Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Quantitative studies on the peroxidation of human low-density lipoprotein initiated by superoxide and by charged and neutral alkylperoxyl radicals.

Rates of peroxidation of human LDL and rates of consumption of the LDL's alpha-tocopherol (TocH) have been measured at 37 degrees C. Peroxidation was initiated by radicals generated in the aerated aqueous phase at known rates by thermal decomposition of appropriate precursors: superoxide (O2(*-)/HOO(*)) from a hyponitrite and alkylperoxyls (ROO(*), two positively charged, one negatively charged and one neutral) from azo compounds. The efficiencies of escape from the solvent cage of the geminate pair of neutral carbon-centered radicals was found to be 0.1, but it was 0.5 for the three charged radicals, a result attributed to radical/radical Coulombic repulsion within the cage. All four alkylperoxyls initiated and terminated tocopherol-mediated peroxidation (TMP) with about equal efficiency and essentially all of these radicals that were generated were consumed in these two reactions. TMP is a radical chain process, and when initiated by the alkylperoxyls, the rate of LDL peroxidation was faster in the early stages while TocH was present than later, after all of this "antioxidant" had been consumed. In contrast, only about 3-4% of the generated superoxide radicals reacted in any measurable fashion with TocH-containing LDL at pH's from 7.6 to 6.5 and peroxidation was much slower than with a similar rate of generation of alkylperoxyls. After all the TocH had been consumed, LDL peroxidation was negligible at pH 7.6 and 7.4, but at pH 6.8 and 6.5, the peroxidation rates showed a large increase over the rates while the TocH had been present. That is, endogenous TocH behaves as an antioxidant in LDL subjected to attack by the physiologically relevant superoxide radical, whereas TocH behaves as a prooxidant in LDL subjected to attack by the probably far less physiologically important alkylperoxyls. Rates of LDL peroxidation initiated by superoxide increased as the pH was decreased, and the results are consistent with the initiation of peroxidation of fresh LDL occurring via H-atom abstraction from TocH by HOO(*) to form the Toc(*) radical and termination by reaction of O2(*-) with Toc(*), a process that occurs partly by addition leading to TocH consumption and partly by electron plus proton transfer leading to the regeneration of TocH.     

Abnormal solvent effects on hydrogen atom abstractions. 1. The reactions of phenols with 2,2-diphenyl-1-picrylhydrazyl (dpph*) in alcohols

Rate constants, k(ArOH/dpph*)(S), for hydrogen atom abstraction from 13 hindered and nonhindered phenols by the diphenylpicrylhydrazyl radical, dpph*, have been determined in n-heptane and a number of alcoholic and nonalcoholic, hydrogen-bond accepting solvents. Abnormally enhanced k(ArOH/dpph*)(S) values of have been observed in alcohols. It is proposed that this is due to partial ionization of the phenols and a very fast electron transfer from phenoxide anion to dpph*. The popular assessment of the antioxidant activities of phenols with dpph* in alcohol solvents will generally lead to an overestimation of their activities.     

A carbon-centered radical unreactive toward oxygen: unusual radical stabilization by a lactone ring

A lactone ring confers unusual stability to a diphenylmethyl-like radical that is virtually unreactive toward oxygen. Thus, the radical derived from HP-136 is about 10,000 times less reactive than typical carbon-centered radicals. A reversible reaction with oxygen is proposed by analogy with triphenylmethyl; however, the association constant is about 1000 times smaller for HP-136 than for triphenylmethyl. While the lactone ring greatly influences the reactivity, the spectroscopy of the HP-136-derived radical is in line with that expected for a substituted diphenylmethyl radical.     

New insight into solvent effects on the formal HOO. + HOO. reaction

The 2,2'-azobis(isobutyronitrile)(AIBN)-induced autoxidation of gamma-terpinene (TH) at 50 degrees C produces p-cymene and hydrogen peroxide in a radical-chain reaction having HOO* as one of the chain-carrying radicals. The kinetics of this reaction in cyclohexane and tert-butyl alcohol show that chain termination involves the formal HOO. + HOO. self-reaction over a wide range of gamma-terpinene, AIBN, and O2 concentrations. However, in acetonitrile this termination process is accompanied by termination via the cross-reaction of the terpinenyl radical, T., with the HOO. radical under conditions of relatively high [TH] (140-1000 mM) and low [O2] (2.0-5.5 mM). This is because the formal HOO. + HOO. reaction is comparatively slow in acetonitrile (2k approximately 8 x 10(7) M(-1) s(-1)), whereas, this reaction is almost diffusion-controlled in tert-butyl alcohol and cyclohexane, 2k approximately 6.5 x 10(8) and 1.3 x 10(9) M(-1) s(-1), respectively. Three mechanisms for the bimolecular self-reaction of HOO. radicals are considered: 1) a head-to-tail hydrogen-atom transfer from one radical to the other, 2) a head-to-head reaction to form an intermediate tetroxide, and 3) an electron-transfer between HOO. and its conjugate base, the superoxide radical anion, O2-.. The rate constant for reaction by mechanism (1) is shown to be dependent on the hydrogen bond (HB) accepting ability of the solvent; that by mechanism (2) is shown to be too slow for this process to be of any importance; and that by mechanism (3) is dependent on the pH of the solvent and its ability to support ionization. Mechanism (3) was found to be the main termination process in tert-butyl alcohol and acetonitrile. In the gas phase, the rate constant for the HOO. + HOO. reaction (mechanism (1)) is about 1.8 x 10(9) M(-1) s(-1) but in water at pH< or =2 where the ionization of HOO. is completely suppressed, this rate constant is only 8.6 x 10(5) M(-1) s(-1). The very large retarding effect of water on this reaction has not previously been explained. We find that it can be quantitatively accounted for by using Abraham's HB acceptor parameter, beta(2)(H), for water of 0.38 and an estimated HB donor parameter, alpha(2)(H), for HOO. of about 0.87. These Abraham parameters allow us to predict a rate constant for the HOO. + HOO. reaction in water at 25 degrees C of 1.2 x 10(6) M(-1) s(-1) in excellent agreement with experiment.     

Absolute rate constants for some hydrogen atom abstraction reactions by a primary fluoroalkyl radical in water

A combination of laser flash photolysis and competitive kinetic methods have been used to measure the absolute bimolecular rate constants for hydrogen atom abstraction in water from a variety of organic substrates including alcohols, ethers, and carboxylic acids by the perfluoroalkyl radical, *CF(2)CF(2)OCF(2)CF(2)SO(3)(-) Na(+). Comparison, where possible, of these rate constants with those previously measured for analogous reactions in the non-polar organic solvent, 1,3-bis(trifluoromethyl)benzene (J. Am. Chem. Soc, 1999, 121, 7335) show that the alcohols react 2-5 times more rapidly in the water solvent and that the ethers react at the same rate in both solvents. A transition state for hydrogen abstraction that is more reminiscent of an "intimate ion pair" than a "solvent separated ion pair" is invoked to explain these modest solvent effects.     

Absolute Rate Constants for the Reactions of Primary Alkyl Radicals with Aromatic Amines(1)

Hydrogen abstraction from diarylamines (4-X-C(6)H(4))(2)NH [X = H, CH(3), C(8)H(17), CH(3)O, and Br] by the 2-methyl-2-phenylpropyl radical in n-dodecane solution was investigated by thermolysis of 3-methyl-3-phenylbutanoyl peroxide in the presence of various concentrations of the amines. The reaction is a non-chain process in which the 2-methyl-2-phenylpropyl radical and its rearrangement product, the 2-benzylpropan-2-yl radical, abstract hydrogen from both the solvent and the amine. Cross-disproportionation reactions of the rearranged radical led to the formation of significant amounts of beta,beta-dimethylstyrene. Rate constants for hydrogen abstraction by the unrearranged, primary alkyl radical from n-dodecane (k(373K) = 3.5 x 10(3) M(-)(1) s(-)(1)), diphenylamine (k(373K) = 1.3 x 10(6) M(-)(1) s(-)(1)), and the substituted diarylamines were determined from the product yields and the known rate constant for the radical rearrangement. From kinetic experiments with N-deuteriodiphenylamine the deuterium kinetic isotope effect,k(NH)/k(ND), was found to be 2.3 at 373 K.     

Critical re-evaluation of the O-H bond dissociation enthalpy in phenol

The gas-phase O-H bond dissociation enthalpy, BDE, in phenol provides an essential benchmark for calibrating the O-H BDEs of other phenols, data which aids our understanding of the reactivities of phenols, such as their relevant antioxidant activities. In a recent review, the O-H BDE for phenol was presented as 90 +/- 3 kcal mol(-1) (Acc. Chem. Res. 2003, 36, 255-263). Due to the large margin of error, such a parameter cannot be used for dynamic interpretations nor can it be used as an anchor point in the development of more advanced computational models. We have reevaluated the existing experimental gas-phase data (thermolyses and ion chemistry). The large errors and variations in thermodynamic parameters associated with the gas-phase ion chemistry methods produce inconsistent results, but the thermolytic data has afforded a value of 87.0 +/- 0.5 kcal mol(-1). Next, the effect of solvent has been carefully scrutinized in four liquid-phase methods for measuring the O-H BDE in phenol: photoacoustic calorimetry, one-electron potential measurements, an electrochemical cycle, and radical equilibrium electron paramagnetic resonance (REqEPR). The enthalpic effect due to solvation, by, e.g., water, could be rigorously accounted for by means of an empirical model and the difference in hydrogen bond interactions of the solvent with phenol and the phenoxyl radical. For the REqEPR method, a second correction is required since the calibration standard, the O-H BDE in 2,4,6-tri-tert-butylphenol, had to be revised. From the gas-phase thermolysis data and three liquid-phase techniques (excluding the electrochemical cycle method), the present analysis yields a gas-phase BDE of 86.7 +/- 0.7 kcal mol(-1). The O-H BDE was also estimated by state-of-the-art computational approaches (G3, CBS-APNO, and CBS-QB3) providing a range from 86.4 to 87.7 kcal mol(-1). We therefore recommend that in the future, and until further refinement is possible, the gas-phase O-H BDE in phenol should be presented as 86.7 +/- 0.7 kcal mol(-1).     

Kinetic studies on stilbazulenyl-bis-nitrone (STAZN), a nonphenolic chain-breaking antioxidant in solution, micelles, and lipid membranes

The rate constants, k(inh), for reaction of stilbazulenyl-bis-nitrone (STAZN, 1) with peroxyl radicals and the number of radicals trapped, n, are compared with those of phenolic antioxidants 2,2,5,7,8-pentamethyl-6-hydroxychroman (PMHC, 4a), 2,5,7,8-tetramethyl-6-hydroxychroman-2-carboxylic acid (Trolox, 4b), and 2,6-di-tert-butyl-4-methoxyphenol (DBHA, 5). The behavior of STAZN depended markedly on the media and type of initiator used, water-soluble or lipid-soluble. In styrene/chlorobenzene and initiation by azo-bis(isobutyronitrile) (AIBN), k(inh) (STAZN) = 0.64 k(inh) (5) = 0.02k(inh) (4a). On addition of methanol, the k(inh) of STAZN increased 6-fold to be four times that of 5 while that of 4a decreased 6-fold. In aqueous SDS-micelles containing methyl linoleate and initiation with water-soluble azo-bis(amidinopropane)2HCl, ABAP, the relative k(inh) values were 1 >or= 4b > 5. In dilinoleoylphosphatidyl choline (DLPC) bilayers and initiation with lipid-soluble azo-bis-2,4(dimethylvaleronitrile) (DMVN), the k(inh) order was 5 > 4b > 1. During initiation with ABAP in micelles and bilayers, the calculated values of k(inh) for STAZN changed during the induction period. The experimental results are interpreted in terms of the conformation of STAZN, which is transoid in homogeneous solution but cisoid in aqueous dispersions of lipids. In such dispersions, the STAZN lies at the lipid-water interface where it traps water-soluble peroxyl radicals by a single electron-transfer mechanism. The cisoid conformation at lipid-water interfaces is supported by theoretical calculations.