General properties probe diffusion

Here we examine the literature on diffusion of probes through polymer solutions. Nearly 200 probe size polymer molecular weight combinations have been examined at a range of polymer concentrations. There is a solid but not extremely extensive body of work on the temperature dependence of probe diffusion in polymer solutions. A half-dozen studies of probe rotational motion and more than a dozen reports based on particle tracking are noted, along with a half-dozen sets of true microrheological measurements, in which mesoscopic objects perform driven motion in polymer solutions. 

Results on probe diffusion fall into three phenomenological classes. In the first two classes, diffusion is usefully characterized by a single relaxation time and hence a well-defined probe diffusion coefficient In the third class, light scattering spectra are more complex. The classes are  

We begin with systems having a well-defined probe diffusion coefficient. 

As seen above, in almost every system whose relaxations can be characterized by a single diffusion coefficient Dp, the concentration dependence of Dp is described by a stretched exponential in c, see Eq. 9.4. If Dp instead followed a power law 

A few systems show re-entrant behavior in which a relaxation rate increases with increasing c, and then perhaps decreases again at an even larger c, as reported by Bremmell, et a/.(35,36), Dunstan and Stokes(37), and Ullmann, et al.OT). In a very few systems, an apparent small-c plateau is observed Dp or r p is nearly independent of c for c up to some small concentration, and then declines at larger c, as described by Yang and Jamieson(57) and by Papagiannopolis, et a/. (89). 

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The high-temperature superionic properties of the Ag + and Cu + chalcogenides (of general formula A2X, with A = Ag, Cu and X=S, Se, Te) have been extensively studied. These compounds provide an interesting comparison with their halide counterparts, particularly when probing the effects of the doubled cation density on the ionic diffusion mechanisms and macroscopic ionic conductivity [37]. 

There are a number of factors which may influence the activity or selectivity of a polymer-immobilized catalyst. Substrate diffusion is but one. This article has reviewed the mathematical formalism for interpreting reaction rate data. The same approach that has been employed extensively in heterogeneous systems is applicable to polymer-immobilized systems. The formalism requires an understanding of the extent of substrate partitioning, the appropriate intrinsic kinetic expression and a value for the substrate s diffusion coefficient. A simple method for estimating diffusion coefficients was discussed as were general criteria for establishing the presence of substrate transport limitations. Application of these principles should permit one to identify experimental conditions which will result in the intrinsic reaction rate data needed to probe the catalytic properties of immobilized catalysts. 

The orientations of the principal diffusion axes xr, yR, zr depend critically on the hydrodynamic properties and geometry of the spin label as well as its attachment to the polymer backbone. The rotational diffusion constants Ry, and associated with each axis are in general different from each other however, nitroxides that are covalently tethered to a polymer backbone generally exhibit a principal rotation axis, around which the probe rotation is significantly faster than for any other axis. This principal direction is assigned to be the Zr axis and its orientation is typically determined by the tether bonds of the nitroxide to the polymer backbone. 

In comparisons of muons with protons and of muonium with hydrogen atoms, pronounced quantum effects occur whenever dynamics are involved. In this way, muons have been utilized to probe a large variety of properties and materials insulators, semiconductors, metals, superconductors, insulators, gases, liquids, crystalline and amorphous solids, static and dynamic magnetic properties of all kinds, electron mobility, quantum diffusion, chemical reactivity and molecular structure and dynamics. The term adopted for the broad field of muon spin spectroscopy techniques, fiSR, emphasizes the analogy with other types of magnetic resonance for example EPR. juS represents muon spin , and R in a more general sense stands simultaneously for rotation , relaxation and resonance . 

The kinetic interactions between solvent and solute molecules in free solution determine their rotational and translational diffusion characteristics. Fluorescence polarization is a spectroscopic technique that allows the determination of motional preferences of reporter molecules in fluids with respect to both the rate of motion and the orientational restriction of that motion [1,2], For spherical molecules in isotropic fluids at low concentrations, these motions can be described by the Stokes-Einstein and Perrin relationships, and if these motions have an equal probability of occurring in any dimension they are referred to as isotropic. However, when a fluid displays structure, or anisotropy, the motion of diffusing molecules may be restricted, generally to different extents in different dimensions, and these motions are said to be anisotropic. New approaches must then be taken in order to describe the probe s hydrodynamic behavior. By measuring the hydrodynamic properties of a fluorescent probe in solution, it is possible to extract valuable information on the physical structure and properties of a fluid. Knowledge of the physical structure and properties of food fluids and matrices is essential for solving practical problems in food research. 

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