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Data availability: Data will be made available on request. Appendix A. Supplementary data: Supplementary data to this article can be found online at: https://doi.org/10.1016/j.ultsonch.2022.106158. Copyright © 2022 The Authors. The volume of fluid (VOF) and continuous surface force (CSF) methods were used to develop a bubble dynamics model for the simulation of bubble oscillation and implosion dynamics under ultrasound. The model was calibrated and validated by the X-ray image data acquired by ultrafast synchrotron X-ray. Coupled bubble interactions with bulk graphite and freely moving particles were also simulated based on the validated model. Simulation and experiments quantified the surface instability developed along the bubble surface under the influence of ultrasound pressure fields. Once the surface instability exceeds a certain amplitude, bubble implosion occurs, creating shock waves and highly deformed, irregular gas-liquid boundaries and smaller bubble fragments. Bubble implosion can produce cyclic impulsive stresses sufficient enough to cause µs fatigue exfoliation of graphite layers. Bubble-particle interaction simulations reveal the underlying mechanisms for efficient particle dispersion or particle wrapping which are all strongly related to the oscillation dynamics of the bubbles and the particle surface properties. UK Engineering and Physical Sciences Research Council (Grant Nos. EP/R031819/1; EP/R031665/1; EP/R031401/1; EP/R031975/1); Royal Society.

The surface energy based solubility parameters theory was applied\ud to model the degree of polystyrene-functionalisation of MWCNTs\ud in six different organic solvents. The experimental characterization of\ud the polymer-functionalized MWCNTs is consistent with the predictions of this model providing a breakthrough towards the rational design of functionalized MWCNTs based on thermodynamic parameters.

By addressing the challenge of controlling molecular motion, mechanically interlocked molecular machines are primed for a variety of applications in the field of nanotechnology. Specifically, the designed manipulation of communication pathways between electron donor and acceptor moieties that are strategically integrated into dynamic photoactive rotaxanes and catenanes may lead to efficient artificial photosynthetic devices. In this pursuit, a novel [3]rotaxane molecular shuttle consisting of a four-station bis-naphthalene diimide (NDI) and central C60 fullerene bis-triazolium axle component and two mechanically bonded ferrocenyl-functionalized isophthalamide anion binding site-containing macrocycles is constructed using an anion template synthetic methodology. Dynamic coconformational anion recognition-mediated shuttling, which alters the relative positions of the electron donor and acceptor motifs of the [3]rotaxane’s macrocycle and axle components, is demonstrated initially by 1H NMR spectroscopy. Detailed steady-state and time-resolved UV–vis–IR absorption and emission spectroscopies as well as electrochemical studies are employed to further probe the anion-dependent positional macrocycle–axle station state of the molecular shuttle, revealing a striking on/off switchable emission response induced by anion binding. Specifically, the [3]rotaxane chloride coconformation, where the ferrocenyl-functionalized macrocycles reside at the center of the axle component, precludes electron transfer to NDI, resulting in the switching-on of emission from the NDI fluorophore and concomitant formation of a C60 fullerene-based charge-separated state. By stark contrast, in the absence of chloride as the hexafluorophosphate salt, the ferrocenyl-functionalized macrocycles shuttle to the peripheral NDI axle stations, quenching the NDI emission via formation of a NDI-containing charge-separated state. Such anion-mediated control of the photophysical behavior of a rotaxane through molecular motion is unprecedented.

Fullerene dyads bridged with perfluorinated linking groups have been synthesized through a modified arc-discharge procedure. The addition of Teflon inside an arc-discharge reactor leads to the formation of dyads, consisting of two C60 fullerenes bridged by -CF2- groups. The bridging groups consisting of electronegative atoms, lead to different energy levels and to new features in the photoluminescence spectrum. A suppression of the singlet oxygen photosensitization, indicated that the radiative decay from singlet to singlet state is favoured against the intersystem crossing singlet to triplet transition.

The endohedral fullerene 15N@C60 has narrow electron paramagnetic resonance lines which have been proposed as the basis for a condensed-matter portable atomic clock. We measure the low-frequency spectrum of this molecule, identifying and characterizing a clock transition at which the frequency becomes insensitive to magnetic field. We infer a linewidth at the clock field of 100 kHz. Using experimental data, we are able to place a bound on the clock’s projected frequency stability. We discuss ways to improve the frequency stability to be competitive with existing miniature clocks.

The endohedral fullerene 15N@C60 has narrow electron paramagnetic resonance lines which have been proposed as the basis for a condensed-matter portable atomic clock. We measure the low-frequency spectrum of this molecule, identifying and characterizing a clock transition at which the frequency becomes insensitive to magnetic field. We infer a linewidth at the clock field of 100 kHz. Using experimental data, we are able to place a bound on the clock's projected frequency stability. We discuss ways to improve the frequency stability to be competitive with existing miniature clocks.

Electron spin qubits in molecular systems offer high reproducibility and the ability to self-assemble into larger architectures. However, interactions between neighboring qubits are "always on," and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both effectively turn on or off interqubit coupling mediated by dipolar interactions and benefit from the long nuclear spin decoherence times (T2n). We transfer qubit states between the electron and N15 nuclear spin in N15@C60 with a two-way process fidelity of 88%, using a series of tuned microwave and radio frequency pulses and measure a nuclear spin coherence lifetime of over 100 ms. © 2011 American Physical Society.

We examine the temperature dependence of the electron spin relaxation times of the molecules N@C60 and N@C70 (which comprise atomic nitrogen trapped within a carbon cage) in liquid CS2 solution. The results are inconsistent with the fluctuating zero-field splitting (ZFS) mechanism, which is commonly invoked to explain electron spin relaxation for S> or =1 spins in liquid solution, and is the mechanism postulated in the literature for these systems. Instead, we find an Arrhenius temperature dependence for N@C60 , indicating the spin relaxation is driven primarily by an Orbach process. For the asymmetric N@C70 molecule, which has a permanent ZFS, we resolve an additional relaxation mechanism caused by the rapid reorientation of its ZFS. We also report the longest coherence time (T2) ever observed for a molecular electron spin, being 0.25 ms at 170 K.

Photoluminescence spectroscopic measurements have allowed the acquisition of high resolution spectra at low temperature for the endohedral metallofullerenes, Er2 @ C82 (isomer I) and Er2 C2 @ C82 (isomer I). The characteristic emission in the 1.5-1.6 μm region corresponds to the 4 I13 / 2 (m) → 4 I15 / 2 (n) transitions of the Er3 + ion for both molecules. The emission arising from Er2 C2 @ C82 (I) appears acuminated (narrow lines that taper to a point) when compared with that of Er2 @ C82 (I). The Er2 C2 @ C82 (I) emission linewidths are comparable to those found in crystals, making this molecule of interest for applications where accessible, well-defined quantum states are required. © 2009 Elsevier B.V. All rights reserved.

Motivated by the possibility of observing photoluminescence and electron paramagnetic resonance from the same species located within a fullerene molecule, we initiated an EPR study of Er3+ in ErSc2N@C80. Two orientations of the ErSc2N rotor within the C80 fullerene are observed in EPR, consistent with earlier studies using photoluminescence excitation (PLE) spectroscopy. For some crystal field orientations, electron spin relaxation is driven by an Orbach process via the first excited electronic state of the 4I15/2 multiplet. We observe a change in the relative populations of the two ErSc2N configurations upon the application of 532 nm illumination, and are thus able to switch the majority cage symmetry. This photoisomerization, observable by both EPR and PLE, is metastable, lasting many hours at 20 K. © 2008 The American Physical Society.

We review recent progress towards implementing quantum information processing protocols using electron and nuclear magnetic resonance in the molecule N-14@C-60. Using conventional spectrometers, we measure the errors inherent in quantum manipulations of spins. By applying composite pulses, we correct the dominant error to a high degree. Identifying a two qubit computational basis out of the electron and oF nuclear spin levels of N-14@C-60, we implement an ultrafast phase gate on the nuclear qubit by exciting an electron spin transition. (c) 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.

The endohedral fullerene molecule, N@C60, is a candidate for molecular spin qubits (quantum bits) and spin probes owing to its exceptional electron spin properties. Advancements in the processing of N@C60 are key to obtaining samples of high purity on a reasonable timescale. We investigate enrichment by high throughput processing (flow rate of 18 L h(-1) and operating pressure of 1.5-2 MPa) using high performance liquid chromatography (HPLC) as a means of scaling N@C60 production. We use detection by electron paramagnetic resonance (EPR) spectroscopy to map N@C60 during processing, and through the reconstruction of the peak position in the chromatogram, we are able to determine the retention time and relative purity of N@C60 without the need for its isolation. Based on this, we establish a procedure for time-efficient, high throughput processing to isolate N@C60 in high purity.

A method has been developed for the attachment of a dithiolane group to endohedral metallofullerenes via a 1,3-dipolar cycloaddition reaction. This sulfur-containing functional group serves as an anchor, enabling efficient immobilisation of endohedral fullerenes on Au(111) surfaces at room temperature, directly from the solution phase. The functionalised fullerenes form disordered monolayers that exhibit no long-range ordering, which is attributed to both the strong bonding of the dithiolane anchor to the surface and to the conformational flexibility of the functional group. Endohedral fullerenes Er(3)N@C(80) and Sc(3)N@C(80) have been used as models for functionalisation and subsequent surface deposition. Their chemical reactivity towards dithiolane functionalisation and their surface behaviour have been compared to that of C(60). The endohedral fullerenes appear to be significantly less reactive towards the functionalisation than C(60), however they bind in a similar manner to a gold surface as their dithiolane terminated C(60) counterparts. The optical activity of Er(3)N@C(80) molecules is preserved after attachment of the functional group. We report a splitting of the endohedral Er(3+) emission lines due to the reduction in symmetry of the functionalised fullerene cage, as compared to the highly symmetrical icosahedral C(80) cage of pristine Er(3)N@C(80).

Electron spin qubits in molecular systems offer high reproducibility and the ability to self assemble into larger architectures. However, interactions between neighbouring qubits are 'always-on' and although the electron spin coherence times can be several hundred microseconds, these are still much shorter than typical times for nuclear spins. Here we implement an electron-nuclear hybrid scheme which uses coherent transfer between electron and nuclear spin degrees of freedom in order to both controllably turn on/off dipolar interactions between neighbouring spins and benefit from the long nuclear spin decoherence times (T2n). We transfer qubit states between the electron and 15N nuclear spin in 15N@C60 with a two-way process fidelity of 88%, using a series of tuned microwave and radiofrequency pulses and measure a nuclear spin coherence lifetime of over 100 ms., Comment: 5 pages, 3 figures with supplementary material (8 pages)

Endohedral fullerenes encapsulating single nitrogen atoms (N@C60 and N@C70) are spin active, due to the presence of unpaired nitrogen electron spins. High reactivity of nitrogen leads to a poor stability of these molecules at elevated temperatures, drastically restricting possibilities of their chemical treatment. In this study, N@C60 and N@C70 in toluene solutions were subjected to high pressure (HP) up to 0.8 GPa and annealed for 1, 2, 10 or 24 h, at either room or elevated temperatures. In each case the number of surviving molecules was evaluated based on the relative spin counts of ex situ EPR spectra obtained before and after the treatment. The enhanced thermal stability of N@C60 and N@C70 under HP conditions is attributed to inhibited formation of azabridges, which under normal pressure facilitate the escape of nitrogen from the fullerene cage. © 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim.

The magnetic properties of ErSc2 N @ C80, Er2 ScN @ C80 and Er3 N @ C80 metallofullerenes are characterized in the temperature range 2 to 300 K up to a magnetic field of 7 T. The magnetic susceptibility of these fullerenes follows the Curie-Weiss law. The fitting parameters to the Curie-Weiss law provide an effective magnetic moment μeff of Er3 + ion in each of the fullerenes. The magnetic moment decreases with the increase in number of Er3 + ions inside the cage. This is related to crystal-field effects, intramolecular interactions and the local quenching of the angular momentum of the ion within the fullerene cage. © 2008 Elsevier B.V. All rights reserved.

We examine environmental effects of surrounding nuclear spins on the electron spin relaxation of the N@C60 molecule (which consists of a nitrogen atom at the centre of a fullerene cage). Using dilute solutions of N@C60 in regular and deuterated toluene, we observe and model the effect of translational diffusion of nuclear spins of the solvent molecules on the N@C60 electron spin relaxation times. We also study spin relaxation in frozen solutions of N@C60 in CS2, to which small quantities of a glassing agent, S2Cl2 are added. At low temperatures, spin relaxation is caused by spectral diffusion of surrounding nuclear 35Cl and 37Cl spins in the S2Cl2, but nevertheless, at 20 K, T2 times as long as 0.23 ms are observed., Comment: 7 pages, 6 figures

We examine the temperature dependence of the relaxation times of the molecules N@C60 and N@C70 (which comprise atomic nitrogen trapped within a carbon cage) in liquid CS2 solution. The results are inconsistent with the fluctuating zero field splitting (ZFS) mechanism, which is commonly invoked to explain electron spin relaxation for S > 1/2 spins in liquid solution, and is the mechanism postulated in the literature for these systems. Instead, we find a clear Arrhenius temperature dependence for N@C60, indicating the spin relaxation is driven primarily by an Orbach process. For the asymmetric N@C70 molecule, which has a permanent non-zero ZFS, we resolve an additional relaxation mechanism caused by the rapid reorientation of its ZFS. We also report the longest coherence time (T2) ever observed for a molecular electron spin, being 0.25 ms at 170K., 6 pages, 6 figures V2: Updated to published version

The long spin lifetimes exhibited by endohedral fullerenes imply that they can store quantum information and hence have the potential to be used as qubits. Production of asymmetrical endohedral fullerene dimers (e.g. iNC(60)-iNC(70)) could lead to ordered arrays of ABABAB sequences. This kind of molecular self-assembly offers potential for creating large qubit arrays, a precondition for any scalable quantum computer. We present our progress towards the production and characterisation of endohedral fullerenes, fullerene dimers and array structures and their potential use in quantum computation.