Transport measurements

A very wide range of techniques can be used to probe atomic transport in solids, and these have been detailed in various books [204—208] and reviews [21, 209-212[ (see also Chapters 13, 8, 11 and 12). The most commonly used are tracer methods, ionic conductivity, and NMR measurements. Less commonly used (but more specialized) techniques include creep, quasi-elastic neutron scattering (QENS), and Mbssbauer spectroscopy (M S). An elegant survey ofthe methods that have been used on nanoionic materials has been made by Heitjans and Indris [210]. The principles, procedures, and limitations of the more common techniques are outlined in the following sections. 

Some general comments might be useful, however, before considering the individual methods. First, the techniques may be divided into (i) macroscopic methods, which are used to measure the effect of long-range motion of atoms and (ii) microscopic methods, which are used to measure the effect of jump frequencies of atoms [210, 212]. In principle, for a simple jump process via point defects in a solid, the two are interconnected by the classical Einstein-Smoluchowski equation [204]  

The techniques that have been described so far to measure the molar masses of polymers in solution depend upon the equilibrium properties of the polymer solution. It is possible to relate the molar mass of the polymer to the solution properties through theoretical (e.g. thermodynamic) equations and the measurements are normally extrapolated to zero concentration where the solutions exhibit ideal behaviour. It is also possible to determine molar masses by studying the transport properties of polymer solutions which are usually analysed in terms of hydrodynamic models. These properties can be divided into two categories one of which involves the motion of the molecules through a solvent which is itself stationary (e.g. ultracentifuge) and the other deals with the effect of polymer molecules upon the motion of the whole solution (e.g. solution viscosity). The theoretical models which have been devised to explain the transport properties are by no means as well developed as those used to explain, for example, the thermodynamic properties of polymer solutions and so transport properties are normally analysed using semi-empirical 

The presence of polymer molecules in particular solvents can give rise to a dramatic increase in viscosity which is very much greater than that found for equivalent concentrations of low-molar-mass solutes. This is because of the enormous difference in dimensions between the polymer and solvent molecules and in good solvents the polymer coils are expanded even further. In general the increase in viscosity depends upon a number of factors which are as follows. 

Polymer scientists are normally interested in the variation of the solution viscosity with molar mass. Unfortunately no theories have been developed to relate them to each other and empirical relationships are used to determine the molar mass of a polymer sample from measurements of solution viscosity. However, this method does have the distinct advantage of being a rapid technique that can be carried out quickly using relatively simple apparatus. 

The necessity of using identical volumes of liquid in the Ostwald viscometer clearly leads to a potential source of error and this problem is overcome in the Ubbelohde or suspended-level viscometer also shown in 

From a practical viewpoint it is necessary with all viscometers to make sure that the solutions and capillaries are clean and free from dust or dirt. It may be necessary to filter the solutions and flush out the capillary with solvent from time to time otherwise serious errors may occur in the results. The viscometer is usually kept in a water bath during measurements and sufficient time must be allowed for the temperature of the solution and apparatus to equilibriate as the viscosity of the solution varies strongly with temperature. 

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Ion transport measurements indicate that Na" ions carry most of the current, yet aluminum is deposited. A charge transfer probably occurs at the cathode interface and hexafluoroaluminate ions are discharged, forming aluminum and F ions to neutralize the charge of the current carrying Na" ... 

Carbon Dioxide Transport. Measuring the permeation of carbon dioxide occurs far less often than measuring the permeation of oxygen or water. A variety of methods ate used however, the simplest method uses the Permatran-C instmment (Modem Controls, Inc.). In this method, air is circulated past a test film in a loop that includes an infrared detector. Carbon dioxide is appHed to the other side of the film. AH the carbon dioxide that permeates through the film is captured in the loop. As the experiment progresses, the carbon dioxide concentration increases. First, there is a transient period before the steady-state rate is achieved. The steady-state rate is achieved when the concentration of carbon dioxide increases at a constant rate. This rate is used to calculate the permeabiUty. Figure 18 shows how the diffusion coefficient can be deterrnined in this type of experiment. The time lag is substituted into equation 21. The solubiUty coefficient can be calculated with equation 2. 

Figure 3.5 The apparent vapour pressure of gold in gas transportation measurements as a function of the gas flow rate. Low flow rates, which were used earlier to assure equilibrium, are now known to be too high as a result of thermal diffusion in the gas mixture which is saturated with gold vapour...

Early transport measurements on individual multi-wall nanotubes [187] were carried out on nanotubes with too large an outer diameter to be sensitive to ID quantum effects. Furthermore, contributions from the inner constituent shells which may not make electrical contact with the current source complicate the interpretation of the transport results, and in some cases the measurements were not made at low enough temperatures to be sensitive to 1D effects. Early transport measurements on multiple ropes (arrays) of single-wall armchair carbon nanotubes [188], addressed general issues such as the temperature dependence of the resistivity of nanotube bundles, each containing many single-wall nanotubes with a distribution of diameters d/ and chiral angles 6. Their results confirmed the theoretical prediction that many of the individual nanotubes are metallic. 

From our transport measurements, we can conclude that at low temperatures, the conductivity of the bundle of buckytubes shows two-dimensional weak localization behavior and the MR is negative above 60 K the MR is positive and increases approximately... 

Fig. 6. The magnetic field dependence of the high- and low-temperature MR, respeetively the solid lines are caleulated. The inset shows a sehematic of the eontact eonfiguration for the transport measurements.

Mass transport measurements have shown that cation transport predominates in FeO (Fe ) and Fej04 (Fe, Fe ), whereas anion transport predominates in FejOj (0 ). This leads to the well-accepted growth scheme for multi-layered scale growth on iron shown in Fig. 7.3, with the governing equations for individual layer growth being ... 

In situ electron transport measurements on conducting polymers are commonly made by using a pair of parallel-band electrodes bridged by the polymer [Fig. 9(A)].141142 Other dual-electrode techniques in which the polymer film is sandwiched between two electrodes [Fig. 9(B)],139,140 rotating-disk voltammetry [Fig. 9(C)],60,143 impedance spectroscopy,144,145 chronoamperometry,146 and chronopotentiometry147 have also been used. 

Figure 9. Schematic diagrams of (A) parallel-band electrode,141 142 (B) sandwiched electrode,139 140 and (C) rotating-disk voltammetry60 143 methods for making in situ electron transport measurements on polymer films.

In the previous chapters, examples of ID arrays of nanoclusters have been given, where self-assembly or ET were used to address the arrays for electrical transport measurements. So far it is evident that these methods did not lead to strictly ID defect-free arrangements. Furthermore, inherent disorder cannot be avoided. This means that the electrical transport properties through a perfect array could only be studies theoretically up to now. 

By inspection, the flux is directly proportional to the solubility to the first power and directly proportional to the diffusion coefficient to the two-thirds power. If, for example, the proposed study involves mass transport measurements for series of compounds in which the solubility and diffusion coefficient change incrementally, then the flux is expected to follow this relationship when the viscosity and stirring rate are held constant. This model allows the investigator to simulate the flux under a variety of conditions, which may be useful in planning experiments or in estimating the impact of complexation, self-association, and other physicochemical phenomena on mass transport. 

In whole tissue or cell monolayer experiments, transcellular membrane resistance (Rm = Pm1) lumps mucosal to serosal compartment elements in series with aqueous resistance (R = P ). The operational definition of Lm depends on the experimental procedure for solute transport measurement (see Section VII), but its magnitude can be considered relatively constant within any given experimental system. Since the Kp range dwarfs the range of Dm, solute differences in partition coefficient dominate solute differences in transcellular membrane transport. The lumped precellular resistance and lumped membrane resistance add in series to define an effective resistance to solute transport ... 

S.B. Cronin, R. Barnett, M. Tinkham, S.G. Chou, O. Rabin, M.S. Dresselhaus, A.K. Swan, M.S. Unlu, and B.B. Goldberg, Electrochemical gating of individual single-wall carbon nanotubes observed by electron transport measurements and resonant Raman spectroscopy. Appl. Phys. Lett. 84, 2052—2054 (2004). 

Salomon A, Cahen D, Lindsay S, Tomfohr J, Engelkes VB, Frisbie CD (2003) Comparison of electronic transport measurements on organic molecules. Adv Mater 15 1881-1890... 

Apart from the more conventional transport measurements of molecular junctions at constant bias voltage, alkane(di)thiols-based molecular junctions were also characterized by transition voltage spectroscopy [258, 259], AC voltage modulation [260], and inelastic electron tunneling spectroscopies [261],... 

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