Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47920/1/10107_2005_Article_BF01582296.pd

Interface development in polycarbonate/poly(methyl methacrylate) bilayer films

We report the effect of annealing over a range of temperatures and times on the mixing, stability, and interfacial width in thin bilayer films of bisphenol A-polycarbonate (PC) on deuterated poly(methyl methacrylate) (dPMMA). These bilayer films were highly stable when annealed at temperatures of up to 438 K, the temperature at which the degradation of the blends of these materials was first detectable by thermogravimetric analysis. At higher temperatures, dewetting of the PC upper layer of the film occurred at an increasing rate. Nuclear reaction analysis showed that the PC and dPMMA layers remained segregated. Neutron reflectometry data showed that the interfacial width between the two polymer layers grew rapidly from 0.5 nm for an unannealed sample to approximately 4.0 nm, the latter value being in good agreement with the predicted value for the interfacial width in the absence of any reaction. Extended annealing at 438 K and lower temperatures had no effect on the interfacial width, whereas at higher temperatures, the interfacial width increased to approximately 5.5 nm before the films became unstable. The broadening of the interface found at higher annealing temperatures was attributed to an increase in the miscibility of the polymers induced by the monomer from the unzipping of the dPMMA chains. There was no evidence of a thermally induced chemical reaction between the two polymers. (C) 2001 John Wiley & Sons, Inc

Partitioning of a heterotelechelic polystyrene to separate interfaces of thin films

Heteratelechelic deuteropolystyrenes have been synthesised with a tertiary amine functionality at one end and a fluorocarbon group at the other end of the polymer chain. A layer of this polymer. circa 120 Angstrom thick, has been attached to the surface of a silicon substrate and subsequently covered with a much thicker layer of hydrogenous polystyrene. The combination has then been annealed at 413 K under vacuum for defined times and the subsequent distribution of the deutero heterotelechelic polymer determined using nuclear reaction analysis and neutron reflectometry. The influences of annealing time, molecular weight and thickness of the hydrogenous polymer have been examined. Nuclear reaction analysis showed that an excess of the heterotelechelic polymer formed at both interfaces with a larger excess remaining at the substrate-polymer interface. When the molecular weight of the hydrogenous polymer is lower than that of the deuteropolymer, the deutero layer is initially swollen by the hydrogenous polymer but the thickness then decreases as deutero polymer becomes detached from the silicon substrate and an additional excess layer is eventually formed at the vacuum-polymer surface. When the molecular weight of the hydrogenous polymer is higher, there is an initial shrinkage of the deuteropolymer layer. but the original thickness (similar to radius of gyration of the. deuteropolymer) is regained on prolonged annealing. There is no evidence for bridging between the two interfaces by the heterotelechelic polymer. After five days annealing the volume fraction distribution of the deuteropolymer at the silicon substrate was well described by a self-consistent field model where the only adjustable parameter was the sticking energy of the tertiary amine group to the silicon substrate for which a value of 8 k(B)T was obtained. Comparison of the dependence of the equilibrium layer thickness of the deuteropolymer on the equilibrium grafting density at the silicon surface with the predictions of scaling theory for brush-like polymer layers suggested that the grafted molecules were in the ideal, unperturbed brush region

In situ water permeation measurement using an external He-3(2+) ion beam

A new approach for water vapour transmission rate (WVTR) measurement is demonstrated that uses an external ion beam. ‘Sandwich’ specimens were prepared comprising two films of the barrier material (PET) surrounding a thin film of hydrophilic poly(ethylene-oxide), “PEO”. Deuterated water (D2O) permeating PET barrier films was trapped by the PEO, and quantified using 3He2+ nuclear reaction analysis and proton detection. WVTR was determined from the rate of D2O accumulation in the PEO layer. This approach may be applied both to poor barrier films with WVTRs of >200 g m−2 day−1, and may extend to films whose barrier properties exceed levels that can be characterised with conventional techniques. Variation in the proton energy distribution provides a means of measuring D2O migration within test samples, and could be used to detect the approach to failure in complex barrier films. In these experiments, D2O migration toward the irradiated face of the sample was attributed to ion beam-induced reactive sites or increased hydrophilicity of the barrier film, and was verified by separate measurements of the D2O content of PET films. Strategies for improving the sensitivity and accuracy of this method for WVTR characterisation towards a lower detection limit 1 μg m−2 day−1 are discussed