Response of thin-film SQUIDs to applied fields and vortex fields: Linear SQUIDs

In this paper we analyze the properties of a dc SQUID when the London penetration depth \lambda is larger than the superconducting film thickness d. We present equations that govern the static behavior for arbitrary values of \Lambda = \lambda^2/d relative to the linear dimensions of the SQUID. The SQUID's critical current I_c depends upon the effective flux \Phi, the magnetic flux through a contour surrounding the central hole plus a term proportional to the line integral of the current density around this contour. While it is well known that the SQUID inductance depends upon \Lambda, we show here that the focusing of magnetic flux from applied fields and vortex-generated fields into the central hole of the SQUID also depends upon \Lambda. We apply this formalism to the simplest case of a linear SQUID of width 2w, consisting of a coplanar pair of long superconducting strips of separation 2a, connected by two small Josephson junctions to a superconducting current-input lead at one end and by a superconducting lead at the other end. The central region of this SQUID shares many properties with a superconducting coplanar stripline. We calculate magnetic-field and current-density profiles, the inductance (including both geometric and kinetic inductances), magnetic moments, and the effective area as a function of \Lambda/w and a/w.Comment: 18 pages, 20 figures, revised for Phys. Rev. B, the main revisions being to denote the effective flux by \Phi rather than

Self-Healing Polyphosphonium Ionic Networks

Self healing, ionically crosslinked networks were prepared from poly(acrylic acid) (PAA) and poly(triethyl(4-vinylbenzyl)phosphonium chloride (P-Et-P) and their properties were studied. Three different ratios of PAA/P-Et-P were incorporated into the networks by varying the addition orders of the components. Swelling of the networks increased with increasing NaCl concentration when they were immersed in aqueous solution. All networks retained their structural integrity in 0.1 M NaCl. Studies of the rheological and tensile properties of the networks swelled in 0.1 M NaCl showed that PAA\u3eP-Et-Pexhibited high elongation and viscoelastic properties suitable for self-healing with a relaxation time of ~30 s, whereas the other networks exhibited predominantly elastic behavior. The moduli were similar to those of soft tissues. Self-healing of PAA\u3eP-Et-Pin 0.1 M NaCl was demonstrated through repair of a 0.5 mm diameter puncture in the material whereas healing was incomplete for the other networks and also for PAA\u3eP-Et-Pin the absence of NaCl. Healing after completely severing a tensile testing sample showed significant recovery of the modulus, strength, and elongation. The properties of these materials and their ability to self-heal in low and physiologically relevant salt concentrations make them promising candidates for a variety of applications, particularly in the biomedical area

Phosphonium Polyelectrolyte Complexes for the Encapsulation and Slow Release of Ionic Cargo

© 2019 American Chemical Society. Polyelectrolyte complexation, the combination of anionically and cationically charged polymers through ionic interactions, can be used to form hydrogel networks. These networks can be used to encapsulate and release cargo, but the release of cargo is typically rapid, occurring over a period of hours to a few days and they often exhibit weak, fluid-like mechanical properties. Here we report the preparation and study of polyelectrolyte complexes (PECs) from sodium hyaluronate (HA) and poly[tris(hydroxypropyl)(4-vinylbenzyl)phosphonium chloride], poly[triphenyl(4-vinylbenzyl)phosphonium chloride], poly[tri(n-butyl)(4-vinylbenzyl)phosphonium chloride], or poly[triethyl(4-vinylbenzyl)phosphonium chloride]. The networks were compacted by ultracentrifugation, then their composition, swelling, rheological, and self-healing properties were studied. Their properties depended on the structure of the phosphonium polymer and the salt concentration, but in general, they exhibited predominantly gel-like behavior with relaxation times greater than 40 s and self-healing over 2-18 h. Anionic molecules, including fluorescein, diclofenac, and adenosine-5′-triphosphate, were encapsulated into the PECs with high loading capacities of up to 16 wt %. Fluorescein and diclofenac were slowly released over 60 days, which was attributed to a combination of hydrophobic and ionic interactions with the dense PEC network. The cytotoxicities of the polymers and their corresponding networks with HA to C2C12 mouse myoblast cells was investigated and found to depend on the structure of the polymer and the properties of the network. Overall, this work demonstrates the utility of polyphosphonium-HA networks for the loading and slow release of ionic drugs and that their physical and biological properties can be readily tuned according to the structure of the phosphonium polymer

Early stages of ramified growth in quasi-two-dimensional electrochemical deposition

I have measured the early stages of the growth of branched metal aggregates formed by electrochemical deposition in very thin layers. The growth rate of spatial Fourier modes is described qualitatively by the results of a linear stability analysis [D.P. Barkey, R.H. Muller, and C.W. Tobias, J. Electrochem. Soc. {\bf 136}, 2207 (1989)]. The maximum growth rate is proportional to $(I/c)^\delta$ where $I$ is the current through the electrochemical cell, $c$ the electrolyte concentration, and $\delta = 1.37 \pm 0.08$. Differences between my results and the theoretical predictions suggest that electroconvection in the electrolyte has a large influence on the instability leading to ramified growth.Comment: REVTeX, four ps figure

Rheology of the Electric Double Layer in Electrolyte Solutions

Electric double layers (EDLs) are ionic structures formed on charged surfaces and play an important role in various biological and industrial processes. An extensive study in the past decade has revealed the structure of the EDL in concentrated electrolyte solutions of both ordinary salts and ionic liquids. However, how the EDL structure affects their material properties remains a challenging topic due to technical difficulties of these measurements at nanoscale. In this work, we report the first detailed characterization of the viscoelasticity of the EDL formed over a wide range of ion concentrations, including concentrated electrolyte solutions. Specifically, we investigate the complex shear modulus of the EDL by measuring the resonant frequency and the energy dissipation of a quartz crystal microbalance (QCM), a surface-sensitive device, immersed in aqueous solutions containing three types of solutes: an ionic liquid, 1-butyl-3-methylimidazolium chloride (BmimCl); an ordinary salt, sodium chloride (NaCl); and a nonelectrolyte, ethylene glycol (EG). For the two electrolyte solutions, we observe a monotonic decrease in the resonant frequency and a monotonic increase in the energy dissipation with increasing ion concentrations due to the presence of the EDL. The complex shear modulus of the EDL is estimated through a wave propagation model in which the density and shear modulus of the EDL decay exponentially toward those of the bulk solution. Our results show that both the storage and the loss modulus of the EDL increase rapidly with increasing ion concentrations in the low ion concentration regime (<1 M) but reach saturation values with similar magnitude at a sufficiently high ion concentration. The shear viscosity of the EDL near the charged QCM surface is approximately 50 times for NaCl solutions and 500 times for BmimCl solutions of the bulk solution value at the saturation concentration. We also demonstrate that QCM can be utilized for analyzing the rheological properties of the EDL, thus providing a complementary, low-cost, and portable alternative to conventional laboratory instruments such as the surface force apparatus. Our results elucidate new perspectives on the viscoelastic properties of the EDL and can potentially guide device optimization for applications such as biosensing and fast charging of batteries

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c

Early Radio and X-Ray Observations of the Youngest Nearby Type Ia Supernova PTF 11kly (SN 2011fe)

On 2011 August 24 (UT) the Palomar Transient Factory (PTF) discovered PTF11kly (SN 2011fe), the youngest and most nearby Type Ia supernova (SN Ia) in decades. We followed this event up in the radio (centimeter and millimeter bands) and X-ray bands, starting about a day after the estimated explosion time.We present our analysis of the radio and X-ray observations, yielding the tightest constraints yet placed on the pre-explosion mass-loss rate from the progenitor system of this supernova. We find a robust limit of Ṁ ≾ 10^(−8)(w/100 km s^(−1))M_☉ yr^(−1) from sensitive X-ray non-detections, as well as a similar limit from radio data, which depends, however, on assumptions about microphysical parameters. We discuss our results in the context of single-degenerate models for SNe Ia and find that our observations modestly disfavor symbiotic progenitor models involving a red giant donor, but cannot constrain systems accreting from main-sequence or sub-giant stars, including the popular supersoft channel. In view of the proximity of PTF11kly and the sensitivity of our prompt observations, we would have to wait for a long time (a decade or longer) in order to more meaningfully probe the circumstellar matter of SNe Ia

Development and geometry of isotropic and directional shrinkage crack patterns

We have studied shrinkage crack patterns which form when a thin layer of an alumina/water slurry dries. Both isotropic and directional drying were studied. The dynamics of the pattern formation process and the geometric properties of the isotropic crack patterns are similar to what is expected from recent models, assuming weak disorder. There is some evidence for a gradual increase in disorder as the drying layer become thinner, but no sudden transition, in contrast to what has been seen in previous experiments. The morphology of the crack patterns is influenced by drying gradients and front propagation effects, with sharp gradients having a strong orienting and ordering effect.Comment: 8 pages, 11 figures, 8 in jpg format, 3 in postscript. See also http://mobydick.physics.utoronto.ca/mud.htm