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Mohapatra DK, Camp PJ, Philip J. Influence of size polydispersity on magnetic field tunable structures in magnetic nanofluids containing superparamagnetic nanoparticles. NANOSCALE ADVANCES 2021; 3:3573-3592. [PMID: 36133709 PMCID: PMC9419785 DOI: 10.1039/d1na00131k] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 04/23/2021] [Indexed: 06/01/2023]
Abstract
We probe the influence of particle size polydispersity on field-induced structures and structural transitions in magnetic fluids (ferrofluids) using phase contrast optical microscopy, light scattering and Brownian dynamics simulations. Three different ferrofluids containing superparamagnetic nanoparticles of different polydispersity indices (PDIs) are used. In a ferrofluid with a high PDI (∼0.79), thin chains, thick chains, and sheets are formed on increasing the in-plane magnetic field, whereas isotropic bubbles, and hexagonal and lamellar/stripe structures are formed on increasing the out-of-plane magnetic field over the same range. In contrast, no field-induced aggregates are seen in the sample with low polydispersity under the above conditions. In a polydisperse sample, bubbles are formed at a very low magnetic field strength of 30 G. Insights into the structural evolution with increasing magnetic field strength are obtained by carrying out Brownian dynamics simulations. The crossovers from isotropic, through hexagonal columnar, to lamellar/stripe structures observed with increasing field strength in the high-polydispersity sample indicate the prominent roles of large, more strongly interacting particles in structural transitions in ferrofluids. Based on the observed microstructures, a phase diagram is constructed. Our work opens up new opportunities to develop optical devices and access diverse structures by tuning size polydispersity.
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Affiliation(s)
- Dillip Kumar Mohapatra
- Smart Materials Section, Corrosion Science and Technology Division, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, HBNI Kalpakkam-603102 India
| | - Philip J Camp
- School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ Scotland UK
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University 51 Lenin Avenue Ekaterinburg 620000 Russia
| | - John Philip
- Smart Materials Section, Corrosion Science and Technology Division, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, HBNI Kalpakkam-603102 India
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Mohapatra DK, Laskar JM, Philip J. Temporal evolution of equilibrium and non-equilibrium magnetic field driven microstructures in a magnetic fluid. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.112737] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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3
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Cai G, Wang S, Zheng L, Lin J. A Fluidic Device for Immunomagnetic Separation of Foodborne Bacteria Using Self-Assembled Magnetic Nanoparticle Chains. MICROMACHINES 2018; 9:mi9120624. [PMID: 30486364 PMCID: PMC6315333 DOI: 10.3390/mi9120624] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2018] [Revised: 11/22/2018] [Accepted: 11/23/2018] [Indexed: 12/12/2022]
Abstract
Immunomagnetic separation has been widely used for the separation and concentration of foodborne pathogens from complex food samples, however it can only handle a small volume of samples. In this paper, we presented a novel fluidic device for the specific and efficient separation and concentration of salmonellatyphimurium using self-assembled magnetic nanoparticle chains. The laminated sawtooth-shaped iron foils were first mounted in the 3D-printed matrix and magnetized by a strong magnet to generate dot-array high gradient magnetic fields in the fluidic channel, which was simulated using COMSOL (5.3a, Burlington, MA, USA). Then, magnetic nanoparticles with a diameter of 150 nm, which were modified with the anti-salmonella polyclonal antibodies, were injected into the channel, and the magnetic nanoparticle chains were vertically formed at the dots and verified using a fluorescence inverted microscope. Finally, the bacterial sample was continuous-flow injected, and the target bacteria could be captured by the antibodies on the chains, followed by gold standard culture plating to determine the amount of the target bacteria. Under the optimal conditions, the target bacteria could be separated with a separation efficiency of 80% in 45 min. This fluidic device could be further improved using thinner sawtooth-shaped iron foils and stronger magnets to obtain a better dot-array magnetic field with larger magnetic intensity and denser dot distribution, and has the potential to be integrated with the existing biological assays for rapid and sensitive detection of foodborne bacteria.
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Affiliation(s)
- Gaozhe Cai
- Key Laboratory of Agricultural Information Acquisition Technology, Ministry of Agriculture, China Agricultural University, Beijing 100083, China.
| | - Siyuan Wang
- Key Laboratory of Modern Precision Agriculture System Integration Research, Ministry of Education, China Agricultural University, Beijing 100083, China.
| | - Lingyan Zheng
- Key Laboratory of Modern Precision Agriculture System Integration Research, Ministry of Education, China Agricultural University, Beijing 100083, China.
| | - Jianhan Lin
- Key Laboratory of Agricultural Information Acquisition Technology, Ministry of Agriculture, China Agricultural University, Beijing 100083, China.
- Key Laboratory of Modern Precision Agriculture System Integration Research, Ministry of Education, China Agricultural University, Beijing 100083, China.
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Higashi T, Minegishi H, Echigo A, Nagaoka Y, Fukuda T, Usami R, Maekawa T, Hanajiri T. Nanomaterial-assisted PCR based on thermal generation from magnetic nanoparticles under high-frequency AC magnetic fields. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.06.070] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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5
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Chae HS, Piao SH, Maity A, Choi HJ. Additive role of attapulgite nanoclay on carbonyl iron-based magnetorheological suspension. Colloid Polym Sci 2014. [DOI: 10.1007/s00396-014-3389-3] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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6
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Richardi J, Weis JJ. Influence of short range potential on field induced chain aggregation in low density dipolar particles. J Chem Phys 2013; 138:244704. [DOI: 10.1063/1.4811290] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
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Zhang Q, Janner M, He L, Wang M, Hu Y, Lu Y, Yin Y. Photonic labyrinths: two-dimensional dynamic magnetic assembly and in situ solidification. NANO LETTERS 2013; 13:1770-1775. [PMID: 23464735 DOI: 10.1021/nl400351k] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Creating novel structures by self-assembly processes and fixing the resultant assemblies are both critical to the design and fabrication of functional materials through bottom-up approaches. We demonstrate magnetically induced self-assembly of 2D photonic labyrinth structures and their solidification through a sol-gel method. The photonic labyrinth structures can be patterned into more regular arrangements using nonmagnetic substrates. This work may provide a platform for fabricating novel materials and devices with complex morphologies and spatial configurations.
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Affiliation(s)
- Qiao Zhang
- Department of Chemistry, University of California, Riverside, Riverside, California 92521, United States
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8
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An HN, Sun B, Picken SJ, Mendes E. Long Time Response of Soft Magnetorheological Gels. J Phys Chem B 2012; 116:4702-11. [DOI: 10.1021/jp301482a] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hai-Ning An
- Nanostructured Materials, Department
of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628
BL Delft, The Netherlands
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Bin Sun
- Nanostructured Materials, Department
of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628
BL Delft, The Netherlands
| | - Stephen J Picken
- Nanostructured Materials, Department
of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628
BL Delft, The Netherlands
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
| | - Eduardo Mendes
- Nanostructured Materials, Department
of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Julianalaan 136, 2628
BL Delft, The Netherlands
- Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands
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9
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Effects of Superparamagnetic Nanoparticle Clusters on the Polymerase Chain Reaction. APPLIED SCIENCES-BASEL 2012. [DOI: 10.3390/app2020303] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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10
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Richardi J, Weis JJ. Low density mesostructures of confined dipolar particles in an external field. J Chem Phys 2011; 135:124502. [DOI: 10.1063/1.3638048] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Ukai T, Morimoto H, Maekawa T. Cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:061406. [PMID: 21797363 DOI: 10.1103/physreve.83.061406] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2011] [Indexed: 05/31/2023]
Abstract
We investigate the cluster-cluster aggregations of superparamagnetic particles in a rotational magnetic field numerically by the Brownian dynamics method, focusing on the cases of ϕ = 0.01 and 0.03 and Ma = 0, 0.001, 0.01, and 0.1, where ϕ is the area fraction of superparamagnetic particles and Ma is the Mason number, i.e., the ratio of viscous drag to magnetic force acting on a magnetic particle. We clarify the effect of ϕ and Ma on the cluster-cluster aggregation process from the point of view of dynamic scaling law.
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Affiliation(s)
- Tomofumi Ukai
- Bio-Nano Electronics Research Centre, Toyo University, Kawagoe, Saitama, Japan
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12
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Higashi T, Nagaoka Y, Minegishi H, Echigo A, Usami R, Maekawa T, Hanajiri T. Regulation of PCR efficiency with magnetic nanoparticles in a rotating magnetic field. Chem Phys Lett 2011. [DOI: 10.1016/j.cplett.2011.03.017] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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13
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Laskar JM, Philip J, Raj B. Experimental investigation of magnetic-field-induced aggregation kinetics in nonaqueous ferrofluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021402. [PMID: 20866804 DOI: 10.1103/physreve.82.021402] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2010] [Revised: 06/22/2010] [Indexed: 05/15/2023]
Abstract
We investigate the influence of field ramp rate on the kinetics of magnetic dipole-dipole induced chainlike structure formation in a nonaqueous nanoparticle dispersion using light scattering studies. With increase in magnetic field, at a constant ramp rate, the transmitted light intensity diminishes and the transmitted light spot is transformed to a diffused ring due to scattering from the self-assembled linear aggregates. The decay rate of transmitted intensity increases up to an optimum ramp rate, above which the trend becomes reverse. At an optimum ramp rate, the minimum time for initial aggregation coincides with the exposure time where the intensity decay is fastest. The variation of transmitted intensity at different ramp rate is explained on the basis of initial aggregation time that depends on Brownian motion, dipolar magnetic attraction and multibody hydrodynamic interactions. The slope of the transmitted light intensity after the removal of magnetic field depends on the time required for dissociation of ordered linear structures. Disappearance of the ring pattern and the reappearance of original light spot, upon removal of the magnetic field, confirm the perfect reversibility of the linear aggregates. The observed concentration dependant decay rates are in good agreement with aggregation theory.
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Affiliation(s)
- Junaid M Laskar
- SMARTS, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, India
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14
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Activity of an enzyme immobilized on superparamagnetic particles in a rotational magnetic field. Biochem Biophys Res Commun 2010; 393:779-82. [DOI: 10.1016/j.bbrc.2010.02.081] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2010] [Accepted: 02/12/2010] [Indexed: 11/20/2022]
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15
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Laskar JM, Philip J, Raj B. Experimental evidence for reversible zippering of chains in magnetic nanofluids under external magnetic fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041401. [PMID: 19905308 DOI: 10.1103/physreve.80.041401] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2009] [Revised: 08/24/2009] [Indexed: 05/28/2023]
Abstract
We study the time-dependent transmitted intensity and the scattered pattern from magnetic nanofluids at constant ramping of uniform external magnetic field. The nanofluid used is the dispersion of magnetite particles with an average diameter of 6.5 nm with a protective surfactant coating. We observe several critical fields at which the transmitted light intensity decreases drastically followed by the formation of a ringlike pattern on a screen placed perpendicular to the field direction. Interestingly, the critical fields occur at a regular interval of 20 G. The observed critical fields are attributed to zippering transitions of the chains due to attractive energy well when the chains are of different lengths or shifted with respect to one another. Interaction energy calculations show a decrease in the energy of the system due to dipolar interactions at different critical fields confirming the lowering of the system energy through lateral coalescence. The observed zippering phenomenon is perfectly reversible.
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Affiliation(s)
- Junaid M Laskar
- Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, India
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16
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Morimoto H, Katano K, Maekawa T. Ring-chain structural transitions in a ferromagnetic particles system induced by a dc magnetic field. J Chem Phys 2009; 131:034905. [DOI: 10.1063/1.3179687] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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17
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Richardi J, Pileni MP, Weis JJ. Self-organization of confined dipolar particles in a parallel field. J Chem Phys 2009; 130:124515. [DOI: 10.1063/1.3100304] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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18
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Morimoto H, Ukai T, Nagaoka Y, Grobert N, Maekawa T. Tumbling motion of magnetic particles on a magnetic substrate induced by a rotational magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021403. [PMID: 18850832 DOI: 10.1103/physreve.78.021403] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2008] [Revised: 06/20/2008] [Indexed: 05/26/2023]
Abstract
We analyze the dynamics of paramagnetic particles on a paramagnetic substrate under a rotational magnetic field. When the paramagnetic particles are subjected to a rotational magnetic field, the rotational plane of which is perpendicular to the substrate surface, the particles form chain clusters caused by the dipole-dipole interaction between the particles and these clusters display a tumbling motion under certain conditions. In this case, the angular momentum of the clusters is converted to a translational one through the force of friction acting between the particles and substrate and, as a result, the clusters move along the surface of the substrate. We analyze the conditions under which the tumbling motion occurs and the dependence of the translational velocity of a cluster on the control parameters by the Stokesian dynamics method. Based on the dynamics of magnetic particles, we propose a method of manipulating nano- and microparticles using a rotational magnetic field. We demonstrate the manipulation of magnetic and nonmagnetic particles, a carbon nanotube, and a biological cell.
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Affiliation(s)
- Hisao Morimoto
- Bio-Nano Electronics Research Center, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585, Japan
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Haghgooie R, Doyle PS. Transition from two-dimensional to three-dimensional behavior in the self-assembly of magnetorheological fluids confined in thin slits. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061406. [PMID: 17677262 DOI: 10.1103/physreve.75.061406] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2007] [Indexed: 05/16/2023]
Abstract
We study the effects of extreme confinement on the self assembly of the colloids found in magnetorheological (MR) fluids using Brownian dynamics simulations. The MR fluid is confined in a thin slit with a uniform external magnetic field directed normal to the slit. We find a crossover in the behavior of the system from two dimensions to three dimensions as the slit thickness is increased. A simple model is presented to describe this crossover as a function of the slit thickness and volume fraction of the MR fluid. The model is able to predict the salient features of the structure formation that has been observed in these systems. Furthermore, the model predicts the approximate time scales for structure formation under a variety of conditions. We present a quantitative analysis of the effect of volume fraction on the behavior of the system. Additionally, we show quantitatively how energy barriers to structure formation play a crucial role in determining the steady state structure of these systems. Our analysis explains the discrepancies between previous experimental and theoretical work on the self-assembly of MR fluids confined in thin slits.
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Affiliation(s)
- Ramin Haghgooie
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Bentz JL, Kozak JJ. Aggregation of dipolar colloidal particles: geometric effects. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:011414. [PMID: 16486147 DOI: 10.1103/physreve.73.011414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2005] [Indexed: 05/06/2023]
Abstract
To understand the importance of confinement and the influence of translational degrees of freedom on aggregation of dipolar colloidal particles, we calculate numerically-exact values for the mean encounter time for two nonspherically symmetric molecules to form a two-molecule cluster, regarded here as a precursor to aggregation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a "dimer" in the sense that each molecule is specified to occupy two adjacent lattice sites. The two dimers undergo simultaneous translation, and the mean times for their encounter are determined. Exact numerical results are obtained via application of the theory of finite Markov processes. The results allow one to examine in a detailed way the interplay among such factors as geometrical confinement, system size, translational motion, and specific orientational effects in influencing the aggregation event. The results are compared with previously reported theoretical predictions and experiments on the behavior of dipolar colloidal particles in the presence of an applied magnetic field.
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Affiliation(s)
- Jonathan L Bentz
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames, IA 50011, USA.
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21
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Self-assembly of magnetic nanoparticles into complex superstructures: Spokes and spirals. Colloids Surf A Physicochem Eng Asp 2005. [DOI: 10.1016/j.colsurfa.2005.06.072] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Haghgooie R, Doyle PS. Structure and dynamics of repulsive magnetorheological colloids in two-dimensional channels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:011405. [PMID: 16089959 DOI: 10.1103/physreve.72.011405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2005] [Revised: 05/07/2005] [Indexed: 05/03/2023]
Abstract
We study a system of colloidal spheres with induced magnetic dipoles confined in two-dimensional (2D) hard-wall channels using Brownian dynamics simulations. The external magnetic field is directed normal to the 2D plane and therefore the colloids interact with a purely repulsive r(-3) potential. The effects of confinement between parallel walls are determined by analyzing the structure and dynamics of these confined systems and comparing to the unbounded (infinite) 2D plane limit. The bond-order correlation function is analyzed as a function of time and exhibits unique characteristics associated with the channel-like confinement. The existence of a plateau in this correlation function is observed over an intermediate time scale and the fate of the plateau (decay or persistence) depends upon the channel width, the strength of the external magnetic field, and the number density. The plateau is analyzed in further detail and an explanation is put forth for its existence and subsequent long time behavior. Additionally, re-entrant behavior with respect to dimensionless channel width is observed in the structural properties and an associated state-diagram is presented for these systems.
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Affiliation(s)
- Ramin Haghgooie
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, 02139, USA
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Nagaoka Y, Morimoto H, Maekawa T. Dynamics of disklike clusters formed in a magnetorheological fluid under a rotational magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:032502. [PMID: 15903473 DOI: 10.1103/physreve.71.032502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2004] [Indexed: 05/02/2023]
Abstract
We investigate the cluster formations and dynamics in a magnetorheological fluid under a rotational magnetic field focusing on the case of a relatively high volume fraction. We find that isotropic disklike clusters, which rotate more slowly than the field rotation, are formed at low Mason numbers (the ratio of viscous to magnetic forces) and, what is more, we show short rod clusters, which rotate stably thanks to the low Mason numbers and circulate along the surface of the disklike clusters. The circulation velocity of the surface particles is much higher than the rotational surface velocity of the rigid disklike clusters.
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Affiliation(s)
- Yutaka Nagaoka
- Bio-Nano Electronics Research Center, Toyo University, Saitama, Japan
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