Radius of clusters at the percolation threshold: A position space renormalization group study

Using a direct position-space renormalization-group approach we study percolation clusters in the limits , wheres is the number of occupied elements in a cluster. We do this by assigning a fugacityK per cluster element; asK approaches a critical valueK _c , the conjugate variables . All exponents along the path (K–K _c ) 0 are then related to a corresponding exponent along the paths . We calculate the exponent , which describes how the radius of ans-site cluster grows withs at the percolation threshold, in dimensionsd=2, 3. Ind=2 our numerical estimate of =0.52±0.02, obtained from extrapolation and from cell-to-cell transformation procedures, is in agreement with the best known estimates. We combine this result with previous PSRG calculations for the connectedness-length exponent , to make an indirect test of cluster-radius scaling by calculating the scaling function exponent using the relation =/. Our result for is in agreement with direct Monte-Carlo calculations of , and thus supports the cluster-radius scaling assumption. We also calculate ind=3 for both site and bond percolation, using a cell of linear sizeb=2 on the simple-cubic lattice. Although the result of such small-cell calculations are at best only approximate, they nevertheless are consistent with the most recent numerical estimates.Supported in part by grants from ARO and ONR     

Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using fluorescence, near-infrared reflectance imaging: a case study

We present in vivo fluorescent, near-infrared (NIR), reflectance images of indocyanine green (ICG) and carotene-conjugated 2-devinyl-2-(1-hexyloxyethyl) pyropheophorbide (HPPH-car) to discriminate spontaneous canine adenocarcinoma from normal mammary tissue. Following intravenous administration of 1.0 mg kg-1 ICG or 0.3 mg kg-1 HPPH-car into the canine, a 25 mW, 778 nm or 70 mW, 660 nm laser diode beam, expanded by a diverging lens to approximately 4 cm in diameter, illuminated the surface of the mammary tissue. Successfully propagating to the tissue surface, ICG or HPPH-car fluorescence generated from within the tissue was collected by an image-intensified, charge-coupled device camera fitted with an 830 or 710 nm bandpass interference filter. Upon collecting time-dependent fluorescence images at the tissue surface overlying both normal and diseased tissue volumes, and fitting these images to a pharmacokinetic model describing the uptake (wash-in) and release (wash-out) of fluorescent dye, the pharmacokinetics of fluorescent dye was spatially determined. Mapping the fluorescence intensity owing to ICG indicates that the dye acts as a blood pool or blood persistent agent, for the model parameters show no difference in the ICG uptake rates between normal and diseased tissue regions. The wash-out of ICG was delayed for up to 72 h after intravenous injection in tissue volumes associated with disease, because ICG fluorescence was still detected in the diseased tissue 72 h after injection. In contrast, HPPH-car pharmacokinetics illustrated active uptake into diseased tissues, perhaps owing to the overexpression of LDL receptors associated with the malignant cells. HPPH-car fluorescence was not discernable after 24 h. This work illustrates the ability to monitor the pharmacokinetic delivery of NIR fluorescent dyes within tissue volumes as great as 0.5-1 cm from the tissue surface in order to differentiate normal from diseased tissue volumes on the basis of parameters obtained from the pharmacokinetic models.     

Simultaneous analysis of methionine- and leucine-enkephalin from rat brain: quantification by liquid chromatography-electrochemistry

This study focuses on the application of liquid chromatography with electrochemical detection (LC-ED) for the analysis of methionine-enkephalin (ME) and leucine-enkephalin (LE) extracted from rat brain regions. The high applied potentials necessary for enkephalin detection required the development of an efficient sample processing protocol. Brain extracts were processed using chromatographic mode sequencing (CMS). The decrease in electroactive interfering substances by CMS improved the chromatographic resolution of ME and LE and the electrode performance. Other qualitative and analytical methods were used to evaluate the enkephalin data obtained by LC-ED for rat brain regions. This study demonstrates that LC-ED provides both the sensitivity and specificity necessary for the analysis of enkephalins from rat brain regions.     

13C NMR studies of molecular relaxation processes in polar fluids

A study of the dynamical molecular structure of a dilute polar fluid is reported, in which ¹³C spin-lattice relaxation times of decanol in deuterated cyclohexane are presented for the individual carbon atoms, and the results are discussed in the context of viscosity data of decanol in alkane systems. The two techniques provide complementary information about the mobility of the alcohol chains and the onset of multimer formation, which is also pertinent to the dynamics of electron solvation in the same systems.     

Density functional calculation of quinone electrode potentials

Here, we have applied density functional methods, in combination with free energy hydration calculations, to calculate two-electron electrode potentials for quinones and naphthoquinones. While we find that the free-energy perturbation method, implemented within a molecular dynamics framework, is superior to the PM 3—SM 3 continuum method for determining free energies of hydration, the computationally less expensive PM 3—SM 3 method does perform well when there is not an internal hydrogen bond. Generally, all the density functional approaches investigated gave good energetics when applied to this problem, but the Beck '88—Vosko—Wilk—Nusair combination of functionals for the exchange-correlation energy gave the best results. The density functional results are marginally better than the Møller-Plesset second-order perturbation results. Moreover, because the results are obtained using a thermodynamic cycle which involves taking differences in total energies, the results are not too dependent on the quadrature scheme used to calculate the exchange-correlation energy. By using semiempirically optimized geometries and the PM 3—SM 3 method for determining free energies of hydration, it has been possible to calculate electrode potentials for a series of large molecules (naphthoquinones) to within about 30 mV of experiment. This result is extremely encouraging and shows that density functional methods offer great promise in the design of redox-active molecules such as bioreductive anticancer agents. © 1995 John Wiley & Sons, Inc.     

Mechanistic studies on the formation and reactivity of dioxygen adducts of diiron complexes supported by sterically hindered carboxylates

Dioxygen activation by enzymes such as methane monooxygenase, ribonucleotide reductase, and fatty acid desaturases occurs at a nonheme diiron active site supported by two histidines and four carboxylates, typically involving a (peroxo)diiron(III,III) intermediate in an early step of the catalytic cycle. Biomimetic tetracarboxylatodiiron(II,II) complexes with the familiar "paddlewheel" topology comprising sterically bulky o-dixylylbenzoate ligands with pyridine, 1-methylimidazole, or THF at apical sites readily react with O(2) to afford thermally labile peroxo intermediates that can be trapped and characterized spectroscopically at low temperatures (193 K). Cryogenic stopped-flow kinetic analysis of O(2) adduct formation carried out for the three complexes reveals that dioxygen binds to the diiron(II,II) center with concentration dependences and activation parameters indicative of a direct associative pathway. The pyridine and 1-methylimidazole intermediates decay by self-decomposition. However, the THF intermediate decays much faster by oxygen transfer to added PPh(3), the kinetics of which has been studied with double mixing experiments in a cryogenic stopped-flow apparatus. The results show that the decay of the THF intermediate is kinetically controlled by the dissociation of a THF ligand, a conclusion supported by the observation of saturation kinetic behavior with respect to PPh(3), inhibition by added THF, and invariant saturation rate constants for the oxidation of various phosphines. It is proposed that the proximity of the reducing substrate to the peroxide ligand on the diiron coordination sphere facilitates the oxygen-atom transfer. This unique investigation of the reaction of an O(2) adduct of a biomimetic tetracarboxylatodiiron(II,II) complex provides a synthetic precedent for understanding the electrophilic reactivity of like adducts in the active sties of nonheme diiron enzymes.     

Trends in 19F-19F and 29Si-19F coupling constants in organosilicon derivatives containing SiF2 and Si2F4 units

Consideration of ¹⁹F-¹⁹F and ²⁹Si-¹⁹F coupling constants in a series of organosilicon derivatives containing SiF₂ and Si₂F₄ units reveals a number of trends which are useful for structural and stereochemical assignments. For example the vicinal ¹⁹F-¹⁹F coupling constants in a number of CSiF₂SiF₂C- derivatives (including straight chain compounds, disilacyclobutanes and disilacyclohexanes) show an apparent linear dependence on dihedral angle, varying in magnitude from near zero for small values of φ up to ca. 19 Hz for φ ～ 180°. This is particularly useful for stereochemical assignments [1,2]. In addition ²⁹Si-¹⁹F coupling constants appear to fall in quite distinct ranges (¹J_SiF > 300 Hz, 29 Hz < ²J_SiF < 55 Hz, ³J_SiF < 10 Hz). This is quite useful for structural assignments [1,6]. Reaction of SiF₂ with 1,3-cyclohexadiene gives two new silicon fluorine compounds: a disilabicyclo[2,2,2]octene and an HSi₂F₅-substituted cyclohexadiene.     

The reactions of 4-dicyanomethylene-2-phenyl-4H-1-benzopyran and some benzologs with nucleophiles

4-Dicyanomethylene-2-phenyl-4H-1-benzopyran (1) reacts with primary amines under mild conditions to give 4-imino-3-alkyl-5-alkylimino-2-phenyl-3,4-dihydro-5H-[1]benzopyrano[3,4-c]-pyridine derivatives which, in turn, are hydrolyzed with acid to 4-imino-3-alkyl-2-phenyl-3,4-dihydro-5H-[1]benzopyrano[3,4-c]pyridin-5-ones. When more vigorous conditions are employed for the reactions of 1 with primary amines, Dimroth rearrangements take place and the products are derivatives of 4-alkyl- (or aryl)amino-5-alkyl- (or aryl)imino-2-phenyl-5H-[1]benzopyrano-[3,4-c]pyridine. The latter compounds are hydrolyzed by acid to the corresponding 5-pyridone derivatives. The reaction of 1 with piperidine gives 2-phenyl-4-piperidyl-5H-[1]benzopyrano-[3,4-c]pyridin-5-one. Sodium methoxide reacts with 1 to give 3-cyano-2-methoxy-4-(2-hydroxyphenyl)-6-phenylpyridine. Two benzologs of 1 have been allowed to react with primary and secondary amines and the products are analogous to those obtained from 1 .     

Joule heating in packed capillaries used in capillary electrochromatography

Effective heat dissipation is critical for reproducible and efficient separations in electrically driven separation systems. Flow rate, retention kinetics, and analyte diffusion rates are some of the characteristics that are affected by variation in the temperature of the mobile phase inside the column. In this study, we examine the issue of Joule heating in packed capillary columns used in capillary electrochromatography (CEC). As almost all commonly used CEC packings are poor thermal conductors, it is assumed that the packing particles do not conduct heat and heat transfer is solely through the mobile phase flowing through the system. The electrical conductivity of various mobile phases was measured at different temperatures by a conductivity meter and the temperature coefficient for each mobile phase was calculated. This was followed by measurement of the electrical current at several applied voltages to calculate the conductivity of the solution within the column as a function of the applied voltage. An overall increase in the conductivity is attributed to Joule heating within the column, while a constant conductivity means good heat dissipation. A plot of conductivity versus applied voltage was used as the indicator of poor heat dissipation. Using theories that have been proposed earlier for modeling of Joule heating effects in capillary electrophoresis (CE), we estimated the temperature within CEC columns. Under mobile and stationary phase conditions typically used in CEC, heat dissipation was found to be not always efficient. Elevated temperatures within the columns in excess of 23 degrees C above ambient temperature were calculated for packed columns, and about 35 degrees C for an open column, under a given set of conditions. The results agree with recently published experimental findings with nuclear magnetic resonance (NMR) thermometry, and Raman spectroscopic measurements.