The projective dimension of three cubics is at most 5

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\le 5$. In the present paper we prove this conjectured sharp bound.     

Melting temperatures of poly(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride solutions: Thermodynamic analysis

Melting temperatures were observed visually for poly-(2,6-dimethyl-1,4-phenylene oxide) in methylene chloride at nine concentrations (polymer weight fractions ranging from 0.0042 to 0.2362). The data were analyzed upon the assumptions that ΔH_u and ΔS_u, the molar heat and entropy of fusion per polymer unit, are constant over the temperature range studied, and that a Flory-Huggins chemical potential expression with a concentration-independent pair interaction parameter, χ₁ = (0.5 + ψ₁) + ψ₁Φ/T, satisfactorily describes the polymer unit activity in the binary solutions. Computation gave ΔH_u = 1404 cal/mole of units (therefore Δh = 11.7 cal/g), ψ₁ = ?0.569₁, and Φ = 342.₄°K. The effect of using various combinations of data points upon the values of these three parameters, as determined by least-squares linear regression treatment of the melting temperature expression, is indicated.     

On-line reaction monitoring by extractive electrospray ionisation

The design and development of a novel extractive electrospray ionisation (EESI) device for on-line reaction monitoring is described. The EESI apparatus uses a secondary, grounded nebuliser to produce an analyte aerosol and a Venturi pump is then used to transfer a sample of the aerosol to an electrospray source where it is ionised. The EESI apparatus was then tested with a variety of small, organic molecules to assess sensitivity, linearity and dynamic range. The performance of the technique will depend on the mass spectrometer used for the experiments; in the configurations used here it has a usable dynamic range of around 3.5 orders of magnitude with a linear range of around 2.5 orders of magnitude and is capable of analysing species present down to low μg/mL with signal-to-noise ratio greater than 2.5. The use of EESI for reaction monitoring was validated using a series of mock reaction mixtures and then used to monitor the base hydrolysis of ethyl salicylate to salicylic acid.     

Insight into the permeation barrier of glued Langmuir-Blodgett bilayers

Permeation measurements have been made for He, CO2, and N2 across single Langmuir-Blodgett (LB) bilayers derived from 1,2,4,5-tetrakis[(N-(undecanoamidoethyl)-N,N-dimethyl ammonium) methyl]benzene tetrabromide (2) and 1,2,4,5-tetrakis[(N-(perfluoroundecanoamidoethyl)-N,N-dimethyl ammonium)methyl]benzene tetrabromide (3) in the absence and in the presence of entrapped poly(acrylic acid) (PAA). In the absence of PAA, single LB bilayers of 3 show a higher permeance for He and N2 but a lower permeation rate of CO2, as compared with analogous LB bilayers made from 2. The relatively low permeation rate of CO2 for the former has been attributed to reduced associative interactions with the fluorocarbon-rich bilayer. The same behavior has also been observed for LB bilayers containing PAA, formed under conditions that yield glued bilayers of 2 and 3 having similar diffusional pathways, as judged by He/N2 selectivities. These results, together with the fact that glued bilayers of 2 (having a thinner PAA layer as compared with those made from 3) exhibit lower He and N2 permeances, provide compelling evidence that the main barrier for gas transport is the combination of surfactant plus PAA and not simply a thin PAA layer that is encased within the surfactant bilayer.     

Low energy 13C+ and 13C2+ ion irradiation of water ice

In this paper we report the results of the first experimental study of the irradiation of low temperature water ice (30 and 90 K) using low energy (4 keV) 13C+ and 13C2+ ions. 13CO(2) and H2O(2) were readily formed within the H2O ice with the product yield and growth rate observed to be highly dependent on both the sample temperature and ion charge state.     

A free-volume-based approach to modeling thermoset cure behavior

The free-volume theory for the temperature dependence of transport properties of glass-forming polymers is extended to obtain their relationship to the extent of cure. This treatment centers on the unifying role of molecular mobility and yields a model which connects extent of reaction, viscosity, diffusivity, ionic conductivity and dipole relaxation time. The temporal dependence of these properties is expressed by coupling the extended free-volume model with a relationship for the rate of cure, which included diffusional limitations. Analyses based on this model are applied to the observed behavior of a model epoxy-amine resin system. The intrinsic kinetics of this model system are shown to be first order. It is shown that diffusional limitations strongly affected the progress of the reaction in the final stages of cure. The diffusion-modified rate expression predictions agree with extent of reaction versus time data over the range of experimental temperatures. The temporal dependence of viscous behavior of the curing resin is measured. The extended free-volume model accurately describes the evolution of resin viscosity during cure. The dielectric behavior is similarly characterized and is in close agreement with the predictions of the general free-volume expression. The results of this study indicate that the free-volume theory modified to account for molecular weight effects allows prediction of resin properties with a two-parameter model. The results show that a power-law relationship exists between viscosity and ionic conductivity. This result suggests that electrical properties may be used for on-line measurement of resin viscosity during cure.     

Micro-interferometry for measurement of thermal displacements at fiber/matrix interfaces

A micro-interferometric technique for measuring out-of-plane thermal displacements on a scale commensurate with the dimensions of the fiber/matrix unit cell is described. A scanning micro-interferometer is used to image surface displacements of samples containing a single-pitch-based carbon fiber embedded in an epoxy matrix. The interferometer design gives the necessary resolution to detect small changes in thermal displacements in the fiber/matrix interface region. The samples were heated electrically through the fiber to create radially symmetric temperature and displacement fields. Repeatable displacement measurements were obtained on a radial line across the interface region with an accuracy of ±25 Å. A sharp expansion of the matrix surrounding the fiber was observed with each heating. Overall, the experiments demonstrate the utility of micro-interferometry for measuring submicron displacements.