An NMR study of methanol diffusion in polymer electrolyte fuel cell membranes

Methanol diffusion in two polymer electrolyte membranes, Nafion 117 and BPSH 40 (a 40% disulfonated wholly aromatic polyarylene ether sulfone), was measured using a modified pulsed field gradient NMR method. This method allowed for the diffusion coefficient of methanol within the membrane to be determined while immersed in a methanol solution of known concentration. A second set of gradient pulses suppressed the signal from the solvent in solution, thus allowing the methanol within the membrane to be monitored unambiguously. Over a methanol concentration range of 0.5–8 M, methanol diffusion coefficients in Nafion 117 were found to increase from 2.9 × 10⁻⁶ to 4.0 × 10⁻⁶ cm² s⁻¹. For BPSH 40, the diffusion coefficient dropped significantly over the same concentration range, from 7.7 × 10⁻⁶ to 2.5 × 10⁻⁶cm² s⁻¹. The difference in diffusion behavior is largely related to the amount of solvent sorbed by the membranes. Increasing the methanol concentration results in an increase in solvent uptake for Nafion 117, while BPSH 40 actually excludes the solvent at higher concentrations. In contrast, diffusion of methanol measured via permeability measurements (assuming a partition coefficient of 1) was lower (1.3 × 10⁻⁶ and 6.4 × 10⁻⁷ cm² s⁻¹ for Nafion 117 and BPSH 40 respectively) and showed no concentration dependence. The differences observed between the two techniques are related to the length scale over which diffusion is monitored and the partition coefficient, or solubility, of methanol in the membranes as a function of concentration. For the permeability measurements, this length is equal to the thickness of the membrane (178 and 132 μm for Nafion 117 and BPSH 40 respectively) whereas the NMR method observes diffusion over a length of approximately 4–8 μm. Regardless of the measurement technique, BPSH 40 is a greater barrier to methanol permeability at high methanol concentrations.     

Geometrical factors in the dispersion of ballistic heat pulses

The dispersion of ballistic heat pulses in dielectric crystals can partly be ascribed to geometrical factors that include the sample thickness, the contact areas of the source and detector and their relative positioning, and the acoustic anisotropy of the transmission medium. These factors are involved in determining the spread in the path lengths and group velocities of the phonons that are transmitted. In this paper we derive a simple expression, valid when the source and detector dimensions are small compared with the thickness of the slab-shaped sample, which relates the temporal width of a ballistic heat pulse to the average in-plane component of the slowness vector s of the transmitted phonons. A comparison is made between the predictions of this expression, Monte Carlo simulations and published experimental ballistic heat pulse data on paratellurite.     

Plasticized single conductung polyelectrolytes based on poly (AMPS)

Poly(2-acrylamido-2-methyl-propane-1-sulphonic acid), poly(AMPS), has been ion exchanged with lithium and sodium to form alkali metal ion conducting polyelectrolytes. In the pure form these materials are rigid and would thus show limited conductivity. However addition of water or dimethylsulphoxide, as plasticizers, increases the conductivity by several orders or magnitude. The thermal analysis and NMR relaxation studies of these systems suggest that the increase in conductivity is as a direct result of increased ion mobility although the FTIR evidence still suggests significant ion association consistent with weak electrolytes. Although the T_g's of the sodium form of the polymer were higher, this system displayed higher conductivities than lithium which can be explained by a greater degree of ion dissociation and hence a larger number of charge carriers in the case of sodium poly(AMPS).     

Diffuse reflection and polarization modulation FT-IR spectrometry of surface species

Summary Two techniques for measuring the infrared spectra of adsorbed species on surfaces of different types are described. Diffuse reflectance spectra of species adsorbed on powdered substrates with a high surface area can be measured with an exceptionally high signal-to-noise ratio. The technique is illustrated by the adsorption of carbon monoxide on rhodium supported on alumina at metal loadings between 0.1 and 10%. Some doubt is cast on previous band assignments for adsorbed CO molecules. Grazing incidence reflection-absorption spectrometry can be used to measure the spectra of molecules on flat metallic substrates of very low surface area. Attempts to develop a technique for observing the intermolecular vibration between the adsorbate and the substrate using a unique triple modulation approach are discussed.

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FT-IR-Spektrometrie mit diffuser Reflexions- und Polari-sations-Modulation von Adsorbaten an Oberflächen

Zusammenfassung Zwei Techniken zur Messung von Infrarot-Spektren von Adsorbaten verschiedener Art werden beschrieben. Diffuse Reflexionsspektren von Adsorbaten an pulverförmigen Substraten mit einer großen Oberfläche können mit einem außerordentlich großen Signal-zu-RauschVerhältnis gemessen werden. Als Beispiel dient die Adsorption von Kohlenstoffmonoxid an Rhodium auf Aluminiumoxid bei Metallgehalten von 0,1 bis 10%. Einige Zweifel an früheren Bandzuweisungen für adsorbierte CO-Moleküle werden geäußert. Reflexions-Absorptions-Spektrometrie mit streifendem Einfall kann zur Messung der Spektren von Molekülen an flachen metallischen Substraten mit sehr geringer Oberfläche benutzt werden. Versuche zur Entwicklung einer Technik für die Beobachtung der intermolekularen Schwingungen zwischen dem Adsorbaten und dem Substrat mittels einer einzigartigen Dreifach-Modulationstechnik werden diskutiert.

     

Electroacoustic waves in piezoelectric crystals: Certain limiting cases

The Christoffel equations for electroacoustic waves in unbounded piezoelectric crystals are solved in the limits of weak and strong electromechanical coupling and for the case where the unstiffened elastic constants satisfy the conditions of elastic isotropy. Lyubimov's proof that piezoelectric stiffening of the elastic constants increases acoustic velocities is extended to cover degenerate modes. It is shown that when the elastic contribution to the stiffened elastic constants is zero, only one acoustic branch survives with a finite velocity. When the unstiffened elastic constants satisfy the conditions of elastic isotropy one of the acoustic branches is unaffected by the piezoelectric stiffening and, moreover, Lyubimov's theorem holds nonperturbatively.     

Acoustic field radiated into a transversely isotropic solid from a small aperture spherical surface

The acoustic field modelling reported in this paper finds application in the design of a scanning probe tip for measuring the near-surface elastic properties of solids and surface structures at high frequencies and with high spatial resolution. The underlying concept is for a longitudinally polarized pulse to be launched from a spherically-shaped portion of the upper surface of the pyramidal or conical shaped tip, and focused towards the narrow lower end. The change in the reflectivity when the narrow end is brought into contact with a solid will provide a measure of the local frequency dependent compliance of that solid. The calculations assume the material from which the tip is fabricated to be transversely isotropic, with symmetry axis coinciding with the axis of the tip. The main issue addressed in this paper is the role of the curvature of the radiating surface and anisotropy of the medium in determining the focal length and focal spread of the radiated field. Two complementary approaches are taken, firstly the discretization of the equations of motion on an irregular mesh of around 3 × 10⁵ triangular elements and solution using the commercial FE package ABAQUS/Explicit, and secondly an analytical approach based on ray tracing and a Green’s function method exploiting the angular spectrum method and stationary phase approximation in its evaluation. Consistency is achieved between these approaches regarding the characteristics of the focal region. With the combination of the two approaches it is thus possible to model the wave field from low frequencies, where the FE method is computationally economical and able to handle complex geometries, to high frequencies, where advantage increasingly lies with ray tracing and the Green’s function method.     

Effect of spatial dispersion on transient acoustic wave propagation in 3D

Spatial dispersion is the variation of wave speed with wavelength. It sets in when the acoustic wavelength approaches the natural scale of length of the medium, which could, for example, be the lattice constant of a crystal, the repeat distance in a superlattice, or the grain size in a granular material. In centrosymmetric media, the first onset of dispersion is accommodated by the introduction of fourth order spatial derivatives into the wave equation. These lead to a correction to the phase velocity which is quadratic in the spatial frequency. This paper treats the effect of spatial dispersion on the point force elastodynamic Green's functions of solids. The effects of dispersion are shown to be most pronounced in the vicinity of wave arrivals. These lose their singular form, and are transformed into wave trains known as quasi-arrivals. The step and ramp function wave arrivals are treated, and it is shown that their unfolded quasi-arrival forms can be expressed in terms of integrals involving the Airy function.     

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.