Reply to a note by T. G. Shepherd

Summary In a recent note by Shepherd it is claimed that the main conclusions discussed in a paper by Petroniet al. about certain instability mechanisms for steady equivalent barotropic flows are incorrect and, although no criticism is made regarding the analytical treatment, two counterexamples are presented to support this thesis. In addition to this it is asserted that the envisaged necessity for energy and enstrophy to be transferred in both spatial directions in a normal-mode instability is ?extremely well known?. Here we demonstrate that Shepherd's conclusions are without foundation and confirm the validity and originality of Petroniet al. results by showing that:a) the first counterexample describes a situation that is in fact provided for by Petroniet al.'s analysis;b) the second counterexample is not dynamically realizable and, even if it were, the related conclusions would not apply to flows defined in doubly periodic or bounded domains such as those considered by Petroniet al.; c) the mechanism cited above is not known at all in the specific context dealt with by Petroniet al. We emphasize this by pointing out that for steady equivalent barotropic flows the range of parameters for which such an instability mechanism is allowed complements exactly the range for which the steady states are stable according to Benziet al.     

Tides and seiches in gulfs

Summary In this paper Garrett's theory of tides in gulfs is extended so that its formalism includes the free oscillations (seiches) of the gulf. The elevation of the free surface ξ and the velocity fieldu are obtained in a rectangular, one-dimensional gulf opening into an infinite ocean. An application of the results to the Adriatic sea can explain qualitatively the long life of the uninodal seiche of that basin.

---

Riassunto In questo lavoro la teoria delle maree nei golfi dovuta a Garrett è estesa al fine di introdurre nel formalismo le oscillazioni libere (sesse) del golfo. Si ottengono l'elevazione della superficie libera ξ ed il campo di velocitàu in un golfo rettangolare ed unidimensionale che si affaccia su un oceano infinito. Un'applicazione dei risultati al Mare Adriatico fornisce una spiegazione qualitativa della lunga vita della sessa uninodale di tale bacino.

---

Резюме В этой статье теория Гаррета обобщается таким образом, чтобы формализм теории включал свободные осцилляции (сейши) уровня залива. Определяются подъем свободной поверхности ξ и поле скоростейu в прямоутольном одномерном заливе, открытом в бесконечный океан. Применение полученных результатов к Адриатическому морю может обЪяснить качественно большое время жизни одно-узлового сейша этого бассейна.

---

---

Research supported by C.N.R.: ?Progetto Finalizzato Oceanografia?.     

Solvent effects on the rate of the keto-enol interconversion of 2-nitrocyclohexanone

The rates of tautomerization of 2-nitrocyclohexanone (2-NCH) have been measured spectrophotometrically at 25.0 +/- 0.1 degrees C in several organic aprotic solvents and their binary mixtures. In cyclohexane the reaction is effectively catalyzed by bases and inhibited by acids while the so-called "spontaneous reaction" appears essentially due to autocatalysis. Apparent second order rate constants (k(app)(B)) for the reaction catalyzed by triethylamine (TEA) and pyridine (Pyr) have been obtained. From the experimental k(app)(B) values rate constants for the enolization (k(1)(B)) and ketonization (k(-1)(B)) reactions have been calculated. A Kamlet-Taft type linear solvation energy relationship (LSER) adequately accounts for the observed solvent effects. Activation parameters for both reactions show that solvent effects are mainly entropic in origin and that there is a shift of the transition state from a ketone-like to an enol-like structure on passing from less to more polar solvents.     

Synthesis of cyclohexadienylstannanes - Novel example of vinylic SRN1 mechanism: A theoretical and experimental study

The reaction of trimethyltinsodium (1) with 1-(diethoxyphosphoryl)oxy-1,3-cyclohexadienes in liquid ammonia under irradiation affords the corresponding 1-trimethylstannylcyclohexadienes. We suggest that these reactions occur by an S_RN1 mechanism. On the other hand, 2-(diethoxyphosphoryl)oxy-1,3-cyclohexadiene reacts very slowly towards 1 and the substitution product decomposes under the reaction conditions employed. Thus, structurally similar compounds do not behave in the same way under ET conditions. We suggest that this behavior is mainly due to differences in spin density of their radical anions, which affect their fragmentation rates. Our results are supported by computational calculations.     

Ionization and tautomerization of 2-nitrocyclohexanone in aqueous solution

The keto-enol tautomerism of 2-nitrocyclohexanone (2-NCH) was studied in aqueous solution under different experimental conditions. Ketonization rate constants were measured spectrophotometrically at 25 degrees C at an ionic strength of 0.4 mol dm-3 (NaCl) in diluted hydrochloric acid, in diluted sodium hydroxide, and in several buffers by using NaHSO3 as the scavenger of the keto form. A value of pK(a)(EH) = 4.78 for the enol form was obtained from the rate-pH profile of the reaction. A value of pK(a)(KH) = 5.97 for the keto form was directly obtained from the UV-vis spectra of 2-NCH recorded at different pHs. The equilibrium constant for the keto-enol tautomerism, pK(T) = -log([enol]/[ketone]) = 1.19, was obtained by combining the two pKa values (pK(T) = pK(a)(KH) - pK(a)(EH)). A comparison of these results with the corresponding values (Keefe, J. R.; Kresge, A. J. In The Chemistry of Enols; Rappoport, Z., Ed.; Wiley & Sons: New York, 1990; pp 399-480) for cyclohexanone shows the dramatic effects of an alpha-nitro substituent on the keto-enol acidities and the tautomerization constant of alicyclic ketones. Rates and equilibria were discussed in the light of the Br?nsted equation, the principle of nonperfect synchronization, and the Marcus theory. It turns out that, on passing from nitroalkanes to nitroketones, the resonance contribution to pKa and deprotonation rate decreases, being overwhelmed by steric and inductive effects.     

A “quasi‐flexible” automatic docking processing for studying stereoselective recognition mechanisms. Part I. Protocol validation

The main purpose of this work is the development and validation of a general scheme based on a systematic and automatic “quasi‐flexible” docking approach for studying stereoselective recognition mechanisms. To achieve our goals we explore the conformational and configurational space for small‐ or medium‐size flexible molecules in a systematic way, seeking a method that is both reasonably accurate and relatively fast from the computational point of view. In particular, we have developed a general computational protocol for the global molecular interaction evaluation (“Glob‐MolInE”) to efficiently explore the orientational and conformational space of flexible selectors and selectands used in modern chiral high‐performance liquid chromatography (HPLC); the enantioselective binding of the selector (S)‐N‐(3,5‐dinitrobenzoyl)‐leucine‐ n‐propylamide (S)‐ 1 towards the selectand N‐(2‐naphthyl)‐alanine methyl ester 2 has been studied; the global minimum obtained for the homochiral associate [S( 1 )/S( 2 )] (Pop. >99%) is very close (RMS≃0.20) to the crystallographically determined structure. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 515–530, 2000     

Kinetic and theoretical studies on the mechanism of intramolecular catalysis in phenyl ester hydrolysis

The kinetic study of the hydrolysis reaction of Z-substituted phenyl hydrogen maleates (Z = H, m-CH3, p-CH3, m-Cl, p-Cl and m-CN) was carried out in aqueous solution, and the results were complemented with theoretical studies. Under some experimental conditions, two kinetic processes were observed. One of them was ascribed to maleic anhydride formation and the other to the anhydride hydrolysis. The Br?nsted-type plot for the leaving-group dependence was linear with slope beta(lg) = -1. The experimental results are consistent with a mechanism that involves significant bond breaking in the rate-limiting transition state (alpha(lg) = 0.64). Theoretical results for the reaction in the gas phase showed an excellent Br?nsted-type dependence with a beta(lg) of -1.03. A tetrahedral intermediate (TI) could not be found through DFT gas-phase studies (B3LYP/6-311+G*). Calculations carried out within a continuous solvation model or with discrete water molecules failed to find a stable TI. With both models, a flat region on the potential-energy surface is found and a tight optimization of the structures led back to starting materials. The theoretical results do not discard the possible existence of an unstable intermediate on the free-energy surface, but the analysis of the whole body of results compared with other acyl transfer reactions lead us to suggest that an enforced concerted mechanism is the most appropriate to describe these reactions.     

Discussion of thermodynamic data obtained by adsorption gas chromatography of hydrocarbons on a new graphitized carbon black with a high specific surface area

Summary A new graphitized carbon black (Carbograph 5) with a specific surface area (560 m² g⁻¹) greater than those of commerically available graphitized carbons was studied by gas chromatography to determine the enthalpy, entropy, and free energy of adsorption of a series of alkanes (C₂−C₆). The adsorption properties were also investigated by considering changes in the isosteric heats and entropies of adsorption when a nonpolar stationary phase (squalane) was added to the adsorbent. The data obtained are discussed and compared with literature values for other graphitized carbon blacks.     

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.