Shear- free perfect fluids with solenoidal magnetic curvature and a γ-law equation of state

We show that shear-free perfect fluids obeying an equation of state p = (γ − 1)μ are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.

Structural characterization of conducting polypyrrole using 13C cross-polarization/magic-angle spinning solid-state nuclear magnetic resonance spectroscopy

¹³C nuclear magnetic resonance (n.m.r.) has been used to study polypyrrole and N-substituted polypyrrole in the solid state. The extent of oxidation appears to be counterion-dependent; in particular, the quinoid structure appears favoured in the films prepared with dodecyl sulfate. Resonances associated with the quinoid unit are lost upon reduction of the polypyrrole film, which supports the idea that the quinoid structure is associated with the oxidized form of polypyrrole. N-substituted polypyrroles have a more distinct resonance at 110 ppm, which is linked to lower degrees of oxidation or charge delocalization in these systems. The decrease in conductivity of polypyrrole upon thermal ageing in air is associated with both the loss of counterion (‘thermal dedoping’) and the decomposition of the quinoid structure in the polymer backbone. There is no indication of carbonyl formation in the solid-state n.m.r. spectra obtained in the present study.

Probing ion exchange in the triflic acid-guanidinium triflate system: a solid-state nuclear magnetic resonance study

Knowledge of ion exchange and transport behavior in electrolyte materials is crucial for designing and developing novel electrolytes for electrochemical device applications such as fuel cells or batteries. In the present study, we show that, upon the addition of triflic acid (HTf) to the guanidinium triflate (GTf) solid-state matrix, several orders of magnitude enhancement in the proton conductivity can be achieved. The static 1H and 19F solid-state NMR results show that the addition of HTf has no apparent effect on local molecular mobility of the GTf matrix at room temperature. At higher temperatures, however, the HTf exhibits fast ion exchange with the GTf matrix. The exchange rate, as quantified by our continuum T2 fitting analysis, increases with increasing temperature. The activation energy for the chemical exchange process was estimated to be 58.4 kJ/mol. It is anticipated that the solid-state NMR techniques used in this study may be also applied to other organic solid-state electrolyte systems to investigate their ion-exchange processes.

Sodium ion dynamics in a sulfonate based ionomer system studied by 23Na solid-state nuclear magnetic resonance and impedance spectroscopy

A poly(2-acrylamido-2-methyl-1-propane-sulphonate) (PAMPS) ionomer containing both sodium and quaternary ammonium cations functionalised with an ether group, has been characterised in terms of its thermal properties, ionic conductivity and sodium ion dynamics. The ether oxygen was incorporated to reduce the Na+ association with the anionic sulfonate groups tethered to the polymer backbone, thereby promoting ion dissociation and ultimately enhancing the ionic conductivity. This functionalised ammonium cation led to a significant reduction in the ionomer Tg compared to an analogue system without an ether group, resulting in an increase in ionic conductivity of approximately four orders of magnitude. The sodium ion dynamics were probed by 23Na solid-state NMR, which allowed the signals from the dissociated (mobile) and bound Na+ cations to be distinguished. This demonstrates the utility of 23Na solid-state NMR as a probe of sodium dynamics in ionomer systems.

Shear-free perfect fluids with a solenoidal magnetic curvature

We investigate shear-free perfect fluid solutions of the Einstein field equations where the fluid pressure satisfies a barotropic equation of state and the spatial divergence of the magnetic part of the Weyl tensor is zero. We prove, with the exception of certain quite restricted special cases within the class of solutions in which there exists a Killing vector aligned with the vorticity and for which the magnitude of the vorticity ω is not a function of the matter density μ alone, that such a fluid is either non-rotating or non-expanding. In the restricted cases the equation of state must satisfy an over-determined differential system.

Solid state ion transport and phase behaviour in composites of N,N-methyl propylpyrrolidinium tetrafluoroborate and amorphous polyethylene oxide

The binary and ternary addition of 2 wt.% LiBF₄ and 2 wt.% amorphous polyethylene oxide (aPEO) respectively to the plastic crystal forming salt P₁₃BF₄ (where P₁₃⁺=methylpropyl pyrrolidinium cation) was investigated with specific focus on the phase behaviour and evaluation of transport characteristics. Differential scanning calorimetry (DSC), optical thermomicroscopy, solid state nuclear magnetic resonance (NMR), and AC impedance spectroscopy were used to develop an understanding of the conduction process in the pure and mixed systems. The morphology of the ternary compound appeared as hexagonal spherulites upon solidification. Multinuclear NMR Pulsed Field Gradient measurements (¹H,¹⁹F,⁷Li) to probe both cation and anion diffusion coefficients are reported. The anion is shown to be the most diffusive (at 320 K:¹⁹F=2.5×10⁻¹¹ m² s⁻¹; 1H: 1.8×10⁻¹¹ m² s⁻¹; ⁷Li: 1.1×10⁻¹¹ m² s⁻¹) in the ternary compound, with enhanced conductivity (2.7×10⁻⁵ S cm⁻¹ at 310 K) just below the melt.

Plastic crystal electrolyte materials : new perspectives on solid state ionics

Plastic crystal materials have long been known but have only relatively recently become of interest as solid–state ion conductors. Their properties are often associated with dynamic orientational disorder or rotator motions in the crystalline lattice. This paper describes recent work in the field including the range of organic ionic compounds that exhibit ion conduction at room temperature. Conductivity in some cases is high enough to render the compounds of interest as electrolyte materials in all solid state electrochemical devices. Doping of the plastic crystal phase with a small ion such as Li+ in some cases produces an even higher conductivity. In this case the plastic crystal acts as a solid state “solvent” for the doped ion and supports the conductive motion of the dopant via motions of the matrix ions. These doped materials are also described in detail.

Solid state NMR analysis of polypyrrole grown in a phosphonium ionic liquid

³¹P, ¹⁹F and ¹³C solid state NMR analysis has been used to investigate the intercalation/de-intercalation of both anions and cations in electrochemically synthesized polypyrrole films. Use of a phosphonium-based ionic liquid, tri(hexyl)(tetradecyl)phosphonium bis(trifluoromethanesulfonyl)amide, allows the separate detection of the cation and anion by analysis of the phosphorous and fluorine resonances, respectively. Initial results indicate the incorporation of both cations and anions during film growth in the ionic liquid. There is a notable change in the ³¹P chemical shift of the cation on incorporation into the film, consistent with a significant change in environment compared to the pure ionic liquid. Despite its large size, the phosphonium cation can be completely expelled from the film by oxidation.

Insight into local structure and molecular dynamics in organic solid-state ionic conductors

Elucidating the rate and geometry of molecular dynamics is particularly important for unravelling ion-conduction mechanisms in electrochemical materials. The local molecular motions in the plastic crystal 1-ethyl-1-methylpyrrolidinium tetrafluoroborate ([C2 mpyr][BF4 ]) are studied by a combination of quantum chemical calculations and advanced solid-state nuclear magnetic resonance spectroscopy. For the first time, a restricted puckering motion with a small fluctuation angle of 25° in the pyrrolidinium ring has been observed, even in the low-temperature phase (-45 °C). This local molecular motion is deemed to be particularly important for the material to maintain its plasticity, and hence, its ion mobility at low temperatures.

New insights into the thermal behaviour of organic ionic plastic crystals: magnetic resonance imaging of polycrystalline morphology alterations induced by solid-solid phase transitions

Organic ionic plastic crystals (OIPCs) show strong potential as solid-state electrolytes for lithium battery applications, demonstrating promising electrochemical performance and eliminating the need for a volatile and flammable liquid electrolyte. The ionic conductivity (σ) in these systems has recently been shown to depend strongly on polycrystalline morphology, which is largely determined by the sample's thermal history. [K. Romanenko et al., J. Am. Chem. Soc., 2014, 136, 15638]. Tailoring this morphology could lead to conductivities sufficiently high for battery applications, so a more complete understanding of how phenomena such as solid-solid phase transitions can affect the sample morphology is of significant interest. Anisotropic relaxation of nuclear spin magnetisation provides a new MRI based approach for studies of polycrystalline materials at both a macroscopic and molecular level. In this contribution, morphology alterations induced by solid-solid phase transitions in triisobutyl(methyl)phosphonium bis(fluorosulfonyl)imide (P1444FSI) and diethyl(methyl)(isobutyl)phosphonium hexafluorophosphate (P1224PF6) are examined using magnetic resonance imaging (MRI), alongside nuclear magnetic resonance (NMR) spectroscopy, diffusion measurements and conductivity data. These observations are linked to molecular dynamics and structural behaviour crucial for the conductive properties of OIPCs. A distinct correlation is established between the conductivity at a given temperature, σ(T), and the intensity of the narrow NMR signal that is attributed to a mobile fraction, fm(T), of ions in the OIPC. To explain these findings we propose an analogy with the well-studied relationship between permeability (k) and void fraction (θ) in porous media, with k(θ) commonly quantified by a power-law dependence that can also be employed to describe σ(fm).

Atom probe tomography investigation of heterogeneous short-range ordering in the 'komplex' phase state (K-state) of Fe-18Al (at.%)

We study an Fe-18Al (at.%) alloy after various thermal treatments at different times (24-336 h) and temperatures (250-1100 °C) to determine the nature of the so-called 'komplex' phase state (or "K-state"), which is common to other alloy systems having compositions at the boundaries of known order-disorder transitions and is characterised by heterogeneous short-range-ordering (SRO). This has been done by direct observation using atom probe tomography (APT), which reveals that nano-sized, ordered regions/particles do not exist. Also, by employing shell-based analysis of the three-dimensional atomic positions, we have determined chemically sensitive, generalised multicomponent short-range order (GM-SRO) parameters, which are compared with published pairwise SRO parameters derived from bulk, volume-averaged measurement techniques (e.g. X-ray and neutron scattering, Mössbauer spectroscopy) and combined ab-initio and Monte Carlo simulations. This analysis procedure has general relevance for other alloy systems where quantitative chemical-structure evaluation of local atomic environments is required to understand ordering and partial ordering phenomena that affect physical and mechanical properties.

Regional homogeneity of resting-state brain abnormalities in violent juvenile offenders: A biomarker of brain immaturity?

The authors investigated whether male violent juvenile offenders demonstrate any differences in local functional connectivity indicative of delayed maturation of the brain that may serve as a biomarker of violence. Twenty-nine violent juvenile offenders and 28 age-matched controls were recruited. Regional homogeneity (ReHo) method was used to analyze resting-state magnetic resonance images. Violent offenders showed significantly lower ReHo values in the right caudate, right medial prefrontal cortex, and left precuneus, and higher values in the right supramarginal gyrus than the controls. These regions had both high sensitivity and specificity in distinguishing between the two groups suggesting that dysfunction in these regions can be used to correctly classify those individuals who are violent. Dysfunction in the right medial prefrontal-caudate circuit may, therefore, represent an important biomarker of violence juvenile males.