Single-site beta-diiminate zinc catalysts for the ring-opening polymerization of beta-butyrolactone and beta-valerolactone to poly(3-hydroxyalkanoates)

Polymerization of beta-butyrolactone (BBL) and beta-valerolactone (BVL) using the zinc alkoxide initiator (BDI-1)ZnO(i)()Pr [(BDI-1) = 2-((2,6-diisopropylphenyl)amido)-4-((2,6-diisopropylphenyl)imino)-2-pentene] proceeds very rapidly under mild conditions to produce poly(3-hydroxybutyrate) (PHB) and poly(3-hydroxyvalerate) (PHV), respectively. For the monomer-to-initiator ratio 200:1, PHB number-average molecular weights (M(n)) are proportional to conversion throughout the reaction and polydispersity indices (PDIs) are narrow, consistent with a living polymerization. Higher monomer-to-initiator ratios can be used to achieve high molecular weight PHB (M(n) > 100 000). End-group analysis verifies that the polymerization of BBL follows a coordination-insertion mechanism, where complexes of the form (BDI-1)ZnOCH(Me)CH(2)CO(2)R are the active species. Variable temperature NMR experiments show that (BDI-1)ZnO(i)()Pr is monomeric in benzene-d(6) solution. In contrast, (BDI-2)ZnO(i)()Pr [(BDI-2) = 2-((2,6-diethylphenyl)amido)-4-((2,6-diethylphenyl)imino)-2-pentene] is a poor initiator at room temperature because it prefers to form a bis-mu-isopropoxide dimer in solution. According to kinetic studies, propagation by (BDI-1)ZnO(i)()Pr is first order in both monomer as well as (BDI-1)ZnO(i)()Pr concentration. These results lead us to propose a monometallic active species. Several results suggest that elimination side reactions are slowly catalyzed by zinc alkoxides, leading to degradation of the polymer.     

Nitrogen inversion in cyclic amines and the bicyclic effect

The hitherto unsolved problem of the origin of the unusually high nitrogen inversion-rotation (NIR) barriers in 7-azabicyclo[2.2.1]heptanes (the bicyclic effect) was examined using the natural bond orbital (NBO) approach. Reinvestigating the NIR barrier for tropane by DNMR, we found that NIR barriers increase smoothly on going from nitrogen-bridged bicyclic systems of a larger ring size to the smaller ring homologous systems. The experimental NIR barriers are reproduced with good accuracy using the MP2/6-31G level of theory. The NBO analysis for these and other azabicycles led to the conclusion that the height of these barriers is mostly determined by the energy of the sigma-orbitals of the C(alpha)(-)C(beta) bonds as well as the nitrogen lone pair. Thus, the bicyclic effect is actually an extreme case of a common C(alpha-)N-C(alpha) tripyramid geometry-NIR barrier dependence for N-bridged bicyclic amines. By establishing the rate-determining role of the C(alpha-)N-C(alpha) tripyramid fragment for NIR, we have derived the first sufficiently accurate quantitative correlations amine geometry-NIR barrier for monocyclic as well as bicyclic N-H and N-Me amines (i.e., for an amine set which also includes the bicyclic effect systems).     

On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

Structure of V(2)O(5)*nH(2)O xerogel solved by the atomic pair distribution function technique

A long-standing issue regarding the local and long-range structure of V(2)O(5)*nH(2)O xerogel has been successfully addressed. The full three-dimensional structure of the lamellar turbostratic V(2)O(5)*nH(2)O xerogel was determined by the atomic pair distribution function technique. We show that on the atomic scale the slabs of the xerogel can be described well as almost perfect pairs (i.e., bilayers) of single V(2)O(5) layers made of square pyramidal VO(5) units. These slabs are separated by water molecules and stack along the z-axis of a monoclinic unit cell (space group C2/m) with parameters a = 11.722(3) A, b = 3.570(3) A, c = 11.520(3) A, and beta = 88.65 degrees. The stacking sequence shows signatures of turbostratic disorder and a structural coherence limited to 50 A.     

Tunneling from a 3-dimensional quantum well in an electric field: an analytic solution

We derive the stationary tunneling solution for charged particles moving in a spherical, 3-dimensional zero-range potential plus a constant electric field. From the analytic expression for the wave function we calculate the distribution of the current inside and outside the vacuum barrier. At low field strengths there is a constant spreading of the tunnel current orthogonal to the direction of the applied field. At intermediate field strengths the exact results for the current distribution behave different from the semiclassical predictions.     

Focal shift in focused truncated gaussian beams

It is known that under certain circumstances the point of maximum intensity in a focused aberration-free wave is not at the geometrical focus, but is closer to the focusing lens. In the present note such a focal shift is analyzed for the case of a gaussian beam, focused by a thin lens, which fills a circular aperture of any prescribed radius, the waist of the beam being assumed to be located in the aperture plane. Many previously known results follow as limiting cases of our analysis.