Semilog plots

Cake Washing Wash efficiency data are most conveniently represented by a semilog plot of percent remaining B as a function of wash ratio N as shown in Fig. 18-103. Percent remaining refers to that portion of the solute in the dewatered but unwashed cake which is left in the washed and dewatered cake. Since a cake-washing operation... 

Figure 45. Semilog plot of the pit-growth current, J vs. V = 50 mV, [NiCU = 5 mol in 3, (NaCIJ = 1000 mol m 3. T=300 K, J0 is the current component shown in Eq. (Ill), which becomes unstable at the minimum state and Iq is the growth factor of the pits expressed by Eq. (112). (Reprinted from M. Asanuma and R. Aogaki, Nonequilibrium fluctuation theory on pitting dissolution. III. Experimental examinations on critical fluctuation and its growth process in nickel dissolution, J. Chem. Phys. 106,9944, 1997, Fig. 14. Copyright 1997, American Institute of Physics.)...

Figure 47. Semilog plot of the growth factor of the pitting current vs. r,/2. 0, [NiCl2] = 1 mol nT3 , [Nidj = 5...

These can be solved by classical methods (i.e., eliminate Sout to obtain a second-order ODE in Cout), by Laplace transformation techniques, or by numerical integration. The initial conditions for the washout experiment are that the entire system is full of tracer at unit concentration, Cout = Sout = L Figure 15.7 shows the result of a numerical simulation. The difference between the model curve and that for a normal CSTR is subtle, and would not normally be detected by a washout experiment. The semilog plot in Figure 15.8 clearly shows the two time constants for the system, but the second one emerges at such low values of W t) that it would be missed using experiments of ordinary accuracy. 

FIGURE 15.8 Semilog plot of washout function showing two slopes that correspond to the two time constants in the side capacity model. 

Semilog plot of the real part of heat release response, Re[(q /cl)], p /p) of a ZFK flame to acoustic pressure oscillations [31]. Dotted line shows response of a simple two-step flame [47]. 

Semilog plot of the frequency-dependent part of heat release response, Im [(479 )/(p7p)/(akF(Tb-Ti)] ZPK flame to acousity velocity oscila-... 

FIGURE 21 Semilog plot of the in vitro rate of hydrolytic chain scission of various copolymers of e-caprolactone, measured under in vitro conditions. (From Ref. 95.)... 

FIG. 31 Semilog plot of the force-response time measured over mica and ion-exchanged mica surfaces as a function of relative humidity. The time constant characterizes the mobility of different surface ions at different humidity values. (From Ref. 76.)... 

FIG. 32 Top Semilog plot of the time constant t for ionic motion as a function of RH for KF. Bottom Simultaneously measured contact potential. At a critical humidity A, there is a break or a change in slope in these two surface properties. Below A, water solvates preferentially cations at the step edges. Above A, the rates of dissolution (solvation) of anions and cations are similar and water uni-... 

Fig. 29.—Semilog plot of molecular weight against the reciprocal of the polymerization temperature for isobutylene polymerized in the presence of BF3. Results have been recalculated from the data of Thomas et al. The slope of the line corresponds to an activation energy difference of 4.6 kcal./mole.

The second method assumes that the molecular weight calibration curve is linear on a semilog plot and should be employed where universal calibration is not practical as with aqueous SEC. Several variants of these methods involving different molecular weight data for the standards are discussed. The proposed methods have been evaluated using aqueous SEC and polydextran standards and nonaqueous SEC with polyvinylchloride standards. 

First, we determine the P-phase function on a semilog plot by means of linear regression on the later part of the concentration curve for which the time course is most linear (Fig. 39.13a). This yields ... 

Equation (35) describes the line in Fig. 10, which is a semilog plot of Cp versus time for an orally administered drug absorbed by a first-order process. The plot begins as a rising curve and becomes a straight line with a negative slope after 6 hours. This behavior is the result of the biexponential nature of Eq. (35). Up to 6 hours, both the absorption process [exp(—kat) and the elimination process [exp( keil)] influence the plasma concentration. After 6 hours, only the elimination process influences the plasma concentration. 

Thus after 6 hours the semilog plot of Cp versus time shown in Fig. 10 becomes a straight line and kei can be determined from the slope. Therefore, the overall elimination rate constant for a drug may be accurately determined from the tail of a semilog plot of plasma concentration versus time following extravascular administration if ka is at least five times larger than kei. 

As shown in Fig. 10, a semilog plot of residuals versus time is a straight line with a slope of —ka. 

If the absorption process obeyed first-order kinetics, a semilog plot of the residuals in the sixth column would be a straight line and ka can be determined from the slope. However, the regular Cartesian plot of the... 

It is not necessary to apply the trapezoidal rule to the entire plasma concentration versus time curve in order to calculate the total AUC. After the semilog plot becomes a straight line, the remaining area out to t = can be calculated using the following equation ... 

It follows that if the entire semilog plot were straight, as would be the case for a one-compartment drug following IV administration, the total AUC would be given by... 

Hence semilog plotting of concentration versus time (Fig. 13) will give a straight line with a slope from which K is calculated. But most reactions are catalyzed... 

Michaelis-Menten equation (Equation 2.12). (B) As in (A) but with the substrate concentration axis plotted on a logarithmic scale (a semilog plot). 

Figure 5.2 Concentration-response plot for an enzyme inhibitor displayed on linear (A) and logarithmic (B) concentration scales. The IC50 is identified from the midpoint (i.e., fractional activity = 0.5) of the semilog plot.

When [El] has been reduced to the point that it is equal in concentration to [EI Je, the natural logarithm of the ratio /f/, /[ 7]0 would be ln(l/< ) = -1.0. The length of time required for [EI to decay by this amount can be obtained from the semilog plot shown in Figure A1.4B. This time interval is referred to as the relaxation time or the time constant and is given the symbol x. The relaxation time is the reciprocal of the rate constant ... 

Capsules were equilibrated with a tracer solution overnight. A capsule pellet (0.2-0.5 ml) was then placed in 5 ml test buffer (PBS or RPMI-1640 medium, Gib-co/BRL, New York, NY) on a shaker and a 0.2-ml aliquot was immediately sampled by a screen-protected pipette with further samples being taken over the next 700 s. The tracer quantity was assayed using the methods described below. A final sample was taken after the capsules has been in contact with the buffer for several hours (equilibrated tracer quantity) and the increment to the tracer concentration at each time was calculated. From the progress of tracer to equilibrium on a semilog plot a slope denoted as the zero -order rate flux constant was obtained and has been used as a measure of capsule permeability. [3H] -Glucose (580 daltons),insulin (6.2 kDa), and ovalbumin (45 kDa) have been used as tracers. Radioactivity was measured by means of a Packard 2000CA Liquid Scintillation Counter (Packard Instruments,... 

The U.S. Bureau of Labor Statistics provides information that permits computation of estimated future labor and material costs. You can project costs to the future by fitting a cost index values for several time periods. If the slope b of the index is constant, then the ratio ljly versus t is a semilog plot... 

FIGURE 3.2 Semilog plot of the plasma concentration, C, of a drug as a function of time, where Co is the projected plasma concentration at time zero and -1/2.303 is the slope of the elimination curve. 

Figure 2. Semilog plot of antipyrine uptake data of Figure 1. Each set of points is from a separate experiment using 6 mussels in 300 mL Instant Ocean ...

Fig. 8.15 Semilog plot of H/D liquid-gas separation factors for some chemical equilibria (After Bigeleisen,. 1., Adv. Chem Ser. 89, 1, 1969)... 

To overcome the uncertainty of the actual onset of ionization, among several others, [80] the critical slope method has been developed. [25,81] It makes use of the fact that from theory realistic values of IE are expected at the position of the ionization efficiency curve where the slope of a semilog plot of the curve is... 

---