Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.     

On the Durrmeyer-type modification of some discrete approximation operators

In [10], for continuous functionsf from the domain of certain discrete operatorsL _n the inequalities are proved concerning the modulus of continuity ofL _nf. Here we present analogues of the results obtained for the Durrmeyer-type modification $\tilde L_n $ ofL _n. Moreover, we give the estimates of the rate of convergence of $\tilde L_n f$ in Hölder-type norms     

Kinetics and mechanism of the phenolysis of asymmetric diaryl carbonates

The reactions 4-methylphenyl 4-nitrophenyl carbonate (MPNPC), 4-chlorophenyl 4-nitrophenyl carbonate (CIPNPC), 4-methylphenyl 2,4-dinitrophenyl carbonate (MPDNPC), and 4-chlorophenyl 2,4-dinitrophenyl carbonate (CIPDNPC) with a homogeneous series of phenoxide anions are subjected to a kinetic investigation in aqueous solution (25.0 degrees C, ionic strength 0.2 M (KCI)). Under an excess of phenoxide with respect to the substrate, all of these reactions obey pseudo-first-order kinetics and are first order in phenoxide. The Br?nsted-type plots for the nucleophilic rate constants (k(N)) are linear, with slopes beta = 0.48 (MPNPC), 0.67 (ClPNPC), 0.41 (MPDNPC), and 0.32 (ClPDNPC). The magnitude of these slopes and the absence of a curvature in the Br?nsted plot at pK(a) = 7.1 for the CIPNPC reactions are consistent with concerted mechanisms (one step). The carbonates MPDNPC and ClPDNPC are more reactive than MPNPC and CIPNPC, respectively, toward phenoxide nucleophiles. This can be explained by the presence of a second nitro group in the nucleofuge of the dinitro derivatives, which (i) leaves their carbonyl carbon more positively charged, making them better electrophiles, and (ii) makes 2,4-dinitrophenoxide a better leaving group than 4-nitrophenoxide. The 4-chloro derivatives are more reactive than the corresponding 4-methyl derivatives. This should be due to the greater electron withdrawal of 4-chloro than 4-methyl, which makes the former carbonyl more electrophilic. Comparison of the concerted phenolysis of MPNPC with the stepwise reactions of secondary alicyclic amines with the same substrate indicates that substitution of a secondary alicyclic amine group in a zwitterionic tetrahedral intermediate by a phenoxy group greatly destabilizes the intermediate. An equation is deduced for log k(N) in terms of the basicity of the nucleophile, the nonleaving moiety, and the leaving group. This equation shows that for these reactions, the sensitivity of log k(N) to the basicity of the nonleaving moiety (beta(nlg) = -0.27) is very similar to that of the nucleofuge (beta(lg) = -0.25).     

H-bonding dependent structures of (NH4+)3H+(SO4 2-)2. Mechanisms of phase transitions

The role of different H-bonds in phases II, III, IV, and V of triammonium hydrogen disulfate, (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), has been studied by X-ray diffraction and (1)H solid-state MAS NMR. The proper space group for phase II is C2/c, for phases III and IV is P2/n, and for phase V is P onemacr;. The structures of phases III and IV seem to be the same. The hydrogen atom participating in the O(-)-H(+).O(-) H-bond in phase II of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) at room temperature is split at two positions around the center of the crucial O(-)-H(+).O(-) H-bonding, joining two SO(4)(2)(-) tetrahedra. With decreasing temperature, it becomes localized at one of the oxygen atoms. Further cooling causes additional differentiation of possibly equivalent sulfate dimers. The NH(4)(+) ions participate mainly in bifurcated H-bonds with two oxygen atoms from sulfate anions. On cooling, the major contribution of the bifurcated H-bond becomes stronger, whereas the minor one becomes weaker. This is coupled with rotation of sulfate ions. In all the phases of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), some additional, weak but significant, reflections are observed. They are located between the layers of the reciprocal lattice, suggesting possible modulation of the host (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) structure(s). According to (1)H MAS NMR obtained for phases II and III, the nature of the acidic proton disorder is dynamic, and localization of the proton takes place in a broader range of temperatures, as can be expected from the X-ray diffraction data.     

Fine tuning the structure of the Cu2+ complex with the prion protein chicken repeat by proline isomerization

The interaction between the single hexarepeat unit of chicken prion protein [ChPrP(54-59)] and Cu(II) was investigated by NMR, finding different coordination modes for the trans/trans and cis/trans isomers.     

Dual Nucleophilic Substitution Reactions of O,O‐Diethyl 2,4‐dinitrophenyl Phosphate and Thionophosphate Triesters

The reactions of the title compounds with phenoxides, secondary alicyclic (SA) amines, and pyridines, in 44 wt% ethanol–water, at 25°C and an ionic strength of 0.2 M, were subjected to kinetic and product studies. From analytical techniques (HPLC and NMR), two pathways were detected (nucleophilic attack at the phosphoryl center and at the C‐1 aromatic carbon) for the reactions of all the nucleophiles with the phosphate ( 2 ) and for the pyridinolysis of the thionophosphate ( 1 ). Only aromatic nucleophilic substitution was found for the reactions of 1 with phenoxides and SA amines. For the dual reactions, the nucleophilic rate constants (k_N) were separated in two terms: $k_{\rm N}^{\rm P}$ and $k_{\rm N}^{{\rm Ar}}$, which are the rate constants for the corresponding electrophilic centers. The absence of a break in the Brønsted‐type plots for the attack at P is consistent with concerted mechanisms. The Brønsted slopes, β_Ar 0.32–0.71, for the attack at the aromatic C‐1, are in agreement with stepwise mechanisms where formation of a Meisenheimer complex is the rate‐determining step. © 2013 Wiley Periodicals, Inc. Int J Chem Kinet 45: 202–211, 2013