De-mixing dynamics of a binary liquid system in a controlled-pore glass

The European Physical Journal E - The temperature-induced microphase separation of the binary liquid system iso-butyric acid+heavy water (iBA + D2O) in a mesoporous silica glass (CPG-10-75) of...     

Bifurcation for a semilinear elliptic equation on ℛN with radially symmetric coefficients

We consider the semilinear eigenvalue problem on ^N (N 2) (N2) and investigate the question under which conditions on the radially symmetric function q, =0 is a bifurcation point for this equation in H¹, In H² and in L^p for 2p+.     

Goodisman's correction of the Thomas-Fermi-von Weizsäcker theory of atoms

Summary Following a suggestion of J. Goodisman, we substitute the therm by in the Thomas-Fermi-von Weizsäcker energy functional for atoms.f _z³ [0,1] is a function depending on the nuclear chargez.We establish conditions for the functionsf _z such that the ratio of this modified TFW-energyE _kz ^/TFWG (z) (kz is the total number of electrons) and the exact quantum mechanical energy converges to 1 asz. Moreover, we prove thatE _kz ^/TFWG (z)=E _kz ^/TFW (z)+Dz ²+o(z ²) (z) and determineD. Here,E _kz ^/TFW (z) is the unmodified TFW energy.

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Zusammenfassung Einem Vorschlag J. Goodismans folgend, ersetzen wir in dem Thomas-Fermi-von Weizsäcker Energiefunktional für Atome den Term durch .f _z³ [0,1] ist hierbei eine Funktion, die von der Kernladungszahlz abhängt.Wir geben dann Bedingungen für die Funktionenf _z an, unter denen der Quotient der so modifizierten TFW-energieE _kz ^/TFWG (z) (kz=Anzahl der Elektronen) und der exakten quantenmechanischen Energie fürz gegen 1 konvergiert. Darüber hinaus beweisen wir, daßE _kz ^/TFWG (z)=E _kz ^/TFW (z)+D·o(itz) ² (z) gilt und bestimmmenD. E _kz ^/TFW (z) ist hierbei die nicht-modifizierte TFW-Energie.

     

Monolayer films of PS-b-PEO diblock copolymers at the air/water- and an oil/water-interface

 Amphiphilic diblock copolymers consisting of a hydrophobic polystyrene block (PS) and a hydrophilic poly(ethylene oxide) block (PEO) with block sizes of 1000 or 3000 g/mol for both blocks were studied at the air/water and toluene/water interface. Measurements of the film pressure π of spread monolayers at the water surface reveal two limiting regimes of the π−a _m isotherms, in which the mean molecular area a _m is determined either by the size of the hydrophilic or the hydrophobic blocks of the PS-PEO molecules. The interfacial activity of the block copolymers at the toluene/water interface was studied by measuring the interfacial tension σ over a wide range of concentrations. Pronounced differences in the temperature dependence of the interfacial tension were observed, depending mostly on the block length of the hydrophilic PEO block. From the temperature dependence of σ it is inferred that for the block copolymers with the PEO block size of 3000 g/mol the phase inversion temperature (PIT) is well above 60 °C while for those with a PEO block size of 1000 g/mol the PIT is below or near 25 °C in the toluene/water system. Received: 5 February 1998 Accepted: 16 February 1998     

A Nonlinear Dirichlet Problem on the Unit Ball

In the present paper, we consider the nonlinear Dirichlet problem - Δu(x) u^β(x) = 0 is the unit ball and q is a continuous radially symmetric function on B which may be singular on ?B. We state some mild conditions for the function q so that the Dirichlet problem has a positive classical solution.     

16, 18O induced transfer reactions on122, 120Sn

The reactions¹²⁰Sn+72 MeV¹⁸O and¹²²Sn+74 MeV¹⁶O were investigated with time of-flightE-E-telescopes. Data are presented for all quasi-elastic reaction channels. The two neutron stripping and pickup reactions (¹⁸O,¹⁶O), (¹⁸O,²⁰O) and (¹⁶O,¹⁸O) are analyzed in detail. It is shown that these heavy ion induced two neutron transfer reactions proceed with essentially the same type of selectivity as the corresponding light ion induced reactions. The differential cross sections for transfer reactions leaving the^{120, 122}Sn nuclei in their 2⁺ first excited states are shown to be influenced by interference effects due to additional inelastic excitations.     

Nonlinear Poisson autoregression

We study statistical properties of a class of non-linear models for regression analysis of count time series. Under mild conditions, it is shown that a perturbed version of the model is geometrically ergodic and possesses moments of any order. This result turns out to be instrumental on deriving large sample properties of the maximum likelihood estimators of the regression parameters. The theory is illustrated with examples.     

Lyotropic Liquid Crystal to Soft Mesocrystal Transformation in Hydrated Salt–Surfactant Mixtures

Hydrated CaCl₂, LiI, and MgCl₂ salts induce self‐assembly in nonionic surfactants (such as C₁₂H₂₅(OCH₂CH₂)₁₀OH) to form lyotropic liquid‐crystalline (LLC) mesophases that undergo a phase transition to a new type of soft mesocrystal (SMC) under ambient conditions. The SMC samples can be obtained by aging the LLC samples, which were prepared as thin films by spin‐coating, dip‐coating, or drop‐casting of a clear homogenized solution of water, salt, and surfactant over a substrate surface. The LLC mesophase exists up to a salt/surfactant mole ratio of 8, 10, and 4 (corresponding to 59, 68, and 40 wt % salt/surfactant) in the CaCl₂, LiI, and MgCl₂ mesophases, respectively. The SMC phase can transform back to a LLC mesophase at a higher relative humidity. The phase transformations have been monitored using powder X‐ray diffraction (PXRD), polarized optical microscopy (POM), and FTIR techniques. The LLC mesophases only diffract at small angles, but the SMCs diffract at both small and wide angles. The broad surfactant features in the FTIR spectra of the LLC mesophases become sharp and well resolved upon SMC formation. The unit cell of the mesophases expands upon SMC transformation, in which the expansion is largest in the MgCl₂ and smallest in the CaCl₂ systems. The POM images of the SMCs display birefringent textures with well‐defined edges, similar to crystals. However, the surface of the crystals is highly patterned, like buckling patterns, which indicates that these crystals are quite soft. This unusual phase behavior could be beneficial in designing new soft materials in the fields of phase‐changing materials and mesostructured materials, and it demonstrates the richness of the phase behavior in the salt–surfactant mesophases.