Reduced parabolic model for radical addition reactions

The transition state of addition of free radicals and atoms to multiple bonds is considered as a result of intersecting of two parabolic potential curves. One of them characterizes the stretching vibration of the attacked multiple bond, and another curve characterizes the stretching vibration of the bond formed in the transition state. The force constant of the latter is calculated by an empirical equation that correlates the force constant with the bond dissociation energy. In the framework of this model, the thermally neutral activation energy (E _e0) and the elongation of the attacked and formed bonds (r _e) in the transition state were calculated from the experimental data (activation energy (E _e) and enthalpy of reaction (H _e)) for the addition of an H atom and methyl, alkoxyl, aminyl, triethylsilyl, and peroxyl radicals to the C=C bond and the addition of H and CH₃ to the C=O and CC bonds. Analysis of the data obtained showed that E _e0 depends linearly on the |H _e| + E_e sum, i.e., E_e0/kJ mol^–1 = 14.2 + 0.61 · (E_e – H _e), and the bond elongation in the transition state for addition of the most part of radicals to ethylene and acetylene vary within (0.65–0.87)·10_–10 m. The factors affecting the activation energy of the radical addition reactions are discussed.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1542–August, 2004.     

Ion Association and Hydration in Aqueous Solutions of Nickel(II) and Cobalt(II) Sulfate

Aqueous solutions of nickel(II) and cobalt(II) sulfate have been investigated at 25 ^∘C by dielectric relaxation spectroscopy (DRS) over a wide range of frequencies (0.2 ≤ ν (GHz) ≤ 89) and salt concentrations (0.025 ≤ c(mol-L⁻¹) ≤ 1.4). The spectra indicate, as for MgSO₄(aq) studied previously, the simultaneous presence of double solvent-separated, solvent-shared and contact ion pairs in both NiSO₄(aq) and CoSO₄(aq). The stepwise formation constants for each ion-pair type and the overall association constant, obtained from the data are in good agreement with ultrasonic relaxation and other estimates. The DR spectra at higher concentrations (c ≥ 0.5 mol-L⁻¹) suggest the existence of a nonlinear triple ion M₂SO₄²⁺(aq). Consistent with the very strong hydration of the salts, which have ‘effective’ hydration numbers approaching 27 at infinite dilution, there are no significant differences in any of the relaxation or thermodynamic parameters for NiSO₄(aq) and CoSO₄(aq), except that the triple ion appears to be somewhat more stable for the latter.     

The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

Conformational Studies on Polytripeptides as a Model of Collagen

To study the role of glycine residues in stabilizing the collagen triple helix, the glycine residues in the polytripeptide (Pro-Ala-Gly)_n were partially replaced by alanine. The proline content was kept constant. The stability of the helical conformation of these polypeptides was studied by IR- and X-ray measurements in the solid state and by ORD, CD and viscometry in solution. The renaturation was followed as a function of time. All the polytripeptides studied, with the exception of (-Pro-Ala-Ala-)_n attained the polyproline II conformation. However the stability decreased with increasing alanine content. Obviously the molecules of (-Pro-Ala-Gly-) are highly associated by intermolecular hydrogen bonds and one may therefore suppose that a triple-stranded helix aggregation occurs. The results of the refolding process show that the stability of the helices seems to also affect the refolding rate in terms of the optical rotation, Two transitions appeared: the first one is responsible for a rapid reversible change in conformation and the second one for a further slow and irreversible change in the hydrodynamic shape. The latter seems to be due to the partial helical nature, leading to higher chain mobility.     

Characterization of the Converging Jet Region in a Triple Torch Plasma Reactor

Enthalpy probe measurements were taken of the converging plasma plume in a triple torch plasma reactor and related to substrate heat flux measurements. Results show excellent entrainment of process gases injected into the converging plasma plume by way of the central injection probe. At lower pressures (40 kPa), the plasma volume is equivalent to at least a 3 cm diameter, 4 cm long cylinder, with relatively uniform temperature, velocity, and substrate heat flux profiles when compared to a typical dc arc jet. Converging plasma plume size, substrate heat flux, and enthalpy profiles are also shown to be a strong function of applied system power. Substrate heat flux measurements show smaller radial gradients than enthalpy probe measurements, because of the high radial velocity component of gases above the substrate boundary layer. Enthalpy probe measurements were also conducted for diamond deposition conditions and approximate temperature and velocity profiles obtained. Problems with the uniform gas mixture assumption prohibited more accurate measurements. Reproducibility of enthalpy measurement results was shown with an average standard deviation of 11.8% for the velocity and 7.6% for the temperature measurements.     

Recent development of non-faradaic potentiometry

Non-faradaic potentiometry has been plagued by a great many fundamental errors and a lack of conceptualization. Of greatest concern is the second Nernst equation hiatus. Potentiometry may be generally classified as faradaic and non-faradaic. The former deals with the redox reactions using the Nernst equation to explain the potential origin. The latter deals with the non-redox reactions using the Boltzmann and modified Boltzmann equations to explain the origin of electrode potential. Redox faradaic potentiometry has been well described in the textbooks. However, non-faradaic potentiometry has been almost completely neglected in the literature. Many well-known electrodes, such as the pH glass electrode, common reference electrodes, and ion selective electrodes (ISE) have been mistakenly interpreted as redox reactions or ion exchange reactions. New theories and experimental results show their mechanisms to be non-faradaic in nature. Furthermore, the reaction mechanisms for ISE have been confused in textbooks with redox reactions and the Nernst equation. The ISE potentials originating from adsorption of ions or charged particles based on surface charge density will be explained using the double and counterion triple layers concept. The new counterion triple layer concept may be applied to the potential development of sensors. The reason for a new concept, theory, or mechanism is to better explain the phenomena. Examples will be given of how our new concept explains the capacitor, counterion triple layer, surface adsorbed layers interactions, and the interface structure. We will also discuss the new sensor development based on the new adsorption concept. For the first time a new type of Ag/AgCl reference electrode for non-faradaic potentiometry will be presented, one without a liquid junction and with a Pt wire instead of a salt bridge. They will help open up a new horizon for electrochemical sensor research and may be used under unusual conditions, such as high temperature and high pressure, stirring, etc.     

A study for quality evaluation of Taxilli Herba from different hosts based on fingerprint-activity relationship modeling and multivariate statistical analysis

In this study, a fingerprint-activity relationship modeling between chemical fingerprints and antirheumatic activity was established, and multivariate statistical analysis was used to evaluate the quality of Taxilli Herba (TH) from different hosts. Characteristic fingerprints of 20 batches of TH samples were generated by high-performance liquid chromatography coupled with triple quadrupole-time of flight tandem mass spectrometry (HPLC-Triple TOF-MS/MS), and the similarity analysis was calculated based on thirteen common characteristic peaks by hierarchical clustering analysis (HCA). Subsequently, nine efficacy markers were discovered by combining fingerprints and antirheumatic activity through grey correlation analysis (GCA) and bivariate correlation analysis (BCA). Meanwhile, the content of 5 constituents in 9 markers was determined by high-performance liquid chromatography coupled with triple quadrupole-linear ion trap tandem mass spectrometry (HPLC-QTRAP-MS/MS). The comprehensive quality of TH was assessed using multivariate statistical analysis, including principal components analysis (PCA) and technique for order preference by similarity to ideal solution (TOPSIS). The results showed that a high dose of TH extract could markedly ameliorate arthritis damage compared to other doses, with flavonoids playing an important role in the antirheumatic activity. The comprehensive quality of samples from Morus alba L. (SS) was superior to those from Liquidambar formosana Hance (FXS). The present study will demonstrate the markers associated with efficacy, and provide an applicable strategy for more comprehensive quality control and evaluation of TH.     

A convergence result for a sequence of distributed-parameter optimal control problems

In this paper, we consider a sequence of abstract optimal control problems by allowing the cost integrand, the partial differential operator, and the control constraint set all to vary simultaneously. Using the notions of -convergence of functions,G-convergence of operators, and Kuratowski-Mosco convergence of sets, we show that the values of the approximating problems converge to that of the limit problem. Also we show that a convergent sequence of optimal pairs for the approximating problems has a limit which is optimal for the limit problem. A concrete example of parabolic optimal control problems is worked out in detail.This research was supported by NSF Grant No. DMS-88-02688.