A derivation is given of the effect of a time‐dependent magnetic field gradient on the spin‐echo experiment, particularly in the presence of spin diffusion. There are several reasons for preferring certain kinds of time‐dependent magnetic field gradients to the more usual steady gradient. If the gradient is reduced during the rf pulses, H1 need not be particularly large; if the gradient is small at the time of the echo, the echo will be broad and its amplitude easy to measure. Both of these relaxations of restrictions on the measurement of diffusion coefficients by the spin‐echo technique serve to extend its range of applicability. Furthermore, a pulsed gradient can be recommended when it is critical to define the precise time period over which diffusion is being measured.The theoretical expression derived has been verified experimentally for several choices of time dependent magnetic field gradient. An apparatus is described suitable for the production of pulsed gradients with amplitudes as large as 100 ...

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Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient

Equivalent weight (EW) is the number of grams of dry Nafion per mole of sulfonic acid groups when the material is in the acid form. This is an average EW in the sense that the comonomer sequence distribution (that is usually unknown to the investigator and largely unreported) gives a distribution in m in this formula. EW can be ascertained by acid-base titration, by analysis of atomic sulfur, and by FT-IR spectroscopy. The relationship between EW and m is EW ) 100m + 446 so that, for example, the side chains are separated by around 14 CF2 units in a membrane of 1100 EW. Common at the time of this writing are Nafion 117 films. The designation “117” refers to a film having 1100 EW and a nominal thickness of 0.007 in., although 115 and 112 films have also been available. Early-reported studies involved 1200 EW samples as well as special experimental varieties, some being rather thin. The equivalent weight is related to the property more often seen in the field of conventional ion exchange resins, namely the ion exchange capacity (IEC), by the equation IEC ) 1000/EW. The mention of the molecular weight of high equivalent weight (EW > 1000 g‚mol-1) Nafion is almost absent in the literature, although the range 105-106 Da has been mentioned. As this polymer does not form true solutions, the common methods of light scattering and gel permeation chromatography cannot be used to determine molecular weight as well as the size and shape of isolated, truly dissolved molecules. Studies of the structure of this polymer in solvent (albeit not a true solution) will be mentioned in the scattering section of this review. It should be noted that Curtin et al. performed size exclusion chromatography determinations of the molecular weight distribution in Nafion aqueous dispersions after they were heated to high temperatures (230, 250, and 270 °C).1 Before heating, there was a high molecular weight shoulder on a bimodal distribution, due to molecular aggregates, but this shoulder disappeared upon heating, which indicated that the aggregates were disrupted. The peaks for the monomodal distribution for the heated samples were all located at molecular weights slightly higher than 105 g‚mol-1. Also, light scattering experiments revealed that the radius of gyration had a linear dependence on the molar mass of the aggregates, which suggests that the particles are in the form of rods or ribbons, or at least some elongated structure. Nafion ionomers are usually derived from the thermoplastic -SO2F precursor form that can be extruded into sheets of required thickness. Strong interactions between the ionic groups are an obstacle to melt processing. This precursor does not possess the clustered morphology that will be of great concern in this article but does possess Teflon-like crystallinity which persists when the sulfonyl fluoride form is converted to, for example, the K+ form by reacting it with KOH in water and DMSO. Thereafter, the -SO3H form is achieved by soaking the film in a sufficiently concentrated aqueous acid solution. Extrusion of the sulfonyl fluoride precursor can cause microstructural orientation in the machine direction, * Address correspondence to either author. Phone: 601-266-5595/ 4480. Fax: 601-266-5635. E-mail: Kenneth.Mauritz@usm.edu; RBMoore@usm.edu. 4535 Chem. Rev. 2004, 104, 4535−4585

State of Understanding of Nafion

Striking convergent evolution is found in the properties of the organic osmotic solute (osmolyte) systems observed in bacteria, plants, and animals Polyhydric alcohols, free amino acids and their derivatives, and combinations of urea and methylamines are the three types of osmolyte systems found in all water-stressed organisms except the halobacteria The selective advantages of the organic osmolyte systems are, first, a compatibility with macromolecular structure and function at high or variable (or both) osmolyte concentrations, and, second, greatly reduced needs for modifying proteins to function in concentrated intracellular solutions Osmolyte compatibility is proposed to result from the absence of osmolyte interactions with substrates and cofactors, and the nonperturbing or favorable effects of osmolytes on macromolecular-solvent interactions

https://science.sciencemag.org/content/sci/217/4566/1214.full.pdf

Living with water stress: evolution of osmolyte systems

Molecular diffusion and microcirculation in the capillary network result in a distribution of phases in a single voxel in the presence of magnetic field gradients. This distribution produces a spin-echo attenuation. The authors have developed a magnetic resonance (MR) method to image such intravoxel incoherent motions (IVIMs) by using appropriate gradient pulses. Images were generated at 0.5 T in a high-resolution, multisection mode. Diffusion coefficients measured on images of water and acetone phantoms were consistent with published values. Images obtained in the neurologic area from healthy subjects and patients were analyzed in terms of an apparent diffusion coefficient (ADC) incorporating the effect of all IVIMs. Differences were found between various normal and pathologic tissues. The ADC of in vivo water differed from the diffusion coefficient of pure water. Results were assessed in relation to water compartmentation in biologic tissues (restricted diffusion) and tissue perfusion. Nonuniform slow flow of cerebrospinal fluid appeared as a useful feature on IVIM images. Observation of these motions may significantly extend the diagnostic capabilities of MR imaging.

MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders.

We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

Reptation of a Polymer Chain in the Presence of Fixed Obstacles

The pressure dependence of the self‐diffusion coefficients of several normal paraffin hydrocarbons and the isomers of hexane have been determined. In addition, the temperature dependence of self‐diffusion coefficients has been measured for the isomers of hexane. Energies and volumes of activation have been calculated. With the exception of 2, 2‐dimethyl butane, these parameters do not change significantly with branching in the isomers of hexane. The volumes of activation are about 10–20% of the molar volumes in all cases. Diffusion coefficients computed from a semiempirical modification of an equation derived by Longuet‐Higgins and Pople are compared with the experimental results.

Self‐Diffusion in Liquids: Paraffin Hydrocarbons

NMR shift and diffusion study of dioxane-H2O and pyridine-H2O mixtures

The behavior of water in Nafion membranes

Approximate expressions for the self‐diffusion coefficients of spherical molecules in solid, liquid, and gas phases are obtained from the relation D=(kT/m) ∫ 0∞ρ(s)ds, where D is the diffusion coefficient and ρ(s) is the velocity correlation function of the spherical molecules. The correlation function is approximated by the function cosαδs/coshαs and the parameters α and δ are expressed in terms of molecular properties for liquids and gases. The approximate diffusion coefficient is found to obey an Arrhenius relation in the solid phase and a Sutherland equation for the gas phase. The results of a crude calculation of the self‐diffusion coefficient for liquid neopentane are within a factor of two of the experimental diffusion coefficients. The temperature coefficient of the calculated diffusion coefficients is also within a factor of two of the observed temperature coefficient.

Self‐Diffusion and Velocity Correlation

Nuclear magnetic relaxation times have been studied in some polymer liquids and solutions. The nonexponential decay of the transverse magnetization has been ascribed to the distribution of molecular weights. The use of such measurements as a means of determining average molecular weights and distributions is discussed. A preliminary application of this use is made for polyethylene. The implications of nuclear magnetic relaxation measurements are discussed in terms of molecular motional processes of the polymer chains.

Dean C. Douglass

Papers

Self‐Diffusion in Liquids: Paraffin Hydrocarbons

NMR shift and diffusion study of dioxane-H2O and pyridine-H2O mixtures

The behavior of water in Nafion membranes

Self‐Diffusion and Velocity Correlation

Nuclear magnetic relaxation in polymer melts and solutions