Preparation and evaluation of carbon coated alumina as a high surface area packing material for high performance liquid chromatography

The retention of polar compounds, the separation of structural isomers and thermal stability make carbonaceous materials very attractive stationary phases for liquid chromatography (LC). Carbon clad zirconia (C/ZrO₂), one of the most interesting, exhibits unparalleled chemical and thermal stability, but its characteristically low surface area (20–30 m²/g) limits broader application as a second dimension separation in two-dimensional liquid chromatography (2DLC) where high retentivity and therefore high stationary phase surface area are required. In this work, we used a high surface area commercial HPLC alumina (153 m²/g) as a support material to develop a carbon phase by chemical vapor deposition (CVD) at elevated temperature using hexane vapor as the carbon source. The loading of carbon was varied by changing the CVD time and temperature, and the carbon coated alumina (C/Al₂O₃) was characterized both physically and chromatographically. The resulting carbon phases behaved as a reversed phase similar to C/ZrO₂. At all carbon loadings, C/Al₂O₃ closely matched the unique chromatographic selectivity of carbon phases, and as expected the retentivity was increased over C/ZrO₂. Excess carbon – the amount equivalent to 5 monolayers – was required to fully cover the oxide support in C/Al₂O₃, but this was less excess than needed with C/ZrO₂. Plate counts were 60,000–76,000/m for 5 μm particles. Spectroscopic studies (XPS and FT-IR) were also conducted; they showed that the two materials were chemically very similar.     

Independent sets in regular graphs and sum-free subsets of finite groups

It is shown that there exists a function∈(k) which tends to 0 ask tends to infinity, such that anyk-regular graph onn vertices contains at most 2^{(1/2+∈(k))n} independent sets. This settles a conjecture of A. Granville and has several applications in Combinatorial Group Theory. Research supported in part by the United States-Israel Binational Science Foundation and by a Bergmann Memorial Grant.     

Molecular weight control of polyacrylamide with sodium formate as a chain‐transfer agent: Characterization via size exclusion chromatography/multi‐angle laser light scattering and determination of chain‐transfer constant

We discuss the synthesis and characterization of polyacrylamide (PAM) homopolymers with carefully controlled molecular weights (MWs). PAM was synthesized via free‐radical solution polymerization under conditions that yield highly linear polymer with minimal levels of hydrolysis. The MW of the PAM homopolymers was controlled by the addition of sodium formate (NaOOCH) to the polymerization medium as a conventional chain‐transfer agent. MWs and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi‐angle laser light scattering analysis; for polymerizations carried out to high conversion, PAM MWs ranged from 0.23 to 6.19 × 10⁶ g/mol, with most samples having PDI ≈2.0. Zero‐shear intrinsic viscosities of the polymers were determined via low‐shear viscometry in 0.514 M NaCl at 25 °C. Data derived from the polymer characterization were used to determine the chain‐transfer constant to NaOOCH under the given polymerization conditions and to calculate Mark–Houwink–Sakurada K and a values for PAM in 0.514 M NaCl at 25 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 560–568, 2003     

Random Cayley graphs and expanders

For every 1 > δ > 0 there exists a c = c(δ) > 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G, S) is at most (1 - δ). This implies that almost every such a graph is an ?(δ)-expander. For Abelian groups this is essentially tight, and explicit constructions can be given in some cases. © 1994 John Wiley & Sons, Inc.     

Influence of Solution Volume on the Dissolution Rate of Silicon Dioxide in Hydrofluoric Acid

Experimental data and modeling of the dissolution of various Si/SiO₂ thermal coatings in different volumes of hydrofluoric acid (HF) are reported. The rates of SiO₂‐film dissolution, measured by means of various electrochemical techniques, and alteration in HF activity depend on the thickness of the film coating. Despite the small volumes (0.6–1.2 mL) of the HF solution, an effect of SiO₂‐coating thickness on the dissolution rate was detected. To explain alterations detected in HF activity after SiO₂ dissolution, spectroscopic analyses (NMR and FTIR) of the chemical composition of the solutions were conducted. This is associated with a modification in the chemical composition of the HF solution, which results in either the formation of an oxidized species in solution or the precipitation of dissolution products. HF₂^? accumulation in the HF solution, owing to SiO₂ dissolution was identified as the source of the chemical alteration.     

Protection of flows under targeted attacks

We present a new robust optimization model for the problem of maximizing the amount of flow surviving the attack of an interdictor. Given some path flow, our model allows the interdictor to specify the amount of flow removed from each path individually. In contrast to previous models, for which no efficient algorithms are known, the most important basic variants of our model can be solved in poly-time. We also consider extensions where there is a budget to set the interdiction costs.