Frequency measuring diffusion

Impedance Some of the errors arising from the use of linear polarisation resistance led to interest and development in a.c. systems.An early development used a fixed a.c. frequency and a commercial instrument was produced in the UK. Inaccuracies still occurred, however, and were due to the electrode impedance which is fequency dependent. Electrode reactions have a capacitance component, in addition to resistance, resulting in a requirement to measure the impedance. However, the total impedance comprises values for the reaction, solution, diffusion and capacitance. Measurements at different frequency are more reliable, particularly where high solution resistances occur. Simplifications for industrial monitoring have been developed consisting of two measurements, i.e. at a high (10 kHz) and low frequency (0-1 Hz). The high-frequency measurement can identify the... 

For a number of calculated properties (average dipole moment, dielectric permittivity and its frequency dependence, diffusion coefficient and dielectric and NMR relaxation time) the TIP4Pfq potential performs better than SPCfq, presumably thanks to its more realistic molecular geometry [100]. All calculated properties, except D = 1.9 10 cm /s vs =2.4 10 cm /s at 25 C, are in good agreement with the corresponding measured data. 

Frequency response methods have been found useful in both theoretical and experimental analysis of gas mixing in fluidized beds. Experiments in a fluidized-bed reactor related to mixing theory were made by Bamstone and Harriott 24). Testin and Stuart have measured diffusion coefficients in gas-solid adsorption studies 25). 

The range of measurable diffusivities depends on the size and the shape of the adsorbent crystals as well as the range of frequencies covered by the FR apparatus, as demonstrated in Fig. 2. Appropriate size of the crystals has to be, therefore, chosen in order to be able to detected the diffusivities of the sorbate molecules in the system. 

A method for measuring diffusivity of solid polymers based on this type of boundary condition has been developed by Berlot [49, 50], and by Gehrig et al. [51], A disc sample of thickness 2a is held at a uniform temperature and then a sinusoidal temperature fluctuation of angular frequency ta is imposed on the outer surfaces. The amplitude ratio and phase of the temperature at the center are monitored with a thermocouple. Under these conditions the amplitude ratio A and phase 0 are given by [52]... 

Field gradient A magnetic field applied to make the resonance frequencies depend - usually linearly - on the location of the spins in the sample. Specifically oriented coils in the probe generate fields ( 100mTm ) in the x, y, and z directions. More complex gradients can be created by appropriate coil design (e.g., shim coils). Pulsed field gradients are used to measure diffusion and to select multiple quantum coherences. See also MRI. 

For species in solution undergoing diffusion (without forced convection) the lowest frequency that can be used depends also on the hydrodynamic conditions. It is well known that the chronoamperometric curves in solutions might be measured up to 60 s, after which natural convection affects the linearity of diffusion. This means that measurements of the mass transport impedance are limited to approximately 0.1 Hz (or slightly lower). However, measuring diffusion in solid materials (e.g., hydrogen absorption in metals and alloys, lithium intercalation) is not influenced by convection, and the measurements might be carried out to the... 

The diffusion coefficient /), was introduced in eqs. (5-4) and (5-13). From eq.(5-ll) it can be seen that is a measure of the mobility or of the jump frequency of the particles of type L Ever since sufficient quantities of stable or radioactive isotopes for most elements have become available, the so-called tracer method of measuring diffusion coefficients has been widely used. In this method, small quantities of isotope are permitted to diffuse into the system under investigation, and isotopic effects are neglected. In completely homogeneous material, the mean square displacement xf of the tracer atoms is experimentally determined. The following formula then applies [13] ... 

A novel one-sided NMR magnet has been developed for self-diffusion measurements in thin samples [7]. Using this technique, researchers have demonstrated measurements in bulk [BMIM][TFSI] and [BMIM][TFSI] confined in nanoporous anodized aluminum oxide membranes, as shown in Fig. 3. This operates at a proton Larmor frequency of 14.08 MFlz, and the expected appHcation is toward in situ measurements in portable energy devices. This method utilizes the fringe field to measure diffusion coefficients instead of conventional PFG-NMR. 

The letters s, p, and d originate in the names sharp, principal, and diffuse. These were the terms that were given to absorption and emission lines in the atomic spectra of alkali atoms on the basis of the appearance of those lines, usually on a photographic plate. Lines of similar type formed series, and it was learned that the transition frequencies measured for a series followed a simple mathematical progression. With quantum mechanics the progressions and spectral characteristics became understandable consequences of the allowed energy levels and transitions. From this association with types of lines come the orbital letters in use today. 

Substituting Eq. (1.92) into Eq. (2.70), we obtain spectra proper to the gas phase at k < 1. These spectra for t = 1 are depicted in Fig. 2.6. There co for the IR spectra is measured from the vibrational frequency and only the right-hand half of the symmetrical band is shown. The spectra deviate only slightly from those arising in the J-diffusion model. It is hardly possible to see that their wings are not Lorentzian. The effect... 

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