A Final Remark

The investigation of viscoelasticity of dilute blends confirms that the reptation dynamics does not determine correctly the terminal quantities characterising viscoelasticity of linear polymers. The reason for this, as has already been noted, that the reptation effect is an effect due to terms of order higher than the first in the equation of motion of the macromolecule, and it is actually the first-order terms that dominate the relaxation phenomena. Attempts to describe viscoelasticity without the leading linear terms lead to a distorted picture, so that one begins to understand the lack of success of the reptation model in the description of the viscoelasticity of polymers. Reptation is important and have to be included when one considers the non-linear effects in viscoelasticity. 

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A final remark should be added that applies to both of the methods outlined above. As both are iterative, any computer program must specify either the number of iterations or the precision of the desired result Or better, both should be included and employed - whichever comes first. 

As a final remark it must be mentioned that theoretical and experimental works have been dedicated to investigating the effect of the finite size of the chains [65]. In fact, as grows exponentially, at low temperatures it can become comparable with the distance between two consecutive defects (e.g. impurities and vacancies) which are always present in real systems and hardly separated by more than 103 -104 elementary units. In case of Z < , the nucleation of the DW is energetically favoured if occurring at the boundaries, because the energy cost is halved. However the probability to have a boundary spin is inversely proportional to L thus the pre-exponential factor becomes linearly dependent on L, as experimentally found in doped SCMs. As doping occurs at random positions on the chain, a distribution of lengths is observed in a real system. However, as the relaxation time is only linearly dependent on L, a relatively narrow distribution is expected. 

As a final remark in this section, we expect that the results presented herein have shown how theoretical methods allow us to obtain some insight into a great variety of experimental facts, even in the complex case of chemical reactivity. 

A final remark about the line intensities in Fig. 5.10 (left) as the field is directed perpendicular to the y-beam, the situation corresponding to (p=9i)° in Table 5.4 applies and the line intensities from outward to inward are in the proportions of 3 4 1. One can also apply the external field parallel to the y-beam, with the result that the second and fifth lines of the sextet disappear from the spectra ( =0 in Table 5.4). Bpdker et al. [25] used this to simplify the spectrum of small iron particles and could in this way analyze the shape of the outer lines in more detail. 

As a final remark we have to observe that the numbers of compounds, point sets, environment types, etc. evaluated at a certain time are continuously increasing, nevertheless they are sufficiently large to justify the general conclusions drawn. 

As a final remark it may be stated that the predictive simulation of crystal nucleation from a solvent, and of the consequent polymorph selectivity, is the grand challenge of computational crystallography in the next few decades. 

A final remark In Section 20.3 we will see that due to the difference in air diffusivities the evaporation velocity of MCF is smaller than v,a of water vapor. A rough estimate will be given by the ratio of the molecular masses (combine Eqs. 20-27 and 18-46) ... 

A final remark should be made as to the validity of eq. (2.13). This equation suggests the existence of a set of independent relaxation mechanisms. A general proof for the existence of such mechanisms could be given for visco-elastic solids in terms of the thermodynamics of irreversible processes (52) at small deviation from equilibrium. For liquid systems, however, difficulties arise from the fact that in these systems displacements occur which are not related to the thermodynamic functions. 

As a final remark it may be mentioned that the discussed polypropylene melts do not at all behave like second-order fluids in the range of shear rates and angular frequencies accessible to measurement. This is shown in Fig. 4.6. In this figure the doubled extinction angle 2 is plotted... 

As a final remark, the machine costs matched with the innovative character of the technology could confine the application just for industrial laundries, limiting the possibility to extend dry-cleaning machines to an end-user approach. 

As a final remark for this section we note that for nano-particles, for which IJDna is roughly two orders of magnitude smaller than for micro-particles, a subtle control of the balance between the different terms in Ulol may seem more difficult. Nevertheless, reversible assembly may easily be obtained with nanoparticles [127,... 

A final remark to close the section dealing with five-membered rings is that Mathey recently reported a one-pot procedure converting a phospholide ion (which is highly aromatic, as discussed above) to the six-membered ring phosphabenzene (which is also highly aromatic, as will be discussed below) as shown in Scheme 49 [278],... 

A final remark concerns molecular weight, which increases with amount of monomer charged, and is smaller in the case of corrected batch process than in batch process (table V). 

A final remark is to underline the efficiency of the "corrected batch process" to regulate not only the copolymer composition, but also the molecular weight and more importantly particle size. 

As a final remark, from (3), it can be seen that, it is not proper to speak of an electronic transition by mentioning only the configurations involved, such as Is2 - lsW.This is because, in this particular case, it does not specify the final state of the transition. Hence, to cite an electronic transition, we need to specify both the initial and final electronic states. Only stating the initial and final configurations is not precise enough. We will have more discussion on this later. 

A final remark in this Section concerns axially symmetric problems. We usually treat these in radial coordinates and apply a numerical Hankel transform instead of the Fourier transform. This is a slow transform with a dense matrix, but due to the relatively small computational domain radially symmetric problems require, this is not a big problem. Alternatively, one could treat such situations by finite differencing in the radial dimension, but it would mean accepting additional (paraxial) approximation, and would introduce artificial numerical dispersion into the algorithm. 

A final remark concerns complexes, represented by Green s methyltita-nium complex 23 (76) or Schrock s alkylidene complexes [e.g., 24 (77)], in... 

We have, we hope, provided enough detail about the Zeeman effect to show how almost every microwave resonance could be assigned, so far as the J values were concerned. A final remark should be made concerning the parity labels. These depend upon the identification of a J = 1 /2 <- 1/2 transition, and the measured g-factors for the two J = 1/2 levels which identify their e//, and hence total parities. The parities of all other levels then follow because all transitions are electric-dipole allowed, between states of opposite parity. As we have mentioned earlier, the combination of numerical relationships between the resonance frequencies, double resonance studies, and Zeeman effect measurements enabled the pattern of levels lying within 8 cm 1 of the dissociation limit to be established. The highest level, J = 7/2 (—parity), in figure 10.74, was thought to lie within 20 MHz (<0.001 cm-1) of the dissociation limit. 

A final remark the real development of the powder coating process was not as straightforward as in our story. It was the result of many smaller projects, with many dead ends. Even so, it did not take 700 000 years ... 

As a final remark we wish to note that the result of the one-dimensional computer simulation shown in Fig. 9 suggests that the nonlinear version of the itinerant oscillator model should be improved by giving a fluctuating character to the virtual potential, since Rq does not turn out to be a very fast variable. Therefore, the potential of (4.9) should be interpreted as an average potential around which an effective potential would fluctuate. 

A final remark concerns the effect of interfacial curvature. Above we have considered the surface to be flat, i.e., its radius of curvature is supposed to be large with respect to the thickness of the adsorbed layer. Some adsorption studies, however, deal with colloidal particles which are too small to fulfil this condition. Intuitively, one would expect different adsorbed amounts on a strongly convex surface, since the curvature changes the lateral repulsion. Others have argued that also the thickness could be different. Very few studies have dealt explicitly with these effects -2 3 4)... 

As a final remark, a brief comment should be made on the capabilities of other scanning prohe microscopy techniques, particularly atomic force microscopy (AFM), for the visualization of pores in carbon materials. Fig. 6 shows an image of the studied ACFs obtained by tapping mode AFM. It is evident from Fig. 6 that the pore structure of the ACFs is not resolved and the surface appears extremely smooth. Such deficient performance of the AFM is mainly attributed to the relatively large curvature radius of the tips used (5-10 nm, among the shaipest available). This limits the width of the trenches that can be probed with reasonable accuracy and, in this case, prevents the detection of the micro- and mesopores of the ACF sample. 

We close this introduction with a final remark about the modelling of the failure. In a real situation, failure takes place in solid samples which are, by nature, continuous in space. However, many studies (numerical and experimental) have been made on lattices. In all these studies, it is an implicit assumption that one can replace a continuous solid by a lattice. For example, a conducting solid can be described by a lattice in which the bonds between sites are identical resistors. It is a very common practice in percolation type models of disordered solids. We stress that this transformation (continuous solid to lattice) defines a particular length scale the length of the unit cell of the lattice. This implies that defects appear by discrete steps and this does not correspond always to real situations. We shall see later how to remove this limitation. 

As a final remark in this chapter, a very important investigation concerning the experimental verification of lone pair electron density has been reported for dimethyltellurium dichloride, (CH3)2TeCl2 (451). High-resolution X-ray experiments on the deformation density at 151 K, which are the first ones of this kind for a heavy main-group element molecule, give clear and quantitative evidence for the localized electron density predicted at one of the equatorial positions of the ( (-trigonal bipyramidal molecule. 

As a final remark, a class of selenium(II) and tellurium(II) compounds should be mentioned that are another example of the strong... 

A final remark about effects of steric hindrance of solvation of polar groups shall complete the discussion of optical rotations at the wavelength of the sodium-D-line. It seems that the truncated TTOR approach (equations 2, 3 and 5) remains valid for 1,1-diphenylcyclopropanes, if the target group for solvation (such as COOH or CH2OH) is sterically not strongly hindered. This is seen from the calculated and observed rotations of 71-74. 

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