Characterization of PDMS model junctions and networks by solution and solid-state silicon-29 NMR spectroscopy

The application of ²⁹Si solution and solid-state cross-polarization/magic-angle spinning (CP/MAS) nuclear magnetic resonance (NMR) techniques to the study of structural features in polydimethylsiloxane (PDMS) model endlinked elastomeric networks is explored. The relationship between the topological (network) functionality of a structural moiety, which determines network mechanical properties, and its chemical (spectral) functionality, which is reported by the NMR, is discussed. The second-order spectral shifts corresponding to topographical functionality variation within a chemical functionality class are usually sufficiently well resolved in these networks to allow positive identification of a variety of structural features. The basic PDMS repeat unit, ? OSi(CH₃)₂? , is found to possess an axially symmetric chemical shift tensor with σ_∥ = ?56.8 ppm downfield from TMS, and σ_⊥ = ?4.4 ppm. This axial symmetry does not result from rapid reorientation about the chain axis. The NMR spectrum reveals defects in model endlinked networks. In the case of vinyl-endlinked systems, the defects are ascribed to the formation of elastically ineffective loops. Hydroxyl-endlinked systems contain either loops or else trifunctional junctions (hydrolyzed before chain coupling could take place) and dangling chain ends. The CP/MAS technique provides an order-of-magnitude reduction over standard solution techniques in the time to acquire a spectrum from a network not containing paramagnetic doping. ¹³C spectra of PDMS systems are not as informative as ²⁹Si spectra.     

Non-isothermal film casting: Determination of draw resonance

The important industrial process of casting polymeric films suffers from the “draw resonance” instability that appears as sudden oscillations in the product dimensions. This instability influences the quality of the end-product and negatively limits productivity and efficiency of the process. The draw resonance originates when a material is being processed beyond the limits of its intrinsic properties. Research is conducted with the intention to find those process and material properties that allow to optimize the production process while keeping it stable.This paper concentrates on a non-isothermal analysis of the stability of the film casting. The mathematical model of the process is given by a quasi-linear system of first order PDEs with two point boundary conditions. The constitutive polymer behavior is approximated by the modified Giesekus model. Linear stability analysis combined with the Laplace transformation of the resulting linear system is applied to find parameters that determine mathematical and thus process instability. It all comes down to determining the spectrum of a compact operator; corresponding eigenfunctions can be regarded as the characteristic modes of the system. For implementation, the modification of Galerkin approach is used. The major advantage of the mathematical and numerical method is that the full spectrum is calculated in a matter of seconds. Our results agree perfectly with the ones from literature for isothermal case, and with the experimental data for the non-isothermal case. The results also indicate that non-isothermality is highly important and cannot be excluded from modeling.     

A bounded compactness theorem forL 1-embeddability of metric spaces in the plane

LetM=(W, d) be a metric space. LetL ¹ denote theL ¹ metric. AnL ¹-embedding ofM into Cartesiank-space ℝ ^k is a distance-preserving map from (W, d) into (ℝ ^k ,L ¹). Letc(k) be the smallest integer such that for every metric spaceM, M isL ¹-embeddable inR ^k iff everyc(k)-sized subspace ofM isL ¹-embeddable inR ^k. A special case of a theorem of Menger (see p. 94 of [5]) says thatc(1) exists and equals 4. We show thatc(2) exists and satisfies 6≦c(2)≦11. Whether or notc(k) exists for anyk≧3 is an open question. The research of S. M. Malitz was partially supported by NSF Grant CCR-8909953.     

Obstructions to the Existence of Sasaki–Einstein Metrics

We describe two simple obstructions to the existence of Ricci-flat Kähler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular, this also leads to new obstructions for Kähler–Einstein metrics on Fano orbifolds. We present several families of hypersurface singularities that are obstructed, including 3-fold and 4-fold singularities of ADE type that have been studied previously in the physics literature. We show that the AdS/CFT dual of one obstruction is that the R–charge of a gauge invariant chiral primary operator violates the unitarity bound.     

Size-asymmetric primitive model at low temperature: description of ion pairing and location of the critical point

We argue that Bjerrum's approach to ion pairing is inappropriate for the size-asymmetric primitive model in the neighborhood of its critical point, and propose a new approach based on the Stillinger-Lovett pairing procedure. The new approach recursively scales up the ion size until linear approximations are suitable for analyzing such a model. To locate the critical point, a residual van der Waals interaction between pairs is added, with an energy cutoff adjusted to match the critical temperature of the restricted primitive model. The locations and downward trends of T(c) and rho(c) with asymmetry are found to compare favorably with simulations.     

A structural, magnetic and Mössbauer spectroscopic study of an unusual angular Jahn-Teller distortion in a series of high-spin iron(II) complexes

Single crystal X-ray structures and susceptibility data are described for six homoleptic iron(II) complex salts, of 2,6-di(pyrazol-1-yl)pyridine or a 3,3"-disubstituted derivative of it. Zero field Mossbauer spectroscopic data for four of the complexes, and one previously reported analogue, are also discussed. Four of these compounds exhibit an unusual angular Jahn-Teller distortion towards C(2) symmetry to differing degrees, while the other two exhibit structures close to the "ideal" D(2d) symmetry for this ligand set. This structural distortion has two components: a twisting of the plane of one ligand relative to the other about the N{pyridine}-Fe-N{pyridine} vector, so that the two ligands are no longer perpendicular; and a rotation of one ligand about the Fe ion, so that the N{pyridine}-Fe-N{pyridine} angle < 180 degrees. Susceptibility data show that all the complexes are fully high-spin between 5 and 300 K, but yield an unusually wide range of zero-field splitting parameters for the different compounds of between 2.6 and 13.4 cm(-1). Magnetostructural correlations suggest that a low value of |D| is diagnostic for a high degree of "rotation" distortion. The Mossbauer spectra imply that an increased quadrupole splitting might also be diagnostic for the presence of the angular distortion.     

Can proteins and crystals self-catalyze methyl rotations?

The chi (C(alpha)-C(beta)) torsional barrier in the dipeptide alanine (N-methyl-l-alanyl-N-methylamide) crystal was investigated using ab initio calculations at various levels of theory, molecular mechanics, and molecular dynamics. For one of the two molecules in the asymmetric unit the calculations suggest that rotation around the chi dihedral angle is catalyzed by the crystal environment, reducing by up to approximately 2kT the torsional barrier in the crystal with respect to that in the gas phase. This catalytic effect is present at both low and room temperature and originates from a van der Waals destabilization of the minima in the methyl dihedral potential coming from the nonbonded environment of the side chain. Screening of a subset of the Protein Data Bank with a pharmacophore model reproducing the crystal environment around this side chain methyl identified a protein containing an alanine residue with an environment similar to that in the crystal. Calculations indicate that this chi torsional barrier is also reduced in the protein at low temperature but not at room temperature. This suggests that environment-catalyzed rotation of methyl groups can occur both in the solid phase and in native biological structures, though this effect might be temperature-dependent. The relevance of this catalytic effect is discussed in terms of its natural occurrence and its possible contribution to the low-frequency vibrational modes of molecules.     

X-ray structure analysis of poly[di-(3,4-dimethylphenoxy)phosphazene]

The crystal structure of oriented poly[di-(3,4-dimethylphenoxy) phosphazene] (PDMP) was determined by x-ray diffraction. Unit-cell parameters were found to be a = 15.85, b = 19.43, and c = 9.85 Å. The unit cell is metrically orthorhombic with monoclinic space group P2₁. There were 48 refinable diffraction spots in the observed reciprocal lattice region, of which 28 were observed and 20 were unobserved. A refined model yielded the following residuals: R^(obs) = 0.162 and 0.138. It was shown that a two-chain unit cell with a [T₃C]₂ (trans, trans, trans, cis, trans, trans, trans, cis) backbone conformation was the correct structure. The dimethylphenoxy side groups were arranged in nearly parallel planes, slightly off-normal to the fiber c axis. The polymer chains are extremely tightly packed and contain close but reasonable steric contacts.     

The stoichiometric hydrogenation of 1,1-diphenylethylene with hydridocobalt tetracarbonyl; differences from the hydroformylation reaction

The kinetics of the stoichiometric hydrogenation of 1,1-diphenylethylene with HCo(CO)₄ is cleanly second order, permitting a determination of the activation parameters. The rate is unaffected by the atmosphere over the reaction and is enhanced by substituting DCo(CO)₄ for HCo(CO)₄. These results contrast sharply with those secured in the hydroformylation of 1-alkenes and thus dual mechanistic pathways are available for the reaction of HCo(CO)₄ with unsaturated systems. It is very possible that the stoichiometric hydrogenation of 1,1-diphenylethylene involves a geminate free radical pair but definitive proof is still lacking.