General treatment of paramagnetic relaxation enhancement associated with translational diffusion.
A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented. The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al., Mol. Phys. 48, 329 (1983); Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] for inner-sphere relaxation. It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density. A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S = 7/2 and S = 1, which may correspond to Gd(III) and Ni(II) systems. It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slow relative translational diffusion and fast molecular tumbling.
Simple analytical approximation of the longitudinal electronic relaxation rate of Gd(III) complexes in solutions
More and more sophisticated theoretical models have been developped for a correct description of the relaxation of the electronic spin S = 7/2 of the Gd(III) paramagnetic complexes used as contrast agents in magnetic resonance imaging (MRI). Both the static zero field splitting (ZFS) modulated by the random rotation of the complex and the transient ZFS due to the very fast distortion of this entity must be included in these models. This leads to rather complicated analytical expressions, from which it is difficult to evaluate the respective effects of the physically relevant parameters. However, in the Redfield limit of the theory of electronic spin relaxation, we show that the longitudinal relaxation function G∥(t) has a quasi-monoexponential decay characterized by a unique relaxation rate 1/T1e, which has a simple expression in terms of the applied magnetic field B0, of the static and transient ZFS parameters, and of the rotational and vibrational correlation times. For the typical investigated Gd(III) complexes, this expression is shown to have a very satisfactory accuracy for B0 < 10 T. The various physical parameters as well as the range of validity of the relaxation approximation are discussed in detail.
Effects of reservoir volume on performance of pulse tube cooler.
A pulse tube cooler has the advantages of long-life and low-vibration over conventional cryocoolers such as G-M and Stirling coolers because of the absence of moving parts at low temperature. On the other hand, the combination of a reservoir and orifice is indispensable to optimize the performance of pulse tube coolers. In order to make the pulse tube cooler compact for practical applications, the volume of reservoir should be minimized. This paper analyzes the effects of the reservoir volume on the thermodynamic performance of various components in a simple orifice and a double-inlet pulse tube cooler by combining a linearized model with a thermodynamic analysis. Expressions of entropy production for those components are presented. The results show that the reservoir volume has a significant influence on the entropy production in the various components when the reservoir to pulse tube volume ratio is smaller than about 5. The ratio is important to determine the minimum reservoir volume for a pulse tube cooler. Optimum settings for a double-inlet pulse tube cooler are also discussed.