A proton T1-nuclear magnetic resonance dispersion study of water motion in snowflakes and hexagonal ice

Snowflakes and ordinary hexagonal ice were studied measuring water proton spin–lattice relaxation rate R1(ωI)-nuclear magnetic resonance dispersion (NMRD) profiles at proton Larmor frequencies ranging from 1 to 30 MHz and at different temperatures ranging from −2◦C to −10◦C. The spin–spin relaxation rate 1/ 1/T2(ωI) was determined at a single Larmor frequency of 16.3 MHz. The high-field wing of the proton R1(ωI)-NMRD profile was characterised by two parameters: a correlation time τc which described the dipole–dipole spectral density, and the relaxation rate at low fields R max real (0) which was determined from T 2 . The correlation time τc depended on the dynamic model used. A rotation diffusion model yield approximatively 3μs at −3◦C to about 5μs at 10◦C, whereas for a more realistic six-site discrete exchange model, the correlation times decreased slightly to about 80% for the same temperature interval. Proton dipole–dipole interactions were divided into intramolecular and intermolecular contributions where the intermolecular contribution was about 0.4–0.8 × the intramolecular contribution. It was not possible to discriminate between the dynamic models or to detect ice/water interface effects by comparing the NMRD data from snowflakes with ordinary hexagonal ice data

A Proton Water T1-NMRD Study of Ganglioside Micelles

Ganglioside GM1 (GM1) micelles have been studied by means of water proton T1 NMRD experiment. The field dependent spin-lattice relaxation rates were measured for Larmor frequencies ranging from 0.1 to 40 MHz and for two micelle concentrations at three temperatures (T=10,15,20oC). The proton T1 NMRD-profiles are well described by assuming two proton pools are responsible for the dispersion curves. The proton pools are characterized by an effective correlation time and a proton fraction. The largest correlation time, τc,1 ≈ 130−160 ns, is determined by the low field part of the NMRD profile. The second correlation time, τc,2 ≈ 12 ns, is determined by the high fieldpartoftheNMRDprofile. Theradiusoftheganglioside micelles has previously been determined as about 54 using fluorescence experiments and with Stoke-Einstein relation the reorientation correlation time becomes τR= 120-165 ns depending on the temperature dependence of the water viscosity. It is thus plausible to identify one pool of waterprotons, characterized by the largest effective correlation time, as corresponding to waters residing in the headgroup withanorderparameterS6=0andτc,1 ≈ τR orcorresponding to labile protons with a τc,1as the mean life time. The proton NMRD profile reveal a second Lorenzian which also can eitherbelabileandexchangingGangliosideprotonsorwater moleculesresidingintheheadgroupwithameanlifetimeas approximately 12 ns. The proton NMRD experiment cannot discriminate between these two cases

S. Nicolaus och S. Clemens

Serien Sveriges kyrkor är utgiven av Riksantikvarieämbetet och Kungl. Vitterhets historie och antikvitets akademie

Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device

We analyze the spin coincidence experiment considered by Bell in the derivation of Bells theorem. We solve the equation of motion for the spin system with a spin Hamiltonian, Hz, where the magnetic field is only in the z-direction. For the specific case of the coincidence experiment where the two magnets have the same orientation the Hamiltonian Hz commutes with the total spin Iz, which thus emerges as a constant of the motion. Bells argument is then that an observation of spin up at one magnet A necessarily implies spin down at the other B. For an isolated spin system A-B with classical translational degrees of freedom and an initial spin singlet state there is no force on the spin particles A and B. The spins are fully entangled but none of the spin particles A or B are deflected by the Stern-Gerlach magnets. This result is not compatible with Bells assumption that spin 1/2 particles are deected in a Stern-Gerlach device. Assuming a more realistic Hamiltonian Hz + Hx including a gradient in x direction the total Iz is not conserved and fully entanglement is not expected in this case. The conclusion is that Bells theorem is not applicable to spin coincidence measurement originally discussed by Bell