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Goh S, Menzel AM, Wittmann R, Löwen H. Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels. J Chem Phys 2023; 158:054909. [PMID: 36754783 DOI: 10.1063/5.0133207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.
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Affiliation(s)
- Segun Goh
- Theoretical Physics of Living Matter, Institute of Biological Information Processing, Forschungszentrum Jülich, 52425 Jülich, Germany
| | - Andreas M Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany
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Weeber R, Kreissl P, Holm C. Magnetic field controlled behavior of magnetic gels studied using particle-based simulations. PHYSICAL SCIENCES REVIEWS 2021. [DOI: 10.1515/psr-2019-0106] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
Abstract
This contribution provides an overview of the study of soft magnetic materials using particle-based simulation models. We focus in particular on systems where thermal fluctuations are important. As a basis for further discussion, we first describe two-dimensional models which demonstrate two deformation mechanisms of magnetic gels in a homogeneous field. One is based on the change of magnetic interactions between magnetic particles as a response to an external field; the other is the result of magnetically blocked particles acting as cross-linkers. Based on the qualitative behavior directly observable in the two-dimensional models, we extend our description to three-dimensions. We begin with particle-cross-linked gels, as for those, our three-dimensional model also includes explicitly resolved polymer chains. Here, the polymer chains are represented by entropic springs, and the deformation of the gel is the result of the interaction between magnetic particles. We use this model to examine the influence of the magnetic spatial configuration of magnetic particles (uniaxial or isotropic) on the gel’s magnetomechanical behavior. A further part of the article will be dedicated to scale-bridging approaches such as systematic coarse-graining and models located at the boundary between particle-based and continuum modeling. We will conclude our article with a discussion of recent results for modeling time-dependent phenomena in magnetic-polymer composites. The discussion will be focused on a simulation model suitable for obtaining AC-susceptibility spectra for dilute ferrofluids including hydrodynamic interactions. This model will be the basis for studying the signature of particle–polymer coupling in magnetic hybrid materials. In the long run, we aim to compare material properties probed locally via the AC-susceptibility spectra to elastic moduli obtained for the system at a global level.
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Affiliation(s)
- Rudolf Weeber
- Institute for Computational Physics, University of Stuttgart , Stuttgart , Germany
| | - Patrick Kreissl
- Institute for Computational Physics, University of Stuttgart , Stuttgart , Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart , Stuttgart , Germany
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Veloso SR, Andrade RG, Castanheira EM. Review on the advancements of magnetic gels: towards multifunctional magnetic liposome-hydrogel composites for biomedical applications. Adv Colloid Interface Sci 2021; 288:102351. [PMID: 33387893 DOI: 10.1016/j.cis.2020.102351] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2020] [Revised: 12/18/2020] [Accepted: 12/19/2020] [Indexed: 12/11/2022]
Abstract
Magnetic gels have been gaining great attention in nanomedicine, as they combine features of hydrogels and magnetic nanoparticles into a single system. The incorporation of liposomes in magnetic gels further leads to a more robust multifunctional system enabling more functions and spatiotemporal control required for biomedical applications, which includes on-demand drug release. In this review, magnetic gels components are initially introduced, as well as an overview of advancements on the development, tuneability, manipulation and application of these materials. After a discussion of the advantages of combining hydrogels with liposomes, the properties, fabrication strategies and applications of magnetic liposome-hydrogel composites (magnetic lipogels or magnetolipogels) are reviewed. Overall, the progress of magnetic gels towards smart multifunctional materials are emphasized, considering the contributions for future developments.
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Wittmann R, Löwen H, Brader JM. Order-preserving dynamics in one dimension – single-file diffusion and caging from the perspective of dynamical density functional theory. Mol Phys 2021. [DOI: 10.1080/00268976.2020.1867250] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Joseph M. Brader
- Department of Physics, University of Fribourg, Fribourg, Switzerland
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Menzel AM, Löwen H. Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales. PHYSICAL SCIENCES REVIEWS 2020. [DOI: 10.1515/psr-2019-0088] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
Abstract
Magnetic gels and elastomers consist of magnetic or magnetizable colloidal particles embedded in an elastic polymeric matrix. Outstanding properties of these materials comprise reversible changes in their mechanical stiffness or magnetostrictive distortions under the influence of external magnetic fields. To understand such types of overall material behavior from a theoretical point of view, it is essential to characterize the substances starting from the discrete colloidal particle level. It turns out that the macroscopic material response depends sensitively on the mesoscopic particle arrangement. We have utilized and developed several theoretical approaches to this end, allowing us both to reproduce experimental observations and to make theoretical predictions. Our hope is that both these paths help to further stimulate the interest in these fascinating materials.
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Affiliation(s)
- Andreas M. Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg , Universitätsplatz 2, 39106 Magdeburg , Germany
- Theoretische Physik II : Weiche Materie, Heinrich-Heine-Universität Düsseldorf , Universitätsstr. 1, 40225 Düsseldorf , Germany
| | - Hartmut Löwen
- Theoretische Physik II : Weiche Materie, Heinrich-Heine-Universität Düsseldorf , Universitätsstr. 1, 40225 Düsseldorf , Germany
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Goh S, Wittmann R, Menzel AM, Löwen H. Classical density functional theory for a two-dimensional isotropic ferrogel model with labeled particles. Phys Rev E 2019; 100:012605. [PMID: 31499838 DOI: 10.1103/physreve.100.012605] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Indexed: 01/30/2023]
Abstract
In this study, we formulate a density functional theory (DFT) for systems of labeled particles, considering a two-dimensional bead-spring lattice with a magnetic dipole on every bead as a model for ferrogels. On the one hand, DFT has been widely studied to investigate fluidlike states of materials, in which constituent particles are not labeled as they can exchange their positions without energy cost. On the other hand, in ferrogels consisting of magnetic particles embedded in elastic polymer matrices, the particles are labeled by their positions as their neighbors do not change over time. We resolve such an issue of particle labeling, introducing a mapping of the elastic interaction mediated by springs onto a pairwise additive interaction (pseudosprings) between unlabeled particles. We further investigate magnetostriction and changes in the elastic constants under altered magnetic interactions employing the pseudospring potential. It is revealed that there are two different response scenarios in the mechanical properties of the dipole-spring systems: While systems at low packing fractions are hardened as the magnetic moments increase in magnitude, at high packing fractions softening due to diminishing effects from the steric force, associated with increases in the volume, is observed. The validity of the theory is also verified by Monte Carlo simulations with both real springs and pseudosprings. We expect that our DFT approach may promote our understanding of materials with particle inclusions.
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Affiliation(s)
- Segun Goh
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
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Daddi-Moussa-Ider A, Goh S, Liebchen B, Hoell C, Mathijssen AJTM, Guzmán-Lastra F, Scholz C, Menzel AM, Löwen H. Membrane penetration and trapping of an active particle. J Chem Phys 2019; 150:064906. [DOI: 10.1063/1.5080807] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Abdallah Daddi-Moussa-Ider
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Segun Goh
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Benno Liebchen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | | | - Francisca Guzmán-Lastra
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
- Facultad de Ciencias, Universidad Mayor, Ave. Manuel Montt 367, Providencia, Santiago de Chile, Chile
| | - Christian Scholz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany
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Puljiz M, Menzel AM. Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments. Phys Rev E 2019; 99:012601. [PMID: 30780302 DOI: 10.1103/physreve.99.012601] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2018] [Indexed: 06/09/2023]
Abstract
Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both viscoelastic environments of terminal fluidlike flow and of completely reversible damped elastic behavior are covered. For illustration and to highlight the role of the formalism in potential applications, we briefly address the relevant examples of dragging a rigid sphere through a viscoelastic environment together with subsequent relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel matrices, and the swimming behavior of active microswimmers in viscoelastic solutions. The approach provides a basis for more quantitative and extended investigations of these and related systems in the future.
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Affiliation(s)
- Mate Puljiz
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
| | - Andreas M Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Niemczyk B, Sajkiewicz P, Kolbuk D. Injectable hydrogels as novel materials for central nervous system regeneration. J Neural Eng 2018; 15:051002. [DOI: 10.1088/1741-2552/aacbab] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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Pessot G, Schümann M, Gundermann T, Odenbach S, Löwen H, Menzel AM. Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:125101. [PMID: 29474190 DOI: 10.1088/1361-648x/aaaeaa] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Ferrogels and magnetorheological elastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high responsivity of ferrofluids to external magnetic fields. These materials stand out, for example, for significant magnetostriction as well as a pronounced increase of the elastic moduli in the presence of external magnetic fields. By means of x-ray micro-computed tomography, the position and size of each magnetic particle can be measured with a high degree of accuracy. We here use data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum. More precisely, we assign to each particle a dipole moment proportional to its volume and set a randomized network of springs between them that mimics the behavior of the polymeric elastic matrix. Extending our previously developed methods, we compute the resulting structural changes in the systems as well as the frequency-dependent elastic moduli when magnetic interactions are turned on. Particularly, with increasing magnetization, we observe the formation of chain-like aggregates. Interestingly, the static elastic moduli can first show a slight decrease with growing amplitude of the magnetic interactions, before a pronounced increase appears upon the chain formation. The change of the dynamic moduli with increasing magnetization depends on the frequency and can even feature nonmonotonic behavior. Overall, we demonstrate how theory and experiments can complement each other to learn more about the dynamic behavior of this interesting class of materials.
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Affiliation(s)
- Giorgio Pessot
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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Weeber R, Hermes M, Schmidt AM, Holm C. Polymer architecture of magnetic gels: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:063002. [PMID: 29261097 DOI: 10.1088/1361-648x/aaa344] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this review article, we provide an introduction to ferrogels, i.e. polymeric gels with embedded magnetic particles. Due to the interplay between magnetic and elastic properties of these materials, they are promising candidates for engineering and biomedical applications such as actuation and controlled drug release. Particular emphasis will be put on the polymer architecture of magnetic gels since it controls the degrees of freedom of the magnetic particles in the gel, and it is important for the particle-polymer coupling determining the mechanisms available for the gel deformation in magnetic fields. We report on the different polymer architectures that have been realized so far, and provide an overview of synthesis strategies and experimental techniques for the characterization of these materials. We further focus on theoretical and simulational studies carried out on magnetic gels, and highlight their contributions towards understanding the influence of the gels' polymer architecture.
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Affiliation(s)
- Rudolf Weeber
- Institut für Computerphysik, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, Germany
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12
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Borówko M, Sokołowski S, Staszewski T, Pizio O. Adsorption of hairy particles with mobile ligands: Molecular dynamics and density functional study. J Chem Phys 2018; 148:044705. [PMID: 29390816 DOI: 10.1063/1.5010687] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
We study models of hairy nanoparticles in contact with a hard wall. Each particle is built of a spherical core with a number of ligands attached to it and each ligand is composed of several spherical, tangentially jointed segments. The number of segments is the same for all ligands. Particular models differ by the numbers of ligands and of segments per ligand, but the total number of segments is constant. Moreover, our model assumes that the ligands are tethered to the core in such a manner that they can "slide" over the core surface. Using molecular dynamics simulations we investigate the differences in the structure of a system close to the wall. In order to characterize the distribution of the ligands around the core, we have calculated the end-to-end distances of the ligands and the lengths and orientation of the mass dipoles. Additionally, we also employed a density functional approach to obtain the density profiles. We have found that if the number of ligands is not too high, the proposed version of the theory is capable to predict the structure of the system with a reasonable accuracy.
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Affiliation(s)
- M Borówko
- Department for the Modelling of Physico-Chemical Processes, Maria Curie-Sklodowska University, Gliniana 33, Lublin, Poland
| | - S Sokołowski
- Department for the Modelling of Physico-Chemical Processes, Maria Curie-Sklodowska University, Gliniana 33, Lublin, Poland
| | - T Staszewski
- Department for the Modelling of Physico-Chemical Processes, Maria Curie-Sklodowska University, Gliniana 33, Lublin, Poland
| | - O Pizio
- Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Circuito Exterior, 04510 Ciudad de México, Mexico
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