Correlation length bounds for disordered Ising ferromagnets

Thed-dimensional, nearest-neighbor disordered Ising ferromagnet: $$H = - \sum {J_{ij} \sigma _i \sigma _j }$$ is studied as a function of both temperature,T, and a disorder parameter,λ, which measures the size of fluctuations of couplingsJ _ij ≧0. A finite-size scaling correlation length,ζ _f (T, λ), is defined in terms of the magnetic response of finite samples. This correlation length is shown to be equivalent, in the scaling sense, to the quenched average correlation lengthζ(T, λ), defined as the asymptotic decay rate of the quenched average two-point function. Furthermore, the magnetic response criterion which definesζ _f is shown to have a scale-invariant property at the critical point. The above results enable us to prove that the quenched correlation length satisfies: $$C\left| {\log \xi (T)} \right|\xi (T) \geqq \left| {T - T_c } \right|^{ - {2 \mathord{\left/ {\vphantom {2 d}} \right. \kern-\nulldelimiterspace} d}}$$ which implies the boundv≧2/d for the quenched correlation length exponent.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

Micelle-sequestered dissociation of cationic DNA-intercalated drugs: unexpected surfactant-induced rate enhancement

Detergent sequestration using micelles as a hydrophobic sink for dissociated drug molecules is an established technique for determination of dissociation rates. The anionic surfactant molecules are generally assumed not to interact with the anionic DNA and thereby not to affect the rate of dissociation. By contrast, we here demonstrate that the surfactant molecules sodium dodecyl sulfate (SDS), sodium decyl sulfate, and sodium octyl sulfate all induce substantial rate enhancements of the dissociation of intercalators from DNA. Four different cationic DNA intercalators are studied with respect to surfactant-induced dissociation. Except for the smallest intercalator, ethidium, the dissociation rate constants increase monotonically with surfactant concentration both below cmc and (more strongly) above cmc, much more than expected from electrostatic effects of increased counterion concentration. The rate enhancement, most pronounced for the bulky, multicationic, hydrophobic DNA ligands in this study, indicates a reduction of the activation energy for the ligand to pass out from a deeply penetrating intercalation site of DNA. The discovery that surfactants enhance the rate of dissociation of cationic DNA-intercalators implies that rate constants previously determined by micelle-sequestered dissociation may have been overestimated. As an alternative, more reliable method, we suggest instead the addition of excess of dummy DNA as an absorbent for dissociated ligand.     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

Stereochemistry of contiguous cyclopropane formation from cascade cyclization of a skipped dienyl homoallyl triflate

Solvolysis of asymmetric homoallylic triflates bearing a terminal stannyl substituent gives disubstituted cyclopropanes and bicyclopropanes bearing differentiated termini in high enantiopurity.     

Total synthesis of polycavernoside A, a lethal toxin of the red alga Polycavernosa tsudai

[structure: see text] Two approaches to the synthesis of the aglycon 120 of polycavernoside A (1) were developed, only one of which was completed. The successful "second-generation" route assembled the aglycon seco acids 102 and 106 via Nozaki-Hiyama-Kishi coupling of aldehyde 70, prepared from methyl (S)-3-hydroxy-2-methylpropionate (72) and (S)-pantolactone (73), with vinyl bromide 71. The latter was obtained from a sequence which commenced from the silyl ether 24 of 3-hydroxypropionaldehyde and entailed cyclization of (Z)-zeta-hydroxy-alpha,beta-unsaturated ester 82. Regioselective Yamaguchi lactonization of trihydroxycarboxylic acids 102 and 106 and subsequent functional-group adjustments led to macrolactone 120, to which the fucopyranosylxylopyranoside moiety was attached. Stille coupling of the glycosidated aglycon 128 with dienylstannane 129 furnished polycavernoside A in a synthesis for which the longest linear sequence was 25 steps. The overall yield to lactone 120 was 4.7%.     

Aminocyclodextrins to facilitate the deprotonation of 4-tert-butyl-alpha-nitrotoluene

6A-Amino-6A-deoxy-beta-cyclodextrin enhances the rate of the deprotonation of 4-tert-butyl-alpha-nitrotoluene. The rate constants for reaction of the cyclodextrin-bound species, kinc = 4 x 10(-3), 9 x 10(-3) and 19 x 10(-3) s(-1), at pH 6.0, 6.5 and 7.0, respectively, in 0.1 mol dm(-3) aqueous phosphate buffer containing 1% methanol at 298 K. These rate constants correspond to a rate acceleration (kinc/kun) of ca. 10 times at each pH. Under the same conditions, 6A-dimethylamino-6A-deoxy-beta-cyclodextrin and 6A-(2-aminoethylamino)-6A-deoxy-beta-cyclodextrin are more effective; at pH 6.0, 6.5 and 7.0, for the former, kinc = 3 x 10(-2), 7 x 10(-2) and 12 x 10(-2) s(-1), whilst for the latter, kinc = 4 x 10(-2), 5 x 10(-2) and 9 x 10(-2) s(-1), respectively. Each cyclodextrin also decreases the pKa of the nitrotoluene, from 6.8 in free solution, to 6.2 when bound. The accelerated deprotonation by 6A-amino-6A-deoxy-beta-cyclodextrin is reflected in the enhanced rates of hydrogen-deuterium exchange of the nitrotoluene in deuterium oxide, and in the conjugate addition of the nitrotoluene to methyl vinyl ketone in aqueous solution.     

Effects of methyl substitution on radiative and solvent quenching rate constants of [Ru(phen)2dppz]2+ in polyol solvents and bound to DNA

Methyl substituents on the distant benzene ring of the dppz ligand in the "light switch" complex [Ru(phen)(2)dppz](2+) have profound effects on the photophysics of the complexes in water as well as in the polyol solvents ethylene glycol, glycerol, and 1,2- and 1,3-propanediol. Whereas 11,12-dimethyl substitution decreases the rate of quenching by diminishing hydrogen bonding by solvent, the 10-methyl substituent in addition also decreases both the radiative and the nonradiative rate constant for decay to the ground state of the non-hydrogen-bonded excited state species. For both the 10-methyl and the 11,12-dimethyl derivatives, the effect of methyl substitution on the equilibrium of solvent hydrogen bonding to the excited state is due to changes in the entropy terms, rather than in the enthalpy, indicating that the effect is a steric perturbation of the solvent cage around the molecule. When intercalated into DNA, the effects of methyl substitution is smaller than those in polyol solvent or water, suggesting that the water molecules that quench the excited state by hydrogen bonding to the phenazine aza nitrogens mainly access them from the same groove as in which the Ru(II) ion resides. Since the Delta-enantiomer of [Ru(phen)(2)10-methyl-dppz](2+) has an absolute quantum yield of up to 0.23 when bound to DNA, a value 7000 times higher than in pure water solution, it is promising as a new luminescent DNA probe.