Comparison of Theoretical Predictions with Experimental Data

2 Comparison of Theoretical Predictions with Experimental Data 

FIGURE 9.2 Comparison of experimental calibration data with analytical 

FIGURE 9.3 Comparison of experimental calibration data with analytical predictions in a fluidized bed at ujum] = 2.5 

THE COMPUTER-AIDED PARTICLE-TRACKING FACILITY 9.3.1 Principles of Operation 

The CAPTF was developed by Lin, Chen, and Chao (1981, 1985), and improved later by Liljegren (1983) and Moslemian (1987). The advantage of this technique is that the flow field is not disturbed by the facility and, therefore, the measurement gives the actual movement of particles inside the bed. 

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For a comparison of theoretical predictions with experimental data, the isolation of specific relaxation channels is necessary. Standard techniques for this purpose developed by Raman spectroscopists and adopted for CARS studies are the variation of concentration (e.g., isotopic dilution), temperature, and pressure (40,53). 

Drawing an exhaustive list of experimental studies on Ca oscillations is beyond the scope of this chapter the above-mentioned reviews should be consulted to that end. Here, only those references that pertain directly to the elaboration of the models or allow the comparison of theoretical predictions with experimental data are retained. Before we address theoretical aspects, it is useful to briefly recall the main properties of Ca oscillations as determined from a large number of experimental studies pertaining to a variety of different cell types. The spatial aspects of Ca signalling are considered further below, in section 9.6. 

Figure 3.8 Comparison of theoretical predictions with experimental data for the dimensionless horizontal force between two vertical cylinders. Both cylinders are hydrophilic (a) Both cylinders are partially submerged in water (b) Both cylinders are partially submerged in an 8 X 10 M SDS solution. The dash-dot lines show the lower limit for possible separation between the cylinder centers. 0 = 0 = 0 , = 370...

Recently, the stiff-chain polyelectrolytes termed PPP-1 (Schemel) and PPP-2 (Scheme2) have been the subject of a number of investigations that are reviewed in this chapter. The central question to be discussed here is the correlation of the counterions with the highly charged macroion. These correlations can be detected directly by experiments that probe the activity of the counterions and their spatial distribution around the macroion. Due to the cylindrical symmetry and the well-defined conformation these polyelectrolytes present the most simple system for which the correlation of the counterions to the macroion can be treated by analytical approaches. As a consequence, a comparison of theoretical predictions with experimental results obtained in solution will provide a stringent test of our current model of polyelectrolytes. Moreover, the results obtained on PPP-1 and PPP-2 allow a refined discussion of the concept of counterion condensation introduced more than thirty years ago by Manning and Oosawa [22, 23]. In particular, we can compare the predictions of the Poisson-Boltzmann mean-field theory applied to the cylindrical cell model and the results of Molecular dynamics (MD) simulations of the cell model obtained within the restricted primitive model (RPM) of electrolytes very accurately with experimental data. This allows an estimate when and in which frame this simple theory is applicable, and in which directions the theory needs to be improved. 

COMPARISON OF THEORETICAL PREDICTIONS WITH EXPERIMENTAL CALORIMETRIC DATA... 

The choice of fundamental approximation, combined with the choice of parameter values, defines a particular SEMOT method, analogous to a force field in MM. Several established and novel SEMOT methods have been reviewed and compared elsewhere [54]. Among the three popular SEMOT methods mentioned earlier, MNDO/d is least widely available in commercial software packages. The other two methods, AMI and PM3, differ only in their parameterization. Since the PM3 method was parameterized more recently and more carefully, it is expected to be more reliable and will be the focus of discussion here. However, performance varies, so it should be compared with that of the experiment for related systems before putting faith in the predictions. Note that AMI and PM3 predictions are included in the Computational Chemistry Comparison and Benchmark Database (CCCBDB), which is a convenient, on-line resource for comparing theoretical predictions with experimental data [55]. 

Additionally, the favorable comparison of these theoretical predictions with experimental data (Figure 2A0d) gives some credibility to the conclusions above. In Figure l.lOd we plot experimental water vapor permeabilities of various solvent cast nanocomposite films. The experimental behavior follows closely the theoretical trend and is enclosed between the response of exfoliated systems (especially for low filler loadings) and that of intercalated systems (for moderate and higher loadings). This reflects the same effective filler aspect ratio... 

Xu, Y., Graf J., Painter, P.C., and Coleman, M.M. (1991) Miscibility windows for poly(styrene-co-vinylphenol) blends with poly(n-butyl methacrylate) and poly(n-hexyl methacrylate) a comparison of theoretical predictions with Fourier transform infrared experimental data. Polymer 32, 3103-3118. 

Figure 2.34. Comparison of theoretical predictions (curve, calculated from Eq. (2.8S) according to the dissipative model of non-isothermal curing) with experimental data on the decrease of the induction period at high shear rates for phenolic-based compounds (vertical bars) and silicon-based composites at different initial temperatures 150°C (1) 170°C (2) and 190°C (3).

The models and concepts presented in Sections 1.1 -1.4 have been extensively tested in recent years. Some of these tests involved comparison of quantitative relationships between experimental observables with predictions of simple models. In other tests, the theoretical predictions and experimental data were compared with the results of detailed numerical calculations. We offer several examples of each type of comparison. 

The combined procedure described above, which uses only sorption and steady state permeation data, specifies all five of the sorption and transport model parameters without requiring reference to the independently measured time lags. Comparison of theoretically predicted time lags with the experimentally measured values provides a rigorous test of the internal consistency of the transport and sorption data as well as a check of the applicability of the partial immobilization model for description of the transient processes. 

Figure 11. Comparison of theoretical predictions of critical initiation energy with Elsworth s experimental data.

Experiments are very difficult to conduct with a high degree of accuracy over a wide range of conditions and diffusivity data is notoriously unreliable. Therefore, it is not easy to test the accuracy of different theoretical models by comparison of the predicted and experimental values of the correlating constants, particularly since there are four of them. However, the basic Froessling equation... 

Comparison of predictions based upon the theoretical equations with experimental data. The specific systems considered are ... 

Figure 12.13. Comparison of theoretically predicted transition from spherical to planar structure via the intermediate RO structure with experimental observations [43]. Dimensionless quantities Q = qR are attached to the calculated curves, whereas the experimental data corresponds to Qx 20n. Two sets of experimental values are shown, obtained by observations of droplet textures parallel (squares) and perpendicular (circles) to the field (courtesy of J. Bajc).

A micromechanics-based model recently proposed by Anoukou et al. [7,8] was adopted in the present investigation to develop a pertinent model for describing the viscoelastic response of polyamide-6-based nanocomposite systems. Comparisons between the results from the micromechanical model and experimental data were considered for nanocomposites reinforced with modified and unmodified montmorillonite clay. Reasonable agreement between theoretical predictions and experimental data was noticed, the discrepancies being attributed to both uncertainties in the input data and a possible effect of reduced chain segment mobility in the vicinity of clay nanoplatelets. 

In order to validate the theoretical model, the predictions of the numerical simulations were compared with experimental data. Comparison between the results of the... 

The purpose of performing calculations of physical properties parallel to experimental studies is twofold. First, since calculations by necessity involve approximations, the results have to be compared with experimental data in order to test the validity of these approximations. If the comparison turns out to be favourable, the second step in the evaluation of the theoretical data is to make predictions of physical properties that are inaccessible to experimental investigations. This second step can result in new understanding of material properties and make it possible to tune these properties for specific purposes. In the context of this book, theoretical calculations are aimed at understanding of the basic interfacial chemistry of metal-conjugated polymer interfaces. This understanding should be related to structural properties such as stability of the interface and adhesion of the metallic overlayer to the polymer surface. Problems related to the electronic properties of the interface are also addressed. Such properties include, for instance, the formation of localized interfacial states, charge transfer between the metal and the polymer, and electron mobility across the interface. 

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