Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Hyperaromatic stabilization of arenium ions

Benzene-cis- and trans-1,2-dihydrodiols undergo acid-catalyzed dehydration at remarkably different rates: k(cis)/k(trans) = 4500. This is explained by formation of a β-hydroxycarbocation intermediate in different initial conformations, one of which is stabilized by hyperconjugation amplified by an aromatic no-bond resonance structure (HOC(6)H(6)(+) ? HOC(6)H(5) H(+)). MP2 calculations and an unfavorable effect of benzoannelation on benzenium ion stability, implied by pK(R) measurements of -2.3, -8.0, and -11.9 for benzenium, 1-naphthalenium, and 9-phenanthrenium ions, respectively, support the explanation.     

Hyperaromatic stabilization of arenium ions: a remarkable cis stereoselectivity of nucleophilic trapping of β-hydroxyarenium ions by water

Cis- and trans-1,2-dihydrodiol isomers of benzene undergo acid-catalyzed dehydration to form phenol. In principle the isomeric substrates react through a common β-hydroxybenzenium (cyclohexadienyl) carbocation. Notwithstanding, the isomers show a large difference in reactivity, k(cis)/k(trans) = 4500. This difference is reduced to k(cis)/k(trans) = 440 and 50 for the 1,2-dihydrodiols of naphthalene and 9,10-dihydrodiols of phenanthrene, respectively, and to 6.9 for the dihydrodiols of the nonaromatic 7,8-double bond of acenaphthylene. Because the difference in stabilities of cis- and trans-dihydrodiols should be no more than 2-3-fold, these results imply a high cis stereoselectivity for nucleophilic trapping of a β-hydroxyarenium cation by water in the reverse of the carbocation-forming reaction. This is confirmed by studies of the 10-hydroxy-9-phenanthrenium ion generated from aqueous solvolyses of the trans-9,10-bromohydrin derivative of phenanthrene and the monotrichloroacetate ester of the phenanthrene cis-9,10-dihydrodiol. The cis stereoselectivity of forward and reverse reactions is explained by the formation (in the "forward" reaction) of different conformations of carbocation from cis- and trans-dihydrodiol reactants with respectively β-C-H and β-C-OH bonds in pseudoaxial positions with respect to the charge center of the carbocation optimal for hyperconjugation. Formation of different conformations is constrained by departure of the (protonated) OH leaving group from a pseudoaxial position. The difference in stability of the carbocations is suggested to stem (a) from the greater hyperconjugative ability of a C-H than a C-OH bond and (b) from enhanced conjugation arising from the stabilizing influence of an aromatic ring in the no-bond resonance structures representing the hyperconjugation (C(6)H(6)OH(+) ? C(6)H(5)OH H(+)). This is consistent with an earlier suggestion by Mulliken and a demonstration by Schleyer that the benzenium ion is subject to hyperconjugative aromatic stabilization. It is proposed that, in analogy with the terms homoconjugation and homoaromaticity, arenium ions should be considered as "hyperaromatic".     

Acid-catalyzed dehydration of naphthalene-cis-1,2-dihydrodiols: origin of impaired resonance effect of 3-substituents

Acid-catalyzed dehydrations of substituted naphthalene-cis-1,2-dihydrodiols occur with loss of the 1- or 2-OH group to form 2- and 1-naphthols, respectively. Effects of substituents MeO, Me, H, F, Br, I, and CN at 3-, 6-, and 7-positions of the naphthalene ring are consistent with rate-determining formation of β-hydroxynaphthalenium ion (carbocation) intermediates. For reaction of the 1-hydroxyl group the 3-substituents are correlated by the Yukawa-Tsuno relationship with ρ = -4.7 and r = 0.25 or by σ(p) constants with ρ = -4.25; for reaction of the 2-hydroxyl group the 3-substituents are correlated by σ(m) constants with ρ = -8.1. The correlations for the 1-hydroxyl imply a surprisingly weak resonance interaction of +M substituents (MeO, Me) with a carbocation reaction center but are consistent with the corresponding correlation for acid-catalyzed dehydration of 3-substituted benzene-cis-1,2-dihydrodiols for which ρ = -6.9 and r = 0.43. Substituents at the 6- and 7-positions of the naphthalene rings by contrast are correlated by σ(+) with ρ = -3.2 for reaction of the 1-hydroxyl group and ρ = -2.7 for reaction of the 2-hydroxyl group. The unimpaired resonance implied by these substituent effects appears to be inconsistent with a previous explanation of the weak resonance of the 3-substituents in terms of imbalance of charge development and/or nonplanarity of the benzenium ring in the transition state. An alternative possibility is that the adjacent hydroxyl group interferes sterically with conjugation of +M substituents. "Hyperaromaticity" of the arenium ion intermediates does not appear to be a factor influencing this behavior.     

Permanently oriented antibody immobilization for digoxin determination with a flow-through fluoroimmunosensor

This paper reports a new flow-through fluoroimmunosensor, the function of which is based on antibodies immobilized on an inmunoreactor of controlled-pore glass (CPG), for determination of digoxin, used in the treatment of congestive heart failure and artery disease. The immunosensor has a detection limit of 1.20 microg L(-1) and provides high reproducibility (RSD=4.5% for a concentration of 0.0025 mg L(-1), and RSD=6.7% for 0.01 mg L(-1)). The optimum working concentration range was found to be 1.2 x 10(-3)-4.0 x 10(-2) mg L(-1). The lifetime of the immunosensor was about 50 immunoassays; if stored unused its lifetime can be extended to three months. A sample speed of about 10-12 samples per hour can be attained. Possible interference from substances with structures similar to digoxin (morphine, heroin, tebaine, codeine, pentazocine and narcotine) was investigated. No cross-reactivity was seen at the highest digoxin: interferent ratio studied (1:100). The proposed fluoroimmunosensor was successfully used to determine digoxin concentrations in human serum samples.     

Hyperaromatic stabilization of arenium ions: acid-catalyzed dehydration of 2-substituted 1,2-dihydro-1-naphthols

Rate constants for acid-catalyzed dehydration of cis-2-substituted 1,2-dihydro-naphthols are well correlated by the Taft relationship log k = -0.49 - 8.8σ(I), with minor negative deviations for OH and OMe. By contrast the trans substituents show a poor correlation with σ(I) and in most cases react more slowly than their cis isomers. The behavior is consistent with rate-determining formation of a 2-substituted carbocation (naphthalenium ion) intermediate that for cis reactants possesses a 2-C-H bond suitably oriented for hyperconjugation with the charge center. For the trans isomers the 2-substituent itself is oriented for hyperconjugation in the initially formed conformation of the cation. It is argued that k(cis)/k(trans) rate ratios for substituents (Me, 8.4; Bu(t), 12.7; Ph, 3.8; NH(3)(+), 160; OH, 440) reflect their hyperconjugating ability relative to hydrogen. Faster reactions of trans isomers are observed for substitutents known (RS, N(3)) or suspected (EtSO, EtSO(2)) of stabilizing the cation by a π or σ neighboring group effect. The good Taft correlation is taken to indicate that cis substuents are reacting normally, differentiated only by their inductive effects. The slower reactions of the trans isomers are the judged to be "abnormal". This is confirmed by comparing effects of cis and trans β-OH substituents on the reactivities of dihydro phenols, naphthols, and phenanthrols. Whereas k(H)/k(OH) for cis substituents varies by less than 8-fold and is consistent with the influence of an inductive effect of the OH group (k(H)/k(OH) ≈ 2000), k(H)/k(OH) for the trans substituents varies by 3 orders of magnitude, reflecting the additional influence of the lesser hyperconjugating ability of a C-OH bond compared to a C-H bond. The magnitude and variation of this difference is consistent with C-H hyperconjugation conferring aromatic character on the arenium ions.