Frequency transients

Leonard, E. F., and Ruszkay, R. J., Frequency, transient and moment methods in process analysis. Paper presented at A.I.ChiE. Meeting, New York, December, 1961. (I)... 

When mass loading is not the dominant sensing mechanism, sensor response may not be linear with concentration in the film. This departure from linearity has been observed with polymer films [61,64,86]. An investigation into the possible effect of this nonlinearity on the evaluation of D values fiom SAW frequency transients indicated that errors in D values (factor of two error) could be obtained if the nonlinearity of the response is large [86). However, using small steps in partial pressure, this nonlinearity in the response can be minimized, allowing the effective evaluation of difiiision coefficients based on AW frequency transients. 

The results presented above illustrate the utility of using AW frequency transients to evaluate diffusional processes in thin polymer films. The ability to use thin films allows the rapid evaluation of D values from 10 to 10 cm /sec... 

Figure 4.11 Experimental SAW frequency transients during exposure to methanol iplpo = 0.05) for 360 nm-thick polysiloxane film deposited on bare quartz ( ) and on a 150 nm-thick porous silicate film on the quartz substrate ( ). The larger initial fiequency drop with the porous film is due to permeation of methanol through the polysiloxane film and adsorption onto the surfaces of the underlying porous film. Data points are overlapping at early times. (Reprinted with permission. See Ref. (86).)...

The ability of surface acoustic wave (SAW) devices to monitor adsorption of Nj onto the surfaces of porous films and diffusion of species Into polymer films has been demonstrated. Calculations based on the N2 adsorption Isotherms Illustrate how sol-gel solution chemistry can be used to tailor the surface area and pore size distribution of thin films. BET surface areas from unity to over 30 cm /cm of film have been obtained on various samples with median pore diameters from less than 0.4 nm to greater than 6 nm. SAW frequency transients occurring during the diffusion of small molecular species Into polymer films have been used to determine diffusion coefficients from 10 to 10 cm /sec. 

An example of a fit of Equation 4 to an experimental frequency transient is shown in Figure 5b. The experimental data for the final p/Po step from 0.051 to 0.061 are shown by the points the line is the best fit of Equation 4 to the data. The data are plotted versus /t to show the linear response for the Initial stage of diffusion. It is clear that this analysis fits the data well. The rms error for this fit is less than 0.7% of Af ,. The D value obtained at 25 C is 8.4 X 10 cm /sec. 

Figure 5. (a) SAW frequency transients during diffusion of methanol at various p/p values into a 1.8 iim polyimlde film. (b) Fit of Equation 4 to the final frequency transient (p/p from 0.051 to 0.061). (c) D values calculated from the frequency transients as a function of the average value of p/p for each step. 

The results of this Investigation Illustrate the utility of SAW devices in characterizing the properties of thin films formed on the substrate of the device. Using the SAW device as an extremely sensitive microbalance, N2 adsorption isotherms have been obtained directly on thin films. This has allowed the characterization of the surface area and pore size distribution in the film. In general, these measurements are not possible with conventional instrumentation due to the low total surface area present in thin film samples. As another application, SAW device frequency transients can be used to monitor diffusion of species in polymer films in real-time. The short diffusional length scale present in a thin film makes the time required for saturation of the film orders of magnitude shorter than would be required with bulk samples. This allows for a dramatic decrease in the time required for determining diffusion coefficients. 

In Sect. 2.7.2.1.2, the phenomenon of film resonance was discussed. In this special situation, the film thickness corresponds to one quarter of the acoustic wavelength, that is, the acoustic phase shift defined by Eq. (11) has the numerical value = 7t/2. For a film of given shear modulus, progressive increase in thickness will eventually result in this condition being satisfied. This phenomenon is illustrated in Fig. 27 [41] for a poly(3-hexylthiophene) film as a function of the polymerization charge during deposition. As can be seen, the resonant frequency transiently moves sharply upwards and the peak amplitude... 

Soluble boFCHi suppression reduces corrosion and therefore initiator frequency FuU condoisate polishing reduces steam g erator corrosiem and hence, reduces initiator frequency Transients Soluble boron suppression reduces initiator frequency Natural convection ccmling supress initiatcH ... 

Fig. 19.16 The Medtronic 9790 programmer generates a uniform amplitude pacemaker spike in response to any high-frequency transient. Although the paced rhythm can be seen in the background, the multiple pacing stimuli are arising from an unknown source extrinsic to the pacemaker and distorted the recording markedly impeding the pacing system evaluation.

It is well-known that a transient response in a circuit is significantly influenced by the impedance of a lead wire used for grounding, connecting circuits, and measurements as explained in Section 7.4.2. In Reference 47, it is said that the grounding of the metallic sheath of a control cable may not be effective at all during a high-frequency transient because of the grounding lead inductance. 

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