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Horváth B, Decsi P, Szalai I. Nonlinear contributions to the dynamic magnetic susceptibility of magnetic fluids. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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2
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Ivanov AO, Camp PJ. Effects of interactions on magnetization relaxation dynamics in ferrofluids. Phys Rev E 2020; 102:032610. [PMID: 33075873 DOI: 10.1103/physreve.102.032610] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 09/01/2020] [Indexed: 11/07/2022]
Abstract
The dynamics of magnetization relaxation in ferrofluids are studied with statistical-mechanical theory and Brownian dynamics simulations. The particle dipole moments are initially perfectly aligned, and the magnetization is equal to its saturation value. The magnetization is then allowed to decay under zero-field conditions toward its equilibrium value of zero. The time dependence is predicted by solving the Fokker-Planck equation for the one-particle orientational distribution function. Interactions between particles are included by introducing an effective magnetic field acting on a given particle and arising from all of the other particles. Two different approximations are proposed and tested against simulations: a first-order modified mean-field theory and a modified Weiss model. The theory predicts that the short-time decay is characterized by the Brownian rotation time τ_{B}, independent of the interaction strength. At times much longer than τ_{B}, the asymptotic decay time is predicted to grow with increasing interaction strength. These predictions are borne out by the simulations. The modified Weiss model gives the best agreement with simulation, and its range of validity is limited to moderate, but realistic, values of the dipolar coupling constant.
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Affiliation(s)
- Alexey O Ivanov
- Department of Theoretical and Mathematical Physics, Ural Mathematical Center, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland and Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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3
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Drab M, Gongadze E, Kralj-Iglič V, Iglič A. Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1054. [PMID: 33286823 PMCID: PMC7597128 DOI: 10.3390/e22091054] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2020] [Revised: 09/04/2020] [Accepted: 09/18/2020] [Indexed: 02/05/2023]
Abstract
The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.
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Affiliation(s)
- Mitja Drab
- Faculty of Electrical Engineering, Tržaška Cesta 25, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (M.D.); (E.G.)
| | - Ekaterina Gongadze
- Faculty of Electrical Engineering, Tržaška Cesta 25, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (M.D.); (E.G.)
| | - Veronika Kralj-Iglič
- Faculty of Health Sciences, Zdravstvena Pot 5, University of Ljubljana, SI-1000 Ljubljana, Slovenia;
| | - Aleš Iglič
- Faculty of Electrical Engineering, Tržaška Cesta 25, University of Ljubljana, SI-1000 Ljubljana, Slovenia; (M.D.); (E.G.)
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Koski JP, Moore SG, Grest GS, Stevens MJ. Effect of an external field on capillary waves in a dipolar fluid. Phys Rev E 2017; 96:063106. [PMID: 29347427 DOI: 10.1103/physreve.96.063106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2017] [Indexed: 06/07/2023]
Abstract
The role of an external field on capillary waves at the liquid-vapor interface of a dipolar fluid is investigated using molecular dynamics simulations. For fields parallel to the interface, the interfacial width squared increases linearly with respect to the logarithm of the size of the interface across all field strengths tested. The value of the slope decreases with increasing field strength, indicating that the field dampens the capillary waves. With the inclusion of the parallel field, the surface stiffness increases with increasing field strength faster than the surface tension. For fields perpendicular to the interface, the interfacial width squared is linear with respect to the logarithm of the size of the interface for small field strengths, and the surface stiffness is less than the surface tension. Above a critical field strength that decreases as the size of the interface increases, the interface becomes unstable due to the increased amplitude of the capillary waves.
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Affiliation(s)
- Jason P Koski
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Stan G Moore
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Mark J Stevens
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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Solovyova AY, Elfimova EA, Ivanov AO, Camp PJ. Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids. Phys Rev E 2017; 96:052609. [PMID: 29347762 DOI: 10.1103/physreve.96.052609] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Indexed: 06/07/2023]
Abstract
The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.
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Affiliation(s)
- Anna Yu Solovyova
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Ekaterina A Elfimova
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Alexey O Ivanov
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland and Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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6
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Hod M, Dobroserdova A, Samin S, Dobbrow C, Schmidt AM, Gottlieb M, Kantorovich S. Dilution effects on combined magnetic and electric dipole interactions: A study of ferromagnetic cobalt nanoparticles with tuneable interactions. J Chem Phys 2017; 147:084901. [DOI: 10.1063/1.4995428] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- M. Hod
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
| | - A. Dobroserdova
- Ural Federal University, Lenin Ave. 51, 620083 Ekaterinburg, Russia
| | - S. Samin
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - C. Dobbrow
- Institut für Physikalische Chemie, Department Chemie, Universität zu Köln, Luxemburger Str. 116, D-50939 Köln, Germany
| | - A. M. Schmidt
- Institut für Physikalische Chemie, Department Chemie, Universität zu Köln, Luxemburger Str. 116, D-50939 Köln, Germany
| | - M. Gottlieb
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
| | - S. Kantorovich
- Computational Physics, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
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Szalai I, Nagy S, Dietrich S. Linear and nonlinear magnetic properties of ferrofluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042314. [PMID: 26565247 DOI: 10.1103/physreve.92.042314] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2015] [Indexed: 06/05/2023]
Abstract
Within a high-magnetic-field approximation, employing Ruelle's algebraic perturbation theory, a field-dependent free-energy expression is proposed which allows one to determine the magnetic properties of ferrofluids modeled as dipolar hard-sphere systems. We compare the ensuing magnetization curves, following from this free energy, with those obtained by Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] as well as with new corresponding Monte Carlo simulation data. Based on the power-series expansion of the magnetization, a closed expression for the magnetization is also proposed, which is a high-density extension of the corresponding equation of Ivanov and Kuznetsova. From both magnetization equations the zero-field susceptibility expression due to Tani et al. [Mol. Phys. 48, 863 (1983)] can be obtained, which is in good agreement with our MC simulation results. From the closed expression for the magnetization the second-order nonlinear magnetic susceptibility is also derived, which shows fair agreement with the corresponding MC simulation data.
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Affiliation(s)
- I Szalai
- Institute of Physics and Mechatronics, University of Pannonia, 8200 Veszprém, Hungary
| | - S Nagy
- Institute of Mechanics and Mechatronics, The University of West Hungary, H-9401 Sopron, P. O. Box 132, Hungary
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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Moore SG, Stevens MJ, Grest GS. Liquid-vapor interface of the Stockmayer fluid in a uniform external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:022309. [PMID: 25768507 DOI: 10.1103/physreve.91.022309] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Indexed: 06/04/2023]
Abstract
The effect of a uniform (nonspatially varying) external field on the liquid-vapor interface of the Stockmayer fluid (Lennard-Jones particles embedded with a point dipole) has been investigated by molecular-dynamics simulations. The long-ranged parts of both the dipole and Lennard-Jones interactions are treated using an Ewald summation, which removes the effects of the cutoff. The direction of the field shifts the critical point and interfacial properties in different directions. For an external field parallel to the interface, the critical temperature increases, while for a field applied perpendicular to the interface, it decreases. The effects of the field on surface tension and interfacial width are also investigated. For zero field, dipoles near the liquid-vapor interface show a weak orientation parallel to the interface. For fields parallel to the interface, ordering in the liquid phase is greater than the vapor, while for fields perpendicular to the interface, the opposite is true.
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Affiliation(s)
- Stan G Moore
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Mark J Stevens
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Gary S Grest
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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Camp PJ, Elfimova EA, Ivanov AO. The effects of polydispersity on the initial susceptibilities of ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:456002. [PMID: 25327692 DOI: 10.1088/0953-8984/26/45/456002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
The effects of particle-size polydispersity on the initial susceptibilities of concentrated ferrofluids are analyzed using a combination of theory and computer simulation. The study is focused on a model ferrofluid with a prescribed magnetic-core diameter distribution, a fixed non-magnetic surface layer (corresponding to a demagnetized layer and adsorbed surfactant) and a combination of dipolar and hard-core interactions. The non-trivial effects of polydispersity are identified by comparing the initial susceptibilities of monodisperse and polydisperse ferrofluids with the same Langevin susceptibility. The theory is based on a correction to the second-order modified mean-field theory arising from a formal Mayer-type cluster expansion; this correction is dependent on a parameter similar to the normal dipolar coupling constant, except that it contains a complicated double average over the particle-size distribution, which means that the initial susceptibility should depend significantly on polydispersity. Specifically, the theory predicts that the initial susceptibility is enhanced significantly by polydispersity. This prediction is tested rigorously against results from Monte Carlo simulations and is found to be robust. The qualitative agreement between theory and simulation is already satisfactory, but the quantitative agreement could be improved by a systematic extension of the cluster expansion. The overall conclusion is that polydispersity should be accounted for carefully in magnetogranulometric analyses of real ferrofluids.
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Affiliation(s)
- Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh, EH9 3FJ, UK
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Dussi S, Rovigatti L, Sciortino F. On the gas–liquid phase separation and the self-assembly of charged soft dumbbells. Mol Phys 2013. [DOI: 10.1080/00268976.2013.838315] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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11
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Szalai I, Nagy S, Dietrich S. Comparison between theory and simulations for the magnetization and the susceptibility of polydisperse ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:465108. [PMID: 24153397 DOI: 10.1088/0953-8984/25/46/465108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The influence of polydispersity on the magnetization of ferrofluids is studied based on a previously published magnetization equation of state (Szalai and Dietrich, 2011 J. Phys.: Condens. Matter 23 326004) and computer simulations. The polydispersity of the particle diameter is described by the gamma distribution function. Canonical ensemble Monte Carlo simulations have been performed in order to test these theoretical results for the initial susceptibility and the magnetization. The results for the magnetic properties of the polydisperse systems turn out to be in quantitative agreement with our present simulation data. In addition, we find good agreement between our theory and experimental data for magnetite-based ferrofluids.
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Affiliation(s)
- I Szalai
- Institute of Physics and Mechatronics, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary
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12
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Rovigatti L, Kantorovich S, Ivanov AO, Tavares JM, Sciortino F. Branching points in the low-temperature dipolar hard sphere fluid. J Chem Phys 2013; 139:134901. [PMID: 24116579 DOI: 10.1063/1.4821935] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lorenzo Rovigatti
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, 00185 Roma, Italy
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13
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Kristóf T, Boda D, Szalai I. An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:336002. [PMID: 22810162 DOI: 10.1088/0953-8984/24/33/336002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities.
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Affiliation(s)
- T Kristóf
- Institute of Chemistry, Department of Physical Chemistry, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary.
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Gongadze E, Iglič A. Decrease of permittivity of an electrolyte solution near a charged surface due to saturation and excluded volume effects. Bioelectrochemistry 2011; 87:199-203. [PMID: 22209491 DOI: 10.1016/j.bioelechem.2011.12.001] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2011] [Revised: 10/22/2011] [Accepted: 12/01/2011] [Indexed: 11/17/2022]
Abstract
The dipole moment of a water molecule in liquid water differs from that of an isolated one because each molecule is further polarized by the electric field of its neighbours. In this work a formula for the spatial dependence of the relative permittivity of an electrolyte near a highly charged surface is obtained in which the mutual influence of the water molecules is taken into account by means of the cavity field. The orientational ordering of water dipoles is considered in the saturation regime. It is predicted that the relative permittivity of an electrolyte solution near the highly charged surface (i.e. in saturation regime) may be substantially decreased due to orientational ordering of water (saturation effect) and depletion of water molecules (excluded volume effect) due to accumulation of counterions.
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Affiliation(s)
- Ekaterina Gongadze
- Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia
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Szalai I, Dietrich S. Magnetization of multicomponent ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:326004. [PMID: 21795777 DOI: 10.1088/0953-8984/23/32/326004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The solution of the mean spherical approximation (MSA) integral equation for isotropic multicomponent dipolar hard sphere fluids without external fields is used to construct a density functional theory (DFT), which includes external fields, in order to obtain an analytical expression for the external field dependence of the magnetization of ferrofluidic mixtures. This DFT is based on a second-order Taylor series expansion of the free energy density functional of the anisotropic system around the corresponding isotropic MSA reference system. The ensuing results for the magnetic properties are in quantitative agreement with our canonical ensemble Monte Carlo simulation data presented here.
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Affiliation(s)
- I Szalai
- Institute of Physics and Mechatronics, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary.
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Cerdà JJ, Elfimova E, Ballenegger V, Krutikova E, Ivanov A, Holm C. Behavior of bulky ferrofluids in the diluted low-coupling regime: theory and simulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011501. [PMID: 20365375 DOI: 10.1103/physreve.81.011501] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2009] [Revised: 12/08/2009] [Indexed: 05/29/2023]
Abstract
A theoretical formalism to predict the structure factors observed in dipolar soft-sphere fluids based on a virial expansion of the radial distribution function is presented. The theory is able to account for cases with and without externally applied magnetic fields. A thorough comparison of the theoretical results to molecular-dynamics simulations shows a good agreement between theory and numerical simulations when the fraction of particles involved in clustering is low; i.e., the dipolar coupling parameter is lambda less, similar 2, and the volume fraction is phi less, similar 0.25. When magnetic fields are applied to the system, special attention is paid to the study of the anisotropy of the structure factor. The theory reasonably accounts for the structure factors when the Langevin parameter is smaller than 5.
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Affiliation(s)
- Juan J Cerdà
- Institute for Computational Physics, Universität Stuttgart, 70569 Stuttgart, Germany
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Jia R, Hentschke R. Dipolar particles in an external field: Molecular dynamics simulation and mean field theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:051502. [PMID: 20364987 DOI: 10.1103/physreve.80.051502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2009] [Indexed: 05/29/2023]
Abstract
Using molecular dynamics computer simulation we compute gas-liquid phase coexistence curves for the Stockmayer fluid in an external electric field. We observe a field-induced shift of the critical temperature DeltaTc. The sign of DeltaTc depends on whether the potential or the surface charge density is held constant assuming that the dielectric material fills the space between capacitor plates. Our own as well as previous literature data for DeltaTc are compared to and interpreted in terms of a simple mean field theory. Despite considerable errors in the simulation results, we find consistency between the simulation results obtained by different groups including our own and the mean field description. The latter ties the sign of DeltaTc to the outside constraints via the electric field dependence of the orientation part of the mean field free energy.
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Affiliation(s)
- Ran Jia
- Fachbereich Mathematik und Naturwissenschaften, Bergische Universität, D-42097 Wuppertal, Germany
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19
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Szalai I, Nagy S, Dietrich S. Nonlinear dielectric effect of dipolar fluids. J Chem Phys 2009; 131:154905. [DOI: 10.1063/1.3248242] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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