Frequency sweep data

This chapter gives an overview of relevant statistical methods for the analysis of bioimpedance measurements, with an aim to answer questions such as How do I begin with planning an experiment How many measurements do I need to take How do I deal with large amounts of frequency sweep data Which statistical test should I use How do I validate my results ... 

FIGURE 19. Master curve from various frequency sweep data of pressure-sensitive adhesives. 

The amplitude and phase derived from Eq. (3.20) and Eq. (3.21) are plotted in Fig. 3.30 using the following values 0 = 1 nm, Q = 10 and Oio = 150 kHz. Experimental data of this type is commonly referred to as frequency sweep data. It is used to establish the initial conditions for IC-AFM. When obtained with the probe well away from the surface, it shows the resonant frequency of the system. This is the frequency with maximum amplitude, which coincides with the maximum slope of the phase signal. 

Figure 6.27 was prepared with dynamic frequency sweep data provided by M. J. Struglinski. 

Figures 7.5 and 7.6 were prepared using dynamic frequency sweep data provided by R. H. Colby. 

One may wonder why we have not applied time—temperature superposition (TTS) to the dynamic frequency sweep data given in Figure 8.7, to determine the of SI-9/9, as numerous research groups (Adams et al. 1994 Balsara et al. 1998 Bates 1984 Bates et al. 1990 Floudas et al. 1994, 1996a, 1996b Lin et al. 1994 Modi et al. 1999 Rosedale and Bates 1990 Rosedale et al. 1995 Schulz et al. 1996 Wang et al. 2002 Winey et al. 1994) have done. As discussed in Chapter 6, application of TTS to flexible homopolymers has been practiced by two methods (1) by empirically... 

The dynamic Weissenberg number W can be calculated from data obtained by the strain frequency sweep measurement. It s the ratio of the elastic to the viscous shares in the measured gel and leads to an objective description of the sensoric properties, representing the basis for the standardization of pectins. 

Figure 24.15 Single-sweep data traces of H2O absorption recorded in a hypersonic flow with an enthalpy of 10 MJ/kg. The panels shows the absorbance (as a function of laser frequency, cm ) near 1.400 pm (a) and 1.395 pm (6) recorded simultaneously. V = 4630T50 m/s Ttran.i = 561 15 K Ph20,i = 0.43 0.03 Torr Ttran,2 = 544 35 K and Ph20,2 = 0.45 0.06 Torr...

Dynamic melt viscosity studies on the star blocks and a similar triblock were carried out using a Rheometric Mechanical Spectrometer (RMS) (Rheometrics 800). Circular molded samples with -1.5 mm thickness and 2 cm diameter were subjected to forced sinusoidal oscillations (2% strain) between two parallel plates. The experiment was set in the frequency sweep mode. Data were collected at 180 and 210 °C. 

The protons in each compound will have the shift differences typical of C12CH— and—CHO and, at 60 MHz, can be expected from the data in Table 9-4 (p. 308) and Equation 9-4 to be observed at about 350 Hz and 580 Hz, respectively, from TMS. Now consider a frequency-sweep experiment4 arranged so that the —CH=0 proton will come into resonance first. 

In the frequency sweep test, the idea is to obtain LVE data from the test material over the widest possible (or realistic) range of frequencies. The lower limit of testing is never difficult for a rheometer to achieve physically, but it may be impractical to explore. Typically, the time required to obtain data at frequencies of <0.01 rad/sec or 0.006 Hz is impractical for a laboratory schedule. (At 0.006 Hz, each data point would take 167 sec for a single iteration most rheometers perform at least two or three iterations.) Furthermore, samples may change or degrade in nonsterile conditions over extremely long tests (i.e., hours). If it is desirable to obtain... 

A frequency sweep can reveal these behavior patterns if it is collected over a sufficiently wide range. Low-frequency data are not usually difficult to obtain (provided that time is not a problem), but there are mechanical limitations to obtaining high-frequency data. At frequencies >10 Hz, it becomes impossible to correct for the inertia of the moving parts in the rheometer. 

Figure 14.2 Frequency sweep rheometry data for a supramolecular gel. G is invariant with frequency up to the yield point and ca. one order of magnitude greater than G".

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

The generation of frequency sweeps under computer control, described in Section II, 3 (p. 13) is one small aspect of a general tendency towards control of analytical instrumentation by means of digital computers, through appropriate interfacing devices. Several commercial and individually built systems have appeared in which all of the instrumental parameters for frequency sweeps or pulse-excitation (see Section IV, p. 45) are selected by teletype or numerical keyboard input to the computer, which then acquires the spectral data automatically and performs any further processing required. Automatic analysis of spectral peak positions and areas by a computer, and printing of the numerical results on a teletype or... 

Frequency sweep studies in which G and G" are determined as a function of frequency (o)) at a fixed temperature. When properly conducted, frequency sweep tests provide data over a wide range of frequencies. However, if fundamental parameters are required, each test must be restricted to linear viscoelastic behavior. Figure 3-31... 

For this purpose, the cantilever tune menu is opened and a frequency sweep is performed. From the probe manufacturers data sheet, the resonance frequency is approximately known, e.g., 300 kHz. Hence, we excite the lever with low power (drive amplitude 25 mV) and sweep the frequency for 30 kHz around the expected resonance frequency of 300 kHz. In advanced AFM set-ups, the resonance frequency may also be independently determined before the tuning by a thermal tune (please consult the corresponding manual for details the procedure is globally reviewed in Sect. 2.2.5). 

Small strain-amplitude frequency sweep is usually used to collect linear rheological data, which are reproduced for repeated measurements within a certain experimental error. Generally, rheology is used to assess the state of dispersion of fillers in the melt. 

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