Argon sorption and partial molar volume in poly(ethyl methacrylate) above and below the glass transition temperature

Sorption and dilation isotherms for argon in poly(ethyl methacrylate) (PEMA) are reported for pressures up to 50 atm over the temperature range 5–85°C. At temperatures below the glass transition (T_g=61°C), sorption isotherms are well described by the dual-mode sorption model; and isotherms above T_g follow Henry's law. However, isotherms for dilation due to sorption are linear in pressure at all temperatures over the range investigated. Partial molar volumes of Ar in PEMA are obtained from these isotherms. The volumes are approximately constant above T_g (about 40 cm³/mol), whereas the volumes below T_g are smaller and dependent on both temperature and concentration (19–26 cm³/mol). By analyzing the experimental data according to the dual-mode sorption and dilation model, the volume occupied by a dissolved Ar molecule and the mean size of microvoid in the glass are estimated to be 67 129 ų, respectively. The cohesive energy density of the polymer is also estimated as 61 cal/cm³ from the temperature dependence of the dual-mode parameters.     

Vortex formation in a viscoelastic entry flow of asymmetric planar contraction

Graphical abstract  

     

The surfboard Schrödinger equations

We study the large time behavior of solutions of time dependent Schrödinger equationsiu/t=–(1/2)u+t V(x/t)u with bounded potentialV(x). We show that (1) if>–1, all solutions are asymptotically free ast, (2) if–1 a solution becomes asymptotically free if and only if it has the momentum support outside of suppV for large time, (3) if –1 <0 all solutions are still asymptotically modified free ast and that (4) if 0 <2, for each local minimumx ₀ ofV(x), there exist solutions which are asymptotically Gaussians centered atx=tx ₀ and spreading slowly ast.     

Semiparametric estimation of the long-range parameter

We study two estimators of the long-range parameter of a covariance stationary linear process. We show that one of the estimators achieve the optimal semiparametric rate of convergence, whereas the other has a rate of convergence as close as desired to the optimal rate. Moreover, we show that the estimators are asymptotically normal with a variance, which does not depend on any unknown parameter, smaller than others suggested in the literature. Finally, a small Monte Carlo study is included to illustrate the finite sample relative performance of our estimators compared to other suggested semiparametric estimators. More specifically, the Monte-Carlo experiment shows the superiority of the proposed estimators in terms of the Mean Squared Error. The first author research was funded by the Economic and Social Research Council (ESRC) reference number: R000238212. The second author research was funded by the Ministry of Education, Culture, Sports and Technology of Japan, reference number: 09CE2002 and B(2)10202202.     

Heat of immersion of iron(III) oxides in water at 25°C

The heat of immersion in water was measured at 25°C for three iron(III) oxides using a twin-type microcalorimeter. One of the samples was commercial α-Fe₂O₃ (sample C) and the other two (samples M and F) were prepared by calcining magnetite and iron(III) hydroxide in air at various temperatures, T_p, from 300 to 700°C. The samples were evacuated at outgassing temperature, T_o, between room temperature and 500°C at a pressure of 1 × 10^?2?2.7 × 10^?2N m^?2 for 6 h. The heat of immersion, h_i(J m^?2), of samples C and M increased with an increase in T_o and showed the maximum h_i at T_o =400°C, while sample F did not show the maximum up to T_o =500°C. The systematic correlation was not observed between h_i and T_p of sample F. The heat of reproduction of the surface hydroxyl group on sample F was approximately estimated as 6.6 × 10⁴ J mole^?1 H₂O.     

Substitution of both chloro and sulfinyl groups of aryl 1-chlorocyclopropyl sulfoxides in one-pot via cyclopropylmagnesium carbenoids: a synthesis of multi-substituted cyclopropanes

The rearrangement of cyclopropylmagnesium carbenoids, which were generated from aryl 1-chlorocyclopropyl sulfoxides with a Grignard reagent, to allenes was found to be suppressed by adding HMPA as an additive. Alkylation of the cyclopropylmagnesium carbenoids with the Grignard reagent gives mainly alkylated cyclopropylmagnesium chloride instead. The cyclopropylmagnesium chloride intermediate can be trapped with several electrophiles to afford multi-substituted cyclopropanes. This procedure provides a new method for a synthesis of multi-substituted cyclopropanes.