Effect of crown-ether surfactants on flame atomic absorption and flame emission signals of some monovalent cations

Two surface-active and one surface-inactive 18-crown-6 derivatives were synthesized and evaluated for their abilities to enhance flame atomic absorption and flame emission signals of monovalent cations. Enhancement of potassium signals were noted for the surface-active compounds but not for the surface-inactive compound. The critical micelle concentration was determined and compared to the degree of enhancement. Surfactant-induced signal enhancements are not due to the slight or moderate decrease in the size of the aerosol first produced in the nebulizing chamber. Additional mechanistic considerations are discussed.     

Molecular orientation in biaxially oriented sheets of poly(ethylene terephthalate) II. Correlation of orientation averages with measured mechanical compliances

The aggregate model is extended to examine the relationship between mechanical anisotropy and molecular orientation in one-way drawn sheets of poly(ethylene terephthalate). It is assumed that both the aggregate and the unit of structure have orthorhombic symmetry. On the basis of a number of detailed assumptions regarding the appropriate application of the model, calculated bounds are obtained for the elastic constants that are in reasonable agreement with the experimental values. The implications of these results with regard to molecular orientation are considered, and it is concluded that both the chain orientation and orientation around the chain axis are important in determining the mechanical anisotropy.     

Spot Self-Replication and Dynamics for the Schnakenburg Model in a Two-Dimensional Domain

The dynamical behavior of multi-spot solutions in a two-dimensional domain Ω is analyzed for the two-component Schnakenburg reaction–diffusion model in the singularly perturbed limit of small diffusivity ε for one of the two components. In the limit ε→0, a quasi-equilibrium spot pattern in the region away from the spots is constructed by representing each localized spot as a logarithmic singularity of unknown strength S _j for j=1,…,K at unknown spot locations x _j ∈Ω for j=1,…,K. A formal asymptotic analysis, which has the effect of summing infinite logarithmic series in powers of −1/log ε, is then used to derive an ODE differential algebraic system (DAE) for the collective coordinates S _j and x _j for j=1,…,K, which characterizes the slow dynamics of a spot pattern. This DAE system involves the Neumann Green’s function for the Laplacian. By numerically examining the stability thresholds for a single spot solution, a specific criterion in terms of the source strengths S _j , for j=1,…,K, is then formulated to theoretically predict the initiation of a spot-splitting event. The analytical theory is illustrated for spot patterns in the unit disk and the unit square, and is compared with full numerical results computed directly from the Schnakenburg model.      

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