Muonium diffusion in ice

Muonium (Mu, μ⁺e⁻) is generally regarded as a light isotope of hydrogen. The procession signals of muonium in single crystals of H₂O and D₂O ice have been studied from 8 to 263 K using the muon spin rotation (μSR) technique. Transverse spin relaxation rates have been extracted and interpreted in terms of modulation of the dipolar interaction between muonium and the protons/deuterons in the lattice by translational diffusion of muonium. In contrast to the situation for H and a previous claim for Mu, muonium is found to be diffusing at temperatures as low as 8 K. An activation energy of 40 meV is obtained by fitting the highest temperature data to an Arrhenius expression. At low temperature muonium is thought to diffuse by quantum tunnelling.     

Positive muons in condensed phase ammonia

The chemical behavior of positive muons in condensed phase ammonia has been investigated in order to elucidate the phase and temperature effects on the chemical and physical behavior of the muon and muonium formation in a simple binary compound. Diamagnetic muon yield (P_D) was constant at 0.67±0.01 in both solid and liquid above 125 K. Muonium formation in solids were observed above 100 K with slow muonium spin relaxation. In liquids, the muonium yield and its spin relaxation rate showed temperature dependence. Addition of metallic sodium increased P_D in liquids.     

Dynamics and supramolecular organization of the 1D spin transition polymeric chain compound [Fe(NH2trz)3](NO3)2. Muon spin relaxation

The thermal spin transition that occurs in the polymeric chain compound [Fe(NH(2)trz)3](NO3)2 above room temperature has been investigated by zero-field muon spin relaxation (microSR) over the temperature range approximately 8-402 K. The depolarization curves are best described by a Lorentzian and a Gaussian line that represent fast and slow components, respectively. The spin transition is associated with a hysteresis loop of width DeltaT = 34 K (T1/2 upward arrow = 346 K and T1/2 downward arrow = 312 K) that has been delineated by the temperature variation of the initial asymmetry parameter, in good agreement with previously published magnetic measurements. Zero-field and applied field (20-2000 Oe) microSR measurements show the presence of diamagnetic muon species and paramagnetic muonium radical species (A = 753 +/- 77 MHz) over the entire temperature range. Fast dynamics have been revealed in the high-spin state of [Fe(NH(2)trz)3](NO3)2 with the presence of a Gaussian relaxation mode that is mostly due to the dipolar interaction with static nuclear moments. This situation, where the muonium radicals are totally decoupled and not able to sense paramagnetic fluctuations, implies that the high-spin dynamics fall outside the muon time scale. Insights to the origin of the cooperative effects associated with the spin transition of [Fe(NH(2)trz)3](NO3)2 through muon implantation are presented.     

Spin relaxation of a short-lived radical in zero magnetic field

A short-lived radical containing only one I = 1/2 nucleus, the muoniated 1,2-dicarboxyvinyl radical dianion, was produced in an aqueous solution by the reaction of muonium with the dicarboxyacetylene dianion. The identity of the radical was confirmed by measuring the muon hyperfine coupling constant (hfcc) by transverse field muon spin rotation spectroscopy and comparing this value with the hfcc obtained from DFT calculations. The muon spin relaxation rate of this radical was measured as a function of temperature in zero magnetic field by the zero field muon spin relaxation technique. The results have been interpreted using the theoretical model of Fedin et al. (J. Chem. Phys., 2003, 118, 192). The muon spin polarization decreases exponentially with time after muon implantation and the temperature dependence of the spin relaxation rate indicates that the dominant relaxation mechanism is the modulation of the anisotropic hyperfine interaction due to molecular rotation. The effective radius of the radical in solution was determined to be 1.12 ± 0.04 nm from the dependence of the muon spin relaxation rate on the temperature and viscosity of the solution, and is approximately 3.6 times larger than the value obtained from DFT calculations.     

On the pressure dependence of the muon spin polarization in mixtures of noble gases

In muon spin rotation (μSR) experiments, where spin-polarized positive muons are stopped in condensed matter, three magnetically distinguishable chemical environments can be observed. That is, the Larmor frequencies associated with diamagnetic environments and two types of paramagnetic environments (muonium and radicals) can be resolved. The chemical identities of the latter two are distinct since their Larmor frequencies are distinct, whereas the chemical identities of the possible diamagnetic species are not determined by the Larmor frequency since chemical shifts can not be resolved in μSR experiments. However, two different diamagnetic species have been observed in experiments performed on mixtures of noble gases. Their distinction arises through different thermal rate constants that lead to “fast” and “slow” relaxing components of the diamagnetic signal. The pressure dependencies of the amplitudes associated with these components are related to the stopping dynamics of muons in noble gas targets. A set of coupled rate equations for muon spin dynamics, based upon quantal Boltzmann equations, have been developed to describe this process in single component gases. This theory is now extended to mixtures. In particular, the dynamics of the muon spin is generated by the muonium hyperfine interaction and by time dependent rate constants for the various chemical species that are assumed to be present, namely, muonium and three diamagnetic species. Radicals have not yet been observed in low pressure gases. The coupled quantal rate equations are solved for two models of the stopping dynamics wherein the rates are taken as square box functions of time.     

Solvation of a hydrogen isotope in aqueous methanol, NaCl, and KCl solutions

The muon hyperfine coupling constant (hfc) of the light hydrogen isotope muonium (Mu) was measured in aqueous methanol, NaCl, and KCl solutions with varying concentrations, in deuterated water, and in deuterated methanol. The muon hfc is shown to be sensitive to the size and composition of the primary solvation shell, and the three-dimensional harmonic oscillator model of Roduner et al. (J. Chem. Phys. 1995, 102, 5989) has been modified to account for dependence of the muon hfc on the methanol or salt concentration. The muon hfc of Mu in the aqueous methanol solutions decreases with increasing methanol concentration up to a mole fraction (chiMeOH) of approximately 0.4, above which the muon hfc is approximately constant. The concentration dependence of the muon hfc is due to hydrophobic nature of Mu. It is preferentially solvated by the methyl group of methanol, and the proportion of methanol molecules in the primary solvation shell is greater than that in the bulk solution. Above chiMeOH approximately 0.4, Mu is completely surrounded by methanol. The muon hfc decreases with increasing methanol concentration because more unpaired electron spin density is transferred from Mu to methanol than to water. The unpaired electron spin density is transferred from Mu to the solvent by collisions that stretch one of the solvents bonds. The amount of spin density transferred is likely inversely related to the activation barrier for abstraction from the solvent, which accounts for the larger muon hfc in the deuterated solvents. The muon hfc of Mu in electrolyte solution decreases with increasing concentration of NaCl or KCl. We suggest that the decrease of the muon hfc is due to the amount of spin density transferred from Mu to its surroundings being dependent on the average orientation of the water molecules in the primary solvation shell, which is influenced by both Mu and the ions in solution, and spin density transfer to the ions themselves.     

Muonium addition to DMPO and PBN sorbed in silica-gel

Nitroxyl radicals were formed by adding the light hydrogen isotope, muonium to the spin traps DMPO (5,5-dimethyl-1-pyrroline-N-oxide) and PBN (N-tert-butyl-alpha-phenylnitrone) sorbed as 30 wt% ethanol solutions in silica-gel; evidence is presented for a specific hydrogen-bonded interaction between the DMPO adduct and the silica surface; longitudinal-field muon spin relaxation measurements (LF-MuSRx) were performed which identified two distinct motional regimes in both samples.     

Quantum diffusion of hydrogen and muonium atoms in liquid water and hexagonal ice

We have used the ring polymer molecular dynamics method to study the diffusion of muonium, hydrogen, and deuterium atoms in liquid water and hexagonal ice over a wide temperature range (8-361 K). Quantum effects are found to dramatically reduce the diffusion of muonium in water relative to that predicted by classical simulation. This leads to a simple explanation for the lack of any significant isotope effect in the observed diffusion coefficients of these species in the room temperature liquid. Our results indicate that the mechanism of the diffusion in liquid water is similar to the intercavity hopping mechanism observed in ice, supplemented by the diffusion of the cavities in the liquid. Within the same model, we have also been able to simulate the observed crossover in the c-axis diffusion coefficients of hydrogen and deuterium in hexagonal ice. Finally, we have been able to obtain good agreement with experimental data on the diffusion of muonium in hexagonal ice at 8 K, where the process is entirely quantum mechanical.     

The reactions of imidazol-2-ylidenes with the hydrogen atom: a theoretical study and experimental confirmation with muonium

The possible radicals resulting from hydrogen atom addition to the imidazole rings of 1,3-bis(isopropyl)-4,5-dimethylimidazol-2-ylidene (1) and 1,3-bis(2,4,6-trimethylphenyl)imidazol-2-ylidene (2) have been studied by means of density functional calculations (B3LYP). The calculations included solvent effects estimated via the polarized continuum model (PCM) and an empirical treatment of vibrational averaging of hyperfine constants. Addition of a hydrogen (or muonium) atom to the carbeneic carbon of 1,3-bis(isopropyl)-4,5-dimethylimidazol-2-ylidene was found to give a radical 60.46 kJ mol(-)(1) more stable than the radical resulting from addition to the double bond. Estimation of the activation barriers for reaction at the two sites shows that addition at the carbeneic carbon is favored. The site of addition was confirmed experimentally using muonium (Mu), which can be considered a light isotope of hydrogen. Muon spin rotation and muon level-crossing spectroscopy were used to determine muon, (13)C, and (14)N hyperfine coupling constants (hfc's) for the radical products of addition to the two carbenes. Good agreement between the experimental and calculated hfc's confirms that Mu (and hence H) adds exclusively to the carbeneic carbon. The radicals that are produced have nonplanar radical centers with most of the unpaired electron spin density localized on the alpha-carbon.     

Muonium-substituted organic free radicals in liquids. Isomer distribution and end-of-track radiolytical processes determined from studies of cyclohexadienyl radicals derived from substituted benzenes

Muonium-substituted free radicals are observed by muon spin rotation when positive muons are stopped in liquid substituted benzenes. From muon precession frequencies in high external magnetic fields the isotropic muon-electron hyperfine coupling constants A_μ are determined. 66 radicals are assigned to ortho-, meta- and para-substituted cyclohexadienyl-type radicals. Formally they are produced by addition of the light hydrogen isotope muonium to 24 mono-substituted benzenes. The distribution of muons between radicals and diamagnetic molecules is suggested to be governed by radiolytical processes near the end-of-track of the thermalizing muon.     

Organic free radicals in superheated water studied by muon spin spectroscopy

There is a pressing need to identify and monitor reaction intermediates in water at high temperatures and pressures, but conventional techniques have limited capability for studying transient free radicals under such challenging conditions. Apparatus has now been developed to permit muon avoided-level crossing spectroscopy (muLCR) of organic free radicals in superheated water. The combination of muLCR with transverse-field muon spin rotation (TF-muSR) provides the means to identify and characterize free radicals via their nuclear hyperfine coupling constants. Because the radicals are derived from the addition of muonium (Mu = mu+ e-) to unsaturated compounds, the ensuing muoniated free radicals correspond to conventional organic free radicals but with a muon spin label substituted for one of the protons. Muon spin spectroscopy is the only technique presently being used to characterize transient free radicals under hydrothermal conditions in an unambiguous manner, free from interference from other reaction intermediates. This paper demonstrates how muoniated radicals can be used to monitor the species present in hydrothermal systems, and examples are presented from two classes of reaction: dehydration of alcohols and enolization of ketones. Spectra are displayed and hyperfine constants reported for muoniated forms of the following free radicals in superheated water (typically 350 degrees C at 250 bar): 2-propyl, 2-methyl-2-propyl (tert-butyl), and 2-hydroxy-2-propyl. The latter radical is the product of muonium addition to both the keto and the enol forms of acetone, but different isotopomers are produced according to which reaction channel is dominant. This should prove invaluable in future studies of the role of enols in combustion.     

Muon implantation of metallocenes: ferrocene

Muon Spin Relaxation and Avoided Level Crossing (ALC) measurements of ferrocene are reported. The main features observed are five high field resonances in the ALC spectrum at about 3.26, 2.44, 2.04, 1.19 and 1.17 T, for the low-temperature phase at 18 K. The high-temperature phase at 295 K shows that only the last feature shifted down to about 0.49 T and a muon spin relaxation peak at about 0.106 T which approaches zero field when reaching the phase transition temperature of 164 K. A model involving three muoniated radicals, two with muonium addition to the cyclopentadienyl ring and the other to the metal atom, is postulated to rationalise these observations. A theoretical treatment involving spin-orbit coupling is found to be required to understand the Fe-Mu adduct, where an interesting interplay between the ferrocene ring dynamics and the spin-orbit coupling of the unpaired electron is shown to be important. The limiting temperature above which the full effect of spin-orbit interaction is observable in the muSR spectra of ferrocene was estimated to be 584 K. Correlation time for the ring rotation dynamics of the Fe-Mu radical at this temperature is 3.2 ps. Estimated electron g values and the changes in zero-field splittings for this temperature range are also reported.     

The detection of muonium in water

We report the first direct observation of the muonium atom (μ⁺e^?) in a liquid sample. Using the transverse field μSR technique muonium spin precession signals were detected in water at six different fields between 4 and 80 G.     

Muon Spin Rotation/Resonance (μSR) for Studying Radical Reactivity of Unsaturated Organophosphorus Compounds

The positive muon (μ⁺) can be regarded as a light isotope of proton and has been an important tool to study radical reactions of organic compounds. Recently, muons have been applied to produce short-lived paramagnetic species from the heavier unsaturated organic molecules including the p-block elements. This article overviews recent muon spin rotation/resonance (μSR) studies on the phosphorus analogs of alkenes, anthracenes, and cyclobutane-1,3-diyls together with the fundamentals of μSR. The acyclic phosphaalkene of P=C and phosphasilenes of P=Si can accept muonium (Mu=[μ⁺e⁻]) at the heavier double bonds, and the corresponding radicals have been characterized. The phosphorus atom in 9-phosphaanthracene, whose P=C double bond is stabilized by the peri-substituted CF₃ groups, predominantly captures muonium to provide the corresponding paramagnetic fused heterocyclic system. The peri-trifluoromethyl groups are functional to promote the unprecedented light isotope effect of muon providing the planar three-cyclic molecular structure to consume the increased zero-point energy. The formally open-shell singlet 1,3-diphosphacyclobutane-2,4-diyl unit can accept muonium at the (ylidic) phosphorus or the skeletal radicalic carbon, and the corresponding paramagnetic phosphorus heterocycles can be characterized by μSR. The findings on these muoniation processes to the unsaturated phosphorus-containing compounds will contribute not only to development of novel paramagnetic functional species but also to progress on muon science.     

A μSR study on chemical behaviors of positive muons in crystalline tris/acetylacetonato/metal/III/ complexes

Chemical behaviours of positive muons implanted in crystalline tris/acetylacetonato/chromium/III/, iron/III/, and cobalt/III/ were investigated by means of the muon spin relaxation technique. The muon spin relaxation function was exponential in tris/acetylacetonato/iron/III/ and Gaussian in tris/acetylacetonato/cobalt/III/, suggesting that the muon spin relaxation may be ascribed to the interaction between the muon spin and a fluctuating electronic spin in the former and between the muon and a static nuclear spin in the latter. The yield of diamagnetic muon species was found to be nearly unity in these three complexes. Based on the analysis of the relaxation function, it is likely that the positive muon implanted in the cobalt/III/ complex will reside at a distance of about 1.7 A from the cobalt atom.     

Theoretical calculations of hyperfine coupling constants for muoniated butyl radicals

The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al. J. Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C-Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the β-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C-Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near 0 K, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.     

A new basic motif in cyanometallate coordination polymers: structure and magnetic behavior of M(mu-OH2)2[Au(CN)2]2 (M=Cu, Ni)

The structures of two cyanoaurate-based coordination polymers, M(mu-OH(2))(2)[Au(CN)(2)](2) (M=Cu, Ni), were determined by using a combination of powder and single-crystal X-ray diffraction techniques. The basic structural motif for both polymers contains rarely observed M(mu-OH(2))(2)M double aqua-bridges, which generate an infinite chain; two trans [Au(CN)(2)](-) units also dangle from each metal center. The chains form ribbons that interact three dimensionally through CNH hydrogen bonding. The magnetic properties of both compounds and of the dehydrated analogue Cu[Au(CN)(2)](2) were investigated by direct current (dc) and alternating current (ac) magnetometry; muon spin-relaxation data was also obtained to probe their magnetic properties in zero-field. In M(mu-OH(2))(2)[Au(CN)(2)](2), ferromagnetic chains of M(mu-OH(2))(2)M are present below 20 K. Interchain magnetic interactions mediated through hydrogen bonding, involving water and cyanoaurate units, yield a long-range magnetically ordered system in Cu(mu-OH(2))(2)[Au(CN)(2)](2) below 0.20 K, as indicated by precession in the muon spin polarization decay. Ni(mu-OH(2))(2)[Au(CN)(2)](2) undergoes a transition to a spin-glass state in zero-field at 3.6 K, as indicated by a combination of muon spin-relaxation and ac-susceptibility data. This transition is probably due to competing interactions that lead to spin frustration. A phase transition to a paramagnetic state is possible for Ni(mu-OH(2))(2)[Au(CN)(2)](2) upon application of an external field; the critical field was determined to be 700 Oe at 1.8 K. The dehydrated compound Cu[Au(CN)(2)](2) shows weak antiferromagnetic interactions at low temperatures.     

A radiolabelling study of radicals derived from benzene, toluene and benzaldehyde sorbed in model environmental carbon

Radiolabelled free radicals were formed by the addition of muonium--a radioactive hydrogen atom with a positive muon as its nucleus--to benzene, toluene and benzaldehyde, as sorbed in porous carbon. The activation parameters associated with their reorientational motion were measured using longitudinal-field muon spin relaxation (LF-MuSRx). Two distinct sorbed fractions were detected in each sample, characterised by molecular reorientational activation energies of 5.9/25.8 kJ/mol for benzene, 2.5/5.9 kJ/mol for toluene and 2.9/11.5 kJ/mol for benzaldehyde.     

DFT study of paramagnetic adducts of tris-(8-hydroxyquinoline)aluminum (III)

Radicals formed by the addition of hydrogen (H) or muonium (Mu) to tris(8-hydroxyquinoline)aluminum(III) (Alq(3)) have been studied using density functional theory (DFT) calculations. Drew et al. (Phys. Rev. Lett. 2008, 100, 116601) studied Alq(3) using the longitudinal field muon spin relaxation technique and assumed the formation of muoniated radicals and rapid intermolecular electron hopping with a rate of (1.4 ± 0.2) × 10(12) s(-1). In this work, the results of DFT calculations on Alq(3), the H/Mu adducts of Alq(3), and the corresponding anions and cations are reported. The energy required to transfer an electron to or from the H/Mu adducts of Alq(3) is prohibitively large, ranging from 4.09 to 5.68 eV, which suggests that the unpaired electron does not hop onto neighboring molecules and that there is no long-range diffusion of the unpaired electron. The hyperfine coupling constants for the muoniated radicals were calculated and used to predict avoided level crossing resonance fields, which will allow experimenters to confirm that the unpaired electron is localized in close proximity to the muon.     

Observation of a Metastable P‐Heterocyclic Radical by Muonium Addition to a 1,3‐Diphosphacyclobutane‐2,4‐diyl

A 1,3‐diphosphacyclobutane‐2,4‐diyl contains a unique unsaturated cyclic unit, and the presence of radical‐type centers have been expected as a source of functionality. This study demonstrates that the P‐heterocyclic singlet biradical captures muonium (Mu=[μ⁺e^?]), the light isotope of a hydrogen radical, to generate an observable P‐heterocyclic paramagnetic species. Investigation of a powder sample of 2,4‐bis(2,4,6‐tri‐t‐butylphenyl)‐1‐t‐butyl‐3‐benzyl‐1,3‐diphosphacyclobutane‐2,4‐diyl using muon (avoided) level‐crossing resonance (μLCR) spectroscopy revealed that muonium adds to the cyclic P₂C₂ unit. The muon hyperfine coupling constant (A_μ) indicated that the phosphorus atom bearing the t‐butyl group trapped muonium to provide a metastable P‐heterocyclic radical involving the ylidic MuP(<)=C moiety. The observed regioselective muonium addition correlates the canonical formula of 1,3‐diphosphacyclobutane‐2,4‐diyl.