Copolymerization kinetics of a model siloxane system

Using ²⁹Si NMR, we monitor the copolymerization of trimethylethoxysilane and dimethyldiethoxysilane (model compounds for more complex sol-gel copolymer systems) in a batch reactor. Under the chosen conditions, the extents of self- and cross-condensation reactions are readily determined. Using a nonideal polycondensation kinetic model, we show that the copolymerization rate coefficient for a pair of sites of differing functionality is bounded by their homopolymerization rate coefficients, lying closer to the larger one. This reactivity pattern generates a heterogeneous monomer distribution in the copolymerization products. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 1293–1302, 1997     

Additive latin transversals

We prove that for every odd primep, everyk≤p and every two subsets A={a ₁, …,a _k } andB={b ₁, …,b _k } of cardinalityk each ofZ _p , there is a permutationπ ∈S _k such that the sumsa _i +b _π(i) (inZ _p ) are pairwise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well. Research supported in part by a State of New Jersey grant and by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University.     

Solubility of sodium soaps in aqueous salt solutions

The solubility of sodium soaps in dilute aqueous salt solutions has been systematically investigated by direct visual phase behavior observations. The added electrolytes, including simple inorganic salts and bulky organic salts, influence the solubility of sodium soaps in water, as represented by the varied soap Krafft point. Two inorganic salts, sodium chloride and sodium perchlorate, demonstrate a "salting-out" property. On the other hand, tetraalkylammonium bromides show an excellent ability to depress the soap Krafft point and enhance the soap solubility in water. With increasing the tetraalkylammonium ionic size, the degree of "salting-in" of soaps in water increases. However, solubility of pure tetraalkylammonium bromide in water decreases as the length of the alkyl chains increases. Furthermore, in the ternary water-tetrapentylammonium bromide (TPeAB)-sodium myristate (NaMy) system, we observed an upper cloud point phenomenon, which greatly shrinks the 1-phase micellar solution region in the phase diagram. This miscibility gap, together with the organic salt solubility limitation, restricts the use of tetraalkylammonium bromides with alkyl chains longer than 4 carbon atoms as effective soap solubility enhancement electrolytes. We also found that for sodium soap with a longer hydrocarbon chain, more tetrabutylammonium salt is required to reduce the soap Krafft point to room temperature.     

On the Complexity of Arrangements of Circles in the Plane

Continuing and extending the analysis in a previous paper [15], we establish several combinatorial results on the complexity of arrangements of circles in the plane. The main results are a collection of partial solutions to the conjecture that (a) any arrangement of unit circles with at least one intersecting pair has a vertex incident to at most three circles, and (b) any arrangement of circles of arbitrary radii with at least one intersecting pair has a vertex incident to at most three circles, under appropriate assumptions on the number of intersecting pairs of circles (see below for a more precise statement). Received June 26, 2000, and in revised form January 30, 2001. Online publication October 5, 2001.     

Doublet–triplet splitting in realistic heterotic string derived models

There has been recently a surge of interest in Grand Unified Theories on orbifolds of higher-dimensional spaces. In particular, the higher-dimensional doublet–triplet splitting mechanism has been of much interest. I revisit the superstring doublet–triplet splitting mechanism in which the color triplets are projected out by the GSO projections, while leaving the electroweak doublets in the physical spectrum. The connection with the higher-dimensional theories is elucidated. It is shown that the doublet–triplet splitting depends crucially on the assignment of boundary conditions in the compactified directions. The possibility of reducing the number of Higgs multiplets by using the GSO projections is also discussed.     

Further development of Raman Microprobe spectroscopy for characterization of char reactivity

The effect of heat treatment on reactivity of cellulose char was investigated, using two methods: (1) Raman Microprobe spectroscopy analysis (RMA) and (2) thermogravimetric analysis (TGA). The heat-treatment was in the temperature range of 600–2600 °C, temperature prevailing in combustion of coal-chars. In the RMA, first- and second-order Raman spectra in the range of 800–2000 and 2000–3600 cm⁻¹, respectively, were measured for all samples. In the first-order Raman spectra, the following bands have been observed: D band and G (at 1350 and 1590 cm⁻¹ respectively), 1150 and 1450 cm⁻¹. In the second-order Raman spectra, four bands have been observed at 2450, 2700, 2940 and 3250 cm⁻¹. Both first- and second-order Raman spectra were fitted by Lorentzian functions. The Lorentzian parameters (bandwidth and intensity ratio) showed significant changes with heat treatment, which is consistent with structural modification. Also, from TGA experiments we observed the expected significant influence of heat treatment on char reactivity. Attempts were made to correlate the Lorentzian parameters with char reactivity. A good correlation was found between the 2940 cm⁻¹ bandwidth in the second-order Raman spectrum and char reactivity, confirming the strong connection between char structure and its reactivity, and illustrating the usefulness of RMA in such studies.     

Development of a chemiluminescent optical fiber immunosensor to detect Streptococcus pneumoniae antipolysaccharide antibodies

A chemiluminescent-based optical fiber immunosensor was developed for the detection of antipneumococcal antibodies. This was accomplished by developing a different chemical procedure utilizing 3-aminopropyl trimethoxysilane and cyanuric chloride to conjugate pneumococcal cell wall polysaccharides to the optical fiber tips, and by improving the sensitivity of the photodetection system. The lowest titer of antipneumococcal antibodies detected by the optical fiber was at a 1:819,200 dilution. The lowest corresponding value by standard enzyme-linked immunosorbent assay was at a 1:98,415 dilution. It was concluded that the optical immunosensor system is an accurate and sensitive method to detect antipneumococcal antibodies and may be an adequate tool to monitor antibodies in specimens such as saliva and urine.     

Organometallic polymers I. Solution polymerization of α-ferrocenylmethylcarbonium fluoborate

The self-condensation of α-ferrocenylmethylcarbonium ion in nitroethane yielded polymers of M_n up to 20,000. The change of [η] and M_n with the reaction time indicated that the process consisted of a rapid primary growth stage, an induction period, a second growth stage, and a crosslinking stage. The [η]–M_n correlation for a series of polymeric fractions in the M_n = 0.1–7.2 × 10⁴ range points to a highly branched structure.