A unique graph of minimal elastic energy

Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the integrals has an integrand independent of the derivative of the unknown. Both the linear and the nonlinear cases are illustrated. By lengthening parameterized curves it is possible to reduce the elastic energy to zero. It is shown here that for graphs this is not the case. Specifically, there is a unique graph of minimal elastic energy among all graphs that have turned 90 degrees after traversing one unit.

     

Studies of self-diffusion of poly(dimethylsiloxane) chains in PDMS model networks by pulsed field gradient NMR

We have measured the diffusion of poly(dimethylsiloxane) (PDMS) chains in PDMS model networks by using a pulsed field gradient NMR technique. The model networks have been prepared by tetrafunctional endliking of linear PDMS chains having molecular weights M_n of 3,700 and 7,400 g mol^?1. The diffusants have been incorporated in the networks by immersing pieces of them in PDMS linear chains with molecular weights M_n between 3,000 and 12,000 g mol^?1 and molecular weight distributions M_w/M_n between 1.1 and 1.7. Although spin-echo attenuation results were fitted to a model which takes into account polydispersity of the diffusant, these results did not exhibit any dependency upon the molecular weight distribution. The self-diffusion coefficients of PDMS chains in the PDMS model networks were found to be smaller than in the melt, and the exponents for the diffusion coefficient dependence on M_n in the networks were found to be about-1.3. Free diffusion will give an exponent equal to-1, whereas free volume contributions or behavior intermediate between free and entangled diffusion will increase the magnitude of the exponent.     

Preparation of supported yttrium alkoxides as catalysts for the polymerization of lactones and oxirane

Two methods have been reported that allow yttrium alkoxides to be supported on porous silica and to be used afterward as heterogeneous catalysts in the ring‐opening polymerization of oxirane and ?‐caprolactone. In the two methods, [tris(hexamethyldisilyl)‐amide]yttrium {Y[N(SiMe₃)₂]₃} is the metal alkoxide precursor. It is directly reacted with the silanol groups of the support, in the first method, and this is followed by alcoholysis of the unreacted amide groups. The flexibility of this method seems to be limited because the grafting density and the structure of the grafted Y alkoxide (less than one alkoxide by metal) are independent of the experimental conditions. In the second method, Y[N(SiMe₃)₂]₃ is first reacted with 1 or 2 equiv of alcohol with the formation of the mixed Y alkoxide/amide. The amide functions are used to attach Y to the support. This method is free from side reactions, quite reproducible, and well suited to support one type of active species (monoalkoxide or dialkoxide). Preliminary experiments with ?‐caprolactone polymerization have confirmed the activity of the supported Y alkoxide, whatever preparation method is used. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 569–578, 2003     

Azidocarbonyl-substituted cubanoureas

Despite the angular strain associated with the assembly of small rings, 1,2-diisocyanatocubane reacts with trimethylsilyl azide under mild conditions to form a hexacyclic ring assembly that contains an imidazolidone ring fused to one edge of cubane. This compound was identified as an azidocarbonyl-substituted cubanourea by means of X-ray crystal structure analysis of the nitro-derivative, the energetic compound N-azidocarbonyl-N¹-nitrocubanourea.     

Deflection of rotating marine propellers using projected-grating moiré techniques

A projected-linear-grating moiré technique has been developed to determine the feasibility of studying the behavior of model marine propeliers rotating in a variable-pressure water tunnel. Full-field deflections were determined from photographs of moiré interference fringes on the propeller roating at speeds up to 2000 rpm.     

Low temperature electrical resistivity of α-cerium under pressure

We report a new method which is used to study the α-phase of cerium without inclusions of β-phase. A pressure independent low temperature resistivity has been observed. None of the exchange enhancement effects previously observed in high pressure susceptibility experiments have been detected on transport properties.