Similarity studies

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

Conceptually similar studies have since been carried out for the reaction of Ft atoms with Cl/Aii(l 11). More recently, quantum-state distributions have been obtamed for both the Ft + Cl/Aii(l 11)[, and M and Ft(D) + D (Ft)/Cii(l 11) systems. The results of these studies are in good qualitative agreement widi calculations. Even for the Ft(D) + D (Ft)/Cii(l 11) system [89], where we know that the incident atom caimot be significantly accommodated prior to reaction, reaction may not be direct. Detailed calculations yield much smaller cross sections for direct reaction than the overall experimental cross section, indicating that reaction may occur only after trapping of the incident atom [90]. 

In applying minimal END to processes such as these, one finds that different initial conditions lead to different product channels. In Figure 1, we show a somewhat truncated time lapse picture of a typical trajectory that leads to abstraction. In this rendering, one of the hydrogens of NHaD" " is hidden. As an example of properties whose evolution can be depicted we display interatomic distances and atomic electronic charges. Obviously, one can similarly study the time dependence of various other properties during the reactive encounter. 

The next question asked is whether there are any indications, from ab initio calculations, to the fact that the non-adiabatic transfonnation angles have this feature. Indeed such a study, related to the H3 system, was reported a few years ago [64]. However, it was done for circular contours with exceptionally small radii (at most a few tenths of an atomic unit). Similar studies, for circular and noncircular contours of much larger radii (sometimes up to five atomic units and more) were done for several systems showing that this feature holds for much more general situations [11,12,74]. As a result of the numerous numerical studies on this subject [11,12,64-75] the quantization of a quasi-isolated two-state non-adiabatic coupling term can be considered as established for realistic systems. 

A similar study of the nitration of 2,5-dichloro- and 2,5-dibromo-nitrobenxene under a variety of conditions has been made. At the very high acidities in oleum the o /)-ratio for nitration was less than unity. It increased with decreasing acidity of the medium and became greater than unity at roughly the acidity represented by 89-90 % sulphuric acid. The results were interpreted in terms of the interaction between the nitronium ion and the nitro group, but the results are complicated and the interpretation not compelling. 

The study of the infrared spectrum of thiazole under various physical states (solid, liquid, vapor, in solution) by Sbrana et al. (202) and a similar study, extended to isotopically labeled molecules, by Davidovics et al. (203, 204), gave the symmetry properties of the main vibrations of the thiazole molecule. More recently, the calculation of the normal modes of vibration of the molecule defined a force field for it and confirmed quantitatively the preceeding assignments (205, 206). 

A similar study of the chlorination of 2 methylpropane established that a tertiary hydrogen is removed 5 2 times faster than each primary hydrogen... 

Oral appHcations of 1500 mg/kg/d for two weeks caused death of rats. Repeated oral appHcations (4 wks) of 30 p-L/kg to rats caused no toxic symptoms, 100 pL/kg resulted in minor toxic effects, and 300 pL/kg induced impairment of several organs andlethaHty. Repeated oral appHcations (26 x) of 0.1 mL/kg caused no toxic symptoms in cats or rabbits. Inhalation of 1500 ppm (2 wks) were without effects, whereas in a similar study with... 

Mass spectral fragmentation patterns of alkyl and phenyl hydantoins have been investigated by means of labeling techniques (28—30), and similar studies have also been carried out for thiohydantoins (31,32). In all cases, breakdown of the hydantoin ring occurs by a-ftssion at C-4 with concomitant loss of carbon monoxide and an isocyanate molecule. In the case of aryl derivatives, the ease of formation of Ar—NCO is related to the electronic properties of the aryl ring substituents (33). Mass spectrometry has been used for identification of the phenylthiohydantoin derivatives formed from amino acids during peptide sequence determination by the Edman method (34). 

Other crystallization parameters have been determined for some of the polymers. The dependence of the melting temperature on the crystallization temperature for the orthorhombic form of POX (T = 323K) and both monoclinic (T = 348K) and orthorhombic (T = 329K) modifications of PDMOX has been determined (284). The enthalpy of fusion, Aff, for the same polymers has been determined by the polymer diluent method and by calorimetry at different levels of crystallinity (284). for POX was found to be 150.9 J/g (36.1 cal/g) for the dimethyl derivative, it ranged from 85.6 to 107.0 J/g (20.5—25.6 cal/g). Numerous crystal stmcture studies have been made (285—292). Isothermal crystallization rates of POX from the melt have been determined from 19 to —50 C (293,294). Similar studies have been made for PDMOX from 22 to 44°C (295,296). 

Similar studies have been performed on the formation of mono -butyl phthalate at 80—150°C with sulfuric acid catalyst (31). The reaction of phthahc anhydride with mono -butyl phthalate to afford di -butyl phthalate is complete ia 10 min at 100°C with 1 wt % catalyst. 

The IR (and Raman) spectra of 1,2-benzisoxazole and 2,1-benzisoxazole have been recorded and their fundamental and combined vibrations assigned (80MI41604). Similar studies have been carried out with 2,1-benzisoxazolium salts (74DIS(B)147, 71JOC1543). 

The isoxazolecarboxylic acids are the most intensively investigated of the isoxazole derivatives, and a detailed compilation of their physiochemical properties has been made 62HC(17)l,p. 177). Similar studies have also been carried out with the 5-isoxazolones (62HC(17)l,p. 124), and pK values of 1,2-benzisoxazole derivatives are listed in Table 4. 

Matthews-Akgerman The free-volume approach of Hildebrand was shown to be valid for binary, dilute liquid paraffin mixtures (as well as self-diffusion), consisting of solutes from Cg to Cig and solvents of Cg and C o- The term they referred to as the diffusion volume was simply correlated with the critical volume, as = 0.308 V. We can infer from Table 5-15 that this is approximately related to the volume at the melting point as = 0.945 V, . Their correlation was vahd for diffusion of linear alkanes at temperatures up to 300°C and pressures up to 3.45 MPa. Matthews et al. and Erkey and Akger-man completea similar studies of diffusion of alkanes, restricted to /1-hexadecane and /i-octane, respectively, as the solvents. 

In a similar study, Exxon describes an onshore plant where once again gas processing with a turboexpander was chosen over the other alternatives. The results of that report are detailed in Table 3-7. 

Similar studies have been carried out to characterize C5Hjj+ species. The barrier to 321... 

Similar studies were conducted by Troyanovsky, who concluded that to maintain the airflow pattern in rooms with heated or cooled air supply as in isothermal conditions, it is necessary that the rise of horizontally supplied jet does not exceed Ay = 0.1 BH at the distance from the outlet X = 0.15K BH) -. From this assumption the following equation for the maximum air temperature difference was derived ... 

Similar studies have been carried out on shock-activated zinc oxide. Here, the effects are not so pronounced, but interesting effects are seen [86W04]. 

A similar study of the action of hydrogen bromide on brucine and the resulting derivative of isobrucine is in progress (Leuchs and Schulte, 1942). ... 

Adsorption of hard sphere fluid mixtures in disordered hard sphere matrices has not been studied profoundly and the accuracy of the ROZ-type theory in the description of the structure and thermodynamics of simple mixtures is difficult to discuss. Adsorption of mixtures consisting of argon with ethane and methane in a matrix mimicking silica xerogel has been simulated by Kaminsky and Monson [42,43] in the framework of the Lennard-Jones model. A comparison with experimentally measured properties has also been performed. However, we are not aware of similar studies for simpler hard sphere mixtures, but the work from our laboratory has focused on a two-dimensional partly quenched model of hard discs [44]. That makes it impossible to judge the accuracy of theoretical approaches even for simple binary mixtures in disordered microporous media. 

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