Darken approximation

Skoulidas AI, Sholl DS (2001) Direct tests of the darken approximation for molecular diffusion in zeolites using equilibrium molecular dynamics. J. Phys. Chem. B. 105 3151-3154... 

Abstract Neutron scattering was first used to derive the self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows one to probe diffusion over space scales ranging from a few A to hundreds of A. The mechanism of diffusion can, thus, be followed from the elementary jumps between adsorption sites to Lickian diffusion. The neutron spin-echo technique pushes down the lower limit of diffusion coefficients, traditionally accessible by neutron methods, by two orders of magnitude. The neutron scattering results indicate that the corrected diffusivity is rarely constant and that it follows neither the Darken approximation nor the lattice gas model. The clear minimum and maximum in diffusivity observed by neutron spin-echo for n-alkanes in 5A zeolite is reminiscent of the controversial window effect . 

Fig.lO Normalized corrected diffusivities obtained experimentally for several systems ( ) CF4 in silicalite, (Q) benzene in Na-Y, (A) CO2 in silicalite, (O) Ar in silicalite, (V) N2 in silicalite, ( ) D2 in Na-X. The solid line gives the (1-0) dependence, and the dotted line the Darken approximation ... 

Many reactions encountered in extractive metallurgy involve dilute solutions of one or a number of impurities in the metal, and sometimes the slag phase. Dilute solutions of less than a few atomic per cent content of the impurity usually conform to Henry s law, according to which the activity coefficient of the solute can be taken as constant. However in the complex solutions which usually occur in these reactions, the interactions of the solutes with one another and with the solvent metal change the values of the solute activity coefficients. There are some approximate procedures to make the interaction coefficients in multicomponent liquids calculable using data drawn from binary data. The simplest form of this procedure is the use of the equation deduced by Darken (1950), as a solution of the ternary Gibbs-Duhem equation for a regular ternary solution, A-B-S, where A-B is the binary solvent... 

When the NMR spectrum of a 30% (w./v.) solution of peroxide in toluene was recorded at 34°C., absorption was observed between 8 2.74 and 5.46. There were seven main resonances, all multiplets, which were interpreted in terms of aliphatic hydrogen shifted by oxygen. Resonance from ethylenic hydrogen amounted to only a fraction of a proton. However, the sample darkened while in the instrument and probably decomposed extensively. When the spectrum of a solution of peroxide prepared by oxidation to 10.4 mole % was recorded using a cold probe at —35°C. a different picture was obtained. There was complex absorption from both ethylenic and saturated hydrogen which was interpreted as arising from a mixture of 1,2 and 1,4 oxygen copolymers in an approximate jatio of 1 to 2. In this sample the residual chloroprene amounted to 0.15% of the monomer units in the peroxide and dimers of chloroprene to 0.6% of the peroxide. 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

Lux-ampere characteristics for annealed films are characterized by a sublinear dependence /pj, in a wide light intensity range, n being approximately equal to 0.6 for As2Se3. After darkening, the index n increases. 

In an apparatus set up for steam distillation and containing a rapidly stirred solution of 5.0 gm (0.023 mole) of jV-benzoylphenylhydroxylamine (N-phenylbenzohydroxamic acid) in 100 ml of a 1 1 solution of ethanol-acetic acid, cooled to —20°C, is added 11.5 gm (0.024 mole based on 94% purity) of lead tetraacetate in one portion. After approximately 10 sec (when the initial green color just begins to darken), 100 ml of water is added and the brown or black mixture is rapidly subjected to steam distillation. The distillate is collected in a receiver filled with chopped ice. The product is isolated by filtration of the distillate. Finally, it is dried by pressing dry between filter papers to yield 1.4-2.0 gm (56-80%), m.p. 66°-68°C. 

Dimethyl-2,3-dihydro-1,2-benzoisothiazolel,l-dioxide(60 g,0.304 mol)and NaF(16.8 g)in dry CHCI3 (500 mL) were cooled to — 40°C before the diluted mixture 10% F2/ N2 (w/ w) was introduced at a rate such that the flow in the second trap was about 15-25 mL min 1 (0.275 mol F2). After approximately 2 h, the contents of the second trap started to darken noticeably and the fluorination was discontinued. N2 was bubbled through the apparatus for about 1 h to purge the system of residual F2. The solvent was removed by rotary evaporation from the solution containing precipitate. After evaporation of the solvent, the crude mixture was purified by recrystallization from pentane (500 mL) at 0CC yield 42 g (64% from substrate, 71% from F2) mp 115-116.5 C. 

Octahedral sulphur is a brittle solid of hardness approximately 2-3 the colour is lemon-yellow at the ordinary temperature but darkens somewhat on warming, whilst at —50° C. it almost disappears, leaving the solid practically colourless 6 the refractive index for sodium light is 2-08,7 the mean specific heat is 0-170,8 and the coefficient of cubic... 

In a 500-cc. round-bottom flask are placed 93 g. (1 mole) of aniline and 106 g. (1 mole) of benzaldehyde (Note 1). The reaction mixture becomes quite warm and water distils. The flask is then heated in an oil bath so that the temperature of the contents is maintained at approximately 1250 (Note 2) for about five hours, or until no more steam is evolved. The contents of the flask darken somewhat during the heating, but the material is homogeneous. Without cooling, the reaction mixture is slowly poured into iced water which is stirred constantly. The ben-zalaniline solidifies, and is filtered, washed twice with iced water, and sucked dry on the funnel. The crude wet material weighs 184-193 g. and melts at 48-50°. 

Ibuprofen comes in tablet and liquid forms that range from 50 to 200 mg per dose. Tablets with doses up to 800 mg of ibuprofen are available with a doctor s prescription. The recommended dosage for adults is approximately 1,200 mg per day, but a doctor can suggest that the patient take up to 3,200 mg per day. Ibuprofen is generally well tolerated, but some people can have side effects such as stomach pains, skin rash, vomiting, black or darkened stools, visual problems, or swelling of the hands and feet. Like aspirin and acetaminophen, ibuprofen takes about 30 minutes to start to relieve pain and lasts approximately 4 to 6 hours. 

The mercury blue line is more difficult to read in a polarimeter than the longer visible wave-lengths. The difficulty is greatly magnified by turbidity in the solution or by incomplete exclusion of the mercury lines in the vicinity of 405 m/u. The measurements should be made in a darkened room, allowing approximately a minute for the eye to grow accustomed to the darkness. The zero point of the instrument should be taken at the same wave-length. 

Thermal transmission testing is an excellent way of detecting various types of anomalies such as surface corrosion under paint before the corrosion becomes visually evident. Thin, single-layer structures, such as aircraft skin panels, can be inspected for surface and subsurface discontinuities. This test is simple and inexpensive, although materials with poor heat-transfer properties are difficult to test, and the joint must be accessible from both sides. For nonmetallic materials, the defect diameter must be on the order of 4 times its depth below the surface to obtain a reliable thermal indication. For metals, the defect diameter must be approximately 8 times its depth. Some bright surfaces such as bare copper and aluminum do not emit sufficient infrared radiation and may require a darkening coating on their surface. 

The clathrochelate complexes, [M(ClgH30Ni2)] [BF4]2, are prepared by adding 5.0 g of 37% aqueous formaldehyde solution to a suspension of 5 g of the appropriate tris(2,3-butanedione dihydrazone)metal bis(tetrafluoroborate) complex in acetonitrile. The condensation reaction is catalyzed by the addition of 0.5 mL of concentrated tetrafluoroboric acid. An immediate darkening of the solutions is observed as the condensation reaction proceeds. The iron (II)-containing solution becomes a very intense purple the nickel(II) solution becomes very dark olive-brown. Precipitation of the clathrochelates requires the addition of approximately 30% by volume of diethyl ether and refrigeration. The products are filtered from the solution, washed with methanol, and air dried. The iron(II) complex is somewhat more soluble in acetonitrile than the other complexes, and increased yields can be obtained by the dropwise addition... 

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