Generating an in situ tunable interaction potential for probing 2-D colloidal phase behavior

Du, Di; Li, Dichuan; Thakur, Madhuri; Biswal, Sibani Lisa

doi:10.1039/c3sm27620a

Cited by 51 publications

(60 citation statements)

References 40 publications

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“…For a suspension of several particles, the MDM [15] can be used [Eq. (4)]: where H 0 is the external magnetic field and r kn the connector vector from particle k to particle n. For two particles, an even simpler form can be used which self-consistently assumes the directions of the two dipoles are the same [12]. The first effect is caused by the dipole moment assumption and will not vanish unless multipole terms are added.…”

Section: A Dipolar Model (Dm) and Mutual Dipolar Model (Mdm)mentioning

confidence: 99%

“…The magnetic force between a particle pair in a rotational magnetic field becomes isotropic if the rotation frequency is higher than a critical value [12]. This isotropic force can be calculated by averaging the angular force over one revolution.…”

Section: Force Between Particles In a Rotational Magnetic Fieldmentioning

confidence: 99%

“…Paramagnetic colloidal suspensions have been utilized for a number of innovative applications in a variety of fields such as smart fluids [e.g., magnetorheological (MR) fluids] [1][2][3], biomedical imaging and sensing [4], unique directed assembly structures [5][6][7], self-propelled swimming structures [8,9], force probing [10,11], and models for statistical mechanics [12,13]. In many of these applications, the force between these paramagnetic particles needs to be accurately calculated.…”

Section: Introductionmentioning

confidence: 99%

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Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Toffoletto

Biswal

2014

Phys. Rev. E

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Typically the force between paramagnetic particles in a uniform magnetic field is described using the dipolar model, which is inaccurate when particles are in close proximity to each other. Instead, the exact force between paramagnetic particles can be determined by solving a three-dimensional Laplace's equation for magnetostatics under specified boundary conditions and calculating the Maxwell stress tensor. The analytical solution to this multi-boundary-condition Laplace's equation can be obtained by using a solid harmonics expansion in conjunction with the Hobson formula. However, for a multibody system, finite truncation of the Hobson formula does not lead to convergence of the expansion at all points, which makes the approximation physically unrealistic. Here we present a numerical method for solving this Laplace's equation for magnetostatics. This method uses a smoothed representation to replace all the boundary conditions. A two-step propagation is used to dramatically accelerate the calculation without losing accuracy. Using this method, we calculate the force between two paramagnetic particles in a uniform and a rotational external field and compare our results with other models. Furthermore, the many-body effects for three-particle, ten-particle, and 24-particle systems are examined using the same method. We also calculate the interaction between particles with different magnetic susceptibilities and particle diameters. The Laplace's equation solver method described in this article that is used to determine the force between paramagnetic particles is shown to be very useful for dynamic simulations for both two-particle systems and a large cluster of particles.

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Section: A Dipolar Model (Dm) and Mutual Dipolar Model (Mdm)mentioning

confidence: 99%

Section: Force Between Particles In a Rotational Magnetic Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Toffoletto

Biswal

2014

Phys. Rev. E

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“…In these applications, the magnetic force between paramagnetic particles must be calculated accurately. Typically, dipole-based models, such as the dipolar model (DM) and the mutual-dipolar model (MDM), are used to calculate the force between paramagnetic particles placed in an external magnetic field [2,5,13]. Dipole-based models are usually fast but inaccurate for systems in which particles are close to one another.…”

mentioning

confidence: 99%

“…Paramagnetic colloidal particles suspended in liquid form different structures, such as chains [1], sheets [2], membranes [3], and networks [4], in the presence of different types of magnetic fields. The versatility of structure manipulation enables paramagnetic colloidal suspensions to have numerous applications, such as smart fluids [5,6], biomedical sensing [7,8], propulsion and transportation in fluids [9,10], and force probes [11,12].…”

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confidence: 99%

Micro-mutual-dipolar model for rapid calculation of forces between paramagnetic colloids

Biswal

2014

Phys. Rev. E

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Typically, the force between paramagnetic particles in a uniform magnetic field is calculated using either dipole-based models or the Maxwell stress tensor combined with Laplace's equation for magnetostatics. Dipolebased models are fast but involve many assumptions, leading to inaccuracies in determining forces for clusters of particles. The Maxwell stress tensor yields an exact force calculation, but solving Laplace's equation is very time consuming. Here, we present a more elaborate dipole-based model: the micro-mutual-dipolar model. Our model has a time complexity that is similar to that of other dipole-based models but is much more accurate especially when used to calculate the force of small aggregates. Using this model, we calculate the force between two paramagnetic spheres in a uniform magnetic field and a circular rotational magnetic field and compare our results with those of other models. The forces for three-particle and ten-particle systems dispersed in two-dimensional (2D) space are examined using the same model. We also apply this model to calculate the force between two paramagnetic disks dispersed in 2D space. The micro-mutual-dipolar model is demonstrated to be useful for force calculations in dynamic simulations of small clusters of particles for which both accuracy and efficiency are desirable. [5,6], biomedical sensing [7,8], propulsion and transportation in fluids [9,10], and force probes [11,12]. In these applications, the magnetic force between paramagnetic particles must be calculated accurately. Typically, dipole-based models, such as the dipolar model (DM) and the mutual-dipolar model (MDM), are used to calculate the force between paramagnetic particles placed in an external magnetic field [2,5,13]. Dipole-based models are usually fast but inaccurate for systems in which particles are close to one another. Such models are inaccurate because they do not consider multipolar effects [14]. The exact force can be calculated by solving a Laplace equation for magnetostatics with multiple boundary and initial conditions and calculating the Maxwell stress tensor for each particle [15]. The solution to the Laplace equation can be analytically approximated by a solid harmonics expansion with the Hobson formula applied to unify the coordinate system [14,16]. This coordinate unification is very computationally expensive and suffers from singularity-related issues [17,18]. A numerical solution to Laplace's equation can be obtained by using a smoothed representation of susceptibility to replace the boundary conditions [17]; this method is referred to as the Laplace equation solver (LES) method. This numerical approach is stable in terms of error propagation but still computationally time consuming.Here, we present a more-sophisticated dipole-based model that considers mutual interactions between dipole moments and multipolar effects. All dipole-based models are based on the fact that a single spherical paramagnetic particle is uniformly magnetized in the presence of a uniform magnetic * Correspondin...

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Colloidal Superstructures Programmed into Magnetic Janus Particles

2014

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By engineering thin magnetic films onto homogeneous colloidal particles, various crystalline lattices are induced from simple magnetic Janus spheres. In situ formation of dicolloids amplifies the diversity of achievable dynamic structures. The competition between shape anisotropy and dipole orientation generates mesoscopic isomerism. This opens design space for anisotropic building blocks for smart colloidal materials.

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Generating an in situ tunable interaction potential for probing 2-D colloidal phase behavior

Cited by 51 publications

References 40 publications

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Numerical calculation of interaction forces between paramagnetic colloids in two-dimensional systems

Micro-mutual-dipolar model for rapid calculation of forces between paramagnetic colloids

Colloidal Superstructures Programmed into Magnetic Janus Particles

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