Temperature noise peak

Further details of the time dependence of the Tg peaks as observed with carbon-black-filled PS are evident from Figure 3, which shows the variation of the noise intensity (relative to its 1-min value) with time at different temperatures. The time dependence of this intensity is most pronounced in the vicinity of the noise peak temperature, although it... 

Another advantage of the Savitsky-Golay method is that derivatives of these functions can also be determined from the method of least squares. This method can be used to determine alpha-peak temperatures automatically since the first derivative changes sign at the peak temperature. The advantage of smoothing is that the number of extraneous peaks due to noise has been minimized. 

Reference materials are Aluminum (non-ferromagnetic) and Mild Steel St 37, DIN 1.0116 /AISI 4130 (ferromagnetic) Reference temperature for reported data is 20°C (70 °l resolution data are based on noise peak-to-peak values Resolution and temperature stability refer to midrange (MMI ) 107 Pa (100 bar) 2) 210 6 Pa (20 bar)... 

Noise present in the detector signal may have two components, long-term noise and short-term noise. The former causes a slow baseline wander measured over a 1 h period and may be attributed to fluctuations in temperature, column stationary phase bleed, flow rate variation, or pneumatic leaks. Short-term noise is observed as small, sharp spikes of shorter duration than component peaks and usually arises in the detector. Most integrators smooth the signal so that noise is not apparent unless a direct plot mode is selected. It is important to establish the mean noise level, the baseline, in order to determine the limit of detection. The time period of a peak is most conveniently described by the peak width at half height and the noise, N, is measured as the variation between maxima and minima of the noise peaks over the time period. The contribution of noise to the total component signal should be less than 1% (Figure 5.17). 

Note that the noise spectrum shown in Figure contains a large, continuous noise region ai low frequencies. Thi.s noi.se has the properties of llicker noise its sources arc not fully known. Superimposed on ihe flicker noise are noise peaks associated wiilt early and daily temperature fluctuations and other periodic phenomena associated with the use laboraiory building. 

Figure 3, Thermal noise level ratio (noise time t/noise at 1 min after reaching temperature) vs, time at temperatures far from (25°, 150°C) and close to (110°, 120°C) temperature at which noise peak occurs (120°C) for PS stored 10 hr at 70°C, Samples heated to indicate temperatures at 20°C/min. Bandwidth, 500-1500 Hz,...

Within the range of frequency, temperature, shear rate etc. covered by the experiment, all the measured thermal noise levels agreed well with the predictions based on the Nyquist formula. This implies that the thermal noise level could have been calculated from resistivity measurements and also that the noise peaks in the vicinity of Tg and Tm would have appeared in the corresponding resistivity-temperature diagrams. This was actually verified in numerous experimental runs. On the other hand, the measurement of thermal noise has the advantage that no external voltage has to be applied across the sample. This eliminates the possibility that the observed peaks arise from polarization effects (6,7). 

It is still not clear whether the measurements reported above are an inherent property of the polymer or whether they are associated with the presence of carbon black. Probably the latter explanation is appropriate since the disruption and reformation of a carbon particle network at the critical temperatures is a likely interpretation of the effects observed (J). In this respect, the noise peaks should be distinguished from resistivity peaks measured at Tg on pure polymers. The latter have been shown to be caused by polarization effects (6). 

The temperatures at which the noise peaks occur are higher than the corresponding Tg and Tm peaks observed with other methods such as DSC or TSC. Further, the effects of storage time and heating rate are different. This indicates that the noise method senses other structural changes than those associated with the DCS or TSC peaks. The noise peaks appear to... 

Figure 5 shows a typical mass loss in a decomposition experiment. The obvious definition would seem to be where the mass loss is steepest, which corresponds to the peak temperature T in the DTG plot. However, this is merely the point where reaction is fastest and does not represent the start of reaction, e.g. where bonds in the compound begin to break. The position of T will depend upon the sample size, packing, and heat flow properties. The point Tjis the initial temperature or onset temperature, but is not easy to identify and depends on the sensitivity of the balance and the amount of drift or noise seen. There may be traces of impurities, which decompose or promote some decomposition ahead of the main reaction. A better definition of start of reaction is the extrapolated onset temperature T. This requires drawing of tangents to the curve at the horizontal baseline and the steepest part of the curve and marking their intersection. For a reaction that starts very slowly and only speeds up later, T and Tj will be very different and a more satisfactory point would be shown as temperature where the fraction reacted a is equal to 0.05, i.e. Tq.05- Another definition of reaction temperature, important in kinetic studies, is when the reaction is half over, that is, when the fraction reacted... 

Since the solvent flow rate during the elution step determines the residence time of the polymer solution in the column, slow flow rates broaden Tref profiles and increase the Tref peak temperature, most likely due to an increase in residence time and axial dispersion in the column. Although higher solvent flow rates can help reduce axial dispersion, they also reduce the signal-to-noise ratio. 

FTIR instrumentation is mature. A typical routine mid-IR spectrometer has KBr optics, best resolution of around 1cm-1, and a room temperature DTGS detector. Noise levels below 0.1 % T peak-to-peak can be achieved in a few seconds. The sample compartment will accommodate a variety of sampling accessories such as those for ATR (attenuated total reflection) and diffuse reflection. At present, IR spectra can be obtained with fast and very fast FTIR interferometers with microscopes, in reflection and microreflection, in diffusion, at very low or very high temperatures, in dilute solutions, etc. Hyphenated IR techniques such as PyFTIR, TG-FTIR, GC-FTIR, HPLC-FTIR and SEC-FTIR (Chapter 7) can simplify many problems and streamline the selection process by doing multiple analyses with one sampling. Solvent absorbance limits flow-through IR spectroscopy cells so as to make them impractical for polymer analysis. Advanced FTIR... 

At either frequency the sensitivity of the instrument is quite remarkable. The exact signal-to-noise ratio depends upon a number of factors including apparent line width (including g and hyperfine anisotropy), ease of saturation, the temperature, and the linear density of the sample in the quartz tube. For a relatively narrow line with peak-to-peak separation of two gauss it is possible to observe the spectrum for concentrations as low as 1014 spins per gram of sample. As the spectrum becomes more anisotropic, the sensitivity of course decreases. Lowering the temperature increases the sensitivity since the population difference An increases [(Eqs. (26) and (3°)]. 

The major assumption in the fitting procedure was that the basis spectra (i.e., spectra for individual molecular components) are independent of flow tube temperature. This approximation was tested by running mass spectra of stable molecules such as toluene and st3Tene over the full range of flow tube temperatures, and the peak ratios in these spectra change by no more than l%-2%. Based on this result and the signal-noise ratio in the experiments, the fitting uncertainty was estimated at about 5%. 

UV/VIS/NIR spectroscopy and ESR spectroscopy. The UV/VIS/NIR spectrum shows a sharp peak at 983 nm and a broad peak at 846 nm. These two absorbances are attributed to allowed NIR-transitions and these values are consistent with spectra of the cation obtained with other methods [2]. EPR spectroscopy of Cgg-cations, produced by different methods, leads to a broad distribution of measured g-values. These differences are caused by the short lifetime of the cation, the usually low signal-noise ratio and the uncertainty of the purity. The most reliable value imtil now is probably the one obtained by Reed and co-workers for the salt Cgg"(CBiiHgClg)-(g= 2.0022) [2,9] (see also Section 8.5). Ex situ ESR spectroscopy of above-mentioned bulk electrolysis solutions led to a g-value of2.0027 [8], which is very close to that of the salt, whereas the ESR spectra of this electro lyticaUy formed cation shows features not observed earlier. The observed splitting of the ESR signal at lower modulation amplitudes was assigned to a rhombic symmetry of the cation radical at lower temperatures (5-200 K). 

The peak-to-peak noise value is approximately 8 times the rms value. For example, at room temperature, over a frequency interval of 3 kHz, on a 100 MlQ resistor, the Johnson current noise is... 

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