Force acting on a cluster of magnetic nanoparticles in a gradient field: A Langevin dynamics study

Abstract

Magnetophoretic force acting on a rigid spherical cluster of single-domain nanoparticles in a constant-gradient weak magnetic field is investigated numerically using the Langevin dynamics simulation method. Nanoparticles are randomly and uniformly distributed within the cluster volume. They interact with each other via long-range dipole-dipole interactions. Simulations reveal that if the total amount of particles in the cluster is kept constant, the force decreases with increasing nanoparticle concentration due to the demagnetizing field arising inside the cluster. Numerically obtained force values with great accuracy can be described by the modified mean-field theory, which was previously successfully used for the description of various dipolar media. Within this theory, a new expression is derived, which relates the magnetophoretic mobility of the cluster with the concentration of nanoparticles and their dipolar coupling parameter. The expression shows that if the number of particles in the cluster is fixed, the mobility is a nonmonotonic function of the concentration. The optimal concentration values that maximize the mobility for a given amount of magnetic phase and a given dipolar coupling parameter are determined.

Zero-Field and Field-Induced Interactions between Multicore Magnetic Nanoparticles

“…The effective magnetic moment can also be estimated using a linear response approach [20]:Meff2=χeff3kBTVμ0=m2NχeffχL, χL=μ0m2N3kBTV=8λφ, where χeff is the cluster effective magnetic susceptibility, and χL is the so-called Langevin susceptibility, which describes a linear magnetic response of an “ideal gas” of non-interacting superparamagnetic cores. It was shown in Reference [21,25] that the magnetic response of an isolated spherical magnetic cluster can be accurately described by the so-called modified mean-field theory (MMFT) [27]. It gives the following expression for the effective susceptibility:χeff=χ1+χ/3, χ=χL(1+χL…”

“…Dipolar interaction fields between every pair of cores are calculated directly, without any truncations or approximations. The described approach was previously successfully used in Reference [21,25] to study properties of an isolated MCMNP in uniform and constant-gradient magnetic fields.…”

“…Theoretical and numerical investigations of the last decade have firmly established that the response of an isolated MCMNP to an applied magnetic field can be significantly affected by magnetic interactions (dipole-dipole and/or exchange ones) between cores within the MCMNP. Such intracluster interactions influence the equilibrium magnetic moment [19,20,21], magnetization dynamics [22,23,24], and magnetophoretic mobility [25] of MCMNPs. However, so far, relatively little attention has been paid to the problem of interactions between separate MCMNPs—that is, intercluster interactions.…”

A Critical Review on Selected External Physical Cues and Modulation of Cell Behavior: Magnetic Nanoparticles, Non-thermal Plasma and Lasers

“…Therefore, despite the fact that magnetic particles used in magnetofection and other applications are nanosized, the magnetic complexes form aggregates in cell culture media with sizes of several hundred nanometers to microns [60,62]. For such big clusters magnetic force reaches already 1–50 pN [56,63,64].…”

Feedback controller designs for an electromagnetic micromanipulator

“…These particles are commercially available in sizes ranging from 0.2 to 100 mm and are conjugated with specific antibodies or chemicals to make them functional for various applications. [8][9][10] Under external magnetic field, the magnetic microparticles can be remotely manipulated as a non-invasive tool for cell manipulation, 11 DNA-RNA extracting, 12 immunoassays, 13 targeted drug delivery, [14][15][16] magnetic resonance imaging, 17 hyperthermia therapies 18,19 and signal amplification. 20 Magnetically controlled drug delivery is one of the significant methods among the targeted treatment systems.…”