Microwave frequency measurement

Recent interest has been in the conductivity of more stable ring polymers (there are ordered and disordered regions, see Fig. 3.6). The microwave frequency measure-... 

The field separation and thus the resolution increases with the microwave frequency. Anisotropy of the g-factor occurring in solid materials is also better resolved gi and g2 could correspond to the axial (g ) and perpendicular (gj ) components in a cylindrically symmetric case, or two of the three g-factors of a general g-tensor (Chapter 4). Splittings due to hyperfine- or zero-field interactions are (to first order) independent of the microwave frequency. Measurements at different frequencies can therefore clarify if an observed spectrum is split by Zeeman interactions (different g-factors) or other reasons. 

TABLE 46.5. Typical low frequency plasma frequency and relaxation time obtained from microwave frequency measurements of very highly conducting polymers. 

Figure 15-6. (a) Phoioiuduccd absorption-detected magnetic resonance (ADMR) spectrum of MEH-PPV. HF and FF represents tire half field and full field powder pattern for the triplet (S=l) resonance, respectively, (b) ADMR spectrum ol MEH-PPV/CW, composite film. Both spectra were measured at probe energy 1.35 eV, T=4 K and 3 GHz resonant microwave frequency (reproduced by permission of the American Physical Society from Ref. 1191). 

Another and more accurate microwave method makes use of frequency measurements.1 11 16 28 31 Acetaldehyde is an example of the class of molecules to which this method has been applied. Here there are three equivalent potential minima because of the... 

This situation appears to be different when microwave conductivity measurements are used in parallel with electrochemical measurements. As Fig. 1 shows, there is a marked parallelism between electrochemical processes and microwave conductivity mechanisms. In both cases electrical fields interact with electronic or ionic charge carriers as well as dipoles. In electrochemical processes, it is a static or low-frequency electrical field that is moving electrical charge carriers or orienting dipoles. In a micro-wave measurement, the electric field of the microwave interacts with... 

Microwave measurements are typically performed at frequencies between 8 and 40 Gc/s. The sensitivity with which photogenerated charge carriers can be detected in materials by microwave conductivity measurements depends on the conductivity of the materials, but it can be very high. It has been estimated that 109-1010 electronic charge carriers per cubic centimeter can be detected. Infrared radiation can, of course, also be used to detect and measure free electronic charge carriers. The sensitivity for such measurements, however, is several orders of magnitude less and has been estimated to be around 1015 electronic charge carriers per cubic centimeter.1 Microwave techniques, therefore, promise much more sensitive access to electrochemical mechanisms. 

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

This shows that the penetration depth decreases dramatically with increasing conductivity of the medium to be penetrated. This has been plotted (Fig. 2) for different specific resistivities of the medium and the frequency of 10-40 Gc/s11 at which microwave conductivity measurements are typically performed. It can be seen that with a specific resistivity of 10 Q cm, a penetration depth of only 2 mm can be expected. Figure 2 furthermore shows the doping densities at which the respective penetration depths can be expected for silicon. Whereas the lower frequency X-band of microwaves (8-12.5 Gc/s) offers some advantages for materials with very low resistance, the high-frequency microwave Ka-band (26.5 10... 

A classical setup for microwave conductivity measurements is based on the utilization of the waveguides. A simple installation consists of a microwave generator (typically a gun diode) which, when the Ka-band is used, can be operated in the frequency region of 28-40 Gc/s this is protected by an isolator against back-reflections from the rest of the microwave circuit. The microwave power is conducted by an attenuator across a circulator into the microwave conductor branch at the end of which the electrochemical cell is mounted. The microwave power reflected from the electrochemical sample is conducted via the circulator into the microwave detector. It typically consists of a diode that acts as an antenna, receiving the electrical alternating field, rectifying it, and con-... 

Time-resolved microwave conductivity measurements with electrodes in electrochemical cells can conveniently be made with pulsed lasers (e.g., an Nd-YAG laser) using either normal or frequency-doubled radiation. Instead of a lock-in amplifier, a transient recorder is used to detect the pulse-induced microwave reflection. While transient microwave experiments with semiconducting crystals or powders have been performed... 

Electrochemical cells for microwave conductivity measurements, 445 Electrochemical measurements with microwave frequencies, diagrammated, 448, 449 with microwaves, 478 Electrochemical polymerization... 

Microwave frequencies and electric transport, 438 electrochemical measurements with, 441-419... 

Potential sweep measurements, with microwave frequency effects, 455 Pourbaix diagrams, applied to adlayers on copper, 93... 

Thermal desorption spectra, 171 Thermodynamic equilibrium, phase transitions at, 219 Thermodynamic phase formation, passivation potential and, 218 Time resolved measurements in the microwave frequency range, 447 photo electrodes and 493 Tin... 

FIGURE 9.3 Spectra of the mixture of canthaxanthin (2mM) and A1C13 (2mM) in CH2C12 measured at 60 K at the field B0=3349G and microwave frequency 9.3757 GHz (a) superimposed plot of a set of three-pulse ESEEM spectra as the modulus Fourier transform and (b) HYSCORE spectrum measured with a x=152ns. (From Konovalova, T.A., J. Phys. Chem. B, 105, 8361, 2001. With permission.)... 

Good X-band resonators mounted into a spectrometer and with a sample inside have approximate quality factors of 103 or more, which means that they afford an EPR signal-to-noise ratio that is over circa three orders of magnitude better than that of a measurement on the same sample without a resonator, in free space. This is, of course, a tremendous improvement in sensitivity, and it allows us to do EPR on biomolecules in the sub-pM to mM range, but the flip side of the coin is that we are stuck with the specific resonance frequency of the resonator, and so we cannot vary the microwave frequency, and therefore we have to vary the external magnetic field strength. 

Figure 4. Variation of the linewidth of the parallel signal for Cu(ll) in crosslinked polyacrylamide gels of pore diameter 0.7 nm as a function of the microwave frequency, for mj = -3/2 and -1/2. The solid line is calculated from the values of aH, 6A and 6g given in Table I. Measured values are indicated.

Examination of the ESR spectra measured in this study, Figures 1 and 2, shows no indication of the dipolar broadened line at 77 K in the networks studied even when the samples were cooled to 77 K from ambient temperature during more than four hours. We particularly checked the S-band spectra for this line. We expect the dipolar broadening to be the same at the two frequencies but much more conspicuous at S-band because the spectrum from isolated ions is spread over a smaller range of magnetic fields at this microwave frequency. The absence of the broad line indicates that in all the networks measured Cu(ll) hydrated by freezable, or bulk, water is not detected. These results are in agreement with those presented in ref. 25 which indicate the absence of bulk water in water absorbed on silica gels with pores smaller than 6 nm. 

The Debye equations (9.42) are particularly important in interpreting the large dielectric functions of polar liquids one example is water, the most common liquid on our planet. In Fig. 9.15 measured values of the dielectric functions of water at microwave frequencies are compared with the Debye theory. The parameters tod, e0v, and r were chosen to give the best fit to the experimental data r = 0.8 X 10 -11 sec follows immediately from the frequency at which e" is a maximum e0d — e0v is 2e"ax. 

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