Local Ordering in Liquids: Solvent Effects on the Hyperfine Couplings of the Cyclohexadienyl Radical

Dynamics and local environment of an aromatic counterion bound to di-chain cationic surfactant bilayers studied by avoided level crossing muon spin resonance: evidence for counterion condensation

Avoided level crossing muon spin resonance (ALC-μSR) has been used to study the reorientational dynamics of muon-spin-labelled 2,4,6-trimethylbenzoate (246TMB^-) counterions and their interaction with DODMAC (dioctadecyldimethylammonium chloride) bilayers in the L_α and L_β liquid crystalline states. The muoniated radical anion formed by the addition of muonium to the secondary carbons of the aromatic ring of 246TMB^- is used as a local spin probe. The muon and methylene proton hyperfine parameters and the electron spin relaxation rate (λ_e) of the muoniated spin probe were determined as a function of temperature by modelling the ALC-μSR spectra with Monte Carlo numerical simulations. The observation of a Δ₁ resonance indicates that 246TMB^- is undergoing anisotropic motion and doesn't reside in the aqueous layer in either the L_α and L_β phases. The lack of an abrupt change in the hyperfine parameters or λ_e when the system goes from the L_β to the L_α lamellar liquid crystalline phases suggests that 246TMB^- is located at the oil-water interface rather than within the bilayer. The hyperfine parameters indicate that 246TMB^- is undergoing large amplitude reorientational motion about a preferred orientation resulting from the bilayer's electric field. The interaction between 246TMB^- and the bilayer decreases and the amplitude of the wobbling-in-a-cone motion increases with increasing temperature. The temperature dependence of the electron spin relaxation rate indicates the barrier to reorientation is 41.7 kJ mol^-1.

Partitioning of 2-phenylethanol and limonene cosurfactants in C12E4

Avoided level-crossing muon spin resonance (ALC-μSR) has been used to study the dynamics and local environment of spin probes formed by muonium (Mu) addition to 2-phenylethanol (PEA) and limonene (1-methyl-4-(1-methylethenyl)-cyclohexene) in an aqueous dispersion of the nonionic surfactant C₁₂E₄ (tetra(ethylene glycol) n-dodecyl ether). The spin probes derived from both cosurfactants reside within the micelles in the L₁ phase and the bilayers in the L_α phase rather than in the aqueous region. The local polarity measured by the different isomers of the Mu adducts of PEA suggests there is a water gradient within the micelles and bilayers. Slow rotation of the micelles broadened the Δ₁ resonances with increasing temperature in the L₁ phase while narrower Δ₁ resonances were observed in the L_α phase due to the rapid rotation of the spin probes around a preferred axis, which was wobbling within a cone.

Hyperfine coupling constants of the cyclohexadienyl radical in benzene and dilute aqueous solution

The muon hyperfine coupling constant (Aμ) of the muoniated cyclohexadienyl radical (C6H6Mu) has been directly measured in a 5 mM solution of benzene in water by the radio-frequency muon spin resonance (RF-μSR) technique. The relative shift of Aμ in aqueous solution compared with the value in neat benzene (ΔAμ/Aμ = +0.98(5)% at 293 K) can now be compared directly with theoretical predictions. Application of the RF-μSR method to other dilute systems will provide extremely important information on understanding solvent effects.

Zero-point corrections for isotropic coupling constants for cyclohexadienyl radical, C₆H₇ and C₆H₆Mu: beyond the bond length change approximation

Zero-point vibrational level averaging for electron spin resonance (ESR) and muon spin resonance (µSR) hyperfine coupling constants (HFCCs) are computed for H and Mu isotopomers of the cyclohexadienyl radical. A local mode approximation previously developed for computation of the effect of replacement of H by D on ¹³C-NMR chemical shifts is used. DFT methods are used to compute the change in energy and HFCCs when the geometry is changed from the equilibrium values for the stretch and both bend degrees of freedom. This variation is then averaged over the probability distribution for each degree of freedom. The method is tested using data for the methylene group of C₆H₇, cyclohexadienyl radical and its Mu analog. Good agreement is found for the difference between the HFCCs for Mu and H of CHMu and that for H of CHMu and CH₂ of the parent radical methylene group. All three of these HFCCs are the same in the absence of the zero point average, a one-parameter fit of the static HFCC, a(0), can be computed. That value, 45.2 Gauss, is compared to the results of several fixed geometry electronic structure computations. The HFCC values for the ortho, meta and para H atoms are then discussed.

Isotope effects and the temperature dependences of the hyperfine coupling constants of muoniated sec-butyl radicals in condensed phases

Reported here is the first μSR study of the muon (A(μ)) and proton (A(p)) β-hyperfine coupling constants (Hfcc) of muoniated sec-butyl radicals, formed by muonium (Mu) addition to 1-butene and to cis- and trans-2-butene. The data are compared with in vacuo spin-unrestricted MP2 and hybrid DFT/B3YLP calculations reported in the previous paper (I), which played an important part in the interpretation of the data. The T-dependences of both the (reduced) muon, A(μ)′(T), and proton, A(p)(T), Hfcc are surprisingly well explained by a simple model, in which the calculated Hfcc from paper I at energy minima of 0 and near ±120° are thermally averaged, assuming an energy dependence given by a basic 2-fold torsional potential. Fitted torsional barriers to A(μ)′(T) from this model are similar (~3 kJ/mol) for all muoniated butyl radicals, suggesting that these are dominated by ZPE effects arising from the C−Mu bond, but for A(p)(T) exhibit wide variations depending on environment. For the cis- and trans-2-butyl radicals formed from 2-butene, A(μ)′(T) exhibits clear discontinuities at bulk butene melting points, evidence for molecular interactions enhancing these muon Hfcc in the environment of the solid state, similar to that found in earlier reports for muoniated tert-butyl. In contrast, for Mu−sec-butyl formed from 1-butene, there is no such discontinuity. The muon hfcc for the trans-2-butyl radical are seemingly very well predicted by B3LYP calculations in the solid phase, but for sec-butyl from 1-butene, showing the absence of further interactions, much better agreement is found with the MP2 calculations across the whole temperature range. Examples of large proton Hfcc near 0 K are also reported, due to eclipsed C−H bonds, in like manner to C−Mu, which then also exhibit clear discontinuities in A(p)(T) at bulk melting points. The data suggest that the good agreement found between theory and experiment from the B3LYP calculations for eclipsed bonds in the solid phase may be fortuitous. For the staggered protons of the sec-butyl radicals formed, no discontinuities are seen at all in A(p)(T), also demonstrating no further effects of molecular interactions on these particular proton Hfcc.