Semi-log plots

FIG. 14 Semi-log plot of mean chain length L vs width of the open slit D at various temperatures in 3d. Full symbols denote flexible chains and empty symbols semirigid chains with activation energy a = 0.5 [61]. 

Viscosities of the siloxanes were predicted over a temperature range of 298-348 K. The semi-log plot of viscosity as a function of temperature was linear for the ring compounds. However, for the chain compounds, the viscosity increased rapidly with an increase in the chain length of the molecule. A simple 2-4-1 neural network architecture was used for the viscosity predictions. The molecular configuration was not considered here because of the direct positive effect of addition of both M and D groups on viscosity. The two input variables, therefore, were the siloxane type and the temperature level. Only one hidden layer with four nodes was used. The predicted variable was the viscosity of the siloxane. 

Example. A tablet containing 100 mg of a drug was administered to a healthy volunteer and the plasma concentration (Cp) versus time data shown in Table 6 were obtained. Figure 11 shows a semi-log plot of these Cp versus time data. The half-life for elimination of the drug can be estimated from the straight line tail of the plot to be 4.7 hours. The overall elimination rate constant is then... 

Fig. 4 Distance dependence of hole transfer in DNA. Shown is a semi-log plot of fcht against the distance between Py and G-regions (r). Values of r were calculated assuming an average distance of 3.4 A between base pairs... 

A semi-log plot of the distance dependence of strand cleavage efficiency, see Fig. 8, gives a linear relationship with a slope experimentally indistinguishable from zero. DNA has occasionally been characterized as a molecu-... 

Fig. 8 Semi-log plots of the distance dependence of reaction for DNA(8-11). There is an apparent linear relationship in each case, but the slopes differ according to the specific sequence of DNA bases...

Fig. 11 Semi-log plots of the distance dependence of the reactivity of AQ-DNA(4) and AQ-DNA(5). These oligomers show stepped rather than linear behavior. The size of the step is strongly dependent on the details of the structure...

Results and Discussion on Dynamic Adsorption Measurements. Baker dolomite was used to study the dynamic adsorption experiment. The computed porosity of the rock was 24%. One concentration below the CMC of AEGS, one at CMC, and two concentrations above CMC were chosen to measure the adsorption of this surfactant with Baker dolomite. The mass of surfactant adsorbed per gram of rock is plotted as a function of flow rate in a semi-log plot in Figure 9. 

Dean et al. (1974) use a Langmuir probe technique in a rare gas repetitive afterglow plasma. The electron temperature is extracted from the semi-log plot... 

Figure 9. Semi-log plot and relaxation time constant determination of data from Figure 8. The values of XI and X2 on the plot represent the points used to calculate the relaxation time constants.

Demonstrate that the semi-log plot makes the curve more linear during its rise and fall from baseline. The recirculation hump is still present but is discounted by measuring the area under the curve (AUC) enclosed by a tangent from the initial down stroke. This is the AUC that is used in the calculations. 

A semi-log plot of drug concentration versus time will no longer be linear as the drug has two possible paths to move along, each with their own associated rate constants. 

It is not always easy by inspection to be certain that two reactions are involved. The use of a semi-log plot helps since it shows better the deviation from linearity that a biphasic reaction demands but a computer treatment of the data is now the definitive approach. 

Fig. 1.9 Time dependence of absorbance obtained after mixing Con A (200 pM) and 10 (a) (20 pM). The semi-log plot of the data (inset) shows even clearer the hiphasic nature of the reaction. Reprinted with permission from T. J. Williams, J. A. Shafer, I. T. Goldstein and T. Adamson, J. Biol. Chem. 253, 8538 (1978).

Although autoxidation of Ru(sar) + has similar characteristics in acidic solution, in base hydrogen atom transfer from Ru(sar) + to O2 leads to a deprotonated Ru(III) species which is oxidized to relatively stable Ru" (sar-2 H+) + Ref. 175. The strong deviation from linearity for semi-log plots, with a large excess of O2, is removed when Fe(II) is added. This suppresses the step and doubles the rate. Compare Sec. 2.2.1(b). The value of k can be assessed as 1.3 x 10 M s Ref. 176. The behavior of pentacyanoruthenium complexes has been compared with the iron analogs. Substitution in M"(CN)5L" with both M = Fe and Ru is dissociative, with decreased lability for tbe Ru(II) species. Table 8.10. 

Fig. 3.18 Semi-log plot of the time-dependent single chain dynamic structure factor from a PE melt at T=509 K M =36 kg/mol) for various Q. The solid lines are the fit of the repta-tion model (Eq. 3.39). The dashed lines are a fit using the model of des Cloizeaux (Eq. 3.44). (Reprinted with permission from [4]. Copyright 1998 The American Physical Society)...

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

Equation 5 shows that a semi-log plot of log C vs. t will have a slope equal to -kq Cp... 

Analysis of the relative contributions of the slow and fast decays to the total intensity, by "peeling off the slower from the linear region of a semi-log plot of the autocorrelation function, indicates that it is the ordinary scattering that decreases in intensity. The extraordinary contribution remains roughly constant once it appears. 

The optical rotation of the mixture approaches zero (a racemic mixture) over time, with apparent first-order kinetics. This observation was supported by the semi-log plot [ln(a°D/ aD) vs time], which is linear (Figure 1). It has been shown that this racemization process does in fact follow a true pseudo-first-order rate equation, the details of which have been described by Eliel.t30 Therefore, these processes can be described by the first-order rate constant associated with them, which reflects precisely the intrinsic rate of racemization. Comparison of the half-lives for racemization under conditions of varying amino acid side chain, base, and solvent is the basis for this new general method. 

A second important application of CMD has been to study the dynamics of the hydrated proton. This study involved extensive CMD simulations to determine the proton transport rate in on our Multi-State Empirical Valence Bond (MS-EVB) model for the hydrated proton. = Shown in Fig. 4 are results for the population correlation function, (n(t)n(O)), for the Eigen cation, HsO, in liquid water. Also shown is the correlation function for D3O+ in heavy water. It should be noted that the population correlation function is expected to decay exponentially at long times, the rate of which reflects the excess proton transport rate. The straight line fits (dotted lines) to the semi-log plots of the correlation functions give this rate. For the normal water case, the CMD simulation using the MS-EVB model yields excellent agreement with the experimental proton hopping... 

Figure 4 Semi-log plot of the population correlation function for an Eigen cation in liquid water at 300 K. Shown are the water (solid line) and heavy water (dot-dashed line) results, and the bestfit (dotted line) to each.

Fig. 16. Typical semi-log plots of the peak intensities for the pure homopolypeptides and blend samples against the proton spin-locking time r. (a) PLA/PLV (50/50), (b) PLA/PLIL (50/50), (c) PG/PLV (50/50) and (d) PDA/PLV (50/50).

It is clear that there are significant differences between the two slopes of the semi-log plots for the Cot carbon of pure PLA with the ot-helix form and the Cot carbon of PLA (ot-helix form) in the PLA/PLIL (50/50) blend sample... 

Volatile element abundances in CV chondrites (normalized to Cl chondrites and silicon) lie along a linear array on semi-log plots versus their 50% condensation temperatures. This depletion pattern persists, whether the elements are siderophile, lithophile, or chalcophile. 

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