Effect of microstructure evolution on the mechanical behavior of magneto-active elastomers with different matrix stiffness.

Evolution of microstructure in magneto-active elastomers (MAEs) which can be caused by an applied magnetic field is a fascinating phenomenon with a significant impact on the mechanical behavior of the composite. To gain insight into the underlying mechanisms of this phenomenon, it is essential to create a model that can appropriately describe the field induced change in the particle distribution and its mechanical implications. The magneto-mechanical coupling is driven by magnetic interactions between the particles in the applied field. These magnetic interactions can result in macroscopic deformation of the sample and also in rearrangement of the microstructure, i.e. the local positions of the particles. In the case of initially isotropic MAEs made with a sufficiently soft matrix, this leads to the formation of chains of magnetized particles, creating a significant increase in the mechanical moduli along the field direction. In this paper, we implement a transversely isotropic Neo-Hookean material model to account for such anisotropic elastic behavior. A dipolar mean field approach is used to describe magnetic interactions between the particles. A penalty term is introduced to compensate for the micro-mechanical elastic energy required to move the particles inside the cross-linked elastomer. The resulting model can predict the huge magneto-rheological effects observed in experiments, and improves our understanding of how microstructure evolution affects magnetically induced deformation and stiffness of MAEs.

Theoretical analysis of the elastic free energy contributions to polymer brushes in poor solvent: A refined mean-field theory.

We consider polymer brushes in poor solvent that are grafted onto planar substrates and onto the internal and external surfaces of a cylinder using molecular dynamics simulation, self-consistent field (SCF), and mean-field theory. We derive a unified expression for the mean field free energy for the three geometrical classes. While for low grafting densities, the effect of chain elasticity can be neglected in poor solvent conditions, it becomes relevant at higher grafting densities and, in particular, for concave geometries. Based on the analysis of the end monomer distribution, we introduce an analytical term that describes the elasticity as a function of grafting density. The accuracy of the model is validated with molecular dynamics simulations as well as SCF computations and shown to yield precise values for the layer thickness over a wide range of system parameters. We further apply this model to analyze the gating behavior of switchable brushes inside nanochannels.

Magneto-Mechanical Enhancement of Elastic Moduli in Magnetoactive Elastomers with Anisotropic Microstructures.

Magnetoactive elastomers (MAEs) have gained significant attention in recent years due to their wide range of engineering applications. This paper investigates the important interplay between the particle microstructure and the sample shape of MAEs. A simple analytical expression is derived based on geometrical arguments to describe the particle distribution inside MAEs. In particular, smeared microstructures are considered instead of a discrete particle distribution. As a consequence of considering structured particle arrangements, the elastic free energy is anisotropic. It is formulated with the help of the rule of mixtures. We show that the enhancement of elastic moduli arises not only from the induced dipole-dipole interactions in the presence of an external magnetic field but also considerably from the change in the particle microstructure.

Field-Induced Transversely Isotropic Shear Response of Ellipsoidal Magnetoactive Elastomers.

Magnetoactive elastomers (MAEs) claim a vital place in the class of field-controllable materials due to their tunable stiffness and the ability to change their macroscopic shape in the presence of an external magnetic field. In the present work, three principal geometries of shear deformation were investigated with respect to the applied magnetic field. The physical model that considers dipole-dipole interactions between magnetized particles was used to study the stress-strain behavior of ellipsoidal MAEs. The magneto-rheological effect for different shapes of the MAE sample ranging from disc-like (highly oblate) to rod-like (highly prolate) samples was investigated along and transverse to the field direction. The rotation of the MAE during the shear deformation leads to a non-symmetric Cauchy stress tensor due to a field-induced magnetic torque. We show that the external magnetic field induces a mechanical anisotropy along the field direction by determining the distinct magneto-mechanical behavior of MAEs with respect to the orientation of the magnetic field to shear deformation.

A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers.

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r-3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka's toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Magneto-Mechanical Coupling in Magneto-Active Elastomers.

In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle-interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures.

Giant Extensional Strain of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields.

Elongations of magnetoactive elastomers (MAEs) under ascending-descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics.

Effects of local rearrangement of magnetic particles on deformation in magneto-sensitive elastomers.

Based on the dipole-dipole approach for magnetic interactions we present a comprehensive analysis of spatial rearrangement of magnetic particles under a magnetic field and its effect on the magneto-induced deformation of magneto-sensitive elastomers. The presented formalism allows analyzing non-affine displacements of magnetic particles in a general way and reveals how the local rearrangement of particles under a magnetic field affects the magneto-induced deformation. The formalism includes two contributions: (1) displacements due to elastic coupling with a deformed matrix and (2) rearrangements on the background of the deformed matrix due to magnetic interactions between the particles. We show that in the linear response regime the sign of deformation is defined by the first contribution and the second one amplifies the magnitude of deformation. The sign and magnitude of deformation depend on the factors cos2 θ and cos4 θ, where averaging is over mutual pairs of particles and θ is the angle between the vector connecting the particles and the direction of the magnetic field. We test the new formalism on isotropic-like lattice distributions with cos2 θ = 1/3 and show that the difference in the sign of their deformation is defined by the difference in the factor cos4 θ. The results are compared for 3-dimensional and 2-dimensional systems, which are shown to have a similar behavior as a function of the aspect ratio of a sample.

Impact of Bioactive Peptide Motifs on Molecular Structure, Charging, and Nonfouling Properties of Poly(ethylene oxide) Brushes.

Polymer layers capable of suppressing protein adsorption from biological media while presenting extracellular matrix-derived peptide motifs offer valuable new options for biomimetic surface engineering. Herein, we provide detailed insights into physicochemical changes induced in a nonfouling poly(ethylene oxide) (PEO) brush/polydopamine (PDA) system by incorporation of adhesion ligand (RGD) peptides. Brushes with high surface chain densities (σ ≥ 0.5 chains·nm-2) and pronounced hydrophilicity (water contact angles ≤ 10°) were prepared by end-tethering of heterobifunctional PEOs ( Mn ≈ 20 000 g·mol-1) to PDA-modified surfaces from a reactive melt. Using alkyne distal end group on the PEO chains, azidopentanoic-bearing peptides were coupled through a copper-catalyzed Huisgen azide-alkyne "click" cycloaddition reaction. The surface concentration of RGD was tuned from complete saturation of the PEO surface with peptides (1.7 × 105 fmol·cm-2) to values which may induce distinct differences in cell adhesion (<6.0 × 102 fmol·cm-2). Infrared reflection-absorption and X-ray photoelectron spectroscopies proved the PDA-PEO layers covalent structure and the immobilization of RGD peptides. The complete reconstruction of experimental electrohydrodynamics data utilizing mean-field theory predictions further verified the attained brush structure of the end-tethered PEO chains which provided hydrodynamic screening of the PDA anchor. Increasing the surface concentration of immobilized RGD peptides led to increased interfacial charging. Supported by simulations, this observation was attributed to the ionization of functional groups in the amino acid sequence and to the pH-dependent adsorption of water ions (OH- > H3O+) from the electrolyte. Despite the distinct differences observed in the electrokinetic analysis of the surfaces bearing different amounts of RGD, it was found that the peptide presence on PEO(20 000)-PDA layers does not have a significant effect on the nonfouling properties of the system. Notably, the presented PEO(20 000)-PDA layers bearing RGD peptides in the surface concentration range 5.9 to 1.7 × 105 fmol·cm-2 reduced the protein adsorption from fetal bovine serum to less than 30 ng·cm-2, that is, values comparable to the ones obtained for pristine PEO(20 000)-PDA layers.

Theoretical models for magneto-sensitive elastomers: A comparison between continuum and dipole approaches.

In the literature, different theoretical models have been proposed to describe the properties of systems which consist of magnetizable particles that are embedded into an elastomer matrix. It is well known that such magneto-sensitive elastomers display a strong magneto-mechanical coupling when subjected to an external magnetic field. Nevertheless, the predictions of available models often vary significantly since they are based on different assumptions and approximations. Up to now the actual accuracy and the limits of applicability are widely unknown. In the present work, we compare the results of a microscale continuum and a dipolar mean field approach with regard to their predictions for the magnetostrictive response of magneto-sensitive elastomers and reveal some fundamental relations between the relevant quantities in both theories. It turns out that there is a very good agreement between both modeling strategies, especially for entirely random microstructures. In contrast, a comparison of the finite-element results with a modified approach, which-similar to the continuum model-is based on calculations with discrete particle distributions, reveals clear deviations. Our systematic analysis of the differences shows to what extent the dipolar mean field approach is superior to other dipole models.

Elongated micro-structures in magneto-sensitive elastomers: a dipolar mean field model.

Based on a dipole model for the mutual magnetic interactions among the magnetizable micro-particles in magneto-sensitive elastomers we develop a mean field approach to describe the arrangement of these particles into elongated micro-structures. If these micro-structures are oriented parallel to an external magnetic field the present approach provides an efficient calculation of the behavior of such samples, which is a result of the interplay between micro-structure and shape effects. Accordingly, we are able to draw comprehensive phase diagrams for the resultant deformation and predict for very oblate samples a discontinuous shape change in the presence of a homogeneous external field.

Binary and Bidisperse Polymer Brushes: Coexisting Surface States.

In the present work, we consider polydispersity effects on a mixed polymer brush. Two types of polymer chains with different solvent selectivity being densely grafted together onto an impenetrable surface are forming a binary mixed polymer brush. Using a numerical quasi off-lattice self-consistent field method for heterogeneous chains we study the brush profile upon varying the strength of solvent selectivity (e.g., temperature) and the degree of polymerization of the two chain types (N1 and N2, respectively). For a monodisperse brush (N1 = N2) it is well-known, that the two types of polymers segregate into a two-layer structure, if the difference in solvent selectivity is increased. The state where the chains exposed to their good solvent forming the top layer of the brush can be frustrated for shorter chains and an inversion of the layering takes place. In the inverted state, the top layer is formed by long chains exposed to poor solvent covering the layer of shorter chains. By varying the solvent selectivity of the long chains we show that coexistence of the two states occurs,which indicates a discontinuous phase transition scenario for the switching process. We consider further the case of a very low fraction of short chains and find these chains to undergo a conformational transition of first order from a "coil" state, found deep inside the compact brush layer, to a "flower" state, stretching to the top of the brush upon varying the strength of the solvent selectivity. At the transition both states are found to be quasi-stable with an energy barrier of the order of the chain length in units of kBT. The discontinuous nature of the switching process by combining solvent selectivity and bidispersity can be of high interest for the creation of stimuli-responsive surfaces.

Excluded volume effects in polymer brushes at moderate chain stretching.

We develop a strong stretching approximation for a polymer brush made of self-avoiding polymer chains. The density profile of the brush and the distribution of the end monomer positions in stretching direction are computed and compared with simulation data. We find that our approach leads to a clearly better approximation as compared to previous approaches based upon Gaussian elasticity at low grafting densities (moderate chain stretching), for which corrections due to finite extensibility can be ignored.

Electrokinetics as an alternative to neutron reflectivity for evaluation of segment density distribution in PEO brushes.

Unravelling details of charge, structure and molecular interactions of functional polymer coatings defines an important analytical challenge that requires the extension of current methodologies. In this article we demonstrate how streaming current measurements interpreted with combined self consistent field (SCF) and soft surface electrokinetic theories allow the evaluation of the segment distribution within poly(ethylene oxide) (PEO) brushes beyond the resolution limits of neutron reflectivity technique.