Challenge 7 Conceptual Problems

Currently, research activity in the field of polymer blends - from both theoretical and experimental points of view - is extensive, as is apparent from the many reviews and books available on the subject [27-29]. However, many challenging conceptual problems involving phase separation, phase transition, glass transition, miscibility and immiscibility [30] and optical properties have yet to be resolved for polymer blends [31-34]. 

The intramolecular chemical titration is conceptually and experimentally simple and convenient, but it requires that a particular dioxetane must be made that chemi-energizes the photochemically active carbonyl product K. This is usually a formidable and challenging synthetic problem. Representative intramolecularly chemienergized photochemical transformations include Norrish Type I cleavage (Eq. 44), Norrish Type II (Eq. 45a, b, c) cleavages, cyclohexadienone rearrangement (Eq. 46), and cyclopentenyl ketone rearrangement (Eq. 47). 

The challenge is to evaluate this sum accurately, robustly, and swiftly. As mentioned before, the customary approach is via some form of multipole expansion. FILMS had just such a procedure. Though usually adequate, it shared the conceptual problem of all multipolar schemes of which we are aware, namely, there was no systematic way to sum the entire series with controllable precision. A more practical criticism was that we foimd it difiicult to diagnose when the technique was failing despite appearing to be successful. 

Conventional kinetics is largely concerned with the description of dynamic processes in the time domain, and in consequence few conceptual problems are encountered in understanding time resolved experiments. By contrast, frequency resolved measurements often pose more of a challenge to understanding, in spite of the obvious correspondence between the time and frequency domains. This conceptual difficulty may explain why the only frequency resolved method to achieve universal acceptance in electrochemistry is electrochemical impedance spectroscopy (EIS) [27-29], which analyses the response of electrochemical systems to periodic (sinusoidal) perturbations of voltage or current. It is clear that EIS is a very powerful method, and there... 

Computational quantum chemistry is now a very inexpensive area of study and research, and it is absolutely essential that this accessibility is taken advantage of to provide as broad a base of theoretically informed, reflective and computationally enthusiastic scientists as possible, since, notwithstanding the enormous technical advances of the past decade, some of the most challenging conceptual and scientific problems of molecular electronic structure theory still remain. 

In his speech at the ASSE Symposium, Turner recognized that there are common challenges in applying leading indicators in the practice of safety. He spoke of the conceptual problems since measurement of the effects of the tactics chosen may be difficult. Turner observed that, since there are multiple causal factors for most accidents, choosing the relative leading indicators—the issues for which improvements are to be made in safety management processes— becomes complex. 

Note Answers to all odd-numbered Problems, numbered in blue, can be found in Appendix III. Exercises in the Problems by Topic section are paired, with each odd-numbered problem followed by a similar even-numbered problem. Exercises in the Cumulative Problems section are also paired but somewhat more loosely. (Challenge Problems and Conceptual Problems, because of their nature, are unpaired.)... 

Treatment of structural nonlinearities within the framework of ideas presented in the preceding sections offers several conceptual challenges. For problems involving linear substmctures coupled through nonlinear elements, the fixed- and free-interface methods can be extended in a relatively easy manner. However, for problems involving globally distributed nonlinearities, the extensions... 

The current undergraduate curriculum in chemical engineering, although it provides an excellent conceptual base for graduates who move into the electronics industries, could be improved by the introduction of instractional material and example problems relevant to the challenges outlined in this chapter. This would not require the creation of new courses, but rather the provision of material to emich existing ones. This theme is echoed, more broadly, in Chapter 10. 

The convective diffusion theory was developed by V.G. Levich to solve specific problems in electrochemistry encountered with the rotating disc electrode. Later, he applied the classical concept of the boundary layer to a variety of practical tasks and challenges, such as particle-liquid hydrodynamics and liquid-gas interfacial problems. The conceptual transfer of the hydrodynamic boundary layer is applicable to the hydrodynamics of dissolving particles if the Peclet number (Pe) is greater than unity (Pe > 1) (9). The dimensionless Peclet number describes the relationship between convection and diffusion-driven mass transfer ... 

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