Comparison of Prediction with Experiment

5 Comparison of Prediction with Experiment 4.4.5.1 Steady-State Shear Flow Properties 

We can now relate the step size a with quantities that can be measured by experiment, namely 

Equation (4.186) suggests that at very high values of y the steady-state shear stress a decreases with increasing y that is, a a Since the constitutive equation, 

As pointed out in Chapter 3, some phenomenological constitutive equations predict a decreasing trend of r] with increasing e only when a parameter is adjusted. Such phenomenological constitutive equations cannot be regarded as predictive models. Moreover, there are no molecular parameters involved in those phenomenological equations. Conversely, the constitutive equation, Eq. (4.158), contains all the important molecular parameters namely, that (1) is related to Mg and (2) is related to M, b, f, and M (see Eq. (4.116)). 

Once the expression for a is available, the shear stress relaxation modulus G t, y) can be calculated from 

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Figure 5-4 Comparison of predictions with experiment for the n-pentane-polystyrene system (64,94).

Fig. 6. Comparison of predictions with experiments (after Fu and Zhang, 1991).

In Table II we have presented selectivity predictions as well for several pairs of ions made by the method we have introduced here. In this table we also include the experimentally measured values. Upon comparison of prediction with experiment one observes that when the macroion component is univalent and the trace ion component is divalent (Sr 2, Cd 2, Co+2, ca , and Zn" ) agreement is quite good at the higher degrees of cross-linking (> 4%). At the lower degrees of crosslinking (1% and... 

Comparison of theory with experiment. It will be shown in Section 13.3.2.1 that the flat plate potentials can be used to calculate the osmotic disjoining pressures in concentrated monodisperse sterically stabilized dispersions. Evans and Napper (1977) have compared the theoretical predictions using the above equations with those measured by Homola and Robertson (1976) for polystyrene latex particles stabilized by poly(oxyethylene) of molecular weight ca 2 000 in aqueous dispersion media. The elastic repulsion in the interpenetrational-plus-compressional domain was estimated from the following expression for the constant segment density model... 

A detailed comparison of theory with experiment is given for polyisobutylene in Fig. 10-18, where the components of the complex compliance are chosen for representation. The general aspects of the onset of the glassy zone are evidently semiquantitatively reproduced. However, the distinct difference in slope between theory and experiment for values of J and J less than 10 cm /dyne is apparent. A similar treatment was made by Shibayama and collaborators, who also introduced varying parameters for the springs and dashpots in the ladder model to modify the shapes of the viscoelastic functions predicted. But a more detailed picture of local molecular motions is needed to explain viscoelastic behavior near the glassy zone. 

In general, the major system-analysis codes are equipped to model all of the equipment components and associated physical phenomena and processes that are expected to occur. The codes and modeled namral-circulation and parallel-channel flows for the coupled NCL case require validation by comparisons of predictions with experimental data. The major codes, the several locally developed special-purpose models and codes, and application procedures have been validated by use of many of the simple pure thermal-hydro experiments and analytical results for NCLs and parallel-channel flows. However, in general, the general-purpose major codes must be validated for applications to complete coupled-loop systems for design, development of deep understanding, and safety-grade analyses. 

Accurate ab initio calculations for the hehum dimer and trimer can be used in several other ways in thermal physics. One can use theoretical predictions to calibrate instruments designed to measure the density and dielectric virial coefficients, viscosity, thermal conductivity, speed of sound, and other properties of gases based on comparisons of theory with experiment for helium. 

Dewar and his co-workers, as mentioned above, investigated the reactivities of a number of polycyclic aromatic compounds because such compounds could provide data especially suitable for comparison with theoretical predictions ( 7.2.3). This work was extended to include some compounds related to biphenyl. The results were obtained by successively compounding pairs of results from competitive nitrations to obtain a scale of reactivities relative to that of benzene. Because the compounds studied were very reactive, the concentrations of nitric acid used were relatively small, being o-i8 mol 1 in the comparison of benzene with naphthalene, 5 x io mol 1 when naphthalene and anthanthrene were compared, and 3 x io mol 1 in the experiments with diphenylamine and carbazole. The observed partial rate factors are collected in table 5.3. Use of the competitive method in these experiments makes them of little value as sources of information about the mechanisms of the substitutions which occurred this shortcoming is important because in the experiments fuming nitric acid was used, rather than nitric acid free of nitrous acid, and with the most reactive compounds this leads to a... 

Figure 12.2 shows the results of comparisons between prediction and experiment for the polyimides listed in Table 12.3. The correlation coefficient is determined to be 0.767. Its value can be improved to 0.957 by not considering the polyimide whose predicted dielectric constant value is equal to 3.02. The slope of the best-fit line is equal to 0.737, with a standard deviation of 0.232. 

From active site labelling experiments and from sequence comparison of NRs with homologous proteins, functionally important residues can be predicted and localised on the NR sequences. 

In addition to this mechanistically most valuable result, some other conclusions can also be deduced by comparing the individual similarity indices rRI and rIf which characterise the extent of electron reorganisation in individual reaction steps. In our case it is possible to see that the extent of electron reorganisation is greater in the second step (rRI > rIP). This implies that this step should also be rate determining. The reaction profile of such a process thus corresponds to what Dewar calls the two-step process [78], It would be certainly interesting to confront this theoretical prediction with experiment but unfortunately the lack of convenient data makes such a comparison unfeasible. As we shall see below,... 

A major weakness of semiempirical methods is that they must be assumed to be unreliable outside molecules of the kind used for their training set (the set of molecules used to parameterize them), until shown otherwise by comparison of their predictions with experiment or with high-level ab initio (or probably DFT) calculations. Although, as Dewar and Storch pointed out [125], the reliability of ab initio calculations, too, should be checked against experiment, the situation is somewhat different for these latter, at least at the higher levels studies of exotic species, in particular, are certainly more trustworthy when done ab initio than semiempirically. Semiempirical heats of formation are subject to errors of tens of kJ mol-1, and thus heats (enthalpies) of reaction and activation could be in error by scores of kJ mol-1. AMI and PM3 underestimate steric repulsions, overestimate basicity and underestimate nucleophilicity, and can give unreasonable charges and... 

FIGURE 21.9 Comparison of predicted onset saturation ratios with experiments and the best... 

Hall SE, Floriano WB, Floriano WB, Vaidehi N, Goddard WA 111. Predicted 3-D structures for mouse 17 and rat 17 olfactory receptors and comparison of predicted odor recognition profiles with experiment. Chem. Senses 2004 29 595-616. 

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