Qualitative summary

This chapter presents short descriptions of findings in the previous chapters. There has been a long march to this point. It appears worthwhile to show where we are before considering, in the next chapter, what phenomenology reveals about the nature of polymer dynamics. Each section in the following refers to a previous chapter the reader is directed to those chapters for more detailed remarks, figures, and citations of the primary literature. In discussing parametric behaviors, references are made to simple  

Chapter 2 treats the sedimentation of polymer molecules and the sedimentation of probe particles and tagged polymer molecules through a solution of matrix polymers. What generalizations can be obtained from the extant phenomenology First, s c) for polymers in a homogeneous binary polymer solvent system almost always follows a stretched exponential in polymer concentration. For probe colloids or chains sedimenting through a polymer matrix solution, s(c) also has a stretched-exponential dependence on matrix polymer concentration. 

Chapter 2 introduced an experimental motif to be seen repeatedly in later chapters, notably those on dielectric relaxation, self- and tracer diffusion, colloidal properties, and probe diffusion. Given that one has a molecule whose position or 

In ternary mixtures at small matrix concentration, larger probes sediment more rapidly. However, with increasing matrix concentration the sedimentation coefficient of a larger probe decreases more rapidly than does the sedimentation coefficient of a smaller probe, so at large c large probes sediment more slowly than smaller probes. The a of Eq. 15.1 increases approximately linearly with the hydrodynamic radius of the probe. The a also increases with matrix molecular weight, even when the matrix polymer is much larger than the probes. Indeed, a polymer matrix solution can hinder probe sedimentation when the matrix sediments more rapidly than the probe does. 

Several lines of evidence indicate that a is actually sensitive to the spatial extent of the matrix polymer, not to the matrix molecular weight. The a decreases if one moves the matrix polymer from a good to a Theta solvent. At elevated polymer concentration, three-arm star polymers sediment two or three times faster than do linear polymers of about the same molecular weight. Sedimentation is also slowed if the matrix chains are made more rigid - based on studies on polyelectrolyte matrices - though it is unclear whether the chain rigidity or the polymer spatial extent is the key variable. 

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This expression is called a skeletal equation because it shows the bare bones of the reaction (the identities of the reactants and products) in terms of chemical formulas. A skeletal equation is a qualitative summary of a chemical reaction. 

Luft and Tsuo have presented a qualitative summary of the effects of various plasma parameters on the properties of the deposited a-Si H [6]. These generalized trends are very useful in designing deposition systems. It should be borne in mind, however, that for each individual deposition system the optimum conditions for obtaining device quality material have to be determined by empirical fine tuning. The most important external controls that are available for tuning the deposition processs are the power (or power density), the total pressure, the gas flow(s), and the substrate temperature. In the following the effects of each parameter on material properties will be discussed. 

Figure 37. Qualitative summary of current contributions from the surface path (Is) and the bulk path (7b) for LSM disk microelectrodes on YSZ based on i— measurements in air at 800 °C. (Reprinted with permission from ref 228. Copyright 2002 Elsevier.)...

Figure 23 Qualitative summary of the evolution of steel properties discussed in this chapter as a function of the retained REM content showing an early maximum for all properties associated with sulfide shape control and tramp element control but quite a different story for hydrogen and oxidation resistance...

A qualitative summary of the critical factors for the cities discussed above is given in Table 16. 

Such a summary overview for the Gulf of Mexico, also finds a clear example in the case study of Hydrate Ridge. While Roberts provided a qualitative summary of the three ranges of gas fluxes, his conceptual picture evolved from a career of field experiments, serves as a basis for quantification, such as in the following models. 

Tritium retention mechanisms are reviewed in various papers (e.g., [1, 73] for C-based materials, [1, 74, 75] for beryllium and [1, 76] for tungsten). A qualitative summary of the retention and removal characteristics of the plasma facing materials considered for ITER is shown in Table 12.4 [76]. 

Analysis of all the data on O-atom reactions with squalane and consideration of the various possible reactions of ground state 0( P) and electronically-excited 0( D) lead to a qualitative summary (Fig. 16) of the initial reactions between atomic oxygen and a saturated hydrocarbon surface. The first step leading to the production of volatile reaction products is direct H-atom abstraction by 0( P). The initial OH product may... 

Stated as an abstraction and generalization of engineering observations on the efficiency of heat engines. We start the discussion by presenting a nonmathematical qualitative summary of the arguments on efficiency. Then we define entropy and state the second law. Section 13.5 applies the definition to calculate entropy changes and to predict spontaneity of processes. 

It is possible to give a qualitative summary of London s quantum mechanical treatment on how an instantaneous dipole moment would arise and on the magnitude of its inter-... 

Simulations in the Diffusion-Limited Regime p = 10. None of the profiles listed in Table 23-9 is more effective than uniform deposition at any aspect ratio when the Damkohler number p = 10. This is understandable in the diffusion-controlled regime where the rate of chemical reaction on the catalytic surface is not the primary factor that governs the conversion of reactants to products. However, some profiles perform poorly relative to uniform deposition when diffusion of reactants toward the active surface is slow. Differences among the profiles are more pronounced at higher aspect ratios. A qualitative summary at each aspect ratio is provided in Table 23-10. Identification numbers are underlined when... 

Simulations When p = 1. Now, the rate of reactant diffusion toward the waU is comparable to the rate of reactant consumption via surface-catalyzed chemical reaction. Hence, some of the profiles should be more effective than uniform deposition. This prediction is verified by simulation, but not at the largest aspect ratio (i.e., Ar = 100). The effectiveness of nonuniform deposition is more pronounced when the comer regions exert a stronger influence on reactant conversion at smaller aspect ratio. A qualitative summary at each aspect ratio is provided in Table 23-11. 

In this section we will give a qualitative summary of the role of spin-orbit coupling in molecules. If the separation of spatial and spin parts of the wave function for a state was rigorously justifiable on the grounds that the spin and orbital motions of the electron were completely independent, then electronic transitions between states of different multiplicity would be rigorously forbidden. The ground state of such a system, < o, may be... 

Qualitative Summary of Selected Studies on the Relationship between Organic Matter and Sediments or Soils... 

Indices for measuring the extent of isostructurality of two or more organic crystal structures can be applied not only to homomolecular crystals but also to molecular associates. such as inclusion compounds. A qualitative summary of these descriptors follows, and the reader is referred to a recent account for explicit mathematical definitions. Earlier descriptors of isostructurality included the " d-gree of isostructurahty" Ii(n) (based on the distance differences ARj between the crystal coordinates of identical nonhydrogen atoms within the same section of the asymmetric units of two or more related structures) the packing coefficient increment. A(pc) and the unit cell similarity index... 

In Chapter 4, we discuss the role of three fundamental reactor types in attainable region (AR) theory. Many readers may already be familiar with these reactors, for they are common in chemical reaction engineering. A small, qualitative, summary of these reactors is provided in the following text. 

A CSA is required for operations that involve total amounts of fissile material in excess of the threshold amount for non-aqueous forms (700 g U) where formal criticality safety evaluations and controls are required [Philbin, 1998, Criticality Safety Supplement to the SNL ES H Manual, Applicability Section]. The CSA requires that process designs incorporate a double-contingency principle so that at least two unlikely, independent, and concurrent changes in process conditions must occur before an accidental nuclear criticality is possible. Table 6.4-3 is a qualitative summary of the double contingency analysis from the CSA for isotope processing [Mitchell and Romero, 1999 (draft). Section 5]. 

Although it is possible to cast both quantum and classical mechanics in a similar formal language (i.e., distributions in phase space and a Liouville propagator), standard quantum mechanics is based on a mathematical structure that is substantially different from that of classical Hamiltonian mechanics. We first provide a brief qualitative summary of some results of quantum investigations, and then we present details that can be best appreciated by the reader who is well versed in quantum mechanics. 

The results for beryllium will be qualitatively similar to those for graphite, but the effects of crystalline binding will be somewhat smaller, since the average frequency of the lattice vibrations in beryllium is somewhat lower than in graphite. A brief, qualitative summary of the effects of binding on the spectra for heavy crystalline moderators can be given as follows ... 

The performance criteria that usually determine the choice of one or more FRP resins over another include chemical resistance, mechanical strength, heat resistance, and (for the manufacturer) processability. A qualitative summary of FRP resin performance is presented in Table 5.48. For the final choice of the appropriate FRP resin(s) and liner combination for a given service (chemical environment, weathering exposure, abrasion resistance, etc.) more detailed information, including case history data, should be obtained. 

Table 5.1 Qualitative summary of emissions from alternative-fuel vehicles versus gasoline-fuel vehicles... 

Gaseous materials are well known in our experience, and, under ordinary conditions, we have no trouble in differentiating them from solids, liquids, or glasses, A qualitative summary of the characteristic properties of gases under ordinary conditions is given in Table 2.1. 

Some performance attributes of ETPs and AETPs are summarized in Tables 1.1-1.5. Properties are taken from product data sheets and published technical literature [2], Data were chosen from grades that did not contain any additives for these tables. Since processing and test conditions can play an important role in defining optimum performance, the data should be viewed as a qualitative summary. 

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