Data analysis logarithmic time scale

To reach steady state, the residence time of the fluid in a constant stretch rate needs to be sufficiently long. For some polymer melts, this has been attained however, for polymer solutions this has proved to be a real challenge. It was not until the results of a world wide round robin test using the same polymer solution, code named Ml, became available that the difficulties in attaining steady state in most extensional rheometers became clearer. The fluid Ml consisted of a 0.244% polyisobutylene in a mixed solvent consisting of 7% kerosene in polybutene. The viscosity varied over a couple of decades on a logarithmic scale depending on the instrument used. The data analysis showed the cause to be different residence times in the extensional flow field... 

Regression analysis is considered an appropriate approach to evaluating the stability data for a quantitative attribute and establishing a shelf life. The nature of the relationship between an attribute and time will determine whether data should be transformed for linear regression analysis. The relationship can be represented by a linear or nonlinear function on an arithmetic or logarithmic scale. In some cases, a nonlinear regression can better reflect the true relationship. An appropriate approach to shelf life estimation is to analyze a quantitative attribute (e.g., assay, degradation products) by... 

Figure 6. Disappearance curves of hexameric human insulin (O), the monomeric human insulin analog B9Asp, B27Glu( ), and the dimeric human insulin analog BlOAsp (V) in a logarithmic scale. Straight-line segments were calculated by linear regression analysis using the data fiom the relevant time intervals. (From Brange et ai, 1990, with permission.)...

Regardless of the inherent difficulty in interpreting relaxation data, several researchers have published results on ionic liquids with varying degrees of analysis. Inportantly, relaxation measurements should be made at numerous temperatures to determine the minimum relaxation time to enable detailed analysis. In the simplest terms, the minimum on a variable tenperature (inverse temperature) versus relaxation time (logarithmic scale) plot will shift to lower temperatures (retaining the same relaxation time) if there is only a shift in mobility of the... 

Copper is not expected to follow Cabrera-Mott inverse logaridimic kinetics since its oxide is a modifier according to Table 1. In fact, copper follows direct logarithmic kinetics. This was emphasized by results (Table 2) from die analysis of experimental data [5e,9] including the results shown in Figure 2. No attempt is made here to apply the Fehlner-Mott direct logarithmic expression, Eq. (5) above. This is because the evidenee for oxide recrystallization with time is very complex. Onay [39] reported on the formation of multiphase, multilayer scales on copper at 300°C. He foimd that they result from the dissociation of compact cuprous oxide scale that has lost contact with the copper substrate. 

While time-temperature superposition generally works well for linear polymers, it does not work as well as is often claimed in publications and presentations. The shift factor is often determined by a curve-fitting procedure involving the entire data set. For example, Honerkamp and Weese [63] determined shift factors by assuming a polynomial form for the shift factor. When shift factors are determined by fitting entire data sets, one must keep in mind that the result is a compromise master curve, and when logarithmic scales are used, especially when the range of frequency or time is rather small, the data may seem to superpose well. However, a more careful analysis of the data often reveals that this is not the case. 

---