Evaluation of linear dependent measured values

The standard error of slope is a suitable numerical parameter for the evaluation of linearity. It measures the deviation of the experimental values from the regression line and thus represents a performance parameter with respect to the precision of the regression. Expressed in percent (relative standard error of slope), it is comparable to the RSD obtained in precision studies in the given concentration range (e.g., 10% -20% RSD at the QL, l%-2% for assay). Therefore, this parameter is better suited for evaluation purposes than the residual sum of squares and the residual standard deviation, which are also measures of the deviation between the experimental data and the regression, but they depend on the absolute magnitude of the signal values and are difficult to compare with results from other equipment or with other procedures. 

Comparisons of values quoted in the literature for the physical properties of liquid crystals are often of dubious validity due to differences in the methods of assessment often carried out at different absolute temperatures (e.g. 22°C or 25°C) or reduced temperatures (e.g. T -j— 10°C or 0.95 x 7V /). The use of extrapolated data from a wide variety of nematic mixtures of different composition and properties at various concentrations is also common. Unfortunately non-ideal behaviour is common for such mixtures and non-linear behaviour is not unusual, i.e. the values extrapolated to 100% are more often than not dependent on the matrix used and the concentration of the compound to be evaluated. However, although the absolute values of the data collated in Table 3.13, measured in the same way at the same reduced temperature (0.96 X r r-/), are lower than those reported for the same compounds in the literature, usually measured at 22°C the trends and relative values are very similar. 

The mass-loading effect of a gas was evaluated in a room-temperature pressure cell filled with helium (whose speed of sound, Vf, is 965 m/s at 0°C) at from 1 to 4 atmospheres gauge (Figure 3.47). A linear dependence of velocity on gas density was observed, as expected [62]. The discrepancy between calculated and measured values was thought to be due to insufficient thermal equilibration between measurements. In this application of the FPW device, there is no differ-... 

The differential (isosteric) adsorption heats Qa for negligible adsorbent surface occupation were derived from the linear dependence of log(Vm/T) against 1/T slope, where Vm is the specific retention volume (cm /g) [9]. Direct evaluation of the Vm values over the temperature range 100-150°C and calculation of the isosteric adsorption heats were performed employing hexane as the reference substance. For other adsorbates, the relative retention volumes Vrel = y orbate yhexane gj.g measured experimentally, allowing for the adsorption heat increments with respect to hexane to be estimated. 

The force of cohesion, i.e. the maximum value of attractive force between the particles, may be determined by a direct measurement of force, F required to separate macroscopic (sufficiently large) particles of radius r, brought into a contact with each other. Such a measurement yields the free energy of interaction (cohesion) in a direct contact, A (h0) = Ff n r,. Due to linear dependence of F on r, one can then use F, to evaluate the cohesive force F2 = (r2/r )Fx, acting between particles in real dispersions consisting of particles with the same physico-chemical properties but of much smaller size, e.g. with r2 10 8 m (i.e. in the cases when direct force measurements can not be carried out). At the same time, in agreement with the Derjaguin equation... 

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