Near-thermal reactions of Au(+)(1S,3D) with CH3X (X = F,Cl)

Reactions of Au(+)((1)S) and Au(+)((3)D) with CH(3)F and CH(3)Cl have been carried out in a drift cell in He at a pressure of 3.5 Torr at both room temperature and reduced temperatures in order to explore the influence of the electronic state of the metal on reaction outcomes. State-specific product channels and overall two-body rate constants were identified using electronic state chromatography. These results indicate that Au(+)((1)S) reacts to yield an association product in addition to AuCH(2)(+) in parallel steps with both neutrals. Product distributions for association vs HX elimination were determined to be 79% association/21% HX elimination for X = F and 50% association/50% HX elimination when X = Cl. Reaction of Au(+)((3)D) with CH(3)F also results in HF elimination, which in this case is thought to produce (3)AuCH(2)(+). With CH(3)Cl, Au(+)((3)D) reacts to form AuCH(3)(+) and CH(3)Cl(+) in parallel steps. An additional product channel initiated by Au(+)((3)D) is also observed with both methyl halides, which yields CH(2)X(+) as a higher-order product. Kinetic measurements indicate that the reaction efficiency for both Au(+) states is significantly greater with CH(3)Cl than with CH(3)F. The observed two-body rate constant for depletion of Au(+)((1)S) by CH(3)F represents less than 5% of the limiting rate constant predicted by the average dipole orientation model (ADO) at room temperature and 226 K, whereas CH(3)Cl reacts with Au(+)((1)S) at the ADO limit at both room temperature and 218 K. Rate constants for depletion of Au(+)((3)D) by CH(3)F and CH(3)Cl were measured at 226 and 218 K respectively, and indicate that Au(+)((3)D) is consumed at approximately 2% of the ADO limit by CH(3)F and 69% of the ADO limit by CH(3)Cl. Product formation and overall efficiency for all four reactions are consistent with previous experimental results and available theoretical models.     

Solid state studies of drugs and chemicals by dielectric and calorimetric analysis

Novel dielectric behavior of a linear increase in ionic conductivity prior to melt temperature was observed for active pharmaceutical ingredients (APIs), organic chemicals, amino acids, and carbohydrates. Though, there are solids like polyolefins and long chain organic compounds (tetracosane, pentacosane) which do not exhibit this premelt behavior (i.e., the temperature where the onset of increase in ionic conductivity to melt temperature). We have discovered novel electrical conductivity properties and other physical analytical variations which can lead to unique synthetic routes of certain chemical entities. The above-mentioned unique variations are not related to solid–solid transitions which are quite often observed in pharmaceutical crystalline solids. These new properties are related to amorphous crystalline behavior of a solid. We have also studied the effect of various experimental variables: such as amount of mass tested, applied frequency at a given electric field and heating rate, which results in varying the onset temperature of the increase in ionic conductivity. Melting of the solids was correlated using differential scanning calorimetry (DSC). Activation energies for all the solids were measured in the premelt region using an Arrhenius plot at a specific frequency since we observed changes in the conductivity with frequency. This study focused on frequencies 0.1 to 10 Hz, since the conductivity at these frequencies related to surface analysis. This new physical properties are leading to new electro synthetic procedures to modify or prepare chemicals.     

Thermally-induced dielectric relaxation spectra in three aldohexose monosaccharides

Three aldohexose monosaccharides, d-glucose, d-mannose, and d-galactose, were examined by scanning temperature dielectric analysis (DEA) from ambient temperatures through their melts. Phase transitions, including glass transition (T _g) and melting temperature (T _m), were evaluated by differential scanning calorimetry (DSC). The monosaccharides were found to exhibit thermally-induced dielectric loss spectra in their amorphous-solid phase before melting. Activation energies for electrical charging of each of the monosaccharides were calculated from an Arrhenius plot of the tan delta (e″/e′, dielectric loss factor/relative permittivity) peak frequency versus reciprocal temperature in Kelvin. The DEA profiles were also correlated with the DSC phase diagrams, showing the changes in electrical behavior associated with solid–solid and solid–liquid transitions.     

Model Development in Thermal Styrene Polymerization

Summary: The thermal polymerization of styrene is usually modeled by relying on a reaction scheme and a set of equations that were developed more than three decades ago by Hui and Hamielec. Many detailed models of styrene polymerization are available in the open literature and they are mostly based on the work of Hui and Hamielec, which nearly makes this the standard to follow in explaining the behavior of polystyrene reactors. The model of Hui and Hamielec does a very nice job of describing monomer conversion data but discrepancies are seen between observed and predicted values of number and weight average molecular weights, M_n and M_w. Discrepancies in number average molecular weight seem to be the result of random noise. Discrepancies in weight average molecular weight grow as the polymerization temperature decreases and some of the trends observed in the residuals over the entire temperature range cannot be attributed to random noise. Hui and Hamielec attributed the observed deficiencies to a standard deviation of ±10% in their GPC measurements. A new data set with an experimental error of 2% for average molecular weights is presented. The set contains measured values of M_n, M_w and M_z, so the polymerization scheme has been extended to include third order moments. The data set also includes the effect of ethylbenzene as a chain transfer agent. We present the results of comparing model predictions to our measurements and the adjustments made in the original set of kinetic parameters published by Hui and Hamielec.     

On comparing two chains of numerical semigroups and detecting arf semigroups

If T is a numerical semigroup with maximal ideal N , define associated semigroups B(T):=(N-N) and L(T)= \cup { (hN-hN) \colon h \geq 1 } . If S is a numerical semigroup, define strictly increasing finite sequences { B _i (S) \colon 0 ≤ i ≤β (S) } and { L _i (S) \colon 0 ≤ i ≤λ (S) } of semigroups by B ₀ (S):=S=:L ₀ (S) , B _{β (S)} (S):= \Bbb N =: L _{λ (S)} (S) , B _i+1 (S):=B(B _i (S)) for 0<i< β (S) , L _i+1 (S):=L(L _i (S)) for 0<i< λ (S) . It is shown, contrary to recent claims and conjectures, that B ₂ (S) need not be a subset of L ₂ (S) and that β (S) - λ (S) can be any preassigned integer. On the other hand, B ₂ (S) \subseteq L ₂ (S) in each of the following cases: S is symmetric;S has maximal embedding dimension;S has embedding dimension e(S) ≤ 3 . Moreover, if either e(S)=2 or S is pseudo-symmetric of maximal embedding dimension, then B _i (S) \subseteq L _i (S) for each i , 0 ≤ i ≤λ (S) . For each integer n \geq 2 , an example is given of a (necessarily non-Arf) semigroup S such that β (S) = λ (S)=n , B _i (S) = L _i (S) for all 0 ≤ i ≤ n-2 , and B _n-1 (S) \subsetneqq L _n-1 (S) . April 4, 2000     

Permutation polynomials over algebraic number fields

Let K be an algebraic number field. It is known that any polynomial which induces a permutation on infinitely many residue class fields of K is a composition of cyclic and Chebyshev polynomials. This paper deals with the problem of deciding, for a given K, which compositions of cyclic or Chebyshev polynomials have this property. The problem is reduced to the case where K is an Abelian extension of $\text{Q}$. Then the question is settled for polynomials of prime degree, and the Abelian case for composite degree polynomials is considered. Finally, various special cases are dealt with.