The Positive Muon as a Probe in Chemistry Dr. Iain McKenzie ISIS Neutron and Muon Source STFC Rutherford Appleton Laboratory I.McKenzie@rl.ac.uk
µsr and Chemistry Properties of atoms or molecules containing a µ + Molecular structure Molecular dynamics Reaction rates We study µ + as a substitute for p + 1. Because they are different: isotope effects. 2. Because they are similar: tracer, spin label
Diamagnetic Muons Free muons (µ + ) Diamagnetic states: Molecular ions (N 2 Mu + ) Compounds (MuOH) Muon spin interacts with nuclear spins. J coupling ~ Hz << Δν µ τ µ = 2.2 µs 32 µs time window Δν Δt 1 4π J Δν µ = 2.5 khz Different chemical states are indistinguishable from free µ + Precesses at ν µ [MHz] = 135.5 B [mt]
Muonium A µ = 4.463 GHz Muonium (Mu = [µ +,e - ]) The chemistry of an atom depends primarily on the ionization potential and the radius. Reduced mass = 0.995 m r (H) Ionization energy = 0.9956 R Bohr radius = 1.0044 a 0 Mass Mu = 0.1131 Mass H Chemically identical to H but has 1/9 th the mass!
Muoniated Radicals Mu adds across double bond R R C Mu C R H Delocalized unpaired electron A µ R R C C H Mu R A p Unpaired electron s spin interacts with the spins of the muon and other nuclei (I ½). Hyperfine couplings constants (A µ ) in organic radicals range from 0 to 600 MHz. Hundreds of muoniated radicals have been studied.
TF-µSR of Muonium
TF-µSR of Muonium Low field B ~ 10 G ν 12 and ν 23 are degenerate. γ Mu = 102.88 γ µ (1.394 MHz G -1 ) Measure λ Intermediate field B ~ 250 G ν 12 and ν 23 are not degenerate. Measure A µ
Measuring Mu Reaction Rate Constants λ = λ 0 + k Mu X [ ] Relaxation in pure solvent Pseudo-1 st order rate constant Concentration of reactant X λ / µs -1 Slope = k Mu Units = M -1 s -1 [X] / M
Reactions of Muonium Mu + H X Mu H + X Abstraction Mu + X Mu X Recombination Mu + X n µ + + X n+1 Electron transfer Mu( ) + X( ) Mu( ) + X( ) Spin exchange Mu + Mu H Addition
Muonium Kinetics Abstraction Reactions k Mu < k H Addition Reactions k Mu > k H Mu X + X H H D Isotope effect depends on the width and height of the activation barrier I. D. Reid et al. J. Chem. Phys. 86 (1987) 5578 E. Roduner et al. Ber. Bunsenges. Phys. Chem. 94 (1990) 1224
70 MeV/c Supercritical water P = 400 bar and T = 700 K! e + µ + E max = 52.8 MeV Mu Kinetics in Supercritical Water Mu + C 6 H 6 Extrapolated from low temperature data K. Ghandi et al. PCCP 4 (2002) 586
Hfc of Muonium The hfc of Mu is sensitive to the local environment. Spin density transfer to surrounding solvent molecules. Compression of 1s wavefunction. Methanol / water mixtures Incomplete mixing of methanol and water on the molecular scale. Electrolyte solutions Ordering of water molecules surrounding Mu. I. McKenzie et al. J. Phys. Chem. B 112 (2008) 3070
Allowed transitions TF-µSR of Muoniated Radicals E. Roduner et al. Chem. Soc. Rev. 29 (1993) 337
TF-µSR of Muoniated Radicals CD 2 Mu Radical frequencies ν 12 and ν 43 Linewidth λ R =1/T 2 ν 12 A µ ν 43 Due to transitions between spin states with opposite muon spins. Diamagnetic frequency ν D A µ (MHz) = ν 43 ν 12
RF-µSR of Muoniated Radicals 0.002 B res RF Asymmetry 0.001 0.000-0.001-0.002-0.003-0.004 ν RF = 10 MHz H 3 C C OMu H 3 C 1700 1750 1800 1850 1900 1950 Magnetic Field / Gauss ν RF = γ µ B res 1 2 A µ Measure A µ for slowly formed radicals (slow Mu addition or dilute solutions)
ALC-µSR of Muoniated Radicals ΔM=0 Resonances ΔM=2 Resonances Narrow and weak. Rarely observed. B r A µ A k ( ) 2 γ µ γ k Observed in solids, liquids and gases. ΔM=1 Resonances Sensitive indicator of reorientation dynamics on timescale of 20-50 ns. [ ] B r = A µ + D (3cos 2 θ 1) 1 1 2γ µ 2γ e
Identification of Muoniated Radicals TF-µSR Precession frequencies RF-µSR Resonance field ALC-µSR Resonance fields Hyperfine Coupling Constants Temperature Dependence of HFCs Muon hfc (A µ ) Nuclear hfcs (H, D, 13 C, 14 N.) Distribution of unpaired electron Intramolecular motion
ALC-µSR of Muoniated Radicals P. W. Percival et al. Chem. Phys. Lett. 245 (1995) 90
Structure Determination of Muoniated Radicals Hyperfine coupling constants map out the unpaired spin density but don t provide the structure directly A + - A Fourier Power A µ = 246.4 MHz D R R 0 100 200 300 400 Frequency / MHz A N = 13.7 MHz A + - A A C = 139.6 MHz 3.1 3.5 3.9 4.3 4.7 5.1 5.5 Magnetic Field / kg H 3 C H 3 C N N i-pr 13 C i-pr Mu Identify structure by comparing with DFT calculations of possible radicals. 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 Magnetic Field / kg I. McKenzie et al. J. Am. Chem. Soc. 125 (2004) 11565
Isotope Effects on Intramolecular Dynamics
Isotope Effects on Intramolecular Dynamics CH 2 Mu CH 3 A µ = [ L + M cos 2 ( φ φ 0 ) ]ρ
Isotope Effects on Bond Length r C-Mu ~ 1.049 r C-H m r = m µ m X m µ + m X m µ C Mu ω = k m r C H ZPE = 1 2 ω 1.0 1.2 1.4 Bond length / Å Asymmetric bond stretching potential results in C-Mu bond being longer than C-H bond. E. Roduner et al. Isr. J. Chem. 29 (1989) 3
Measuring Radical Reaction Rates ALC-µSR resonance width ΔB 1/ 2 = ω 2 ALC λ = λ 0 + k R + λ 2 ( ) 2π γ µ γ p [ X] Slope = k R Units = M -1 s -1
Reorientational Dynamics in Solids Hyperfine Tensor B zz B yy B xx Polarization 1 degree 5 degrees 20 degrees 45 degrees 70 degrees 85 degrees 89 degrees B yy 0 B xx = 8.6 MHz B zz = - 8.6 MHz The resonance position depends on the orientation of the molecule with respect to the magnetic field. 14500 15000 15500 16000 16500 Magnetic field / G Resonance lineshape depends on the weigthing of each orientation
Lineshape can provide information about preferred rotation axis Reorientational Dynamics in Solids
Reorientational Dynamics in Solids Δ 1 resonance Asymmetric lineshape indicates preferred rotation axis E. Roduner et al. Chem. Soc. Rev. 29 (1993) 337
µsr as a Probe of Soft Matter Site-directed spin labeling (SDSL) Probe the local environment and dynamics in specific regions Stable spin labels (nitroxides) are a large perturbation compared with Mu
Partitioning of Co-surfactants Surfactant Co-surfactant hydrophobic hydrophilic DHTAC Surfactants can form bilayers, micelles, vesicles, etc. H 2 C CH 2 OH 2-phenylethanol Fragrances Food additives. Drug delivery
Partitioning of Co-surfactants Mu H Anisotropic environment CH 2 H 2 C OH L α phase H Mu L β phase Isotropic environment CH 2 H 2 C OH Mu H CH 2 H 2 C OH 40 mm Phenylethanol in DHTAC Scheuermann et al. PCCP 4 (2002) 1510
Probing the Local Environment of Co-surfactants Non-polar Polar R. Scheuermann et al. PCCP 4 (2002) 1510
Partitioning of Co-surfactants
Spin Labeling of Calamitic Liquid Crystals Δ 0 resonances B C D A A G z (t) = exp[ (λt) β ] B C D Lovett et al. Physica B 289-290 (2000) 612 Phys. Rev. B 63 (2001) 054204
RS 3 2 SR Spin Labeling of Discotic Liquid Crystals 4 1 4a 12b 5 4b 12a 12 RS 6 RS 8a 8b 7 8 9 10 R = -C 6 H 13 11 SR SR 0.00 377 K I 0.25 Cr H Col h I 0.04-0.05 RS RS SR 0.00 RS SR Mu 352 K Col h Mu H 4 H -0.05 4 H 1 H 1 0.00 337 K H SR RS -0.05 0.00 332 K Cr Corrected Asymmetry SR HWHM / T 0.20 0.15 0.10 0.03 0.02 Amplitude / a.u. RS SR RS -0.03 SR 0.01 0.00 302 K Cr 0.05-0.01 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Magnetic Field / T 300 310 320 330 340 350 360 370 380 Temperature / K 0.00 I. McKenzie et al. Unpublished
RS 3 2 SR Spin Labeling of Discotic Liquid Crystals 4 1 4a 12b 5 4b 12a 12 RS 6 RS 8a 8b 7 8 9 10 R = -C 6 H 13 11 SR SR 0.00 377 K I 0.25 Cr H Col h I 0.04-0.05 RS RS SR 0.00 RS SR Mu 352 K Col h Mu H 4 H -0.05 4 H 1 H 1 0.00 337 K H SR RS -0.05 0.00 332 K Cr Corrected Asymmetry SR HWHM / T 0.20 0.15 0.10 0.03 0.02 Amplitude / a.u. RS SR RS -0.03 SR 0.01 0.00 302 K Cr 0.05-0.01 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Magnetic Field / T 300 310 320 330 340 350 360 370 380 Temperature / K 0.00 I. McKenzie et al. Unpublished
Non-Conducting Polymers Poly-butadiene Hfcs provide information about the conformation. Onset of motion at the glass transition temperature. T g F. Pratt et al. Physica B 326 (2003) 34 S. J. Blundell Chem. Rev. 104 (2004) 5717
µsr of Conducting Polymers Interchain diffusion rate D hfc ω 0 D Intrachain diffusion rate λ rate of random electron spin flips 1-D diffusion Risch-Kehr model with λt exp >>1 1-D diffusion 3-D diffusion G z (t) = exp(γt)erfc( Γt ) relaxation function D γ e B c relaxation parameter for Crossover field Γ = ω 4 0 2 2ω e D D > ω 0 > λ
µsr of Conducting Polymers Interchain transport is assisted by thermal motion F. Pratt et al. Physica B 326 (2003) 34
Conclusions Muon spectroscopic techniques are powerful tools for characterizing free radicals in the solid, liquid or gaseous phases. The light mass of the muon can have a large effect on chemical reaction rates and the motion of free radicals. Muon site directed spin labeling can provide information about molecular dynamics in soft matter systems.