New insights into the nature of semi-soft elasticity and “mechanical-Fréedericksz transitions” in liquid crystal elastomers

The mechanical properties of an all-acrylate Liquid Crystal Elastomer (LCE) with a glass transition of 14±1°C are reported. The highly nonlinear load curve has a characteristic shape associated with semi-soft elasticity (SSE). Conversely, measurements of the director orientation throughout tensile loading instead indicate a “mechanical-Fréedericksz” transition (MFT). Values of the step length anisotropy, r, are independently calculated from the theories of SSE (r= 3.2±0.4), MFT (9.3<r<30.0) and thermally-induced length change (r=3.8±0.5). From simultaneously recorded polarising microscopy textures, the consequences of the above discrepancies are considered. Further, a mechanically-induced negative order parameter is observed. Results show the tensile load curve shape cannot solely be used to determine the underlying physics. Consequently, the LCE properties cannot be fully described by theories of SSE or MFTs alone. This suggests that the theory of LCEs is not yet complete. The conclusions suggest that both the LC order parameter and r must be functions of the mechanical deformation

Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory

Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the non-equilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance namely a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.Comment: 14 pages, 2 figures, to appear in PR

Soft elasticity in biaxial smectic and smectic-C elastomers

Ideal (monodomain) smectic-$A$ elastomers crosslinked in the smectic-$A$ phase are simply uniaxial rubbers, provided deformations are small. From these materials smectic-$C$ elastomers are produced by a cooling through the smectic-$A$ to smectic-$C$ phase transition. At least in principle, biaxial smectic elastomers could also be produced via cooling from the smectic-$A$ to a biaxial smectic phase. These phase transitions, respectively from $D_{\infty h}$ to $C_{2h}$ and from $D_{\infty h}$ to $D_{2h}$ symmetry, spontaneously break the rotational symmetry in the smectic planes. We study the above transitions and the elasticity of the smectic-$C$ and biaxial phases in three different but related models: Landau-like phenomenological models as functions of the Cauchy--Saint-Laurent strain tensor for both the biaxial and the smectic-$C$ phases and a detailed model, including contributions from the elastic network, smectic layer compression, and smectic-$C$ tilt for the smectic-$C$ phase as a function of both strain and the $c$-director. We show that the emergent phases exhibit soft elasticity characterized by the vanishing of certain elastic moduli. We analyze in some detail the role of spontaneous symmetry breaking as the origin of soft elasticity and we discuss different manifestations of softness like the absence of restoring forces under certain shears and extensional strains.Comment: 26 pages, 6 figure

Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth

An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding wave number for any combination of thickness and viscosity of the fluid. Applying this method to magnetic fluids of finite depth, these results are quantitatively compared to the wave number of the transient pattern observed experimentally after a jump--like increase of the field. The wave number grows linearly with increasing induction where the theoretical and the experimental data agree well. Thereby a long-standing controversy about the behaviour of the wave number above the critical magnetic field is tackled.Comment: 19 pages, 15 figures, RevTex; revised version with a new figure and references added. submitted to Phys Rev

The Amplitude Equation for the Rosensweig Instability in Magnetic Fluids and Gels

The Rosensweig instability has a special character among the frequently discussed instabilities. One distinct property is the necessary presence of a deformable surface, and another very important fact is, that the driving force acts purely via the surface and shows no bulk effect. These properties make it rather difficult to give a correct weakly nonlinear analysis. In this paper we give a detailed derivation of the appropriate amplitude equation based on the hydrodynamic equations emphasizing the conceptually new procedures necessary to deal with the distinct properties mentioned above. First the deformable surface requires a fully dynamic treatment of the instability and the observed stationary case can be interpreted as the limiting case of a frozen-in characteristic mode. Second, the fact that the driving force is manifest in the boundary conditions, only, requires a considerable change in the formalism of weakly nonlinear bifurcation theory. To obtain the amplitude equations a combination of solubility conditions and (normal stress) boundary conditions has to be invoked in all orders of the expansions.Comment: 46 pages; 4 figure

Vergleich der Kosten der Beschaeftigung von Angestellten und Beamten: Untersuchung fuer das Senatsamt fuer den Verwaltungsdienst der Freien und Hansestadt Hamburg

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Competition between the Bénard-Marangoni and the Rosensweig Instability in Magnetic Fluids

The linear stability analysis of a layer of magnetic fluid with deformable free surface, which is heated from below and exposed to a uniform, vertically applied magnetic field is presented. In this configuration the temperature dependence of the surface tension, the buoyancy and the focusing of the magnetic field due to surface fluctuations act as destabilising effects. We show that this system has for thin layers a stationary codimension–2–point, which can be reached for experimentally relevant values of the material parameters. We also analyse the transition from thin to thicker layers for which there is no codimension–2–point and we show how the codimension–2–point disappears. Finally we demonstrate that there is no oscillatory instability in the regions of parameter space considered here