Theoretical curves

A modem alternative procedure involves computer matching of the entire drop profile to a best fitting theoretical curve in this way the entire profile is used, rather than just d and de, so that precision is increased. Also, drops whose ds is not measurable (how does this happen ) can be used. References 61 and 71-74 provide examples of this type of approach. 

Figure Al.3.16. Reflectivity of silicon. The theoretical curve is from an empirical pseudopotential method calculation [25], The experimental curve is from [31],...

The theoretical curve, deduced from the kinetic expression of the mechanism, fits the experimental points with gratifying exactness, whereas, for pD>12, the simple mechanism reported earlier (428,430) becomes predominant, and the rate increases very rapidly with pD and becomes first order both in thiazole and deuteroxide concentrations (Fig. 

It is, however, possible to calculate the tensile strength of a liquid by extrapolation of an equation of state for the fluid into the metastable region of negative pressure. Burgess and Everett in their comprehensive test of the tensile strength hypothesis, plot the theoretical curves of T /T against zjp, calculated from the equations of state of van der Waals, Guggenheim, and Berthelot (Fig. 3.24) (7], and are the critical temperature and critical... 

Table 2.2 Calculated Values for the Evaluation of Eyring Parameters for the Data and the Theoretical Curve of Fig. 2.5...

Figure 3.16a shows the storage and loss components of the compliance of crystalline polytetrafluoroethylene at 22.6°C. While not identical to the theoretical curve based on a single Voigt element, the general features are readily recognizable. Note that the range of frequencies over which the feature in Fig. 3.16a develops is much narrower than suggested by the scale in Fig. 3.13. This is because the sample under investigation is crystalline. For amorphous polymers, the observed loss peaks are actually broader than predicted by a...

Figure 6.6 Plot of (Rp)blin versus time (a) theoretical curves with...

The superpositioning of experimental and theoretical curves to evaluate a characteristic time is reminiscent of the time-tefnperature superpositioning described in Sec. 4.10. This parallel is even more apparent if the theoretical curve is drawn on a logarithmic scale, in which case the distance by which the curve has to be shifted measures log r. Note that the limiting values of the ordinate in Fig. 6.6 correspond to the limits described in Eqs. (6.46) and (6.47). Because this method effectively averages over both the buildup and the decay phases of radical concentration, it affords an experimentally less demanding method for the determination of r than alternative methods which utilize either the buildup or the decay portions of the non-stationary-state free-radical concentration. 

Figure 8.3 Volume fraction polymer in equilibrium phases for chains of different length, (a) Theoretical curves drawn for the indicated value of n, with the interaction parameter as the ordinate. Note that x increases downward. (Redrawn from Ref. 6.) (b) Experimental curves for the molecular weights indicated, with temperature as the ordinate. [Reprinted with permission from A. R. Shultz and P. J. Flory, J. Am. Chem. Soc. 74 4760 (1952), copyright 1952 by the American Chemical Society.]...

The value of diffusivity calculated from Eq. (12-38) must be recognized as an average value over the entire range of moisture change from W — WJ/(W — WJ = 1 to the value W — WJ/(W — WJ at which Q/d was evaluated. Further, Eq. (12-38) assumes that the theoretical curve is a straight hne for all values of time. This is not true for values W — WJ/(W — W ) less than 0.6. 

FIG. 17-57 Resistance factors for dust layers. Theoretical curves given are based on Eq, (20-78) for a shape factor of 0,5 and a true particle specific gravity of 2,0, [Williams, Hatch, and Greenhurg, Heat, Piping Air, Cond, i2, 259 (1940) Mumford, Markson, and Ravese, Trans, Am, Soc, Mech, Eng, 62, 271 (1940) Capwell, Gas, 15 31 (August 1.93.9)],... 

Fig. 2.18. Electron-impact ionization cross-section for the Ni K shell, as a function of reduced electron energy U [2.128] U = Ep/Ek, where Ep is the primary electron energy and E

Figure 5.3. Variation of grain-boundary specific energy with difference of orientation. Theoretical curve and experimental values ( ) (1950).

A theoretical curve for bi-layer adsorption was calculated from experimental data [3] and is given in Figure 7. The actual values obtained are superimposed on the... 

The magnitude of the variance a represents the square of the distribution spread and has the units of (time). The greater the value of this moment, the greater the spread of the RTD. The variance is particularly useful for matching experimental curves to one of a family of theoretical curves. 

At high temperature, the conductivity was found to increase linearly with temperature and the observed high-temperature MR was positive. In fact, by fitting the data using a simple two-band model] 17] the authors obtained the theoretical curve in Fig. 4 (a). The fitting parameters showed that the ratio Op/ct, where Op and are the partial conductivities of holes and electrons, respectively, decreases with increasing tern-... 

FIGURE 7.32 Effect of supply jet angle on recirculation bubble length. Experimental data and theoretical curve from Sawyer. Reproduced from Awbi. ... 

The theoretical and measured results for E, are shown in Figure 3-41 as a function of resin content by weight. Theoretical results from Equation (3.64) are shown for C = 0,. 2,. 4, and 1, and the data are bounded by the curves for C = 0 and C =. 4. The theoretical curve labeled glass-resin connected in series is a lower, lower bound than the C = 0 curve and is an overly conservative estimate of the stiffness. 

Figure 22.3 shows such theoretical curves as well as experimental points of capillary columns with 0.6- to 1.4-/i.m radii. The separation ranges of these capillary columns are from 5 X 10 to 10. Most of the data points follow the modified DG model. With OTHdC, the molecular hydrodynamic size can be calculated. However, the separation range of a single capillary column is relatively narrow, only about 1.5 order of magnitudes. 

FIGURE 22.3 Experimental points for polystyrene standards in THF and three OTHdC columns (O, 1.342 fjLm, , 0.862 jum and O, 0.630 tm) with theoretical curves according to the modified BG model. (Reprinted with permission from Ref. 7. Copyright 1986 American Chemical Society.)... 

FIGURE 22.7 Elution behavior of polystyrene standards in THE in PCHdC with different packing diameters , 1.40 /tm A, 1.91 m and , 0.87 /tm. Theoretical curves according to Eq. (I), where C = 3.7. (Reprinted from j. Chromatogr., 506,554, Copyright 1990, with permission from Elsevier Science.)... 

Heterogeneous copolymerization of acrylamide causes redistribution comonomers between phases I and II. This leads to a change of copolymer composition in phases I and II. As a result, the values of ri and change. This accounts for anomalous widening of the experimental composition distribution curves as compared with theoretical curves. 

Determine from this plot the Tafel slopes 6, and 6 by curve fitting using the theoretical curves calculated for various values of 6 and 6,.. Calculate from equation 19.14 using the Rp, value evaluated in Step 1 and the Tafel slopes determined in Step 3. 

Fig. 20.9 Experimental capacitance-potential curve for O-OOI m KCl and calculated curve using the Gouy-Chapman model. The experimental curve and the theoretical curve agree at potentials (us R.H.E.) near the p.z.c. Note the constant capacitance of 17 x 10 F m at negative potentials (after Bockris and Drazic )...

An example of the use of (140) is shown in Fig. 41. The small circles in Fig. 41 give the experimental values of log Kx for acetic acid in aqueous solution. The theoretical curve marked 219 is calculated from (140), with a — 1.35, C = 850.2, and d = 219. It will be seen that the agreement is better than might have been expected. To obtain still closer agreement, a somewhat larger value of d is required. The other curve in Fig. 41, calculated with d = 240, gives almost perfect agreement. 

Nakagaki1U) has given a theoretical treatment of the electrostatic interactions by using the Gouy-Chapman equation for the relation between the surface charge density oe and surface potential /. The experimental data for (Lys)n agrees very well with the theoretical curve obtained. 

Figure 9-27. Experimental (dots) and theoretical (solid line) t/V characteristics of. a Ca/PPV/Ca electron-only device with a thickness, L, of 310 nm. The theoretical curve is obtained assuming an exponential trap distribution with a trap density of Nt=5-I()17 cm 1, a trap distribution parameter Tt 1500 K, and an equilibrium electron density n = L5-I011 cm"1. The dashed line gives the hole SLC according to Eq. (9.13). Reproduced from Ref. 85J.

It is only natural that computers present a powerful method for determining yield stress with the help of Eq. (3). A corresponding program of computations is based on such a selection of constants b, n, and m that provides a minimum deviation of the theoretical curve from experimental points. 

Fig. 15. Comparison of the experimental data for the polyelectrolyte effect on ki of NH4-OCN reaction at 50 °C with the theoretical curves obtained from eq. 16. O NaPAA added, [NH4OCN] = 0.0205 M, O DECS added, [NH4OCN] = 0.1025 M (Ref.15 ))...

The PETN Detonation Pressure, P (also called the CJ Pressure), is shown as a function of packing density in Table 7 and in Fig 4. Note that the measured P values in Fig 4 lie quite close to the theoretical curve developed by Lee Homig (Ref 72), which is based on a Wilkin s type equation of state (see Vol 4, D294-L) with a Grueneisen ratio, r, for the detonation products, that is solely a function of specific volume. Shea et al obtained an effective T = 8.077 p-12.288 (Ref 74)... 

The equations resulting from both these studies are extremely complex, and contain several reaction parameters not readily evaluated from separate experiments. Figure 15 shows a comparison between experimental data and the two theoretical presentations. The theoretical curve was obtained by curve-fitting through adjusting the unknown parameters. This comparison shows that the theoretical expressions have sufficient flexibility to adequately correlate experimental burning rates. However, the value of the activation... 

Fig. 5. Sum of gas and liquid holdup in gas-liquid fluidized bed. Experimental data of Turner (T4) and theoretical curves of 0stergaard (03).

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