A semiclassical interpretation of wave mechanics

The single-particle wave function =Re^iS/h has been interpreted classically: At a given point the particle momentum is S, and the relative particle density in an ensemble is R ² . It is first proposed to modify this interpretation by assuming that physical variables undergo rapid fluctuations, so that S is the average of the momentum over a short time interval. However, it appears that this is not enough. It seems necessary to assume that the density also fluctuates. The fluctuations are taken to be random and to satisfy conditions required for agreement with quantum mechanics. In some cases the fluctuating density may take on instantaneous negative values. One gets agreement with quantum mechanics for the spin correlations of two particles in a singlet state. This comes about because of the correlations between the fluctuations of the variables of the two particles, the effect of which is equivalent to an action at a distance. The relation to Bell's inequality is discussed.     

Synergism in the spreading of hydrocarbon-chain surfactants on polyethylene film-anionic and cationic mixtures by a two-step procedure

A study has been made of the adsorption, interaction, and spreading of mixtures of anionic and cationic surfactants at the aqueous solution/polyethylene (PE) interface. When a drop of an aqueous solution of an anionic or cationic hydrocarbon-chain surfactant is placed on a highly hydrophobic PE film (contact angle of water > 90 degrees ), it spreads to an area very little larger than that of a drop of water of the same volume. If the anionic and cationic hydrocarbon-chain surfactant solutions are mixed prior to being applied to PE film, synergism is small, if any, and the reproducibility of the experimental results is poor. However, when the cationic and anionic aqueous solutions are applied on the PE film in a sequential manner, a remarkable synergism in spreading is observed and the results are very reproducible. The area spread by an aqueous solution of the anionic-cationic mixture may be more than 400 times that of aqueous solutions of the same volume and surfactant concentration of the individual surfactant components. Previous work in this laboratory on surfactant systems showing synergism in spreading on PE film, but only weak interaction at the aqueous solution/air interface, showed that the synergy was due to changes at the aqueous solution/PE interface and not to the changes at the aqueous solution/air or PE/air interface. Investigation of the adsorption behavior at the aqueous solution/solid interface of two of the anionic-cationic mixtures studied here indicates the reason for differences in spreading behavior observed with different anionic-cationic mixtures. The more similar the adsorption tendencies at the solid/aqueous solution interface of the anionic and cationic surfactants, and the closer their adsorption to an equimolar monolayer there, the stronger their interaction there and the greater their enhancement of the spreading. A mechanism is proposed for the synergy in spreading observed, based upon the difference between the surface tension in the precursor film at the spreading interface and that at the top of the spreading drop.     

Structural determination of ascorbic acid 2-o-phosphate formed via acid hydrolysis of an ascorbic acid 3-O-phosphinate

The synthesis and X-ray structural determination of 3-O-[(bis-morpholino)phosphinyl]-5,6-O-isopropylidene-l-ascorbate (9) are described. Acid-catalyzed hydrolysis of 9 afforded the 2-O-phosphate 6. Definitive structural proof of 6 is based on a study of the pH profile of its UV spectra as compared with those of ascorbic esters, 2 and 9 (Figs. 1–3).     

Bimetric general relativity and cosmology

A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg _v describing the space-time geometry and gravitation, there exists also a background metric tensor _v The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc ^{5 –1} G ^–210⁹³ g/cm³. The expansion from such a high-density state is similar to that from the singular state (big bang) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.     

Synthesis of a selective estrogen receptor β-modulator via asymmetric phase-transfer catalysis

An efficient asymmetric synthesis of selective estrogen receptor β-modulator (S)-4-bromo-9a-butyl-8-chloro-6-fluoro-7-hydroxy-1,2,9,9a-tetrahydro-fluoren-3-one was developed. The route features a chemoselective aromatic chlorination reaction, an asymmetric phase-transfer-catalyzed alkylation of an indanone with efficient ee upgrade by racemate crystallization, and a robust bromination reaction using imidazole as an in situ bromine trap to avoid overreaction. The synthesis proceeds in 34% yield over 8 steps from 2-fluoroanisole, and provides material with >99.5% ee.     

Ultralow interfacial tension for enhanced oil recovery at very low surfactant concentrations

The interfacial tension (IFT) between alkanes and several individual surfactants and their mixtures has been investigated, using three kinds of alkyl hydrocarbons: decane, dodecane, and tetradecane. For individual and mixed surfactant systems, critical micelle concentrations and areas per molecule at the hydrocarbon-aqueous solution interface were calculated; for the mixed surfactant systems, betasigma(LL), the molecular interaction parameter at the hydrocarbon-aqueous solution interface, and beta(M), the molecular interaction parameter in mixed micelle formation, were calculated. It was found that IFT in the 10(-3) mN/m (ultralow) range can be obtained at surfactant concentrations below 0.05 wt % and even at concentrations below 0.01 wt %, when mixtures of certain surfactants are used at the proper ratio. Surfactants with branched-chain alkyl groups show a much better IFT reduction effectiveness than those with straight-chain alkyl groups. Contrary to what has been observed at the air-aqueous solution surface, mixtures of two homologues with two hydrophobic groups show significant molecular interactions, with both betasigma(LL) and beta(M) having negative values in the 4-5 range in some cases, with the betasigma(LL) value more negative than beta(M). The relationship between micellar shape and ultralow IFT was investigated by calculating the critical packing parameter of the surfactants. It was found that ultralow IFT between the surfactant mixtures and the three hydrocarbons investigated could reach ultralow (<10(-2) mN/m) values when the critical packing parameter is very close to 1.     

Structural effects on surface and micellar properties of alkanediyl-alpha, omega-bis(sodium N-acyl-beta-alaninate) gemini surfactants

A study of the equilibrium surface properties (in water and in the presence of 0.01 M NaCl) of a novel series of anionic gemini surfactants, alkanediyl-alpha,omega-bis(sodium N-acyl-beta-alaninates), is described. Parameters studied include cmc (critical micelle concentration), C20 (required to reduce the surface tension of the solvent by 20 mN/m), gamma(cmc) (the surface tension at the cmc), Gamma(max) (the maximum surface excess concentration at the air/aqueous solution interface), Amin (the minimum area per surfactant molecule at the air/water interface), and the cmc/C20 ratio (a measure of the tendency to form micelles relative to adsorb at the air/water interface). The geminis with a spacer consisting of two methylene groups show premicellar self-aggregation, both in water and in 0.01 M NaCl, when the N-acyl group contains more than 12 carbon atoms; geminis with a spacer consisting of four methylene groups show no premicellar aggregation even when the N-acyl group contains 16 carbon atoms. For the acyl chain lengths where premicellar aggregation does not occur, the values of the cmc of the geminis with a two-methylene spacer are lower than those for the corresponding analogous geminis with a four-methylene spacer. The premicellar formation for the geminis with a two-methylene spacer is due to the short-chain linkage. The geminis show little or no break in their specific conductance-surfactant molar concentration plots and an increase in the pH at the cmc. This is attributed to protonation of the carboxylate group and strong Na+ release during micellization.     

Weyl's geometry and physics

It is proposed to remove the difficulty of nonitegrability of length in the Weyl geometry by modifying the law of parallel displacement and using standard vectors. The field equations are derived from a variational principle slightly different from that of Dirac and involving a parameter . For =0 one has the electromagnetic field. For <0 there is a vector meson field. This could be the electromagnetic field with finite-mass photons, or it could be a meson field providing the missing mass of the universe. In cosmological models the two natural gauges are the Einstein gauge and the cosmic gauge. With the latter the universe has a fixed size, but the sizes of small systems decrease with time and their masses and energies increase, thus producing the Hubble effect. The field of a particle in this gauge is investigated, and it leads to an interesting solution of the Einstein equations that raises a question about the Schwarzschild solution.