembly into Complex Structures,” Nature Materials, Vol. 6, 2007, pp. 557-562. doi:10.1038/nmat1949
[8] K. H. Bhatt and O. D. Velev, “Control and Modeling of the Dielectrophoretic Assembly of On-Chip Nanoparticle Wires,” Langmuir, Vol. 20, No. 2, 2004, Article ID: 467476. doi:10.1021/la0349976
[9] J. J. Weis, “Preliminary Communication Orientational Structure of Quasi-Two-Dimensional Dipolar Hard Spheres,” Molecular Physics: An International Journal at the Interface between Chemistry and Physics, Vol. 93, No. 3, 1998, pp. 361-364. doi:10.1080/002689798169023
[10] J. M. Tavares, J. J. Weis and M. M. Telo da Gama, “Quasi-Two-Dimensional Dipolar Fluid at Low Densities: Monte Carlo Simulations and Theory,” Physical Review E, Vol. 65, No. 6, 2002, Article ID: 061201. doi:10.1103/PhysRevE.65.061201
[11] J. M. Tavares, J. J. Weis and M. M. Telo da Gama, “Phase transition in Two-Dimensional Dipolar Fluids at Low Densities,” Physical Review E, Vol. 73, No. 4, 2006, Article ID: 041507. doi:10.1103/PhysRevE.73.041507
[12] P. D. Duncan and P. J. Camp, “Aggregation Kinetics and the Nature of Phase Separation in Two-Dimensional Dipolar Fluids,” Physical Review Letters, Vol. 121, No. 10, 2006, Article ID: 107202. doi:10.1103/PhysRevLett.97.107202
[13] G. T. Gao, X. C. Zeng and W. Wang, “Vapor-Liquid Coexistence of Quasi-Two-Dimensional Stockmayer Fluids,” Journal of Chemical Physics, Vol. 106, No. 8, 1997, Article ID: 3311. doi:10.1063/1.473079
[14] H. Schmidle and S. H. L. Klapp, Journal of Chemical Physics.
[15] E. Lomba, F. Lado and J. J. Weis, “Structure and Thermodynamics of a Ferrofluid Monolayer,” Physical Review E, Vol. 61, No. 4, 2000, pp. 3838-3849. doi:10.1103/PhysRevE.61.3838
[16] L. Luo and S. H. L. Klapp, “Fluctuations in a ferrofluid Monolayer: An Integral Equation Study,” Journal of Chemical Physics, Vol. 131, No. 3, 2009, Article ID: 034709. doi:10.1063/1.3176210
[17] W.-Z. Ouyang, S.-H. Xu and Z.-W. Sun, “Gas-Liquid Phase Coexistence in Quasi-Two-Dimensional Stockmayer Fluids: A Molecular Dynamics Study,” Journal of Chemical Physics, Vol. 134, No. 1, 2011, Article ID: 014901. doi:10.1063/1.3521393
[18] J.-J. Weis, “Orientational Structure in a Monolayer of Dipolar Hard Spheres,” Molecular Physics: An International Journal at the Interface between Chemistry and Physics, Vol. 100, No. 5, 2002, pp. 579-594. doi:10.1080/00268970110097136
[19] V. Russier, “Calculated Magnetic Properties of Two-Dimensional Arrays of Nanoparticles at vanishing Temperature,” Journal of Applied Physics, Vol. 89, No. 2, 2001, Article ID: 1287. doi:10.1063/1.1333034
[20] P. Politi, M. G. Pini and R. L. Stamps, “Dipolar Ground State of Planar Spins on Triangular Lattices,” Physical Review B, Vol. 73, No. 2, 2006, Article ID: 020405. doi:10.1103/PhysRevB.73.020405
[21] D. Wei and G. N. Patey, “Orientational Order in Simple Dipolar Liquids: Computer Simulation of a Ferroelectric Nematic Phase,” Physical Review Letters, Vol. 68, No. 13, 1992, pp. 2043-2045. doi:10.1103/PhysRevLett.68.2043
[22] D. Levesque, J.-J. Weis and G. J. Zarragoicoechea, “Orientational Order in Simple Dipolar Liquid-Crystal Models,” Physical Review Letters, Vol. 69, No. 6, 1992, pp. 913-916. doi:10.1103/PhysRevLett.69.913
[23] J. J. Weis and D. Levesque, “Orientational Order in High Density Dipolar Hard Sphere Fluids,” Journal of Chemical Physics, Vol. 125, No. 3, 2006, Article ID: 034504. doi:10.1063/1.2215614
[24] S. H. L. Klapp and M. Schoen, “Spontaneous Orientational Order in Confined Dipolar Fluid Films,” Journal of Chemical Physics, Vol. 117, No. 17, 2002, Article ID: 8050. doi:10.1063/1.1512282
[25] R. A. Trasca and S. H. L. Klapp, “Structure Formation in Layered Ferrofluid Nanofilms,” Journal of Chemical Physics, Vol. 129, No. 8, 2008, Article ID: 084702. doi:10.1063/1.2971182
[26] P. I. Teixeira and M. M. Telo da Gama, “Density-Functional Theory for the Interfacial Properties of a Dipolar Fluid,” Journal of Physics: Condensed Matter, Vol. 3, No. 1, 1991, p. 111. doi:10.1088/0953-8984/3/1/009
[27] P. Frodl and S. Dietrich, “Bulk and Interfacial Properties of Polar and Molecular Fluids,” Physical Review A, Vol. 45, No. 10, 1992, pp. 7330-7354. doi:10.1103/PhysRevA.45.7330
[28] J. M. Tavares, M. M. Telo da Gama, P. I. C. Teixeira, J.-J. Weis and M. J. P. Nijmeijer, “Phase Diagram and Critical Behavior of the Ferromagnetic Heisenberg Fluid from Density-Functional Theory,” Physical Review E, Vol. 52, No. 2, 1995, pp. 1915-1929. doi:10.1103/PhysRevE.52.1915
[29] G. M. Range and S. H. L. Klapp, “Density Functional Study of the Phase Behavior of Asymmetric Binary Dipolar Mixtures,” Physical Review E, Vol. 69, No, 4, 2004, Article ID: 041201. doi:10.1103/PhysRevE.69.041201
[30] B. Groh and S. Dietrich, “Long-Ranged Orientational Order in Dipolar Fluids,” Physical Review Letters, Vol. 72, No. 15, 1994, pp. 2422-2425. doi:10.1103/PhysRevLett.72.2422
[31] B. Groh and S. Dietrich, “Ferroelectric Phase in Stockmayer Fluids,” Physical Review E, Vol. 50, No. 5, 1994, pp. 3814-3833. doi:10.1103/PhysRevE.50.3814
[32] B. Groh and S. Dietrich, “Structural and Thermal Properties of Orientationally Ordered Dipolar Fluids,” Physical Review E, Vol. 53, No. 3, 1996, pp. 2509-2530. doi:10.1103/PhysRevE.53.2509
[33] B. Groh and S. Dietrich, “Spatial Structures of Dipolar Ferromagnetic Liquids,” Physical Review Letters, Vol. 79, No. 4, 1997, pp. 749-752. doi:10.1103/PhysRevLett.79.749
[34] M. Gramzow and S. H. L. Klapp, “Capillary Condensation and Orientational Ordering of Confined Polar Fluids,” Physical Review E, Vol. 75, No. 1, 2007, Article ID: 011605. doi:10.1103/PhysRevE.75.011605
[35] I. Szalai and S. Dietrich, “Phase Transitions and Ordering of Confined Dipolar Fluids,” The European Physical Journal E, Vol. 28, No. 3, 2009, pp. 347-359. doi:10.1140/epje/i2008-10424-2
[36] J. A. Barker and D. Henderson, “Perturbation Theory and Equation of State for Fluids. II. A Successful Theory of Liquids,” Journal of Chemical Physics, Vol. 47, No. 11, 1967, Article ID: 4714. doi:10.1063/1.1701689
[37] J. P. Hansen and I. R. McDonald, “Theory of Simple Liquids,” 3rd Edition, Academic Press, Amsterdam, 2006.
[38] R. Geiger, “Long-Range Order in Quasi-Two-Dimensional Dipolar Fluids: A Density Functional Study,” Master Thesis, Technische Universit?t, Berlin, 2008. https://sites.google.com/site/researchgeiger/
[39] P. Nielaba and S. Sengupta, “Perturbative Density Functio-Nal Theory for Phase Transitions in a Two-Dimensional Antiferromagnetic Fluid,” Physical Review E, Vol. 55, No. 3, 1997, pp. 3754-3757. doi:10.1103/PhysRevE.55.3754
[40] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. F. Flannery, “Numerical Recipes 3rd Edition: The Art of Scientific Computing,” Cambridge University Press, Cambridge, 2007.
[41] M. E. van Leeuwen, “Derivation of Stockmayer Potential Parameters for Polar Fluids,” Fluid Phase Equilibria, Vol. 99, 1994, pp. 1-18. doi:10.1016/0378-3812(94)80018-9
[42] A. Schreiber, H. Bock, M. Schoen and G. Findenegg, “Effect of Surface Modification on the Pore Condensation of Fluids: Experimental Results and Density Functional Theory,” Molecular Physics, Vol. 100, No. 13, 2002, pp. 2097-2107. doi:10.1080/00268970210132559
[43] E. Lomba, J. J. Weis, N. G. Almarza, F. Bresme and G. Stell, “Phase Transitions in a Continuum Model of the Classical Heisenberg Magnet: The Ferromagnetic System,” Physical Review E, Vol. 49, No. 6, 1994, pp. 5169-5178. doi:10.1103/PhysRevE.49.5169
[44] To obtain Equation (5) we have taken the limit LZT→∞ of the corresponding equation for slab-like systems (see Equation (2.53) in [34]).

  
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