The optical properties of metal nanoparticles have long been of interest in physical chemistry, starting with Faraday's investigations of colloidal gold in the middle 1800s. More recently, new lithographic techniques as well as improvements to classical wet chemistry methods have made it possible to synthesize noble metal nanoparticles with a wide range of sizes, shapes, and dielectric environments. In this feature article, we describe recent progress in the theory of nanoparticle optical properties, particularly methods for solving Maxwell's equations for light scattering from particles of arbitrary shape in a complex environment. Included is a description of the qualitative features of dipole and quadrupole plasmon resonances for spherical particles; a discussion of analytical and numerical methods for calculating extinction and scattering cross-sections, local fields, and other optical properties for nonspherical particles; and a survey of applications to problems of recent interest involving triangula...

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The Optical Properties of Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment

A spin echo method adapted to the measurement of long nuclear relaxation times (T2) in liquids is described. The pulse sequence is identical to the one proposed by Carr and Purcell, but the rf of the successive pulses is coherent, and a phase shift of 90° is introduced in the first pulse. Very long T2 values can be measured without appreciable effect of diffusion.

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Modified Spin‐Echo Method for Measuring Nuclear Relaxation Times

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

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Peclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world.

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Microfluidics: Fluid physics at the nanoliter scale

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.

Nuclear resonance techniques involving free precession are examined, and, in particular, a convenient variation of Hahn's spin-echo method is described. This variation employs a combination of pulses of different intensity or duration ("90-degree" and "180-degree" pulses). Measurements of the transverse relaxation time ${T}_{2}$ in fluids are often severely compromised by molecular diffusion. Hahn's analysis of the effect of diffusion is reformulated and extended, and a new scheme for measuring ${T}_{2}$ is described which, as predicted by the extended theory, largely circumvents the diffusion effect. On the other hand, the free precession technique, applied in a different way, permits a direct measurement of the molecular self-diffusion constant in suitable fluids. A measurement of the self-diffusion constant of water at 25\ifmmode^\circ\else\textdegree\fi{}C is described which yields $D=2.5(\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in good agreement with previous determinations. An analysis of the effect of convection on free precession is also given. A null method for measuring the longitudinal relaxation time ${T}_{1}$, based on the unequal-pulse technique, is described.

Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments

Resonance Absorption by Nuclear Magnetic Moments in a Solid

The exchange of energy between a system of nuclear spins immersed in a strong magnetic field, and the heat reservoir consisting of the other degrees of freedom (the "lattice") of the substance containing the magnetic nuclei, serves to bring the spin system into equilibrium at a finite temperature. In this condition the system can absorb energy from an applied radiofrequency field. With the absorption of energy, however, the spin temperature tends to rise and the rate of absorption to decrease. Through this "saturation" effect, and in some cases by a more direct method, the spin-lattice relaxation time ${T}_{1}$ can be measured. The interaction among the magnetic nuclei, with which a characteristic time $T_{2}^{}{}_{}{}^{\ensuremath{'}}$ is associated, contributes to the width of the absorption line. Both interactions have been studied in a variety of substances, but with the emphasis on liquids containing hydrogen.Magnetic resonance absorption is observed by means of a radiofrequency bridge; the magnetic field at the sample is modulated at a low frequency. A detailed analysis of the method by which ${T}_{1}$ is derived from saturation experiments is given. Relaxation times observed range from ${10}^{\ensuremath{-}4}$ to ${10}^{2}$ seconds. In liquids ${T}_{1}$ ordinarily decreases with increasing viscosity, in some cases reaching a minimum value after which it increases with further increase in viscosity. The line width meanwhile increases monotonically from an extremely small value toward a value determined by the spin-spin interaction in the rigid lattice. The effect of paramagnetic ions in solution upon the proton relaxation time and line width has been investigated. The relaxation time and line width in ice have been measured at various temperatures.The results can be explained by a theory which takes into account the effect of the thermal motion of the magnetic nuclei upon the spin-spin interaction. The local magnetic field produced at one nucleus by neighboring magnetic nuclei, or even by electronic magnetic moments of paramagnetic ions, is spread out into a spectrum extending to frequencies of the order of $\frac{1}{{\ensuremath{\tau}}_{c}}$, where ${\ensuremath{\tau}}_{c}$ is a correlation time associated with the local Brownian motion and closely related to the characteristic time which occurs in Debye's theory of polar liquids. If the nuclear Larmor frequency $\ensuremath{\omega}$ is much less than $\frac{1}{{\ensuremath{\tau}}_{c}}$, the perturbations caused by the local field nearly average out, ${T}_{1}$ is inversely proportional to ${\ensuremath{\tau}}_{c}$, and the width of the resonance line, in frequency, is about $\frac{1}{{T}_{1}}$. A similar situation is found in hydrogen gas where ${\ensuremath{\tau}}_{c}$ is the time between collisions. In very viscous liquids and in some solids where $\ensuremath{\omega}{\ensuremath{\tau}}_{c}g1$, a quite different behavior is predicted, and observed. Values of ${\ensuremath{\tau}}_{c}$ for ice, inferred from nuclear relaxation measurements, correlate well with dielectric dispersion data.Formulas useful in estimating the detectability of magnetic resonance absorption in various cases are derived in the appendix.

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Relaxation Effects in Nuclear Magnetic Resonance Absorption

Editor’s note: This is a reprint (slightly edited) of a paper of the same title that appeared in the book Physics and Our World: A Symposium in Honor of Victor F. Weisskopf, published by the American Institute of Physics (1976). The personal tone of the original talk has been preserved in the paper, which was itself a slightly edited transcript of a tape. The figures reproduce transparencies used in the talk. The demonstration involved a tall rectangular transparent vessel of corn syrup, projected by an overhead projector turned on its side. Some essential hand waving could not be reproduced.

Edward M. Purcell

Papers

Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments

Resonance Absorption by Nuclear Magnetic Moments in a Solid

Relaxation Effects in Nuclear Magnetic Resonance Absorption

Life at low Reynolds number

Scattering and Absorption of Light by Nonspherical Dielectric Grains