Schmidt rule

Hubbard, N. B. Howell, L. L. Barber, J. P. Conkey, D. B. Hawkins, A. R. Schmidt, H., Mechanical models and design rules for on chip micro channels with sacrificial cores, J Micromech Microeng 2005, 15,720 727... 

Fields et alf and Schmidt made closely parallel observations concerning polar cycloaddition of ethylenes substituted at the a-position by an electron-withdrawing group and having no substituent at the jS-position. In both cases the product observed was that to be expected if the electrophile had added to the j3-carbon atom. Since it is clear that the normal ground-state polarization of acrylonitrile (127) and methyl methacrylate (128) should tend to destabilize the cation produced by j8-addition, it was concluded that the orientation of polar cycloadditions could not be predicted by the rules of electrophilic addition and that this apparent anomaly pointed toward a more concerted type of cycloaddition reaction. 

During the interval between Vongerichten s and Schmidt s investigations, there were discovered several empirical rules through which the configuration of the a-carbon atom of many a-hydroxycarboxylic acids may be inferred. Schmidt applied three of these generalizations, the salt-acid rule and the phenylhydrazide and amide rules, to the appropriate derivatives of apionic acid Table I shows the comparisons which he published. 

Schmidt et al. suggested isotopomer distribution vectors (IDV) to quantitatively describe distributions of positional isotopomers, whereby the elements of an IDV contain molar fractions of single positional isotopomers [14]. The indexing of positional isotopomers as elements of an IDV is based on the binary code with ones for labeled and zeros for non-labeled carbons following the standard rules of numbering the carbons within a molecule. The positional isotopomers in Fig. (1) are ordered in this way. The sum of all elements in the IDV equals 1. The IDV of pyruvate can serve as an example (Eq. 1). 

The experiments discussed above were all carried out with total pressures below 10-4 Torr. However, Hori and Schmidt (187) have also reported non-stationary state experiments for total pressures of approximately 1 Torr in which the temperature of a Pt wire immersed in a CO—02 mixture was suddenly increased to a new value within a second. The rate of C02 production relaxed to a steady-state value characteristic of the higher temperature with three different characteristic relaxation times that are temperature dependent and vary between 3 and 100 seconds between 600 and 1500 K. The extremely long relaxation time compared with the inverse gas phase collision rate rule out an explanation based on changes within the chemisorption layer since this would require unreasonably small sticking coefficients or reaction probabilities of less than 10-6. The authors attribute the relaxation times to characteristic changes of surface multilayers composed of Pt, CO, and O. The effects are due to phases that are only formed at high pressures and, therefore, cannot be compared to the other experiments described here. 

A more complex case of molecular overcrowding of the benzophenanthrene type is found in tetrabenzonaphthalene (86). The crystal structure of this molecule has been studied in its most favourable projection by Herbstein and Schmidt (1954b). The results of this partial analysis rule out a planar centrosymmetric structure and favour a molecule having 222 molecular symmetry with distortions of the benzene rings, as shown in (86), comparable to those found in 3,4-benzophenanthrene no molecular symmetry is required by the crystal. 

Category 2 concerns examples that satisfy Schmidt s rule but remain pho-toinactive. Table 8 records a few of such cases in which the distance between the reactive double bonds is less than 4.2 A. Scheme 9 shows the molecular structures. 

As a general empirical rule for HoNi2B2C samples, the appearance of reentrant behavior caused by stoichiometric effects, disorder, pressure, or magnetic field is always connected with a reduced value of Tc. Thus Schmidt (1997) could systematically reduce Tc and induce reentrant behavior in HoNi2B2C by the substitution of Ni by Co to a minor degree. An example for the influence of heat treatment is... 

Glitsch e rule of thumb (Table 8.6) for CMR random packings when the packing surface area exceeds 43 ft2/ft8. Both Ludwig (63) and the author like these rules, but they only apply to CMR 1, 1.5, and 2. To extend these rules to other packings, the author applied Schmidt s model (102). Equation (8.38) gives... 

Several representatives of this ( lass of compounds wore investigated as to their behavior in alkaline reduction (Hans-STiuatm and Schmidt l). These investigators continued ilio rules which Klb established for nitrophenyl ethers. 

However the dissociation energies of the C3—H bond in propene-i and the C4—C3 bond in butene-1 are also particularly low (Table i8b Schmidt s rule). 

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