Empirically determined time—temperature

Figure 7 - Empirically determined time-temperature shift factors for two blends of 97% 1,2-PBD with PIP. The concentration of the PIP is as indicated.

Timing circuits are provided for measuring precisely the time between ti and t. That time difference can be correlated directly with the temperature of the fluorescent sensor by reference to an empirically determined look up table stored digitally within the instrument. 

In addition to the primary glass-rubber relaxation which follows the empirical shifts determined by Eq. (26), part of the recoverable compliance does not obey time-temperature superposition. The shortest time data at the lowest temperatures has a component which shifts according to the Arrhenius temperature dependence... 

For practical applications empirically determined creep data are being used, such as D(t) or, more often, E(t) curves at various levels of stress and temperature. The most often used way of representing creep data is, however, the bundle of creep isochrones, derived from actual creep curves by intersecting them with lines of constant (log) time (see Figure 7.7). These cr-e-curves should be carefully distinguished from the stress-strain diagram discussed before, as generated in a simple tensile test ... 

Deduction of Shift Factors. Time-temperature shift factors for the blends were obtained by shifting the experimental relaxation isotherms to the calculated master curves (10). The temperature and time dependence of the shift factors of the 75/25 and 50/50 blends are represented in Figures 10a and 10b at t = 10 sec and t = 1000 sec for a reference temperature of 140°C. The empirically determined shift factors of the pure components are given in these figures by dotted lines their temperature dependence is of the WLF type. 

The utility of empirically determined WLF equations was investigated using DMA data obtained on the PVC acoustical damping material. Using a separate software package (available from DuPont Intruments), E, E" and tan 8 were empirically fit using the time-temperature superposition procedure. A reference temperature is first determined by the computer software. The data are then shifted manually and the WLF equation is fit to the resulting temperature shift factors. Values for and calcu-... 

RNA fragmentation is carried out with divalent cations like magnesium in the first strand buffer under high heat [12]. The time for this incubation should be empirically determined due to variations of fragmentation efficiency see Fig. 3). In order to reduce the loss of amplified products under high temperature, the shorter treatment is preferred. 

An Empirical Approach to Demulsifier Selection. Research into emulsion fundamentals added greatly to our understanding of the factors that determine emulsion stability and the surface-active chemicals that can be used to manipulate those factors. In spite of these advances, the requirement for blending demulsifiers in order to achieve acceptable field performance means that empirical approaches are often required for demulsifier selection. In fact, complete characterization of emulsion properties, including process residence times, temperatures, and product requirements still only provides guidance in the selection of process demulsifiers. The costs and time involved in achieving the level of characterization required for a fundamental approach can also be... 

When TTS was originally implemented, the distance that a curve must be shifted in order to transpose it from the temperature of observation T to the reference temperature Tr was determined by the simple empirical curvefitting procedure illustrated above. Pioneering research on this aspect of TTS was carried out by Leaderman (1941, 1943) and Tobolsky (1960), who also modified the procedure to account for the proportionality of modulus to absolute temperature. This has the effect of creating a slight vertical shift in the data. Williams et al. (1955) further modified time-temperature superposition to account for changes in density at different temperatures, which has the... 

Note that a given slope is reached at a higher frequency (shorter relaxation time) as the temperature increases. This observation is consistent with the time-temperature superposition principle which describes viscoelastic behavior. Recognizing the similarity in the curve shapes for each of the data sets in Figure 5a, we determined an empirical shift factor for each temperature (Et) which, when applied to the frequency scale for each curve in Figure 5a, shift the data to a chosen reference temperature (Tq = 142°C). The shifted data are shown in Figure 5b. 

It is not possible to solve these equations with unknown time-dependent boundary conditions. However, we can use the equations to identify the important variables that will affect pressure drop, heat, or mass transfer. The velocity, pressure, temperature, and concentration described with these models should be completely described by the dimensionless variables Re, Fr, Pen, P d, and Eu. Keeping all these dimensionless numbers constant will also give the same solution expressed in the dimensionless form. Equations (4.12) and (4.13) contain Re, Fr, and Eu, and we can find correlations for pressure drop by empirically determining the function... 

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... 

Empirically determine the time for desiccation depending on temperature and humidity. 

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