Synthesis of Colloidal Suspensions of Zeolite ZSM-2

Discrete colloidal particles of zeolite ZSM-2 with crystal sizes less than 100 nm, in the form of aqueous suspensions, have been synthesized in tetramethylammonium (TMA)-aluminosilicate solutions in the presence of either lithium or a combination of lithium and sodium hydroxide. The well-crystallized ZSM-2 has a specific surface area of 781 m²/g after purification and removal of the organic base by calcination. Synthesis times (t) are as short as 3 < t < 12 h and in certain cases, less than 3 h, less than those previously reported in the literature. Prolonged hydrothermal treatment of sols in the presence of sodium cations (>12 h) results in the phase transformation of ZSM-2 to the nitrogeneous edingtonite zeolite (Li,Na)-E. The synthesis of nitrogeneous (Li,Na)-E is also favored by a high TMA content in conjunction with sodium, whereas synthesis of zeolite N-A is favored by a high sodium content. Furthermore, it is shown that colloidal suspensions of TMA sodalite with crystal sizes less than 40 nm are synthesized in the absence of alkali cations.     

Derived Functors of Inverse Limits Revisited

We prove, correct and extend several results of an earlier paperof ours (using and recalling several of our later papers) aboutthe derived functors of projective limit in abelian categories.In particular we prove that if C is an abelian category satisfyingthe Grothendieck axioms AB3 and AB4* and having a set of generatorsthen the first derived functor of projective limit vanisheson so-called Mittag-Leffler sequences in C. The recent examplesgiven by Deligne and Neeman show that the condition that thecategory has a set of generators is necessary. The conditionAB4* is also necessary, and indeed we give for each integerm 1 an example of a Grothendieck category C_m and a Mittag-Lefflersequence in C_m for which the derived functors of its projectivelimit vanish in all positive degrees except m. This leads toa systematic study of derived functors of infinite productsin Grothendieck categories. Several explicit examples of theapplications of these functors are also studied.     

Double excitations of helium in weak static electric fields

A dramatic electric field dependence has been observed in the fluorescence yield spectrum of the doubly excited states in helium, where a rich phenomenology is encountered below the threshold. Fluorescence yields of certain states can be tuned to zero, while other dipole-forbidden states are significantly enhanced, for fields much weaker than 1 kV/cm. Using an R-matrix multichannel quantum defect theory, spherical-to-parabolic frame transformation method, we are able to reproduce the main features of the observed spectrum, and we discuss the qualitative behavior in terms of weak electric field mixing.     

A note on the optimal quadrature inH p

Summary The existence of optimal nodes with preassigned multiplicities is proved for the Hardy spacesH ^p (1<p<). This is then used to show that the exact order of convergence for the optimal qudrature formula withN nodes (including multiplicity) is where 1/p+1/q=1 and 1p.     

Adsorption behavior and cross-linking of EHEC and HM-EHEC at hydrophilic and hydrophobic modified surfaces monitored by SPR and QCM-D

The adsorption behavior of ethyl(hydroxyethyl) cellulose EHEC and hydrophobically modified EHEC (HM-EHEC) at hydrophilic and hydrophobic surfaces has been studied using surface plasmon resonance (SPR) and quartz crystal microbalance with dissipation monitoring (QCM-D) methods. The adsorbed amounts measured with the different methods were different due to large amounts of water in the films. The slow adsorption process made it reasonable to assume a continuous polymer reconfiguration process at the surface. This was mostly seen for HM-EHEC at the hydrophobic surface, where a more flexible structure was adopted during the adsorption process. A cross-linking agent was seen to truly interpolymer cross-link EHEC at the hydrophilic surface and HM-EHEC at the hydrophobic surface. For EHEC at a hydrophobic surface and for HM-EHEC at a hydrophilic surface, the polymers adsorbed in an individually phase-separated manner, making an interpolymer cross-linking reaction unsuccessful.