Elastic deformations in semi-dilute Ni nanorod/hydrogel composites

Schopphoven, Christoph; Birster, Kerstin; Schweitzer, Rouven; Lux, Christian; Huang, Shilin; Kästner, Markus; Auernhammer, Günter K.; Tschöpe, Andreas

doi:10.1007/s00419-018-1461-z

Cited by 12 publications

(11 citation statements)

References 44 publications

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“…Rigid particles introduce a geometric confinement to lateral motion of polymer chains in addition to molecular entanglement . Long-time relaxation is determined by the faster of two processes, reptation with disengagement time constant τ d or constraint release by particle diffusion with time constant τ p . , In PNCs, particle-induced confinement increases the plateau modulus at particle volume fractions of several percent. ,, In the present study, measurements were performed at ϕ vol ≈ 10 –6 so that the nanorods are isolated without interference of their deformation zones . In this dilute limit, the mechanical properties of the local deformation zone, deduced from the motion of probe particles, are independent of particle concentration.…”

Section: Resultsmentioning

confidence: 91%

“…The hydrodynamic length L h of the nanorods determines the spatial range of the polymer solution that is probed by the rotation of a nanorod, as shown for instance by recent FEM simulations on elastic particle−particle interaction. 91 If the interaction zone is characterized by a length λ ≈ L, the scaling relation essentially reflects the share of the region of decreased entanglement density on the deformation zone (Figure 10). The narrow deformation zone of short nanorods captures mainly the close vicinity of the particles dominated by entanglement reduction with a spatial extent of approximately R g .…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…3,4,94 In the present study, measurements were performed at ϕ vol ≈ 10 −6 so that the nanorods are isolated without interference of their deformation zones. 91 In this dilute limit, the mechanical properties of the local deformation zone, deduced from the motion of probe particles, are independent of particle concentration. In all measurements, the nanoviscosities were lower than the macroscopic viscosities of the polymer solutions.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

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Size Effects in the Oscillatory Rotation Dynamics of Ni Nanorods in Poly(ethylene oxide) Solutions

Gratz

Tschöpe

2019

Macromolecules

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The rotation of Ni nanorods, dispersed in dilute and semidilute poly(ethylene oxide) solutions, is investigated. Ni nanorods with similar diameter but different lengths are synthesized using the anodic aluminum oxide template method and characterized by transmission electron microscopy and static magnetic field-dependent optical transmission (SFOT) of linearly polarized light. The rotational motion of nanorods, determined by oscillating magnetic field-dependent optical transmission (OFOT) measurements, is analyzed to retrieve the local dynamic modulus of the polymer solution. The effect of probe size relative to intrinsic length scales of the polymer solution is systematically investigated by variation of the nanorod size, polymer molar mass, and concentration. A significant decrease in the zero-shear rate viscosity is observed in the semidilute entangled regime, which depends on the hydrodynamic length of the nanorods, L h, and polymer radius of gyration, R g, but not on PEO concentration. The relative viscosity can be approximated by η 0 OFOT/η 0 macro = exp ( – 5.6R g/L h). The macroscopic dynamic modulus of the entangled polymer solutions is measured by small-amplitude oscillatory shear. The local dynamic modulus, obtained from nanorod oscillation measurements, exhibits systematic changes with decreasing size of the probe particles, which indicate entanglement reduction as the physical origin of the size effect in this particular particle/polymer system.

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Section: Resultsmentioning

confidence: 91%

Section: ■ Results and Discussionmentioning

confidence: 99%

Section: ■ Results and Discussionmentioning

confidence: 99%

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Size Effects in the Oscillatory Rotation Dynamics of Ni Nanorods in Poly(ethylene oxide) Solutions

Gratz

Tschöpe

2019

Macromolecules

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“…A lot of effort has been spent over the past decades to calculate and quantify such mutual interactions. This concerns both elastic solids [12][13][14][15][16] and viscous fluids [5,[17][18][19] as surrounding media, where in the latter context a focus is on incompressible liquids subject to low-Reynolds-number flows. To be able to perform analytical calculations, a major focus was on bulk states far away from any boundaries and rigid spherical inclusions experiencing no-slip conditions for the surrounding medium on their surfaces.…”

Section: Introductionmentioning

confidence: 99%

Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films

Richter,

Menzel

2021

Preprint

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Interactions between rigid inclusions in continuous three-dimensional linearly elastic solids and low-Reynolds-number viscous fluids have largely been quantified during the past. Prime example systems are given by functionalized elastic composite materials or fluid colloidal suspensions. Here, we address the significantly less frequently studied situation of rigid inclusions in two-dimensional elastic or low-Reynolds-number fluid films. We concentrate on the situation in which disk-like inclusions remain well separated from each other and do not get into contact. Specifically, we demonstrate and explain that the logarithmic divergence of the associated Green's function is lifted in the absence of net external forces on the inclusions, in line with physical intuition. For instance, this situation applies when only pairwise mutual interactions between the inclusions prevail. Our results will support, for example, investigations on membranes functionalized by appropriate inclusions, both of technical or biological origin, or the dynamics of active microswimmers in appropriately prepared thin films.

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“…It is well established that the local elasticity theory cannot be adopted to capture mechanical responses of nano-continua, and consequently, a variety of size-dependent elasticity models are available in literature. Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

et al. 2019

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Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.In the present study, it is proven that HOBC have to be replaced with univocally determined boundary conditions of constitutive type, established by a consistent variational formulation.The treatment, developed in the framework of torsion of elastic beams, provides an effective approach to evaluate scale phenomena in smaller and smaller devices of engineering interest.Both elastostatic torsional responses and torsional free vibrations of nano-beams are investigated by applying a simple analytical method. It is also underlined that the nonlocal strain gradient model, if equipped with the inappropriate HOBC, can lead to torsional structural responses which unacceptably do not exhibit nonlocality. The presented variational strategy is instead able to characterize significantly peculiar softening and stiffening behaviours of structures involved in modern Nano-Electro-Mechanical-Systems (NEMS). KeywordsTorsion; nano-beams; nonlocal strain gradient model; strain gradient elasticity; integral elasticity; size effects; analytical modelling; NEMS. d J J dx J J dx J

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Elastic deformations in semi-dilute Ni nanorod/hydrogel composites

Cited by 12 publications

References 44 publications

Size Effects in the Oscillatory Rotation Dynamics of Ni Nanorods in Poly(ethylene oxide) Solutions

Size Effects in the Oscillatory Rotation Dynamics of Ni Nanorods in Poly(ethylene oxide) Solutions

Mediated interactions between rigid inclusions in two-dimensional elastic or fluid films

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

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