Frequency modulation methods

In this report we present results of a study of a titanium - ethylene complex formed in an ultra high vacuum chamber and collected on a quartz sensor for mass analysis. The technique we use for mass analysis is unique. It is based on the application of a frequency modulation method to unambiguously track the resonant frequency of a quartz sensor to better than 0.1 ppm. A downward shift in the resonant frequency of the sensor, either due to the initial deposition of the complex or due to the absorption of hydrogen gas, indicates a mass accumulation on its face. This shift can be measured with a 0.1 ppm resolution. 

By applying an appropriate perturbation to a relevant parameter of a system under equilibrium, various frequency modulation methods have been used to obtain kinetic parameters of chemical reactions, adsorption-desorption constants on surfaces, effective diffusivities and heat transfer within porous solid materials, etc., in continuous flow or batch systems [1-24]. In principle, it is possible to use the FR technique to discriminate between all of the kinetic mechanisms and to estimate the kinetic parameters of the dynamic processes occurring concurrently in heterogeneous catalytic systems as long as a wide enough frequency range of the perturbation can be accessed experimentally and the theoretical descriptions which properly account for the coupling of all of the dynamic processes can be derived. 

Both harmonic and electrochemical frequency modulation (EFM) methods take advantage of nonlinearity in the E-I response of electrochemiced interfaces to determine corrosion rate [47-50]. A special application of harmonic methods involves harmonic impedance spectroscopy [5i]. The EFM method uses one or more a-c voltage perturbations in order to extract corrosion rate. The electrochemical frequency modulation method has been described in the literature [47-50] and has recently been reviewed [52]. In the most often used EFM method, a potential perturbation by two sine waves of different frequencies is applied across a corroding metal interface. The E-I behavior of corroding interfaces is typically nonlinear, so that such a potential perturbation in the form of a sine wave at one or more frequencies can result in a current response at the same and at other frequencies. The result of such a potential perturbation is various AC current responses at various frequencies such as zero, harmonic, and intermodulation. The magnitude of these current responses can be used to extract information on the corrosion rate of the electrochemical interface or conversely the reduction-oxidation rate of an interface dominated by redox reactions as well as the Tafel parameters. This is an advantage over LPR and EIS methods, which can provide the Z( ) and, at = 0, the polarization resistance of the corroding interface, but do not uniquely determine Tafel parameters in the same set of data. Separate erqreriments must be used to define Tafel parameters. A special extension of the method involves... 

Most NC-AFMs use a frequency modulation (FM) teclmique where the cantilever is mounted on a piezo and serves as the resonant element in an oscillator circuit [101. 102]. The frequency of the oscillator output is instantaneously modulated by variations in the force gradient acting between the cantilever tip and the sample. This teclmique typically employs oscillation amplitudes in excess of 20 mn peak to peak. Associated with this teclmique, two different imaging methods are currently in use namely, fixed excitation and fixed amplitude. 

Selective experiments can also be performed by the tailored excitation method of Tomlinson and Hill. The selective pulse is frequency-modulated with a function designed to yield zero effective field at the resonance offset of the neighboring nuclei. Although this technique is especially promising for studies of more-complex spin systems, its use is as yet very limited, in part because the instrumentation needed is not yet commercially available. 

VHF (50-100 MHz) up to the gigahertz range], the use of remote excitation of the plasma, plasma beams, and modulation of the plasma in time or frequency. Even methods without the assistance of a plasma have evolved, such as the hotwire CVD (HWCVD) method. 

At present, two main streams of techniques exist for the measurement of fluorescence lifetimes, time domain based methods, and frequency domain methods. In the frequency domain, the fluorescence lifetime is derived from the phase shift and demodulation of the fluorescent light with respect to the phase and the modulation depth of a modulated excitation source. Measurements in the time domain are generally performed by recording the fluorescence intensity decay after exciting the specimen with a short excitation pulse. 

As shown in Section 11.2.1.1, more details can be obtained by confocal fluorescence microscopy than by conventional fluorescence microscopy. In principle, the extension of conventional FLIM to confocal FLIM using either time- or frequency-domain methods is possible. However, the time-domain method based on singlephoton timing requires expensive lasers with high repetition rates to acquire an image in a reasonable time, because each pixel requires many photon events to generate a decay curve. In contrast, the frequency-domain method using an inexpensive CW laser coupled with an acoustooptic modulator is well suited to confocal FLIM. 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

There are two widely used methods for measuring fluorescence lifetimes, the time-domain and frequency-domain or phase-modulation methods. The basic principles of time-domain fluorometry are described in Chapter 1, Vol.l of this series(34) and those of frequency-domain in Chapter 5, Vol. 1 of this series.<35) Good accounts of time-resolved measurements using these methods are also given elsewhere/36,37) It is common to represent intensity decays of varying complexity in terms of the multiexponential model... 

Here we will summarize some known results for the simplest example of random frequency modulation as defined by Eq. (2). Let us assume that the process 2( ) in Eq. (2) is a projection of a Markovian process characterized by the evolution operator T. This is possible in principle, because the dynamical motion of the environment can be described in terms of a Liouville operator. The set of variables defining the Markovian process is designated by X. If the variable fi itself is Markovian, X consists only of 2, but in general it has to be supplemented by additional variables to complete the set. Let the function W(x, X, t) be the probability or the probability density for finding the random variables x and X at the respective values at the time t. Then a systematic method of treating the problem, Eq. (2), is to rewrite it in the form... 

As a method to control wavepackets, alternative to the use of ultra-short pulses, I would like to propose use of frequency-modulated light. Since it is very difficult to obtain a well-controlled pulse shape without any chirp, it is even easier to control the frequency by the electro-optic effect and also by appropriate superposition of several continuous-wave tunable laser light beams. 

C spin-lattice relaxation times of individual nuclei can also be measured by PFT 13C H experiments using a 90°, r, 90", r,... pulse train and noise modulation of the proton decoupling frequency. This method is known as progressive saturation [43] and is based on the following concept. 

Key et al., 1959] Key, E., Fowle, E., and Haggarty, R. (1959). A method of pulse compression employing nonlinear frequency modulation, Technical report 207, Lincoln Laboratory, M.I.T. 

Fig. 1. Set-up of the PTB laser system. The Nd YAG laser is frequency stabilized onto a selected iodine absorption line using the phase modulation method. The probe beam is modulated at 2.05 MHz by an electro-optic modulator (EOM), the pumb beam is frequency shifted by an acousto-optical modulator (AOM). The driving AOM rf power is chopped in order to cancel frequency offsets introduced by the Doppler background using a lock-in detection scheme. The transmitted probe beam signal is detected by a photodiode (PD) and mixed with the EOM rf in a double balanced mixer (DBM)...

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