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Metamaterials with simple artificial topological properties made from industrially produced single-phase materials have extraordinary innovation and challenge. In this paper, we investigated wave propagation characteristics of a hexastarchiral lattice metamaterial with periodic assemblies and used the finite element (FE) method to study the band gap properties. Then, in order to understand the mechanism of band gaps, we discussed the mode shapes of unit cells and found that the bending of the ligament and the overall rotation have a high correlation with the generation of omnidirectional band gaps. The relationships between geometric parameters and band gap properties have also been systematically studied, which demonstrated that the band gaps of the proposed metamaterial could be reasonably predicted through the evolution of geometric parameters. Finally, the transmission characteristics of finite sandwich panel structures composed of periodic unit cells were calculated to verify the correctness of the band gap simulation results, which proved that the proposed artificial metastructure has potential application value in vibration and noise reduction projects. [ABSTRACT FROM AUTHOR]

In this work, we investigate the effective parameters of elastic metamaterial thin plates. We find that the out-of-plane rotational resonances can lead to a resonant behavior in the effective bending stiffness of metamaterial thin plates, which provides a route to tune the effective bending stiffness independently, from positive to negative values, and even infinity. By using resonant frequency analysis for metamaterial plates with different sizes, we have verified the resonant nature of the effective bending stiffness. Moreover, by designing a new type of elastic metamaterial plate with enhanced moment of inertia, we demonstrate a convenient way to tune the frequency regime of negative bending stiffness to overlap with that of negative mass density, and thus realize a band of negative group velocity. With the effective mass density and bending stiffness being independently tunable, the resonance properties of the elastic metamaterial thin plate can be engineered efficiently. Our work demonstrates a unique approach for manipulating flexural waves in elastic metamaterial thin plates.

[Display omitted] • Weak homonuclear dipolar interactions affect CPMG echo trains in SSNMR. • Small flip angles for CPMG refocusing pulses attenuate dipolar dephasing. • Measured effective coherence lifetimes (T 2 eff) can be extended. • Significant signal enhancements can be achieved with modified CPMG pulse sequences for weak homonuclear dipolar coupled systems. • These effects manifest in spectra of spin-1/2 and quadrupolar nuclei under static and MAS conditions. The Carr-Purcell/Meiboom-Gill (CPMG) pulse sequence, initially introduced for measuring transverse relaxation time constants (T 2), can provide significant signal enhancements for solid-state NMR (SSNMR) spectra. The proper implementation of CPMG for acquiring spectra influenced by chemical shift anisotropies (CSAs), first and/or second order quadrupolar interactions, or paramagnetic broadening has been well documented to date, as have the effects of heteronuclear dipolar coupling on CPMG echo trains and T 2 lifetimes. Homonuclear dipolar coupling can also impact T 2 lifetimes and CPMG echo trains; these effects have been thoroughly investigated for spectra of homonuclear dipolar coupled spin-1/2 nuclei typically acquired under static conditions that are predominantly influenced by dipolar broadening (e.g. , 1H, 19F, etc.). In particular, it has been shown that short refocusing pulses with small flip angles can extend the effective T 2 (T 2 eff, the observed T 2 constant as impacted by experimental conditions) measured by CPMG sequences for strong homonuclear dipolar coupled spin-1/2 pairs under static conditions. To date, these effects have not been explored for (i) spin-1/2 nuclei that have significant CSAs and simultaneously feature weak homonuclear dipolar couplings, (ii) for quadrupolar nuclei that are also weakly homonuclear dipolar coupled, and (iii) for either of these cases under magic-angle spinning (MAS) conditions. Herein, we demonstrate that short refocusing pulses that cause small flip angles can reduce the attenuation of signal in CPMG echo trains resulting from dipolar dephasing caused by the weak homonuclear dipolar couplings. For both spin-1/2 and quadrupolar nuclei, this can lead to significant extensions in T 2 eff and signal enhancements of up to three times compared to conventional CPMG in favourable cases. These phenomena can occur under both static and magic-angle spinning (MAS) conditions, in the latter of which homonuclear couplings are reintroduced by rotational resonance (R2) recoupling. Experimental examples of 13C (I = 1/2), 2H (I = 1), 87Rb (I = 3/2), 23Na (I = 3/2), and 35Cl (I = 3/2) NMR under static and MAS conditions, as well as simulations of these phenomena, are shown and discussed. [ABSTRACT FROM AUTHOR]

Abstract: Structural measurements in magic-angle-spinning (MAS) solid-state NMR rely heavily on 13C–13C distance measurements. Broadbanded recoupling methods are used to generate many cross-peaks, but have complex polarization transfer mechanisms that limit the precision of distance constraints and can suffer from weak intensities for distant peaks due to relaxation, the broad distribution of polarization, as well as dipolar truncation. Frequency-selective methods that feature narrow-banded recoupling can reduce these effects. Indeed, rotational resonance (R 2) experiments have found application in many different biological systems, where they have afforded improved precision and accuracy. Unfortunately, a highly selective transfer mechanism also leads to few cross-peaks in the resulting spectra, which complicates the extraction of multiple constraints. R 2-width (R 2 W) measurements that scan a range of MAS rates to probe the R 2 matching conditions of one or more sites can improve precision, and also permit multiple simultaneous distance measurements. However, multidimensional R 2 W can be very time-consuming. Here, we present an approach that facilitates the acquisition of 2D-like spectra based on a series of 1D R 2 W experiments, by taking advantage of the chemical shift information encoded in the MAS rates where matching occurs. This yields a more time-efficient experiment with many of the benefits of more conventional multidimensional R 2 W measurements. The obtained spectra reveal long-distance 13C–13C cross-peaks resulting from R 2-mediated polarization transfer. This experiment also enables the efficient setup and targeted implementation of traditional R 2 or R 2 W experiments. Analogous applications may extend to other variable-MAS and frequency-selective solid-state NMR experiments. [Copyright &y& Elsevier]

Abstract: Alzheimer’s disease (AD) is caused by abnormal deposition (fibrillation) of a 42-residue amyloid β-protein (Aβ42) in the brain. During the process of fibrillation, the Aβ42 takes the form of protofibrils with strong neurotoxicity, and is thus believed to play a crucial role in the pathogenesis of AD. To elucidate the supramolecular structure of the Aβ42 protofibrils, the intermolecular proximity of the Ala-21 residues in the Aβ42 protofibrils was analyzed by 13C–13C rotational resonance experiments in the solid state. Unlike the Aβ42 fibrils, an intermolecular 13C–13C correlation was not found in the Aβ42 protofibrils. This result suggests that the β-strands of the Aβ42 protofibrils are not in an in-register parallel orientation. Aβ42 monomers would assemble to form protofibrils with the β-strand conformation, then transform into fibrils by forming intermolecular parallel β-sheets. [Copyright &y& Elsevier]

Abstract: Rotational Resonance (R 2) between different spin Zeeman levels in samples of adamantane C10H16 (homonuclear R 2) and a mixture of C10H16 and C10D16 (both homonuclear and heteronuclear R 2) has been studied. A Field Cycling NMR instrument was used to match the external field frequency to a fixed frequency of sample rotation at , 50 or 60kHz. Rotational Resonance is observed at rational frequency ratios of , such as , , and 1. The method may prove to become a useful tool for the determination of spin–spin distances in condensed matter. [Copyright &y& Elsevier]

The subunit c-ring of H-ATP synthase (F c-ring) plays an essential role in the proton translocation across a membrane driven by the electrochemical potential. To understand its structure and function, we have carried out solid-state NMR analysis under magic-angle sample spinning. The uniformly [C, N]-labeled F c from E. coli (EF c) was reconstituted into lipid membranes as oligomers. Its high resolution two- and three-dimensional spectra were obtained, and the C and N signals were assigned. The obtained chemical shifts suggested that EF c takes on a hairpin-type helix-loop-helix structure in membranes as in an organic solution. The results on the magnetization transfer between the EF c and deuterated lipids indicated that Ile55, Ala62, Gly69 and F76 were lined up on the outer surface of the oligomer. This is in good agreement with the cross-linking results previously reported by Fillingame and his colleagues. This agreement reveals that the reconstituted EF c oligomer takes on a ring structure similar to the intact one in vivo. On the other hand, analysis of the C nuclei distance of [3-C]Ala24 and [4-C]Asp61 in the F c-ring did not agree with the model structures proposed for the EF c-decamer and dodecamer. Interestingly, the carboxyl group of the essential Asp61 in the membrane-embedded EF c-ring turned out to be protonated as COOH even at neutral pH. The hydrophobic surface of the EF c-ring carries relatively short side chains in its central region, which may allow soft and smooth interactions with the hydrocarbon chains of lipids in the liquid-crystalline state. [ABSTRACT FROM AUTHOR]

The application of solid-state NMR methodology for bio-molecular structure determination requires the measurement of constraints in the form of 13C-13C and 13C-15N distances, torsion angles and, in some cases, correlation of the anisotropic interactions. Since the availability of structurally important constraints in the solid state is limited due to lack of sufficient spectral resolution, the accuracy of the measured constraints become vital in studies relating the three-dimensional structure of proteins to its biological functions. Consequently, the theoretical methods employed to quantify the experimental data become important. To accentuate this aspect, we re-examine analytical two-spin models currently employed in the estimation of 13C-13C distances based on the rotational resonance (R2) phenomenon. Although the error bars for the estimated distances tend to be in the range 0.5-1.0 Å, R2 experiments are routinely employed in a variety of systems ranging from simple peptides to more complex amyloidogenic proteins. In this article we address this aspect by highlighting the systematic errors introduced by analytical models employing phenomenological damping terms to describe multi-spin effects. Specifically, the spin dynamics in R2 experiments is described using Floquet theory employing two different operator formalisms. The systematic errors introduced by the phenomenological damping terms and their limitations are elucidated in two analytical models and analysed by comparing the results with rigorous numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: We demonstrate that individual H–C–C–H torsional angles in uniformly labelled organic solids can be estimated by selective excitation of 13C double-quantum coherences under magic-angle spinning at rotational resonance. By adapting a straightforward one-dimensional experiment described earlier [T. Karlsson, M. Eden, H. Luhman, M.H. Levitt, J. Magn. Reson. 145 (2000) 95–107], a double-quantum filtered spectrum selective for Cα and Cβ of uniformly labelled l-[13C,15N]valine is obtained with 25% efficiency. The evolution of Cα–Cβ double-quantum coherence under the influence of the dipolar fields of bonded protons is monitored to provide a value of the Hα–Cα–Cβ–Hβ torsional angle that is consistent with the crystal structure. In addition, double-quantum filtration selective for C6 and C1′ of uniformly labelled [13C,15N]uridine is achieved with 12% efficiency for a 13C–13C distance of 2.5Å, yielding a reliable estimate of the C6–H and C1′–H projection angle defining the relative orientations of the nucleoside pyrimidine and ribose rings. This procedure will be useful, in favourable cases, for structural analysis of fully labelled small molecules such as receptor ligands that are not readily synthesised with labels placed selectively at structurally diagnostic sites. [Copyright &y& Elsevier]

Abstract: Structural analysis of 42-residue amyloid β (Aβ42) aggregates using rotational resonance in solid-state NMR verified that Cβ and/or Cγ of Met-35 and the carboxyl carbon of Ala-42 are proximal enough to form an intramolecular antiparallel β-sheet in the C-terminus. The S-oxidized radical cation at Met-35, an ultimate radical species responsible for neurotoxicity, could be stabilized by the carboxylate anion at the C-terminus, resulting in aggregation to cause long-term oxidative stress. [Copyright &y& Elsevier]

Abstract: In this publication, we introduce a version of the rotational resonance width experiment with a homogeneously broadened matching condition. The increase in the bandwidth is achieved by the reduction of the proton decoupling power during mixing, which results in the reduction of zero-quantum relaxation, and broadens the rotational resonance condition. We show that one can achieve recoupling of the carbonyl-aliphatic side chain dipolar interactions band selectively, while avoiding the recoupling of strongly interacting C′–Cα and C′–Cβ spin pairs. The attenuation of the multi-spin effects in the presence of short zero-quantum relaxation enables a two-spin approximation to be employed for the analysis of the experimental data. The systematic error introduced by this approximation is estimated by comparing the results with a three-spin simulation. The experiment is demonstrated in [U–13C,15N]N-acetyl-l-Val-l-Leu dipeptide, where 11 distances, ranging from 2.5 to 6Å, were measured. [Copyright &y& Elsevier]

Abstract: It is shown that straightforward double-quantum filtered 1H MAS NMR experiments yield spectral lineshapes that permit to estimate the minimum number of 1H spins in a cluster. The approach may offer an alternative to multiple-quantum experiments for the characterisation of 1H spin clusters of moderate size. The duration of the double-quantum excitation period has to be chosen suitably, it is necessary to find a practical compromise between optimum double-quantum filtration efficiency and optimum information content of the spectral lineshapes. Some 1H MAS NMR experiments on partially deuterated maleic acid are reported as well as numerical simulations. [Copyright &y& Elsevier]

Abstract: Spectral lineshapes of MAS NMR spectra of dipolar (re)coupled spin pairs exhibiting considerable chemical shielding anisotropies at and near the so-called n=0 rotational resonance (R2) condition are considered. The n=0 R2 condition is found to be not extremely sharp. Anisotropic interaction parameters such as chemical shielding tensor orientations and the magnitude of the dipolar coupling constant remain sensitively encoded in such lineshapes even when differences in isotropic chemical shielding values of up to 400Hz (corresponding to ca. half the size of the dipolar coupling constant) are present. Additional double-quantum filtration (DQF) may enhance the sensitivity of spectral lineshapes to anisotropic interaction parameters for even larger differences in isotropic chemical shielding values. The dependence of the DQF efficiency on spin-system parameters as well as on external parameters (Larmor and MAS frequencies) is investigated. Away from R2 conditions a trend to lower DQF efficiencies is found whereas some spin-system parameters are more sensitively encoded in the corresponding spectral lineshapes. Our study is based on numerical simulations, with the known parameters of the 31P spin pair in Na4P2O7·10H2O representing our model case. [Copyright &y& Elsevier]

Abstract: The absolute orientations of the three 13C chemical shielding tensors in the phosphoenolpyruvate (PEP) moiety in a PEP-model compound with known crystal structure are reported. The study uses a fully 13C-enriched polycrystalline sample of triammonium phosphoenolpyruvate monohydrate, (NH4)3(PEP)⋅H2O, and 13C MAS NMR experiments fulfilling various different 13C rotational-resonance conditions. The absolute 13C chemical shielding tensor orientations are derived by iterative fitting, employing numerically exact simulations, of various rotational-resonance 13C MAS NMR lineshapes of the three-13C-spin system in fully 13C-enriched (NH4)3(PEP)⋅H2O. The implications of the results of this study for future, biochemically oriented solid-state NMR studies on the PEP moiety are outlined. [Copyright &y& Elsevier]

We describe investigations of the effects of rotational resonance (R2) on solid state 13C NMR spectra of uniformly 13C-labeled samples obtained under magic-angle spinning (MAS), and of the utility of R2 measurements as structural probes of peptides and proteins with multiple uniformly labeled residues. We report results for uniformly 13C-labeled l-alanine and l-valine in polycrystalline form, and for amyloid fibrils formed by the 15-residue peptide Aβ11–25 with uniform labeling of a four-residue segment. The MAS NMR spectra reveal a novel J-decoupling effect at R2 conditions that may be useful in spectral assignments for systems with sharp 13C MAS NMR lines. Pronounced dependences of the apparent isotropic 13C NMR chemical shifts on MAS frequency near R2 conditions are also observed. We demonstrate the feasibility of quantitative 13C–13C distance determinations in l-valine, and qualitative determinations of inter-residue 13C–13C contacts in Aβ11–25 fibrils. Finally, we demonstrate a “relayed” R2 technique that may be useful in structural measurements on systems with poorly resolved 13C MAS NMR lines. [Copyright &y& Elsevier]

In magic angle spinning (MAS) NMR spectra of highly and uniformly 13C,15N-enriched amino acids and proteins, homo-nuclear coupling interactions contribute significantly to the 13C linewidths, particularly for moderate applied magnetic field strengths and sample spinning frequencies. In this work, we attempted to dissect, analyze, and control the contributions of J-coupling and residual homo-nuclear dipolar coupling interactions to the linewidths of uniformly 13C,15N-enriched crystalline alanine; these studies were carried out at 9.4 T using a range of spinning frequencies from 5 to 15 kHz. The anisotropic second-order dipolar shifts and the J-splittings are comparable in their contribution to the linewidths, but behave very differently in terms of experimental protocols for line narrowing. In contrast to the J-coupling interactions, the second-order dipolar broadening cannot be refocused using selective pulses on the passively coupled spin. We carried out experiments to remove or refocus the 13C J-coupling interactions (ω1 J-decoupling) using a selective DANTE pulse in the center of the indirect evolution period. Inversion profiles and bandwidths of selective DANTE pulses acting on transverse magnetization, in the regime of moderate spinning frequencies, were characterized computationally and experimentally. A dramatic improvement in the resolution of the 2D spectrum was achieved when this decoupling protocol was employed. [Copyright &y& Elsevier]

Double-quantum filtered MAS NMR spectra of an isolated homonuclear spin-1/2 pair are considered, at and away from rotational resonance conditions. The pulse sequence used is the solid-state NMR equivalent of double-quantum filtered COSY, known from solution-state NMR. The 119Sn spin pair in [(chex3Sn)2S] is characterized by a difference in isotropic chemical shielding smaller than the two chemical shielding anisotropies and by direct dipolar and isotropic J-coupling constants of similar magnitudes. At rotational resonance, one-dimensional double-quantum filtered 119Sn lineshapes yield the relative orientation of the two 119Sn chemical shielding tensors. Good double-quantum filtration efficiencies are found at and away from rotational resonance conditions, despite the presence of large chemical shielding anisotropies. Numerical simulations illustrate the interplay of the direct dipolar and J-coupling pathways and identify the latter as the main pathway even at rotational resonance conditions. [Copyright &y& Elsevier]