A Comment on the Magnitude of

A Dirty Silicate Story A friend of one of the authors is an astronomer—as well as a professional mineral dealer—who became interested in dirty silicates as candidates for interstellar dust. He therefore selected for determination of the blackest natural silicate mineral in his possession, the coal-black mineral hornblende, which contains a high concentration of impurities such as iron. A slice about 100 jam thick was polished, and transmission was measured in a recording spectrophotometer. The fact that appreciable light was transmitted for all near-infrared and visible wavelengths indicated that k was rather small. Calculations indeed confirmed that k was less than 10 4 between about 6 and 0.3 jum. And yet this was the blackest silicate in the possession of a professional collector. It is not easy to find A = 0.01 in the band gap region of 

5 VALIDITY OF BULK OPTICAL CONSTANTS IN SMALL-PARTICLE CALCULATIONS 

Although we admit that these effects must surely appear in small particles, we cannot countenance the uncritical invocation of vague and esoteric quantum size effects, as is sometimes done, to dispose of optical phenomena in small particles that are not understood. Often the correct interpretation may be much simpler particle shape, for example, which we shall discuss in Sections 12.3 and 12.4. Our best advice, based on calculations (Martin, 1973 Chen et 

There are many ways in which electromagnetic waves can interact with matter in its condensed phases, liquid and solid. Some of these have been treated with simple models in Chapter 9, and examples are given in this chapter. Lest we leave the reader with an oversimplified view of optical constants we list in Table 10.2 several absorption mechanisms in solids together with the spectral regions in which they are important. References, primarily review articles and monographs, are also included to guide the reader in further study. 

Most optical studies of condensed matter have been made near room temperature, but there are applications in which optical properties are required at high temperatures (e.g., particles as solar radiation absorbers) or at low temperatures (e.g., interstellar dust grains). Although we cannot discuss all possibilities, the following brief comments may be helpful. 

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An electron in a hydrogen atom is known to have a velocity of 5 x 10 m/s 1 percent. Using the uncertainty principle, calculate the minimum uncertainty in the position of the electron and, given that the diameter of the hydrogen atom is less than 1 angstrom (A), comment on the magnitude of this uncertainty compared to the size of the atom. 

Comment on the magnitude of the result and the necessity for large pipe sizes in a chemical plant. 

The alkaline hydrolysis of methyl esters of substituted benzoic acids has a Hammett p of 2.23. What would be the Bronsted 3 for the reaction when measured against the of the corresponding benzoic acid Comment on the magnitude of the effective charge at the reaction centre in the transition structure compared with that of the carboxylate anion product in the reference dissociation reaction ... 

EXAMPLE 8 Calculate the value of the equilibrium constant for a reaction with AG° equal to 255 J at 25°C. Comment on the magnitude of the constant. 

What is the estimated velocity for Cu ions moving through water in a Daniell cell in which the electric field is 100.0 V/m Assume that a for Cu is 4 A and the viscosity of water is 0.00894 poise. Comment on the magnitude of your answer. 

S. Bahadur (Iowa State University) For many reasons, the sliding in conventional friction experiments is performed between a hemispherical indentor and a flat plate. Could you therefore comment on the magnitude of error that would be involved if the results of your pyramidal indentor analysis were to be used for the case of hemispherical indentor ... 

A few comments are due on the magnitude of this important result. It is sometimes claimed in the literature that it has an unexpectedly large magnitude. A brief glance at Table 3.3 is sufficient to convince oneself that this is not the case. For the reader who followed closely the discussion of the scales of different contributions above, it should be clear that the natural scale for the correction under discussion is set by the factor 4a Za) / Trn )m. The coefficient before this factor obtained in (3.48) is about —1.9 and there is nothing unusual in its magnitude for a numerical factor corresponding to a radiative correction. It should be compared with the respective coefficient 0.739 before the factor Aa. Za) /n m in the case of the electron-line contribution of the previous order in a. 

I) reduction initially decreased in magnitude from —780 to —580 mV in going from n = 0 to n = 2 (versus Ag wire quasi-reference, 100 mM Bu4NC104 in DMF (dimethyl formamide), GCE). It then was reported to increase in magnitude to —830 mV for n — 3 and —880 mV for n — A. However, from the narrative, it was unclear why the authors were able to measure a thermodynamic redox potential as they commented on the broadness of their CV data. At least for the first few points, the trend in the redox potential follows the established paradigm. As the charge upon reduction decreases, the relatively less polar environment of the dendrimer compared to the solvent destabilizes the reduced form less than the oxidized form. 

Construct a Grunwald-Winstein plot and comment briefly on the magnitude of the slope. The y, Ad parameter is determined from the solvolysis of 1 -adamantyl chloride. 

Q.19.10 Consider Figs. 20.8 and 20.10, comment on the behavior of the superposition of the interactional force and the Lennard-Jones potential when the interactional force between the double layers i/fg = (a) 50, (b) 10, (c) 2.5, and (d) 0.5. Sketching graphs may help. (These numbers are on the same arbitrary magnitude scale as the one used in Fig. 20.10.) Propose a mechanism that could change the interactional force between double layers other the infusion of counter ions (which is mentioned in the text.)... 

The influence of pressure, P, on the miscibility needs a comment. Since pressme reduces the effects of the free volume contributions, for most blends the miscibility increase with P (Walsh and ZoUer 1987 Schwahn 2005). The effects are very sensitive to the monomer structure, as one would expect from free volume considerations, as, for example, in PB/PS blends (Fig. 2.17) In the case of tf-PB/PS blends, the general trend of an increase of the phase boundaries with pressure is observed for all systems (viz., increased binodal and spinodal temperatures with P, due to the reduction of free volume), but the shapes of Ti,i odaAP) and TJiP) are linear for /-PB(l,4)/PS and /-PB(l,4-c )-l,2)/PS blends and are more parabolic for the blend with /-PB(l,2)/PS also the compatibility of PS is best for tf-PB(l,4) and worst for /-PB(l,2), with the d-PB(l,4-co-l,2) copolymer being in between the two, as expected (Fig. 2.17). The P effect generally depends on the magnitude of the heat of mixing For systems with Af/ , < 0, the miscibility is enhanced by compression, whereas for those with Af/ , > 0 it is reduced (Rostami and Walsh, 1984, 1985 Walsh and Rostami 1985). For PS solutions, the pressure gradient of... 

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